%0 Conference Paper %B 2020 SAWE Tech Fair %D 2020 %T 3753. Theoretical and Experimental Evaluation of the Flexibility of the Test Rig on Inertia Property Measurement %A Giorgio Previati %A Mastinu, Gianpiero %A Gobbi, Massimiliano %K 06. Inertia Measurements %K 09. Weighing Equipment %X

In the measurement of inertia properties (mass, centre of gravity and inertia tensor), both the body under investigation and the test rig are commonly considered as rigid bodies. However, in case of heavy or large bodies, these assumptions may not be satisfied. The present paper deals with the consequences of the test rig structure deformations on the measured inertia parameters. In fact, if the forces exchanged by the structure of the test rig and the body are large, the structure may deform changing its geometry and dynamic behavior. These effects, in turn, affect the measured kinematic and dynamic quantities needed for the measurement of the inertia properties.

In the paper, by considering the InTenso+ Measuring System of the Politecnico di Milano, a special type of multi-filar pendulum, the effects of the deformation of the test rig on the measurement of the inertia properties is investigated both numerically and experimentally. A flexible multibody model is employed to understand the dynamic effects of the deformations on the mass properties measurement. Several bodies are measured to validate such analyses. A proper mathematical procedure is then derived to measure the inertia properties of bodies when the realization of a sufficiently stiff structure is impractical.

%B 2020 SAWE Tech Fair %I Society of Allied Weight Engineers, Inc. %C Virtual Conference %P 14 %8 07/2020 %U https://www.sawe.org/papers/3753/buy %L 6, 9 %1

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%2 15 %3 20 %4 SAWE3730 %0 Conference Paper %B 78th Annual Conference, Norfolk, VA %D 2019 %T 3727. Trifilar Pendulum: Non-small Oscillations and Calibration %A Giorgio Previati %K 06. Inertia Measurements %X

The trifilar pendulum is a well-known and established technique for the measurement of the moment of inertia of rigid bodies. For such application, the motion off the pendulum, which is inherently nonlinear, is considered linear. As consequences, only small oscillations and pendula with long cables with respect to their distance should be employed for the measurement. However, in some application either to use non- small oscillation angles or to use pendulum with relative short cables have to be employed. In these cases, the motion cannot be considered linear and some error in the measurement could arise. 

This paper aims to analyze the nonlinear motion off the pendulum. A formula is analytically derived for the calibration of the pendulum for non-small rotation angles. A sensitivity analysis is proposed to highlight the advantages of the proposed approach to the measurement of the moment of inertia of relatively smalll and compact bodies, such as tires and engines, and to full scale vehicles and airplanes.

%B 78th Annual Conference, Norfolk, VA %I Society of Allied Weight Engineers, Inc. %C Norfolk, Virginia %P 16 %8 05/2019 %U https://www.sawe.org/papers/3727/buy %L 6 %1 Non-Member Price: $20.00; Member Price: $15.00 %2 15 %3 20 %4 SAWE3727 %0 Conference Paper %B 78th Annual Conference, Norfolk, VA %D 2019 %T 3728. Investigation on the Mass Properties of Cars %A Giorgio Previati %K 05. Inertia Calculations %K 06. Inertia Measurements %X

The knowledge of the mass properties (center off gravity location and inertia tensor) of cars is crucial for the analysis of their dynamic performances. The measurement of such properties is not always performed and their value is estimated by 3D models off some empirical formula. In this paper, the mass properties off cars are investigated by analyzing the measurements performed at tthe Politecnico di Milano. The measurements have been realized by the InTenso+ test rig off the Politecnico di Milano in the period from 2000 to 2018. The test rig is basically a multi-bar pendulum carrying the body under investigation and oscillating from well-known initial conditions. By means of a proper mathematical procedure, the mass properties of the body are accurately measured in a very short testing time. 

The obtained measures are statistically analyzed and correlations are found with easily accessible vehicle data. On the basis of such correlations, formulae are proposed to have a quick and reasonable estimation of the most relevant mass parameters (center of gravity, heights and diagonal terms of the inertia tensor) of any vehicle.

%B 78th Annual Conference, Norfolk, VA %I Society of Allied Weight Engineers, Inc. %C Norfolk, Virginia %P 14 %8 05/2019 %U https://www.sawe.org/papers/3728/buy %L 5, 6 %1 Non-Member Price: $20.00; Member Price: $15.00 %2 15 %3 20 %4 SAWE3728 %0 Conference Paper %B 78th Annual Conference, Norfolk, VA %D 2019 %T 3730. Path to be an Engineer %A Johnston, Brittany %K 06. Inertia Measurements %X

This is an unconventional Society of Allied Weight Engineers (SAWE) student conference paper that gives insight of how a person can have the will power to navigate on a journey of obtaining a new career. Becoming an engineer is far from easy, but it is possible to obtain. I take that possibility with positivity that enables me to make the great strides that I must complete. This paper gives insight to who I am and why I must make this change.

%B 78th Annual Conference, Norfolk, VA %I Society of Allied Weight Engineers, Inc. %C Norfolk, Virginia %P 6 %8 05/2019 %U https://www.sawe.org/papers/3730/buy %L 6 %1

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%2 15 %3 20 %4 SAWE3730 %0 Conference Paper %B 77th Annual Conference, Irving, Texas %D 2018 %T 3700. On Techniques for Correcting Entrained Air Errors during MOI Measurement of Aircraft Control Surfaces %A Otlowski, Daniel %K 06. Inertia Measurements %X

Knowing the true mass properties of aircraft control surfaces is critical to preventing aerodynamic flutter, a condition that can result in the loss of flight control or outright airframe failure. As the aircraft industry turns to a greater use of composites in airframe construction, layup variations in material density and manufacturing techniques result in as-built deviations from the mass distribution calculated in the CAD model. These moment of inertia (MOI) deviations can be up to 10%, thereby increasing the need to verify MOI of control surfaces through physical measurement.

Control surface MOI measurements are subject to errors when the measurements are conducted in air. Errors in air measurements are principally caused by entrained air. This virtually-attached air adds apparent mass to the control surface and anomalously increases the control surface’s measured MOI. Typical MOI errors range from 5% to 25% of the control surface’s MOI.

Concentrating on entrained air errors, this paper examines viable methods of error correction. Further refined by test article requirements, the methods are evaluated both experimentally and analytically. Application strategies are then developed, and expected outcomes are predicted. Lastly, a new gravity driven horizontal axis instrument, complete with its own novel error compensation, is introduced and compared to a variety of measurement and correction techniques.

%B 77th Annual Conference, Irving, Texas %I Society of Allied Weight Engineers, Inc. %C Irving, Texas %P 64 %8 05/2018 %U https://www.sawe.org/papers/3700/buy %1 Non-Member Price: $20.00; Member Price: $15.00 Members: First 10 product downloads are Free. %2 15 %3 20 %4 SAWE3700 %0 Conference Paper %B 76th Annual Conference, Montreal, Canada %D 2017 %T 3691. Methods to Evaluate the Mass Properties of a Scale Model Aircraft %A Kohtanen, Eetu %A Davis, R. Benjamin %K 06. Inertia Measurements %K 08. Weighing %K 11. Weight Engineering - Aircraft Estimation %K Student Papers %X

Scale model ditching tests are sometimes conducted to study the loads and dynamic behavior associated with an aircraft during water impact. To ensure scalability of the results, the model’s mass properties including weight, center of gravity, and pitch moment of inertia in particular must proportionally reflect the characteristics of the full-scale aircraft. This paper presents the experimental methods used to evaluate these mass characteristics for a 1/20th scale Gulfstream G550 model prior to ditching tests conducted at the University of Georgia. These methods can be used for any similarly sized model.

To determine the center of gravity the aircraft model is placed on a v-block assembly resting on three force transducers arranged in an isosceles triangle formation. The model’s center of gravity along longitudinal and lateral axes is found by summing moments about a known reference axes system using the static forces measured at each transducer. To find the vertical center of gravity, the model is rotated about its longitudinal axis in a v-block fixture, and the force readings along the projection of the rotated plane are then manipulated.

For pitch inertia, a compound pendulum is used to measure the aircraft’s period of oscillation which is related to the inertia about the axis of oscillation through an analytical method [1]. The inertia of the pendulum apparatus by itself is then subtracted from the total experimental inertia, and the parallel axis theorem is used to determine the model’s pitch inertia about its center of gravity. To evaluate the accuracy of the pendulum method, aluminum and steel brackets with known mass properties are attached to the model’s tail, and the pitch inertia is measured again for each bracket. The increase in inertia is then compared against the theoretical increase.

%B 76th Annual Conference, Montreal, Canada %I Society of Allied Weight Engineers, Inc. %C Montreal, Canada %P 12 %8 05/2017 %U https://www.sawe.org/papers/3691/buy %1 Non-Member Price: $20.00; Member Price: $15.00 Members: First 10 product downloads are Free. %2 15 %3 20 %4 SAWE3691 %0 Conference Paper %B 73rd Annual Conference, Long Beach, California %D 2014 %T 3610. Inertia Uncertainity of a Moored FPSO %A Chandrasekaran, Santhosh Kumar %A Schuster, Andreas %K 06. Inertia Measurements %K 13. Weight Engineering - Marine %K 35. Weight Engineering - Offshore %X This paper will address weight requirements t o ensure the delivered mass inertia properties match the initial estimates used for model testing and hydrodynamic performance assessment. It has been assumed that the large dead weight of an FPSO makes the design insensitive to variances in mass inertia over the design cycle. As hydrodynamic engineers improve their mooring design performance and reduce margins, minor changes in mass inertia can have dramatic impact on system response. This paper will compare the mass inertia estimating, uncertainty and detailed calculation with mooring performance to determine optimum thresholds for weight control to mitigate the risk of changes in inertia. %B 73rd Annual Conference, Long Beach, California %I Society of Allied Weight Engineers, Inc. %C Long Beach, California %P 13 %8 05/2014 %U https://www.sawe.org/papers/3610/buy %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3610 %0 Conference Paper %B 73rd Annual Conference, Long Beach, California %D 2014 %T 3612. Measurement of the Inertia Tensor - A Review %A Giorgio Previati %A Gobbi, M. %A Mastinu, G. %K 05. Inertia Calculations %K 06. Inertia Measurements %K 32. Product of Inertia Measurement %X This paper is focused on the measurement of the full inertia tensor of a rigid body. In the literature, many papers can be found addressing this problem. Basically, two different measurement approaches are used. In the first approach, different moments of inertia around different axes are measured and then the inertia tensor is reconstructed from these measurements. In this case, the measurement of the moment of inertia around a given axis can be performed with very high accuracy. In the reconstruction of the inertia tensor is, however, some uncertainty is introduced due to the positioning of the rotation axes with respect to the body. The second measurement approach involves the realization of a test rig able to apply a complex motion to the body under investigation. By a proper measurement of the motion and a suitable mathematical procedure, is possible to derive all the components components of the inertia tensor from a single experiment. Sometimes, the motion is reduced to a vibration of small amplitude and the inertia tensor is derived from a modal analysis. The experimental techniques referring to such two strategies are presented and the underlying theoretical and mathematical aspects involved are discussed. %B 73rd Annual Conference, Long Beach, California %I Society of Allied Weight Engineers, Inc. %C Long Beach, California %P 23 %8 05/2014 %U https://www.sawe.org/papers/3612/buy %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3612 %0 Conference Paper %B 73rd Annual Conference, Long Beach California %D 2014 %T 3624. A Unique Method of Measuring Road Vehicle Moments of Inertia and Centre of Gravity %A Watson, Jim %K 06. Inertia Measurements %X In order for vehicle manufacturers to design their vehicles with accurate test data a technique has been developed and used extensibly to measure the moments of inertia (MOI) and centre of gravity (CoG) for a wide range of vehicles. The rig which was designed and built at Cranfield University uses a reverse pendulum methodology. This is in contrast to other methods of measuring inertia which supports the vehicle or object from the ceiling. Essentially, a vehicle is supported by its chassis and allowed to float on an air bearing and rotate, in a frictionless manner, in three degrees of freedom. The motion of the vehicle is configured to move in one axis of rotation, pitch, roll or yaw. A pair of linear springs is then introduced and simple harmonic motion of the vehicle is obtained by applying small amplitudes. The vehicle oscillates against the springs and the time interval is recorded. From the time period of one oscillation, the inertia for the vehicle and rig with any supporting structures can be calculated. To determine the inertia of the vehicle only, the rig and supporting structure inertia are subtracted. The inertia is defined about the centre of gravity of the vehicle which is obtained by performing a different test. The vehicle is tilted to small angles up-to 2 degrees and the force required to maintain the vehicle at equilibrium with the angle of rotation is measured at various degrees of tilt. This test is performed in pitch and roll to provide verification of results. This paper describes the background to the equations derived for calculations, features of the rig which have arisen from over 25 years of testing with this unique methodology and details of the software used. %B 73rd Annual Conference, Long Beach California %I Society of Allied Weight Engineers, Inc. %C Long Beach, California %P 16 %8 05/2014 %U https://www.sawe.org/papers/3624/buy %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3624 %0 Conference Paper %B 73rd Annual Conference, Long Beach California %D 2014 %T 3625. Methods For Representing Conditions On A Weight Database %A Bjørhovde, Stein %K 06. Inertia Measurements %X This paper will look into several conditions that can appear in a weight control project and where all of them need calculation of weight and center of gravity as a variant of the standard lightweight calculation at point of completion. Requirements and wishes for a weight control system to handle these conditions will be discussed and addressed against methods and solutions. %B 73rd Annual Conference, Long Beach California %I Society of Allied Weight Engineers, Inc. %C Long Beach, California %P 17 %8 05/2014 %U https://www.sawe.org/papers/3625/buy %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3625 %0 Conference Paper %B 72nd Annual Conference, St. Louis, Missouri %D 2013 %T 3603. Mass Property Measurements Of The Mars Science Laboratory Rover %A Keith Fields %K 06. Inertia Measurements %K 07. Section Properties %X The NASA/JPL Mars Science Laboratory (MSL) spacecraft mass properties were measured on a spin balance table prior to launch. This paper discusses the requirements and issues encountered with the setup, qualification, and testing using the spin balance table, and the idiosyncrasies encountered with the test system. The final mass measurements were made in the Payload Hazardous Servicing Facility (PHSF) at Kennedy Space Center on the fully assembled and fueled spacecraft. This set of environmental tests required that the control system for the spin balance machine be at a remote location, which posed additional challenges to the operation of the machine. %B 72nd Annual Conference, St. Louis, Missouri %I Society of Allied Weight Engineers, Inc. %C Saint Louis, Missouri %P 16 %8 05/2013 %U https://www.sawe.org/papers/3603/buy %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3603 %0 Conference Paper %B 69th Annual Conference, Virginia Beach, Virginia %D 2010 %T 3500. Technical Feasibility Study for the Measurement of the Inertia Properties of an Aircraft %A Giorgio Previati %A Mastinu, G. %A Gobbi, M. %K 03. Center Of Gravity %K 06. Inertia Measurements %K 32. Product of Inertia Measurement %X A feasibility study for the measurement of the inertia properties of a full-scale aircraft is presented. The employment of the InTenso+ system developed at Politecnico di Milano is discussed referring to the measurement of the inertia properties of a fighter aircraft. Preliminarily, the InTenso+ system is introduced to highlight its basic features. Then, referring to the addressed non standard aeronautic application, the accuracy of the measurement method is investigated. Both analytical and numerical analyses are presented to estimate the uncertainties of the measurement method. The measurement of the inertia properties of a full scale aircraft is technically feasible within the accuracy quantified in this report. Economic and financial issues are not critical, being the InTenso+ system very simple and consequently inexpensive (the implementation costs are not given in this paper as they depend on the customization of the system). The main result of this paper is that, maybe for the first time since the beginning of aeronautical engineering, the measurement of the full inertia tensor and of the location of the centre of gravity of aircrafts appears feasible in a simple way. Such a measurement can be performed by using the InTenso+ system. %B 69th Annual Conference, Virginia Beach, Virginia %I Society of Allied Weight Engineers, Inc. %C Virginia Beach, Virginia %P 21 %8 05/2010 %U https://www.sawe.org/papers/3500/buy %L 3497 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3500 %0 Conference Paper %B 69th Annual Conference, Virginia Beach, Virginia %D 2010 %T 3507. A Practical Method to Improve Moment of Inertia Measurement Accuracy for Formosat-3 Satellites %A HUNG, HENG-CHUAN %K 06. Inertia Measurements %X The "FORMOSAT-3 Program" is an international collaboration project between Taiwan and the US with joint efforts of Taiwan's National SPace Organization (NSPO) and University Corporation for Atmospheric Research (UCAR) of the US. The primary FORMOSAT-3 mission is to launch a constellation of six micro-satellites into Low-Earth Orbit (LEO) in altitude range 700 ~ 800 Km to collect atmospheric data for weather prediction, atmospheric studies, space weather monitoring and geodetic research. The satellites integration and test were completed at NSPO I&T Facility located in Hsinchu, Taiwan. The objective of this paper is to present the method developed at NSPO to improve Moment Of Inertia (MOI) measurement accuracy for FORMOSAT-3 satellites. The Mass Properties Measurement Facility (MPMF) at NSPO is designed for three axes mass properties measurement of satellite up to 1500 Kg. The MPMF includes a 980 Kg weight L-Fixture for horizontal axes measurement. This “huge” L-Fixture greatly reduces the sensitivity of the MOI measurement for FORMOSAT-3 micro-satellites each weighs only about 62 Kg. Redesign of a smaller L-Fixture is inevitable. However, the L-Fixture is designed so that the test objective is well aligned with the MPMF, to manufacture a new one would be too costly and too time consuming. Decision was made to design a smaller fixture without looking for the alignment problem. The alignment problem is solved later when performing the measurement. The Alignment Measurement Equipment is used to accurately identify the misalignment when the satellite is installed in position for measurement. The misalignment data is then used to correct the MOI data. Although the satellite installed with smaller fixture is not well aligned to the MPMF, the misalignment is well measured. The MOI data can be accurately corrected with the alignment data. The final results show that accuracy has been dramatically improved with this method. %B 69th Annual Conference, Virginia Beach, Virginia %I Society of Allied Weight Engineers, Inc. %C Virginia Beach, Virginia %P 10 %8 05/2010 %U https://www.sawe.org/papers/3507/buy %L 3497 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3507 %0 Conference Paper %B 67th Annual Conference, Seattle, Washington %D 2008 %T 3457. How Mass Properties Affect Satellite Attitude Control %A Boynton, Richard %K 06. Inertia Measurements %K 18. Weight Engineering - Spacecraft Design %X The success of a satellite mission is highly dependent on the accuracy of the measurement of its mass properties before flight and the proper ballasting of the satellite to bring the mass properties within tight limits. Failure to properly control mass properties can result in the satellite tumbling end over end after launch, or quickly using up its thruster capacity in an attempt to point in the correct direction. Solar panels must continue to point toward the sun as the satellite orbits the earth. Telescopes must point earthward. Satellite attitude control systems generally consist of a closed loop of measurement and correction of the spacecraft’s attitude such that it is constantly driven into its desired nominal orientation, effectively rejecting any disturbances imposed on the satellite, such as variations in the earth’s magnetic field, nonspherical shape of the Earth, lunar and solar perturbations, drag of the residual atmosphere on the solar array, and solar radiation pressure, or by movement of mechanical parts within the satellite. This paper discusses the different means of attitude control: thrusters, momentum wheel, spin stabilization, gravity gradient stabilization, and magnetic field control, with emphasis on the relationship of mass properties to these control methods. %B 67th Annual Conference, Seattle, Washington %C Seattle, Washington %P 21 %8 5/19/2008 %U https://www.sawe.org/papers/3457/buy %9 6. Inertia Measurements; 18. Weight Engineering - Spacecraft Design %M 3457 %L 6; 18 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3457 %0 Conference Paper %B 67th Annual Conference, Seattle, Washington %D 2008 %T 3460. Using a Two-Plane Spin Balance Instrument to Balance a Satellite Rotor About Its Own Bearings %A Kennedy, Paul %A Otlowski, Daniel %A Rathbun, Brandon %A Wiener, Kurt %K 06. Inertia Measurements %K 18. Weight Engineering - Spacecraft Design %K Mike Hackney Best Paper Award %X

This paper addresses the problem of statically and dynamically balancing a satellite, mounted antenna rotor supported on its own bearings, and driven by a motor in the satellite body. The satellite body is considered a stationary platform, (stator) for this procedure and is not part of the balancing problem. The antenna rotor is isolated and balanced independently while spinning on its own bearings. In order to measure the unbalance, a method is developed to utilize a two-plane vertical axis spin balance machine. Rather than using the gas bearing rotor of the measuring instrument and spinning the entire satellite, the satellite body (stator) is attached to the balancing machine table, which is held stationary, and the satellite “rotor” is spun on its own bearings. Forces due to the unbalance are measured by the Spin Balance Machine force transducers. The method is compared to a similar procedure using a single plane spin balancer and to methods using “work reversal” methods to balance the rotor by spinning the entire satellite. The accuracy of this procedure is compared to the basic balance capability of the spin balance instrument when used in the conventional manner.

%B 67th Annual Conference, Seattle, Washington %C Seattle, Washington %P 21 %8 5/19/2008 %U https://www.sawe.org/papers/3460/buy %9 6. Inertia Measurements; 18. Weight Engineering - Spacecraft Design %M 3460 %L 6; 18 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3460 %0 Conference Paper %B 66th Annual Conference, Madrid, Spain %D 2007 %T 3414. A Reconfigurable Body for Assessing the Uncertainties Related to the Measurement of Inertia Properties %A Pennati, M. %A Mastinu, G. %A Gobbi, M. %K 06. Inertia Measurements %X The paper presents the design of a reconfigurable body to be taken as the reference body for assessing the uncertainties related to the measurement of inertia properties of rigid bodies. The presented reconfigurable body can be used for the calibration of any rig for measuring the inertia properties of rigid bodies, particularly for the InTenso system of the Politecnico di Milano. The body is composed of a plate, three columns, and a set of masses (disks) that can be arranged in several ways. By changing the position of the columns and the number and the position of the disks along the columns, the mass, the center of gravity (C.G.) location, and the inertia tensor of the body can be modified in whichever fashion. The simple shape of the body components and the construction accuracy allow the difference between the actual inertia properties of the assembled body and the corresponding computed nominal values to be maintained within 0.10 %. The reconfigurable body mass can span from 120 to 500 kg and the diagonal components of the inertia tensor may vary between 9 and 100 kgm2. %B 66th Annual Conference, Madrid, Spain %I Society of Allied Weight Engineers %C Madrid, Spain %P 22 %8 5/28/2007 %G eng %U https://www.sawe.org/papers/3414/buy %9 6. Inertia Measurements %M 3414 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3414 %0 Conference Paper %B 65th Annual Conference, Valencia, California %D 2006 %T 3396. Improve Your Sensor Image with Balance %A Otlowski, Daniel %A Wiener, Kurt %K 06. Inertia Measurements %X This paper reviews the properties which inherently limit the image quality of a gimbal mounted optical imaging system. It further describes how image quality is degraded by external influences, particularly vibration, in the supporting vehicle. The primary emphasis is to quantify, through physical principals, and verify, through experimental demonstration, the degree of static balance required to minimize the detrimental effects of external vibration to an acceptable level. The effects of dynamic balancing will also be discussed. The principles developed for visible light optical systems carried by an Unmanned Air Vehicle (UAV) will be expanded, in a general way, to describe how these principles apply to infra red, ultra violet, and radar systems as well as variations to the requirements as a function of the vehicle on which they are mounted. This discussion will include manned aircraft, missiles, land vehicles and watercraft. %B 65th Annual Conference, Valencia, California %I Society of Allied Weight Engineers %C Valencia, California %P 53 %8 5/20/2006 %G eng %U https://www.sawe.org/papers/3396/buy %9 6. INERTIA MEASUREMENTS %M 3396 %1 Non-Member Price: $26.50; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 26.5 %4 SAWE3396 %0 Conference Paper %B 64th Annual Conference, Annapolis, Maryland %D 2005 %T 3354. The Role of Mass Properties Measurement In The Space Mission %A Wiener, Kurt %K 06. Inertia Measurements %X This paper outlines the requirements for a successful mass properties (MP) measurement program for space missions. It emphasizes the need for cooperation and coordination between the various mission groups in establishing the MP measurement requirements, tolerances equipment, & procedures necessary to meet mission objectives. The typical responsibilities of each group are outlined. The paper also describes the capabilities and limitations of various specific state of the are MP instruments and methods available to measure the weight, center of gravity location (CG), moments of inertia (MOI), and products of inertia (POI) of spacecraft and subassemblies. These MP measuring instruments are compared with regard to the basic principals of measurement, accuracy, cost, and other characteristics. It will also provide guidelines for incorporating design features in the spacecraft to optimize the accuracy of MP measurements and ballasting to meet the design specifications. Examples and design guidelines for locating fixtures are given along with methods and examples used to optimize the accuracy of MP measurements. %B 64th Annual Conference, Annapolis, Maryland %I Society of Allied Weight Engineers, Inc. %C Annapolis, Maryland %P 14 %8 5/14/05 %G eng %U https://www.sawe.org/papers/3354/buy %9 6. INERTIA MEASUREMENTS %M 3354 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3354 %0 Conference Paper %B 63rd Annual Conference, Newport, California %D 2004 %T 3325. Mass Properties Measurement in the X-38 Project %A Peterson, Wayne L. %K 06. Inertia Measurements %K Mike Hackney Best Paper Award %X

This paper details the techniques used in measuring the mass properties for the X-38 family of test vehicles. The X-38 Project was a NASA internal venture in which a series of test vehicles were built in order to develop a Crew Return Vehicle (CRV) for the International Space Station. Three atmospheric test vehicles and one spaceflight vehicle were built to develop the technologies required for a CRV. The three atmospheric test vehicles have undergone flight-testing by a combined team from the NASA Johnson Space Center and the NASA Dryden Flight Research Center. The flight-testing was performed at Edwards Air Force Base in California. The X-38 test vehicles are based on the X-24A, which flew in the ?60s and ?70s. Scaled Composites, Inc. of Mojave, California, built the airframes and the vehicles were outfitted at the NASA Johnson Space Center in Houston, Texas. Mass properties measurements on the atmospheric test vehicles included weight and balance by the three-point suspension method, four-point suspension method, three load cells on jackstands, and on three in-ground platform scales. Inertia measurements were performed as well in which Ixx, Iyy, Izz, and Ixz were obtained. This paper describes each technique and the relative merits of each. The proposed measurement methods for an X-38 spaceflight test vehicle will also be discussed. This vehicle had different measurement challenges, but integrated vehicle measurements were never conducted. The spaceflight test vehicle was also developed by NASA and was scheduled to fly on the Space Shuttle before the project was cancelled.

%B 63rd Annual Conference, Newport, California %I Society of Allied Weight Engineers, Inc. %C Newport, California %P 26 %8 5/15/04 %G eng %U https://www.sawe.org/papers/3325/buy %9 6. INERTIA MEASUREMENTS %M 3325 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3325 %0 Conference Paper %B 63rd Annual Conference, Newport, California %D 2004 %T 3340. Design of an Engine Inertia Measuring Device %A McGarry %A Guenther %A Andreatta %A Heydinger %K 06. Inertia Measurements %X It is sometimes necessary to know the complete inertia matrix (three moments of inertia and three products of inertia) of an engine in order to tune the vibrational dynamics of the engine or the system to which it is added. Typically, one axis about which the moment of inertia is measured is the crankshaft axis, while the other two axes may be any other two mutually perpendicular axes. The device reported on here was designed to measure the components of the inertia matrix, as well as measure the center-of-gravity (CG) location. The CG location must be determined in order to measure the moments of inertia. The device described here was designed for engines in the 200-700 lb range (100-300 kg). Other objects may also be measured, but there is a minimum size and weight below which accurate results cannot be obtained. %B 63rd Annual Conference, Newport, California %I Society of Allied Weight Engineers, Inc. %C Newport, California %P 10 %8 5/15/04 %G eng %U https://www.sawe.org/papers/3340/buy %9 6. INERTIA MEASUREMENTS %M 3340 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3340 %0 Conference Paper %B 63rd Annual Conference, Newport, California %D 2004 %T 3341. A New High Speed Mass Properties Instrument %A Boynton, Richard %A Otlowski %K 06. Inertia Measurements %X In certain industries the amount of time required to make a measurement of moment of inertia and center of gravity can have a dramatic effect on manufacturing cost. For example, thousands of projectiles are measured every year at some proving grounds. This necessitates operating three shifts and using more than one mass properties instrument at the facility. In an effort to reduce measurement cost, Space Electronics has developed a new mass properties instrument that is at least three times faster than our traditional KSR series instrument that has been used throughout the industry for over thirty years. This new instrument employs a different concept. The old instrument rotated to each of the four quadrants, stopped precisely at the correct angle, and then measured the CG offset moment. This required a variable speed motor drive that slowed down as it approached the correct angle, executed motions to damp out any vibration, and then edged slowly to its final destination. The new instrument coasts to a stop at three approximately equally spaced locations. An extremely precise optical encoder then measures the actual angle while a force-restoration transducer determines the moment to better than 0.01% accuracy. The online computer then uses this data to determine X and Y CG of the object being measured. %B 63rd Annual Conference, Newport, California %I Society of Allied Weight Engineers, Inc. %C Newport, California %P 22 %8 5/15/04 %G eng %U https://www.sawe.org/papers/3341/buy %9 6. INERTIA MEASUREMENTS %M 3341 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3341 %0 Conference Paper %B 62nd Annual Conference, New Haven, Connecticut %D 2003 %T 3315. A New Test Rig for the Identification of the Inertia Tensor of a Rigid Body %A Mastinu %A Gobbi %A Giorgio Previati %K 06. Inertia Measurements %X A new method for measuring the inertia tensor of rigid bodies has been developed and applied. A new test-rig, based on the developed method, has been built. The test-rig is basically a three- or four-bar pendulum, carrying the rigid body under investigation. The pendulum is excited either by well defined initial conditions or by a harmonic force. The spatial motion of the pendulum is highly non linear and is recorded by means of accelerometers and gyroscopes. The components of the inertia tensor are identified by a proper numerical procedure which makes use of a mathematical model describing the motion of the pendulum. A proof of the convergence of the identification procedure is given. A validation of the measuring procedure is presented. The maximum error on the main diagonal components of the inertia tensor is less than 0.7%. Further improvements on the precision of the measurement procedure are possible. The rig has been used to measure the inertia tensor of a number of road vehicles and other bodies. %B 62nd Annual Conference, New Haven, Connecticut %I Society of Allied Weight Engineers, Inc. %C New Haven, Connecticut %P 18 %8 5/17/03 %G eng %U https://www.sawe.org/papers/3315/buy %9 6. INERTIA MEASUREMENTS %M 3315 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3315 %0 Conference Paper %B 60th Annual Conference, Arlington, Texas, May 19-23 %D 2001 %T 3130. Inertia Measurements of Large MilitaryVehicles %A Andretta %A Heydinger %A R A Bixel %A Coovert %K 03. Center Of Gravity %K 06. Inertia Measurements %X This paper describes the design and operation of a facility for measuring vehicle center-of-gravity height; roll, pitch, and yaw moments of inertia; and roll/yaw cross product of inertia for a broad range of test specimens. The facility is configurable such that it is capable of measuring these properties for light, single axle trailers; long, heavy vehicles; and tank turrets. The design was driven by the need for accurate, repeatable measurement results and the desire to have a single facility capable of making measurements on a broad range of vehicle sizes. %B 60th Annual Conference, Arlington, Texas, May 19-23 %I Society of Allied Weight Engineers, Inc. %C Arlington, Texas %P 13 %8 5/19/01 %G eng %U https://www.sawe.org/papers/3130/buy %9 3. CENTER OF GRAVIT; 6. INERTIA MEASUREMENTS %M 3130 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3130 %0 Conference Paper %B 60th Annual Conference, Arlington, Texas, May 19-23 %D 2001 %T 3148. Moment of Inertia and Mass Property Measurementsof Control Surfaces of a 747 SP %A Frank, Bill %K 06. Inertia Measurements %X The Stratospheric Observatory for Infrared Astronomy (SOFIA) project is a joint venture between the National Aviation and Space Administration (NASA), the German Space Agency (DLR), Raytheon Aircraft Integration Systems, and several other contractors to build the largest flying infrared observatory. The 2.5 meter diameter infrared telescope will be carried on board a modified 747SP aircraft. The aircraft is being modified to house the telescope by Raytheon Aircraft Integration Systems. The mass properties (weight, center of gravity, and hinge axis moment of inertia) of the control surfaces on the vertical tail of the aircraft were need by engineers at Raytheon to analyze changes in the flight characteristics of the aircraft due to the modifications. This paper presents the testing procedures and the results of the tests performed to achieve the desired objectives. Comparisons are made between the on- and off-aircraft moment of inertia test. The on-aircraft inertia measurement was utilized to verify the numbers calculated using the traditional off-aircraft test and to explore the feasibility of performing inertia measurements without removing the control surfaces from the aircraft. %B 60th Annual Conference, Arlington, Texas, May 19-23 %I Society of Allied Weight Engineers, Inc. %C Arlington, Texas %P 21 %8 5/19/01 %G eng %U https://www.sawe.org/papers/3148/buy %9 6. INERTIA MEASUREMENTS %M 3148 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3148 %0 Conference Paper %B 59th Annual Conference, St. Louis, Missouri, June 5-7 %D 2000 %T 3006. The Moment of Inertia of Fluids - Part 2 %A Boynton, Richard %K 06. Inertia Measurements %X As much as 80% of the mass of a booster rocket or 40% of the mass of a satellite or aircraft can consist of fuel and other liquids. Engineers spend countless hours calculating the mass properties of the solid elements in a flight vehicle with an accuracy of 1 or 2 percent, but the contribution due to the fuel is often based on assumptions that are in error by as much as 50%. Last year one of the authors of this paper (Richard Boynton) published a paper entitled ?The Moment of Inertia of Fluids? (SAWE number 2459). In this paper he summarized a series of measurements which were made on the fluid within different shaped tanks to determine the relationship between total fluid mass and moment of inertia. Some mass properties engineers assume that a tank rotates independently of the fluid contained within it, so that the mass of the fluid has a small effect on the MOI. Others assume that the fluid acts like a solid. As paper number 2459 and this paper show, both assumptions are incorrect. There were a number of issues which Mr. Boynton was unable to resolve when he wrote last year?s paper. This second paper gives the answer to several of them. In particular, this paper: Summarizes experiments on rectangular tanks (the previous paper focused on cylindrical tanks; Confirms the assumption that the roll MOI of fluid in cylindrical tanks is a greater percentage of the solid equivalent MOI for smaller diameter tanks; Gives additional data on the effect of fluid viscosity on MOI; Evaluates the effect of baffles within the tank; Answers the question whether the effective MOI is a function of the rate of angular acceleration of the tank. This is particularly important for satellites that turn very slowly. The experiments we have conducted recently indicate that the relationship between tank geometry and fluid moment of inertia is more complex than we originally surmised. For example, it appears that the rate of oscillation and the size of the tank have a significant effect on the results of our experiments. The conclusions of the previous paper - that moment of inertia increased with aspect ratio and viscosity - are still valid, but additional variables must also be taken into account. %B 59th Annual Conference, St. Louis, Missouri, June 5-7 %I Society of Allied Weight Engineers, Inc. %C St. Louis, Missouri %P 29 %8 6/5/00 %G eng %U https://www.sawe.org/papers/3006/buy %9 6. INERTIA MEASUREMENTS %M 3006 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE3006 %0 Conference Paper %B 58th Annual Conference, San Jose, California, May 24-26 %D 1999 %T 2459. The Moment of Inertia of Fluids %A Boynton, Richard %K 06. Inertia Measurements %K Mike Hackney Best Paper Award %X

This paper describes a first step in trying to measure the MOI of fluids in tanks. The results I measured were not what most mass properties engineers would expect to find. There is a common assumption among mass properties engineers that a tank rotates independently of the fluid contained within it, so that the mass of the fluid has a small effect on the MOI. For this reason, they ignore the mass of the fluid when calculating moment of inertia, even though the mass of the fluid often is a large percentage of the total mass of the vehicle. Although this is often a safe assumption when rotating about the cylindrical axis, the effect of fluid mass on rotation about a transverse axis is usually large enough to be a major contributor to MOI. For a straight walled tank with an aspect ratio of about 3 filled with hydrazine, the MOI is 72% of the value the fluid would have if it were solid. Since the weight of fuel is as much as 85 % of the entire vehicle weight of a rocket, this means that the pitch and yaw MOI of the fuel is more than four times as large as the MOI of the entire rocket before filling it with fuel. If the effect of rocket fuel had been ignored, then the calculated pitch and yaw MOI would be less than 20% of true MOI. The results of a number of different types of experiments are summarized in this paper. It appears that the roll MOI of a rocket can be predicted by knowing the viscosity of the fuel. Additional experiments are necessary to establish a numerical relationship. Also additional work is needed to establish formulas which define the pitch and yaw moment of inertia of fluid-filled tanks of different aspect ratios. I hope that someone reading this paper will take up this cause.

%B 58th Annual Conference, San Jose, California, May 24-26 %I Society of Allied Weight Engineers, Inc. %C San Jose, California %P 24 %8 5/24/99 %G eng %U https://www.sawe.org/papers/2459/buy %9 6. INERTIA MEASUREMENTS %M 2459 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2459 %0 Conference Paper %B 58th Annual Conference, San Jose, California, May 24-26 %D 1999 %T 2461. A New Method for RBP Estimation - The Dynamic Inertia Method %A Witter, M C %A Brown, D L %A Dillon, M %K 06. Inertia Measurements %X A new method for rigid body inertia property estimation is being developed at the University of Cincinnati in conjunction with NASA Dryden, which may have advantages over traditional methods. With the Dynamic Inertia Method (DIM), dynamic forces are applied to an object and its resulting rigid body acceleration is measured. Advances in force sensing technology make this method possible with the advent of a 6 degree of freedom (DOF) load cell. The 6 DOF load cell is used in order to completely measure all forces applied to the test article, including support forces and moments. An array of linear accelerometers is also used to measure the 6 DOF acceleration of the test article. From these measurements, the mass, CG and inertia tenser are estimated. Other dynamic techniques, utilizing the massline of inertance functions to extract RB properties, have been presented in the past with limited success outside the laboratory. What makes this technique different is the ability to measure the 6 DOF support forces. Several examples of the method will be presented, from small automotive components (brake rotor) through large aerospace vehicles (NASA X-38), with independent verification when possible. The DIM shows promise and with adequate development could be an alternative to traditional bifilar and trifilar measurement techniques when vibration testing equipment is available. %B 58th Annual Conference, San Jose, California, May 24-26 %I Society of Allied Weight Engineers, Inc. %C San Jose, California %P 20 %8 5/24/99 %G eng %U https://www.sawe.org/papers/2461/buy %9 6. INERTIA MEASUREMENTS %M 2461 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2461 %0 Conference Paper %B 56th Annual Conference, Bellevue, Washington, May 19-21 %D 1997 %T 2353. Calculating Ellipse of Inertia With Non-Orthogonal Moi Measurements %A Bramante, A %A Cotogni, M %K 06. Inertia Measurements %X When you have to perform a mass property measurement, you can either use your own facility (if you have) or rent one; in the latter case you rent the facility together with its fixtures that may not be fully adequate to your purpose. This study rises from practical difficulties faced when planning to perform the measurement of inertia ellipse points of a big satellite (ARTEMIS) in its launch configuration. The aim of the measurement is to calculate the inertia ellipse on a typical plane of the satellite. Envelope problems have led to the impossibility of investigating all the angles in the plane, being the satellite not allowed to rotate 360deg about its longitudinal axis, using the available L-shaped fixture on a SCHENK machine. Therefore the MOI measurements have been performed about three axes having with a reference satellite axes angles of 0deg, +28deg and -28deg (max allowed rotation). In this paper the problem has been generalized and it is mathematically shown how to calculate the inertia ellipse equation parameters having three MOI values about three different axes at any angular position in the plane of the ellipse. The test results showing the goodness of the method are also presented. %B 56th Annual Conference, Bellevue, Washington, May 19-21 %I Society of Allied Weight Engineers, Inc. %C Bellevue, Washington %P 12 %8 5/19/97 %G eng %U https://www.sawe.org/papers/2353/buy %9 6. INERTIA MEASUREMENTS %M 2353 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2353 %0 Conference Paper %B 55th Annual Conference, Atlanta, Georgia, June 3-5 %D 1996 %T 2299. Sprung/Unsprung Mass Properties Determination Without Vehicle Disassembly %A R A Bixel %A Heydinger, G J %A Guenther, D A %A Novak, J %K 06. Inertia Measurements %X This paper presents a method of measuring a vehicle' s sprung mass without vehicle disassembly. The method involves measuring whole vehicle properties at different trim heights. The accuracy of the method is tested using results for several vehicles. As an extension of the sprung mass determination, this paper also demonstrates the feasibility of determining the inertial properties of a vehicle' s sprung mass without vehicle disassembly. Lastly, measured vehicle roll/yaw product of inertia values are presented for a selection of vehicles. %B 55th Annual Conference, Atlanta, Georgia, June 3-5 %I Society of Allied Weight Engineers, Inc. %C Atlanta, Georgia %P 9 %8 6/3/96 %G eng %U https://www.sawe.org/papers/2299/buy %9 6. INERTIA MEASUREMENTS %M 2299 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2299 %0 Conference Paper %B 55th Annual Conference, Atlanta, Georgia, June 3-5 %D 1996 %T 2300. Mass Properties Control Requirements for Step Mission 4 %A Jones, D L %K 06. Inertia Measurements %X The Space Test Experiment Platform (STEP) Mission 4 is a spinning spacecraft that depends on control of its mass properties in order to achieve the desired pointing. Test operations are performed during spacecraft integration to align the following three axes to the spacecraft geometric axis: Mass principal axis of the spacecraft body. Mass principal axis of the deployed wings. Momentum axis of the momentum wheel. The spacecraft includes an Inertial Properties Adjustment Device (IPAD) that can compensate for small residual errors in the axis alignments by making in-flightadjustments of a movable weight. The error terms associated with each test operation were first identified On a qualitative basis. The tests include a spin balance of the spacecraft body. They also include mass properties and shape measurements of the deployed wings that are not installed for the spin balance of the spacecraft body. Some of the errors could be quantified with high confidence. Others were engineering estimates with lower confidence. The final allocation of allowable errors and sizing of the minimum IPAD weight was made to meet the following constraints: Provide high confidence that the IPAD capacity will be sufficient. Provide test operations that are cost-effective and reliable. %B 55th Annual Conference, Atlanta, Georgia, June 3-5 %I Society of Allied Weight Engineers, Inc. %C Atlanta, Georgia %P 13 %8 6/3/96 %G eng %U https://www.sawe.org/papers/2300/buy %9 6. INERTIA MEASUREMENTS %M 2300 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2300 %0 Conference Paper %B 54th Annual Conference, Huntsville, Alabama, May 22-24 %D 1995 %T 2243. Mass Property Fixture Design for Missile Systems %A Nabity, J %A Seeley, E %A Pritchard, R %K 06. Inertia Measurements %X Fixtures were designed and built to measure the center of gravity and mass moments of inertia (Ixx, Iyy, and Izz) of the Joint Stand-Off Weapon (JSOW). JSOW is a 1200-pound, 60-inch-long air-to-surface missile. One fixture supported the JSOW horizontally for measurement of center of gravity as well as yaw and pitch moments of inertia. This fixture design consisted of a roller plate assembly and required a set of rings to facilitate rotation of the missile. A separate fixture supported the JSOW vertically to measure the roll moment of inertia. It utilized portions of the yaw and pitch fixture, namely the strongback assembly, to minimize cost. This fixture was a gantry design with a yoke pivot, which allowed the JSOW to rotate to the vertical position after it was installed. Both fixtures were designed to mate with a Space Electronics Inc. KSR-5500 Mass Properties Instrument. The fixture designs were strongly influenced by safety considerations. The fixtures had to be easy to use, support an 1800-pound load, and satisfy ordnance handling equipment safety requirements. The other key issue in the fixture designs was to have a measurement uncertainty of less than one percent. Position and lean error are the major sources of fixture errors. Fixture design greatly influences the magnitude of these errors. Lean error is largely caused by poor design and was a major consideration in the design and fabrication of the gantry. ALGOR structural analysis software was used to refine the gantry fixture design and determine static and dynamic stiffness. Measured mass properties were compared to known values and agreed within the desired uncertainties. %B 54th Annual Conference, Huntsville, Alabama, May 22-24 %I Society of Allied Weight Engineers, Inc. %C Huntsville, Alabama %P 21 %8 5/22/95 %G eng %U https://www.sawe.org/papers/2243/buy %9 6. INERTIA MEASUREMENTS %M 2243 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2243 %0 Conference Paper %B 53rd Annual Conference, Long Beach, California, May 23-25 %D 1994 %T 2190. Design of Fixtures for Mass Properties Measurement %A Boynton, Richard %A Wiener, K %K 06. Inertia Measurements %X The number one source of measurement error in most mass properties measurements is the inability to accurately position the object being measured relative to the measurement axis of the instrument. Traditionally this has been accomplished using a precision fixture which supports and locates the object. For horizontal measurements of cylinders, vee blocks are commonly used. For vertical cylinders, an adjustable fixture is often used and the object is centered using dial indicators. Rectangular objects are usually fixtured using a grid plate fixture that has ""fence"" type end stops which interface with a precise pattern of holes on the fixture. For unusual shapes, custom fixtures are designed for the specific object. Although the limiting factor in the accuracy of mass properties measurement is usually the accuracy of fixturing rather than the accuracy of the balancing machine, surprisingly little information is available to improve fixturing accuracy. Other than Space Electronics, very few balancing machine companies offer precision fixtures as standard products. (All the fixtures, accessories, and software described in this paper are available from Space Electronics). Furthermore, mass properties fixturing is often handled as an afterthought and the available funding for the design woefully inadequate. The most important single goal of this paper is to emphasize the importance of fixturing for accurate mass properties measurements. In addition to a discussion of standard and custom fixtures, this paper presents another basic concept of fixturing. Instead of positioning the object at a precise location relative to the instrument, the object can be supported at approximately the right location, and with automatic gaging and software compensation the true location can be determined. A new automated gaging system and position error compensation methods are described. This approach allows payload placement to be made in a fraction of the time that is typically required to move the object to a precise location and introduces no loss of accuracy. This method is particularly useful when measuring large heavy objects that are difficult to reposition. This paper includes drawings and descriptions of a number of specific fixtures, case studies, tips for good fixture design, and recommendations on how to get the best measurement accuracy. This paper also reviews three essential concepts which are related to fixturing: 1. The payload must have precisely defined measurement axes. Both the calculated and measured data are only as good as the definition of the reference axes of the payload. 2. Symbols and polarities must be clearly defined, i.e. which axis is +X, which axis is -Y, etc. These problems can be minimized by following the Recommended Practice for Mass Properties Reporting which we anticipate will be released in 1994 by the SAWE. This recommended practice defines the symbols used for the axes. 3. Methods must be developed to discriminate between true unbalance and apparent unbalance due to fixturing errors. %B 53rd Annual Conference, Long Beach, California, May 23-25 %I Society of Allied Weight Engineers, Inc. %C Long Beach, California %P 48 %8 5/23/94 %G eng %U https://www.sawe.org/papers/2190/buy %9 6. INERTIA MEASUREMENTS %M 2190 %1 Non-Member Price: $24.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 24 %4 SAWE2190 %0 Conference Paper %B 53rd Annual Conference, Long Beach, California, May 23-25 %D 1994 %T 2191. The Rock and Roll Telescope (Using a Gravitational Pendulum to Determine Moment of Inertia) %A Jones, G A %K 06. Inertia Measurements %X Page 19.7 of the SAWE handbook, upper right, shows a method of measuring moment of inertia of a test item using a pendulum. The formulae presented in that figure work only when the pendulum rocks through a small angle. This paper presents an extension of that concept using a pendulum that is supported on a round cross section trunnion in such a way that the test item is simultaneously rocking and rolling. The technique described was actually used in measuring the CG and moment of inertia of a space bound telescope, as described in SAWE paper number 1945. The derivation of the small angle formula is presented. The concept is then extended by deriving the equation for the period NOT assuming a small angle. I chose 45 degrees as an example and worked through the equation. Finally, the implications for moment of inertia measurement are examined. Important Appendix 1. While working out this paper, the author began discovering various errors in the SAWE handbook. There are 160 errors listed. The work was checked by George Strom, who added several of his own findings. Both arc presented. Of these, 47% are misspellings and minor cosmetic defects, the remainder being actual erroneous formulas and factors. Some of this remaining 53% are in rather critical places, such as two erroneous conversion factors in the density units section, page 1.8. Important Appendix 2. This appendix presents an Excel spreadsheet of the formulas in section 4.x.x of the SAWE handbook. The author describes how to embed artwork into a spreadsheet to make the output look identical to section 4 of the handbook. With input of dimensions, the spreadsheet calculates the mass properties of the figure. The package was originally proposed as the San Francisco chapter project. The author intends to offer the package free to SAWE members at the 94 International Conference. %B 53rd Annual Conference, Long Beach, California, May 23-25 %I Society of Allied Weight Engineers, Inc. %C Long Beach, California %P 28 %8 5/23/94 %G eng %U https://www.sawe.org/papers/2191/buy %9 6. INERTIA MEASUREMENTS %M 2191 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2191 %0 Conference Paper %B 52nd Annual Conference, Biloxi, Mississippi, May 24-26 %D 1993 %T 2129. A New Spin Balance Machine %A Boynton, Richard %A Bell, R %K 06. Inertia Measurements %X This paper describes a new low speed vertical axis aerospace gin balance machine which takes advantage of recent advances in technology. This machine measures moment of inertia (MOI) in addition to product of inertia (POI) and center of gravity (CG) offset. Spin speeds as low as 15 RPM yield useful results. This machine has a number of unique features. The operation is totally automatic; even the conversion from spin balance to moment of inertia measurement can be accomplished without the operator touching the machine, Gas bearing technology is used throughout, resulting in unrivaled sensitivity and accuracy. This paper includes a mathematical analysis of the errors of measurement as a function of the relative magnitudes of POI and CG unbalance, the moment equations which relate the transducer forces to payload POI and CG offset, and a practical discussion of fixturing and accessory equipment needed to properly balance an aerospace payload. %B 52nd Annual Conference, Biloxi, Mississippi, May 24-26 %I Society of Allied Weight Engineers, Inc. %C Biloxi, Mississippi %P 38 %8 5/24/93 %G eng %U https://www.sawe.org/papers/2129/buy %9 6. INERTIA MEASUREMENTS %M 2129 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2129 %0 Conference Paper %B 51st Annual Conference, Hartford, Connecticut, May 18-20 %D 1992 %T 2093. Using the ""Moment of Inertia Method"" to Determine Product of Inertia %A Wiener, K %A Boynton, Richard %K 06. Inertia Measurements %X Product of inertia is generally measured using a spin balance machine. In this type of machine, the object is rotated at a speed of about 100 RPM, and the reaction forces against the upper and lower spindle bearings are measured. Product of inertia is then calculated automatically by the machine's on line computer, using formulas that involve the vertical spacing between the upper and lower bearings and the height of the object above the mounting surface of the machine. Objects such as control fins and satellites with extended solar panels cannot be measured using this method because of the large, non-repeatable errors which are introduced by the entrained and entrapped air and turbulence. This paper outlines a method of determining product of inertia by making a series of moment of inertia measurements with the object oriented in six different positions. Product of inertia can then be calculated using formulas which involve the rotation angles of the different fixture positions. Moment of inertia is measured by oscillating the object on a torsion pendulum. Since the object moves very slowly during this measurement, there are negligible centrifugal and windage forces exerted on the object Furthermore, the mass of the entrapped and entrained air can be compensated for by making a second set of measurements in helium and extrapolating the data to predict the mass properties in a vacuum. This paper gives step-by-step instructions on how to measure product of inertia on a torsion pendulum. Special fixtures must be constructed to move the object to the six positions while keeping both the object and the fixture CG near the center of oscillation. We have included design details of such a fixture. Since vacuum data was required, measurements were made in a chamber which could be filled with helium. The design of this chamber is also explained in detail. To illustrate this method, we have used as an example real measurements which were made of airfoil control fins manufactured by one of our customers. For this example, we determined all mass properties: weight, center of gravity along three axes, moment of inertia about three axes, and product of inertia in three planes, all referred to vacuum conditions. %B 51st Annual Conference, Hartford, Connecticut, May 18-20 %I Society of Allied Weight Engineers, Inc. %C Hartford, Connnecticut %P 27 %8 5/18/92 %G eng %U https://www.sawe.org/papers/2093/buy %9 6. INERTIA MEASUREMENTS %M 2093 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2093 %0 Conference Paper %B 51st Annual Conference, Hartford, Connecticut, May 18-20 %D 1992 %T 2095. The Seven Secrets of Accurate Mass Properties Measurment %A Boynton, Richard %K 06. Inertia Measurements %X If you have a mass properties instrument which has an accuracy of 0.1%, how accurately can you measure the mass properties of your payload? Some people think that the answer is 0.1%. In fact, the instrument is usually the least important factor in determining measurement accuracy. There are a number of fatal mistakes which you can make that will produce errors that are 10 or 100 times as large as the inaccuracy of the instrument. Over the years I have concluded that there are seven secrets for accurate mass properties measurement. These are: The payload must have precisely defined measurement axes. The fixture must hold the payload so its measurement axes are precisely located relative to the instrument. You must follow the correct measurement procedure. You must eliminate external influences. The payload must weigh more than 2% of the capacity of the mass properties machine. You must use an accurate instrument. You must define your symbols and polarities. %B 51st Annual Conference, Hartford, Connecticut, May 18-20 %I Society of Allied Weight Engineers, Inc. %C Hartford, Connnecticut %P 15 %8 5/18/92 %G eng %U https://www.sawe.org/papers/2095/buy %9 6. INERTIA MEASUREMENTS %M 2095 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2095 %0 Conference Paper %B 50th Annual Conference, San Diego, California, May 20-22 %D 1991 %T 2024. Using Helium to Predict the Mass Properties of an Object in the Vacuum of Space %A Boynton, Richard %A Bell, R %A Wiener, K %K 06. Inertia Measurements %X How can mass properties of objects designed to operate in space best be measured in an earth based lab? Mass properties measurements of lightweight objects designed to operate in the vacuum of outer space have traditionally been made in a vacuum chamber in order to eliminate the efforts due to the mass of the air surrounding the object. Vacuum chambers are expensive and inconvenient to use. The novel method described in this paper eliminates the effect of the air mass without requiring a vacuum chamber. This method works for any shape object. %B 50th Annual Conference, San Diego, California, May 20-22 %I Society of Allied Weight Engineers, Inc. %C San Diego, California %P 8 %8 5/20/91 %G eng %U https://www.sawe.org/papers/2024/buy %9 6. INERTIA MEASUREMENTS %M 2024 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE2024 %0 Conference Paper %B 47th Annual Conference, Plymouth, Michigan, May 23-25 %D 1988 %T 1829. A Low Speed Dyunamic Balance System %A Jones, D L %K 06. Inertia Measurements %X An existing low-speed dynamic balance system at TRW has been upgraded to handle larger and heavier spacecraft. The upgrade included both the balance machine and the aerodynamic enclosure around the machine. The balance machine is a vertical-axis, single-transducer, hard-bearing machine designed to hold a weight of 5000 pounds with a center of gravity 15 feet above the machine. The upgraded aerodynamic enclosure is a cylinder 26 feet in diameter and 29 feet tall. External fans are used to rotate the air in either direction at speeds up to 12 rpm to reduce the aerodynamic loads on the spacecraft. Dynamic balance operations were performed on test models that were 24 feet in diameter with various heights and weights. An asymmetric aerodynamic appendage was used in some of the operations. The test results showed that the upgraded balance machine operated properly and that the aerodynamic enclosure performed the intended function of reducing the aerodynamic loads. The working range of the balance machine is from zero to 2000 inch-lbs of unbalance moment. A resolution and short term stability of one inch-lb of unbalance moment was demonstrated with a 5000-pound mass model. %B 47th Annual Conference, Plymouth, Michigan, May 23-25 %I Society of Allied Weight Engineers, Inc. %C Plymouth, Michigan %P 14 %8 5/23/88 %G eng %U https://www.sawe.org/papers/1829/buy %9 6. INERTIA MEASUREMENTS %M 1829 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1829 %0 Conference Paper %B 42nd Annual Conference, Anaheim, California, May 23-25 %D 1983 %T 1503. Spacecraft Dynamic Balance With Boundary Layer Control %A Jones, D L %K 06. Inertia Measurements %X Aerodynamic loads can cause problems in the dynamic balance of large diameter spacecraft. The problems include. * Asymmetric loads cause systematic errors. * The steady aerodynamic load limits the spin rate. * Fluctuating aerodynamic loads increase the noise. A method of controlling the air velocity in the boundary layer of a cylindrical enclosure with an external fan has been developed. It was expected that this boundary layer control would cause the air to rotate as a forced vortex, and would greatly reduce the aerodynamic loads on a spacecraft spinning inside the enclosure. The enclosure has a diameter of 20 feet, and is 20 feet all. A reversible fan in a double ended plenum chamber is used to control the air velocity. A maximum vortex spin rate of more than 10 rpm in either direction was achieved. A dynamic balance test program was performed on several test models in the enclosure. The test results indicates that the boundary layer control was generally working as expected. Both the asymmetric and the steady aerodynamic loads were greatly reduced. The boundary layer control did not provide the desired reduction in fluctuating aerodynamic loads in some test configurations. It is expected that an improved enclosure design would provide the desired reduction. This method has particular application to the dynamic balance of large asymmetric spacecraft that are spinning at low angular rates. It is a low cost alternative to performing the balance in a vacuum chamber. %B 42nd Annual Conference, Anaheim, California, May 23-25 %I Society of Allied Weight Engineers, Inc. %C Anaheim, California %P 20 %8 5/23/83 %G eng %U https://www.sawe.org/papers/1503/buy %9 6. INERTIA MEASUREMENTS %M 1503 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1503 %0 Conference Paper %B 42nd Annual Conference, Anaheim, California, May 23-25 %D 1983 %T 1504. Fundamentals of Dynamic Balancing %A Boynton, Richard %K 06. Inertia Measurements %X Most tutorial papers on dynamic balancing discuss the concepts in general terms, but fail to include the necessary mathematics the engineer must have to make use of these concepts. This paper attempts to fill that void. The merits of hard bearing vs soft bearing balancing machines are reviewed and some new conclusions are drawn in light of present day technology. Balancing corrections are discussed from a practical point of view, various types of balancing machines are described, and the advantages of each are summarized. Advantages of the new computer-controlled machines are outlined, including their capability of simultaneously balancing in three axis, calculating angle of inclination of the principal axis, and their remarkable ability to learn from their mistakes in the same way that an experienced balancing machine operator learns special techniques to improve the accuracy of balance. Finally, some comments are made on the practical limits to which various objects can be balanced. %B 42nd Annual Conference, Anaheim, California, May 23-25 %I Society of Allied Weight Engineers, Inc. %C Anaheim, California %P 25 %8 5/23/83 %G eng %U https://www.sawe.org/papers/1504/buy %9 6. INERTIA MEASUREMENTS %M 1504 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1504 %0 Conference Paper %B 42nd Annual Conference, Anaheim, California, May 23-25 %D 1983 %T 1506. Aerodynamic Effects in Mass Properties Determination %A Marshner, R L %K 06. Inertia Measurements %X The atmosphere has an effect on the measurement of mass, moment-of-inertia and product-of-inertia properties of a test object. The effect on mass or weight measurement is due simply to air buoyancy, while the effect o moment-of-inertia and product-of-inertia measurements is more complex. Air drag and/or lift are certainly one factor: Entrapped air, stimulated air and turbulence are other factors. Many dynamic balance machines deduce static moments (for determination) from dynamic data. Thus, atmospheric influence can also be experienced in the determination of CG location. %B 42nd Annual Conference, Anaheim, California, May 23-25 %I Society of Allied Weight Engineers, Inc. %C Anaheim, California %P 21 %8 5/23/83 %G eng %U https://www.sawe.org/papers/1506/buy %9 6. INERTIA MEASUREMENTS %M 1506 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1506 %0 Conference Paper %B 42nd Annual Conference, Anaheim, California, May 23-25 %D 1983 %T 1511A. A High Accuracy Instrument for Measuring MOI %A Boynton, Richard %K 06. Inertia Measurements %X This paper describes an instrument which measures the mass moment of inertia of a test object about a vertical axis, and locates the center of gravity along two axis perpendicular to the vertical axis without the need for re-positioning the test object. This instrument is capable of high accuracy over a wide range of test object weight and moment of inertia, and permits the measurement of moment of inertia about an axis which does not pass through the center of gravity of the test object. The instrument is based on a spherical gas bearing. An inverted torsion pendulum provides time period data which can be easily related to test object moment of inertia; center of gravity is determined by measuring the offset moment and dividing by the weight of the test object. %B 42nd Annual Conference, Anaheim, California, May 23-25 %I Society of Allied Weight Engineers, Inc. %C Anaheim, California %P 16 %8 5/23/83 %G eng %U https://www.sawe.org/papers/1511A/buy %9 6. INERTIA MEASUREMENTS %M 1511A %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1511A %0 Conference Paper %B 41st Annual Conference, San Jose, California, May 17-19 %D 1982 %T 1473. Determining Product of Inertia Using a Torsion Pendulum %A Jodry, C L %A Boynton, Richard %K 06. Inertia Measurements %X This paper presents a method for determining the product of inertia of an object using a high accuracy torsion pendulum moment of inertia instrument. The method chosen requires only three different inertia measurements and minor calculations to determine the principal axes of the object. An air-to-air missile control surface was used as the test article. Simple fixturing was designed so the article could be rotated about its center of gravity, to facilitate making inertia measurements at different angles relative to the reference axes. The center of gravity of the article was determined using a gas bearing center of gravity instrument and utilizing a part of the moment of inertia fixture. Data reduction was handled automatically by the HP 85 computer incorporating a program written for this application. A listing of the program is included in the discussion. Test results were verified by constructing Mohr's Circle for moments of inertia. Minimum and maximum inertia values agreed closely with the measured values. In summary, the method chosen seems to provide a simple and practical approach to product of inertia measurement for some applications. %B 41st Annual Conference, San Jose, California, May 17-19 %I Society of Allied Weight Engineers, Inc. %C San Jose, California %P 35 %8 5/17/82 %G eng %U https://www.sawe.org/papers/1473/buy %9 6. INERTIA MEASUREMENTS %M 1473 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1473 %0 Conference Paper %B 38th Annual Conference, New York, New York, May 7-9 %D 1979 %T 1320. Aerodynamic Effects on Spacecraft Moment of Inertia Measurement %A Jones, D L %K 06. Inertia Measurements %X The effective inertia of a spacecraft is higher in air than it is in a vacuum because of the air that moves with the spacecraft. The uncertainty in knowing the effects of this air is the major error term for large, light-weight spacecraft. Procedures for calculating the effective inertia of the ambient air for several simple geometric shapes are presented. These procedures were obtained from the literature on aircraft, liquid-filled propellant tanks, and hydrodynamic theory. Moment of inertia measurements of an aerodynamic model of a typical spacecraft were made i n a vacuum chamber. The difference in the inertia with and without air was a measure of the aerodynamic effects. Data for both roll and transverse axes .is presented. The application of the calculative procedures to the aerodynamic model is described. Good agreement between .the calculated and measured effects was obtained. %B 38th Annual Conference, New York, New York, May 7-9 %I Society of Allied Weight Engineers, Inc. %C New York, New York %P 22 %8 5/7/79 %G eng %U https://www.sawe.org/papers/1320/buy %9 6. INERTIA MEASUREMENTS %M 1320 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1320 %0 Conference Paper %B 36th Annual Conference, San Diego, California, May 9-12 %D 1977 %T 1166. Aerodynamic Effects on Spacecraft Dynamic Balance %A Jones, D L %K 06. Inertia Measurements %X The requirements for spacecraft dynamic balance are based on vacuum conditions, but the tests are normally performed in air. Asymmetric aerodynamic forces are therefore error terms for spacecraft balance. A test program was performed to investigate these effects. An aerodynamic model of a typical spacecraft with asymmetrical appendage was used. Measurements were made on a TRW-designed low speed balance machine. The tests environments included vacuum, and aerodynamic enclosure, and open air. The final test sequence was performed with the aerodynamic enclosure inside the vacuum chamber. The appendage produced significant asymmetric elastic effects. A special analysis of these effects was required in order to isolate the aerodynamic effects. The measured aerodynamic forces did not vary smoothly with spin rate and with ambient pressure. Extensive data reduction with least squares smoothing techniques was required to obtain meaningful results. The reduced data from the final test sequence is presented in terms aerodynamic moment as a function of the ambient pressure. The associated error in product of inertia is also plotted. The aerodynamic forces were much less in the enclosure than in open air. Using an average from both clockwise and counterclockwise spin directions reduced the errors even further for the measurements in the enclosure. The averaging technique did not provide significant improvement in the open air measurements. Six correction techniques for reducing the aerodynamic error terms were briefly discussed, as follows. • Spin both directions and average the results • Use an aerodynamic enclosure • Replace the ambient air with helium • Provide boundary layer velocity control around the periphery of a cylindrical enclosure • Balance in a vacuum chamber • Use an aerodynamic model to determine correction weights. %B 36th Annual Conference, San Diego, California, May 9-12 %I Society of Allied Weight Engineers, Inc. %C San Diego, California %P 22 %8 5/9/77 %G eng %U https://www.sawe.org/papers/1166/buy %9 6. INERTIA MEASUREMENTS %M 1166 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1166 %0 Conference Paper %B 36th Annual Conference, San Diego, California, May 9-12 %D 1977 %T 1171. Atmospheric Influence on Inertia Measurements %A Lang, W E %A Harbach, T R %K 06. Inertia Measurements %X Mass property measurements are almost always performed in an ambient atmosphere and have been recognized as subject to this environment. This is particularly significant for spacecraft and spacecraft components, where the properties in a space environment are the required input for control of the mission. Atmosphere affects weighing and mass center determinations only to a minimal degree. The major area of concern is measurement of moments of inertia and, in some cases, the products of inertia which are derived from spin balancing operations. The advantage of performing measurements of these parameters in a vacuum environment is obvious, but this is often not possible and is hardly ever convenient The key to deciding the need for vacuum operations lies in estimating the extent of error implicit in atmosphere in measurement, with regard to necessary accuracy. This paper reviews some experience with moment of inertia measurement and spin balancing in vacuum at the NASA Goddard Space Flight Center. Spin balancing of the CTS (Communications Technology Satellite) and moment of inertia measurements of the solar arrays for the IUE (International Ultraviolet Explorer) satellite are discussed in detail. Essential conclusions are that moment of inertia results obtained in atmosphere for items of low density and large frontal area for oscillatory motion may be very inaccurate, primarily due to entrapped or entrained air effects, and that spin balance operations may be adversely affected to the extent that measured items are non-symmetrical about the axis of spin. A method for approximating the atmospheric measurement error for moment of inertia due to air entrapment and entrainment is discussed. %B 36th Annual Conference, San Diego, California, May 9-12 %I Society of Allied Weight Engineers, Inc. %C San Diego, California %P 23 %8 5/9/77 %G eng %U https://www.sawe.org/papers/1171/buy %9 6. INERTIA MEASUREMENTS %M 1171 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1171 %0 Conference Paper %B 35th Annual Conference, Philadelphia, Pennsylvania, May 24-26 %D 1976 %T 1111. Bifilar Pendulum Technique for Determining Mass Properties of Discos Packages %A Mattey, R A %K 06. Inertia Measurements %X A bifilar pendulum was used to determine the mass properties of the Discos packages on the Triad satellite. The pendulum design was unique in that it allowed the package to be rotated into six different angular orientations. Each angular position was located with respect to the center of mass of the package. Analysis and results are given that show that the inertia matrix can be completed using the bifilar pendulum. %B 35th Annual Conference, Philadelphia, Pennsylvania, May 24-26 %I Society of Allied Weight Engineers, Inc. %C Philadelphia, Pennsylvania %P 31 %8 5/24/76 %G eng %U https://www.sawe.org/papers/1111/buy %9 6. INERTIA MEASUREMENTS %M 1111 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1111 %0 Conference Paper %B 35th Annual Conference, Philadelphia, Pennsylvania, May 24-26 %D 1976 %T 1113. Instrumented Gas Bearings Provide a Test Bed for High Accuracy Inertia (Moments & Products) Measurements %A Carpenter, D A %K 06. Inertia Measurements %X This paper discusses the techniques employed in configuring and instrumenting a gas bearing system to provide a sensitive and accurate means of measuring the inertial properties of bodies. The subject system is designed for a single degree of freedom about Z (vertical) axis. Instrumentation is required to provide projected x-x and y-y axis moments and z axis period, speed, and position readouts. Moment data is derived from a single load cell that monitors stabilizing bearing forces in a single plane. A photoelectric pickup system creates the required Z axis data. To aid in understanding the mechanical bearing restraints a series of graphs and explanations are presented in this text. Considerations overall stiffness and the influence on accuracy will be briefly discussed. Presented, also, are instrumentation and hardware techniques that take advantage of the high resolution and low noise profile characteristic of properly configured gas bearing test beds. In summary the combination of low noise and high resolution spells wide dynamic range thus allowing large CG offsets while preserving product of inertia capability at very low rotational speeds. Increasingly, spacecraft construction has moved away from a "rigidbody" approach to construction. Current trends are toward vehicles that display long appendages such as antennas and solar panels. Such a system has a static or quiescent mass distribution and a very different dynamic characteristic. Future facilities designed for complete operation in a vacuum or helium environment will have controlled tensional acceleration and readout capabilities that will provide dynamic as well as static inertial profiles of these difficult to measure payloads. Gas bearing systems easily adapt to these new requirements of the future. %B 35th Annual Conference, Philadelphia, Pennsylvania, May 24-26 %I Society of Allied Weight Engineers, Inc. %C Philadelphia, Pennsylvania %P 15 %8 5/24/76 %G eng %U https://www.sawe.org/papers/1113/buy %9 6. INERTIA MEASUREMENTS %M 1113 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1113 %0 Conference Paper %B 34th Annual Conference, Seattle, Washington, May 5-7 %D 1975 %T 1052. Measurement of the Inertial Properties of the Helios F-1 Spacecraft %A Gayman, W H %K 06. Inertia Measurements %X This paper presents methods of measuring moment of inertia with very high accuracy. The moment of inertia of the Helios Spacecraft about its spin was axis determined by use of a "roll-fixture" using two sets of crossed flexure pivots as elastic constraints. The test procedure entailed measurement of system oscillation period with each of a set of added moment-of-inertia increments. The tare effect of the fixture was determined a like process by and was subtracted from the gross value to yield the spacecraft roll moment of inertia to an estimated accuracy of 0.2%. "Lateral" moments of inertia (i.e., about each of three axes normal to the spin axis) were determined by a gravity pendulum method that makes use of the fact that any physical pendulum has a minimal period of oscillation determined by a particular distance from the axis of rotation to the system center of gravity. In situations where a knife-edge support is used, this distance is equal to the system centroidal radius of gyration. In the subject tests, the pivoting action was provided by hardened pins rolling on flat ways. The effect of the finite radius of the pins was considered in deriving the equations of motion, from which an error analysis revealed the criterion for maximum accuracy in determining the square of the centroidal radius of gyration. The swing fixture provided for a number of optional pivot-pin locations giving precisely known distances between successive axes of oscillation. This fixture, with provisions to support the spacecraft, was ballasted to bring its vertical c.g. close to that predicted for the spacecraft. This ballasting was done not because the test method requires an accurate foreknowledge of specimen c.g. position but, rather, to minimize errors in the parallel-axis transfer term while removing the tare of the fixture. Though the centroidal moment of inertia of the swing fixture was over twice that of the spacecraft, an error analysis of measurements performed on the flight spacecraft showed that accuracies of better than 0.2% were realized for the two lateral principal moments of inertia. The methods presented allow all measurements test to be made with the specimen in an essentially upright position. The vertical center-of-gravity location is derived in the process. Comments are made on the potential importance of aerodynamic effects on measurements made in the earth's atmosphere. It is shown that, for the Helios configuration, these effects must be taken into account by some means to give an assessment of spin stability in the space environment. %B 34th Annual Conference, Seattle, Washington, May 5-7 %I Society of Allied Weight Engineers, Inc. %C Seattle, Washington %P 16 %8 5/5/75 %G eng %U https://www.sawe.org/papers/1052/buy %9 6. INERTIA MEASUREMENTS %M 1052 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1052 %0 Conference Paper %B 34th Annual Conference, Seattle, Washington, May 5-7 %D 1975 %T 1066. Mass Properties Measurements of Large Objects %A Hawks, H H %K 06. Inertia Measurements %X The measuring and testing of mass properties is not new to the weights engineer. Numerous papers have been presented on methods, procedures, facilities, and analyses of various mass properties tests. However, when confronted with the task of measuring a heavy, outsized object, it is found that most previous experience is with smaller aerospace components. Even so, the theory of moment-of-inertia testing remains constant; it should be simply a matter of applying the same proven test procedure to a larger item, but as will be shown in this paper, there were other considerations. The method of moment-of-inertia testing selected was the bifilar pendulum. The mechanics of the bifilar method seemed most workable and the measured parameters relatively easy to obtain. The task was to determine the weight, center of gravity, and three-axis (yaw, pitch, and roll) moment of inertia of two similar Boeing747 engine pod buildups, each weighing 4950 kilograms (11040 pounds) in a space envelope about 2.5 meters (8 feet) in diameter by 6 meters (20 feet) in length. Solving the logistics and ground handling problems of such a large and expensive object proved interesting but uneventful. However, during the first round of tests it became evident that we were at the low end of a learning curve in applying the bifilar pendulum method techniques. In determining the moment of inertia via the bifilar pendulum method, four parameters were measured: filar length, filar radius, system weight, and period of swing. Other considerations in determining the values of these parameters were the effect of load cells installed within the filars; filar end connections; filar elongation, flexibility, and energy-absorbing properties; system calibration; alignment of fixture and object center of gravity; and the effect of air damping. During the tests many problems were encountered and solutions determined. When testing was completed, not only did we have a fair determination of the moments of inertia, but also a good idea of what to avoid on future tests. %B 34th Annual Conference, Seattle, Washington, May 5-7 %I Society of Allied Weight Engineers, Inc. %C Seattle, Washington %P 28 %8 5/5/75 %G eng %U https://www.sawe.org/papers/1066/buy %9 6. INERTIA MEASUREMENTS %M 1066 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1066 %0 Conference Paper %B 33rd Annual Conference, Fort Worth, Texas, May 6-8 %D 1974 %T 1012. Dynamic Unbalance Correction Weight Determination %A Marshner, R L %K 06. Inertia Measurements %X This paper is intended to promote a better understanding of dynamic balancing. First, a brief explanation is given of the technique used by MRC to measure unbalance. A discussion of the validity of dual correction weights to perfectly balance any rigid body is then given, using an interesting approach-resolving the test specimen into two centers-of-mass rather than one. Several simple cases of interest are then analyzed qualitatively using the dual mass centers to promote an appreciation of the dual correction weights. A practical explanation of the concept of product of inertia is given. Following is a summary of the points established. Once the basic understanding of both the measurement technique and the correction technique has been established, the general problem of determining correction weight values and locations is treated in vector notation. The vector use is simple but effective, and brief definitions are given to support the analysis. The resultant equations are translated into a BASIC computer program, which is listed in the paper. In particular, the method used for determination of the angular position of the correction weight is discussed. Finally, several simple cases are reviewed using computer run results to support the intuitive judgments that can be made beforehand. This paper should provide useful reference material for those interested in balancing rigid bodies. Since the analysis, computer program listing and example runs are contained in the same document, it serves as a solid basis for reference, %B 33rd Annual Conference, Fort Worth, Texas, May 6-8 %I Society of Allied Weight Engineers, Inc. %C Fort Worth, Texas %P 15 %8 5/6/74 %G eng %U https://www.sawe.org/papers/1012/buy %9 6. INERTIA MEASUREMENTS %M 1012 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1012 %0 Conference Paper %B 33rd Annual Conference, Fort Worth, Texas, May 6-8 %D 1974 %T 1013. Error Terms for Moment of Inertia Measurement %A Jones, D L %K 06. Inertia Measurements %X This paper presents error terms that are associated with the measurement of moment of inertia (MOI). Major emphasis is placed on the measurement techniques that are currently used in the aerospace industry for high-accuracy measurements of spacecraft MOI. These methods use period measurements of an oscillatory system and also use calibration weights as an integral part of the measurement process. Measurement accuracies better than 1% are typical. Both random and systematic error terms are discussed. Random errors include errors in period measurement and errors in calibration MOI measurement. The contribution of these terms to the total error is presented in parametric form. Sample cases using typical data are included. One systematic error term is the effect of ambient air. This effect is negligible for some configurations but becomes significant for large, lightweight spacecraft. Methods for estimating ambient air effects are discussed. Another systematic error term is the effect of test article elasticity. This term is analyzed as a multiple spring-mass system. Methods for estimating the effects of elasticity are presented. %B 33rd Annual Conference, Fort Worth, Texas, May 6-8 %I Society of Allied Weight Engineers, Inc. %C Fort Worth, Texas %P 16 %8 5/6/74 %G eng %U https://www.sawe.org/papers/1013/buy %9 6. INERTIA MEASUREMENTS %M 1013 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE1013 %0 Conference Paper %B 30th Annual Conference, Newport Beach, California, May 3-5 %D 1971 %T 878. A New Aerospace Balancing System for Small Work Pieces %A Elliot, G R %A Norris, G R %K 06. Inertia Measurements %X This paper describes the design and operating characteristics of a small dynamic balancing machine for measuring unbalance forces of small objects and components. It uses light weight aluminum construction throughout to minimize inertial masses, and is completely air supported and air driven. Air bearings support thrust and radial loads. The air drive system will be shut off during readouts to reduce noise. Force components are read out from two plane transducers directly through signal conditioners to a PDP8 computer on a real time basis. %B 30th Annual Conference, Newport Beach, California, May 3-5 %I Society of Allied Weight Engineers, Inc. %C Newport Beach, California %P 9 %8 5/3/71 %G eng %U https://www.sawe.org/papers/0878/buy %9 6. INERTIA MEASUREMENTS %M 0878 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0878 %0 Conference Paper %B 30th Annual Conference, Newport Beach, California, May 3-5 %D 1971 %T 882. Preflight Balance Error Analysis for Dual-Spin Satellites %A Lagana, J D %A Lotta, J G %K 06. Inertia Measurements %K Mike Hackney Best Paper Award %X

This paper provides a basic format for preflight balance analysis of the dual-spin satellite the dual-spin satellite, having a roll-to-pitch inertia ratio of less than unity, provides a more stable platform than the pancake-shaped spin-stabilized satellite having an inertia ratio greater than unity. Platform stability varies inversely with dynamic imbalance of the satellite's spun section. Several balance error sources are discussed and equations are developed solving the satellite imbalance resulting from these errors. By this discussion and development, the analysis attempts to present the logic involved in identifying the satellite imbalance. The analysis does not account for uncertainties in the mass properties of the satellite, but assumes nominal values. Errors that may be caused by aerodynamic effects, thermal effects, or effects resulting from balancing in a one-g field are neglected. A sample problem is presented to demonstrate the use of the equations. The values of the error sources used in the sample problem indicate that a dual-spin satellite would meet a wobble requirement in the arc-second level. These same error sources would produce a wobble angle that is an order of magnitude larger on a spin-stabilized satellite having a roll-to-pitch inertia close to unity.

%B 30th Annual Conference, Newport Beach, California, May 3-5 %I Society of Allied Weight Engineers, Inc. %C Newport Beach, California %P 29 %8 5/3/71 %G eng %U https://www.sawe.org/papers/0882/buy %9 6. INERTIA MEASUREMENTS %M 0882 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0882 %0 Conference Paper %B 30th Annual Conference, Newport Beach, California, May 3-5 %D 1971 %T 883. Curtailment of Mass Property Measurements Due to Tolerance and Regression Analysis %A Myzel, S J %K 06. Inertia Measurements %X This paper describes a method of curtailing measurements of mass, center of gravity, moment of inertia, and product of inertia. The method yields at least two benefits. Before production, optimum selection of materials and tolerances is possible consistent with established mass property limits. During the production phase mass property measurements are curtailed, and possibly omitted if deemed appropriate. In the pre-production design phase, measurements cannot be performed . However it is shown with a chosen degree of confidence that established mass property limits will not be exceeded. This is possible by using tolerance analysis coupled with a Monte Carlo Creation of a sample production run of components, and regression analysis. Subsequently, in production, complete measured mass properties normally can be limited to the first twelve components if deemed appropriate. Regression analysis curves can be generated by use of the measured data. Comparison with pre-production data can be made. Subsequent production measurements of only mass and center of gravity can be performed on a limited spotcheck basis. Associated moment of inertia and product of inertia limits are available from the regression curves. The curtailed.measurement scheme can be statistically monitored to detect any undesirable trends. A sample model configuration is analyzed by the Direct Approach Concept (DAC) and twelve models are assembled by Random Assembly Method (RAM). %B 30th Annual Conference, Newport Beach, California, May 3-5 %I Society of Allied Weight Engineers, Inc. %C Newport Beach, California %P 85 %8 5/3/71 %G eng %U https://www.sawe.org/papers/0883/buy %9 6. INERTIA MEASUREMENTS %M 0883 %1 Non-Member Price: $42.50; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 42.5 %4 SAWE0883 %0 Conference Paper %B 28th Annual Conference, San Francisco, California, May 5-8 %D 1969 %T 735. Introduction to the Second SAWE Dynamic Balance Symposium %A Boseker, F J %K 06. Inertia Measurements %X As a result of the recognized increasing importance of dynamic balancing to the aerospace mass properties discipline, the 27th annual conference of the SAWE held in New Orleans, LA., on May 13-16, 1968 scheduled a session devoted exclusively to this subject. The response to the request for papers was so overwhelming that two sessions were required to accommodate the total. This paper describes the papers presented at both sessions. %B 28th Annual Conference, San Francisco, California, May 5-8 %I Society of Allied Weight Engineers, Inc. %C San Francisco, California %P 23 %8 5/5/69 %G eng %U https://www.sawe.org/papers/0735/buy %9 6. INERTIA MEASUREMENTS %M 0735 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0735 %0 Conference Paper %B 28th Annual Conference, San Francisco, California, May 5-8 %D 1969 %T 736. Mechanics of Dynamic Balancing %A Wylie, G W %K 06. Inertia Measurements %X Dynamic balance machines, their readout capabilities, and the interpretation of those readouts are described. The basic equations of dynamic imbalance are derived. Figures that represent an unbalanced test specimen along with a mathematical example are provided. The body/machine reference axis relationship is discussed. Equations to determine balance weight locations, including a minimum weight solution, are provided. %B 28th Annual Conference, San Francisco, California, May 5-8 %I Society of Allied Weight Engineers, Inc. %C San Francisco, California %P 13 %8 5/5/69 %G eng %U https://www.sawe.org/papers/0736/buy %9 6. INERTIA MEASUREMENTS %M 0736 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0736 %0 Conference Paper %B 28th Annual Conference, San Francisco, California, May 5-8 %D 1969 %T 737. A New Aerospace Balancing System for Mass Properties Determination %A Stadelbauer, D G %K 06. Inertia Measurements %X A new "hard bearing" aerospace balancing system with hydrostatic spindle is described. Separate hydraulic pumps furnish high pressure oil to radial and axial bearing recesses to let the machine's spindle rotate on a thin film of oil. Bearing noise is thus largely eliminated; permitting extreme amplification of minute unbalance forces generated at very low spin rates. Simultaneous read out for both measuring planes occurs instantaneously on two special vectorial display units. These give a graphic representation of pay load unbalance directly in ounces and degrees by means of an illuminated target. Interchangeable coordinate scales permit direct read out of CoG displacement in pitch and yaw axes and/or POI values for Izy and Izy during the first spin up. Earlier associated hardware such as non-rotating mounting rings, slip ring sets, or gas film bearings for measuring MOI have been extended to include constant monitoring of unbalance forces, contour pickups for determining the geometric axis of a payload, and digital readout with printer. %B 28th Annual Conference, San Francisco, California, May 5-8 %I Society of Allied Weight Engineers, Inc. %C San Francisco, California %P 27 %8 5/5/69 %G eng %U https://www.sawe.org/papers/0737/buy %9 6. INERTIA MEASUREMENTS %M 0737 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0737 %0 Conference Paper %B 28th Annual Conference, San Francisco, California, May 5-8 %D 1969 %T 739. Mass Property Measurements at Extremely Low Angular Rates %A Bocksruker, R W %K 06. Inertia Measurements %X The trend toward larger spin stabilized spacecraft spinning at lower speeds prompted a company funded study program to develop improved methods for measuring mass properties at extremely low angular rates. The culmination of this effort was the design and fabrication of a facility with a capacity up to 10,000 pounds and an operating speed range of 2 to 120 rpm and capable of making moment of inertia measurements concurrent with balancing operations. Separation of critical functions in the machine has resulted in a semi-portable hard bearing machine w i t h a wide range of adjustable sensitivities t h a t may be matched to individual test articles for optimum performance. A method of gravitationally reacting unbalance forces w i t h accurately located precision weights has been employed to eliminate system performance dependence upon precise electrical calibration. %B 28th Annual Conference, San Francisco, California, May 5-8 %I Society of Allied Weight Engineers, Inc. %C San Francisco, California %P 38 %8 5/5/69 %G eng %U https://www.sawe.org/papers/0739/buy %9 6. INERTIA MEASUREMENTS %M 0739 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0739 %0 Conference Paper %B 28th Annual Conference, San Francisco, California, May 5-8 %D 1969 %T 740. Dynamic Balance Error Terms for Rotating Aerospace Vehicles %A Jones, D L %K 06. Inertia Measurements %X Rotating aerospace vehicles are usually balanced as a rotor on a dynamic balance machine to determine the position of their principal axes. This paper discusses the error terms in principal axis location that can exist between a rotor on the machine and a free body in space. The mass properties of a rigid body are defined with respect to a reference system and with respect to a free body. Methods for expressing principal axis location are presented. Several sets of units that can be used are described. The error terms in using a balance machine to locate the principal axis are discussed. Two types of vertical balance machines are included - two-transducer single-speed and single-transducer two-speed. The machine related errors include machine residual unbalance, induced effects of residual static unbalance, and effects of test article vibration. The effects of non-ideal structural reference systems are discussed. The effects of ambient air are divided into velocity-dependent terms and acceleration-dependent terms. The added mass of air is included in the acceleration-dependent terms. Elastic effects are caused by internal deflections under centrifugal loads. These effects can be important for single-transducer two-speed machines. Other error terms, including configuration changes, are briefly discussed. The conclusion presents some guides for making error analyses and for selecting the type of balance machine. %B 28th Annual Conference, San Francisco, California, May 5-8 %I Society of Allied Weight Engineers, Inc. %C San Francisco, California %P 29 %8 5/5/69 %G eng %U https://www.sawe.org/papers/0740/buy %9 6. INERTIA MEASUREMENTS %M 0740 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0740 %0 Conference Paper %B 28th Annual Conference, San Francisco, California, May 5-8 %D 1969 %T 772. Comments on Aerospace Vehicle Dynamic Balancing %A Kelly, O A %K 06. Inertia Measurements %B 28th Annual Conference, San Francisco, California, May 5-8 %I Society of Allied Weight Engineers, Inc. %C San Francisco, California %P 22 %8 5/5/69 %G eng %U https://www.sawe.org/papers/0772/buy %9 6. INERTIA MEASUREMENTS %M 0772 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0772 %0 Conference Paper %B 27th Annual Conference, New Orleans, Louisiana, May 13-16 %D 1968 %T 718. Measuring Moment-Of-Inertia on an Aerospace Balancing System %A Boynton, Richard %A Stadelbauer, D G %K 06. Inertia Measurements %X Moment of inertia measurement is described with a torsional pendulum and inverted torsional pendulum using a gas film bearing. Theoretical aspects of the torsional pendulum are discussed, with particular emphasis on main sources of error. The use of small calibration weights at the end of a hollow aluminum beam is demonstrated to be not only convenient, but also very accurate and versatile. Design criteria for a suitable gas film bearing are described. A method is shown of mounting a gas film bearing on top of the vertical spindle of a balancing machine. The associated hardware and instrumentation is explained, including that of the balancing system. %B 27th Annual Conference, New Orleans, Louisiana, May 13-16 %I Society of Allied Weight Engineers, Inc. %C New Orleans, Louisiana %P 32 %8 5/13/68 %G eng %U https://www.sawe.org/papers/0718/buy %9 6. INERTIA MEASUREMENTS %M 0718 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0718 %0 Conference Paper %B 26th Annual Conference, Boston, Massachusetts, May 1-4 %D 1967 %T 628. Some Problems Associated With Product of Inertia Verification of a Large Blunted Cones %A Harris, J B %K 06. Inertia Measurements %X This paper presents the results of a study to determine the feasibility of verifying the products of inertia of a large blunted cone, considered a rigid structure, using a quadrafilar pendulum. The feasibility study encompassed the following activities: 1) A survey to determine what apparatus and procedures have been used to measure the products of inertia of aeronautical and aerospace vehicles and what accuracies have been achieved; 2) Consideration of advantages and disadvantages of several types of measurement systems and selection of one or more that appear to be best suited for the particular application in mind; 3) Analytical investigation of the characteristics of the selected system and prediction of the error inherent in its use. Brief system descriptions, including advantages and disadvantages are presented in Figures 1, 2, and 3 for types of systems that seem best suited for the cone application. These systems are the spin table/inverted torsion bar, the torsion bar suspension, and the quadrafilar pendulum. Reasons for selecting the quadrafilar pendulum are discussed. A study of the characteristics of the quadrafilar pendulum as applied to the cone application has uncovered some interesting possibilities and advantages. The most interesting is the possibility of defining the moment of inertia ellipsoid by testing with the cone inclined at large angles to the roll reference axis only. %B 26th Annual Conference, Boston, Massachusetts, May 1-4 %I Society of Allied Weight Engineers, Inc. %C Boston, Massachusetts %P 50 %8 5/1/67 %G eng %U https://www.sawe.org/papers/0628/buy %9 6. INERTIA MEASUREMENTS %M 0628 %1 Non-Member Price: $25.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 25 %4 SAWE0628 %0 Conference Paper %B 25th Annual Conference, San Diego, California, May 2-5 %D 1966 %T 568. The Moment of Inertia of Liquid Filled Cylindrical Tanks About Various Axes %A Phillips, M S %K 06. Inertia Measurements %X This paper gives the results of a series of experiments performed to determine the moment of inertia of filled cylindrical tanks as they oscillate about various axes. The purpose of this investigation was to find an approximate analytical expression for determining liquid moments of inertia to better predict the dynamic behavior of launch vehicles. The experiments were divided into four categories: 1. Roll Axis about Center of Mass 2. Displaced Roll Axis 3. Yaw-Pitch Axis about Center of Mass 4. Displaced Yaw- Pitch Axis Torsional and compound pendulums were used for oscillating the tanks. The results of these tests verified the available analytical expressions. These expressions can be applied to Launch vehicle fuel tanks. By definition, the moment of inertia is the property of a solid which depends on its mass distribution and its axis of rotation. Since liquid is non-rigid, the amount of liquid which participates in rotation depends on the boundary conditions placed on the liquid, the liquid viscosity, the frequency of rotation, and the axis of rotation. The dependency of the liquid behavior on so many variables shows that the terms, liquid and solid moment of inertia, are not synonymous. Therefore, the liquid moment of inertia is normally referred to as the effective moment of inertia. That is. the solid moment of inertia which would yield the same apparent moment of inertia of the liquid. The experimental results agree well with the analytical expressions derived from classical hydrodynamic theory. The yaw-pitch expression is obtained by using velocity potential theory with the aspect ratio as the only variable. The roll axis moment of inertia is dependent on the liquid viscosity, oscillation frequency, arid the tank geometry, but for cylindrical fuel tanks it is very close to zero. The moment of inertia transfer theorem for solids was proved to be valid for liquids. The equations herein, which have been verified experimentally, can be easily applied, if the proper variables are known. %B 25th Annual Conference, San Diego, California, May 2-5 %I Society of Allied Weight Engineers, Inc. %C San Diego, California %P 42 %8 5/2/66 %G eng %U https://www.sawe.org/papers/0568/buy %9 6. INERTIA MEASUREMENTS %M 0568 %1 Non-Member Price: $21.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 21 %4 SAWE0568 %0 Conference Paper %B 25th Annual Conference, San Diego, California, May 2-5 %D 1966 %T 569. A Universal Facility for Mass Properties Measurement %A Detwiler, R L %K 06. Inertia Measurements %X The methods and equipment used, at the present time, for the measurement of the mass properties of an object have evolved from simple laboratory devices to rather sophisticated systems. However, with a few exceptions, these systems such as weighing instruments, pendulums, spin balancers and the like are independent devices each one requiring its own instrumentation, fixturing, and measurement set up. Analysis of the types of systems being used has indicated that the functions of the various systems could be combined into one universal facility. Rather than being a compromise, because of its universality, this facility could exhibit improved accuracy and operating convenience. This improvement would result from minimization of positioning errors, and optimization of certain instrumentation and mechanical features. The latter is possible since it becomes economically feasible to utilize certain rather expensive devices when their use is shared in several types of measurements. The objective of the universal facility program at Miller Research Corporation has been the achievement of the above design and performance characteristics. The development of the universal mass properties facility should provide a useful tool to the missile and space industry. It should permit the routine measurement and control of mass property parameters to an order of accuracy previously achieved only in special Laboratory setups. In addition it will permit measurements on a variety of test objects with only fixturing changes required and thus eliminate the “development” program previously necessary to devise a measurement setup for each different object to be measured. %B 25th Annual Conference, San Diego, California, May 2-5 %I Society of Allied Weight Engineers, Inc. %C San Diego, California %P 23 %8 5/2/66 %G eng %U https://www.sawe.org/papers/0569/buy %9 6. INERTIA MEASUREMENTS %M 0569 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0569 %0 Conference Paper %B 25th Annual Conference, San Diego, California, May 2-5 %D 1966 %T 570. Dynamic Balancing of Spin Stabilized Systems %A McKeever, J R %K 06. Inertia Measurements %X Dynamic balancing of spin-stabilized systems in the aerospace industry is generally done at low rotational velocities about a vertical spin axis. This has led to development of a new family of dynamic/static balancing machines. This paper is a discussion of the development of this family of dynamic/static balancing equipment. Section 2, “Dynamic/Static Balancing Theory,” describes the theory of two-plane dynamic/static balancing. Section 3, “Why Balance’ reviews the types of assemblies which require balancing and why they require it. Section 4, “Principles of Balance Machine Design,” covers design considerations that have led to the development of this new family of dynamic/static balancing machines. Section 5, “A Look into the Near Future,” is a short range projection of what considerations are now influencing balance machine development. %B 25th Annual Conference, San Diego, California, May 2-5 %I Society of Allied Weight Engineers, Inc. %C San Diego, California %P 26 %8 5/2/66 %G eng %U https://www.sawe.org/papers/0570/buy %9 6. INERTIA MEASUREMENTS %M 0570 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0570 %0 Conference Paper %B 24th Annual Conference, Denver, Colorado, May 17-19 %D 1965 %T 503. Selection of Techniques for Measurement of Moment of Inertia %A Harris, E C %K 06. Inertia Measurements %X The MOI (moment of inertia) of a body is a relatively difficult mass distribution property to measure even though it may be found in a number of different ways. Before any test method is considered the need for the measurement should be clearly established. In some cases the MOI of the object may be determined more accurately and at less expense by means other than testing. If testing is necessary it is very important that the axis about which the MOI is to be measured be properly defined. A measurement of MOI is generally of most significance when it occurs about an axis through the cg (center of gravity) of the test specimen. The easiest methods of measuring MOI are based on a particular type of oscillating system where the test article is supported in such a manner that it may oscillate about the defined axis of rotation with angular harmonic motion. Angular harmonic motion occurs when the restoring torque is proportional to the angular displacement. The MOI of the test object is deduced from the natural period of the oscillating system and from a system constant. The system constant depends on how the restoring torque is produced. Consideration of various MOI measuring methods, where angular harmonic motion is utilized, shows that each technique generally has its own unique advantages and disadvantages. However, there is usually one technique most suitable to a given situation. The selection is influenced by such factors as: 1) the characteristics of the particular test specimen, including means of attachment; 2) the axis about which the MOI is required; 3) ground handling considerations; 4) other mass properties to be measured; 5) required accuracy of the measurements; 6) available test facilities and experience. It is not believed that any one technique is always superior to all others. The weight and balance test engineer cannot select the most appropriate technique for each situation unless he has a working knowledge of a variety of methods. Such knowledge is, however, very difficult to acquire except through practical experience combined with R&D (research and development) testing. It is recommended that the aerospace industries, the customer (federal agencies) and the professional society unite in a common and coordinated effort to develop more efficient mass properties testing methods and to provide detailed design criteria for this kind of test equipment. %B 24th Annual Conference, Denver, Colorado, May 17-19 %I Society of Allied Weight Engineers, Inc. %C Denver, Colorado %P 49 %8 5/17/65 %G eng %U https://www.sawe.org/papers/0503/buy %9 6. INERTIA MEASUREMENTS %M 0503 %1 Non-Member Price: $24.50; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 24.5 %4 SAWE0503 %0 Conference Paper %B 24th Annual Conference, Denver, Colorado, May 17-19 %D 1965 %T 504. Determining Moments of Inertia by Using the Period Decay Rate of a Mechanical Oscillating System %A Phillips, M S %K 06. Inertia Measurements %X This paper presents the results of a series of experiments designed to develop a rapid, accurate, and economical method of measuring mass moments of inertia. In a perfect oscillating system, no “additional mass effects” from environmental atmosphere and no other frictional losses occur. Therefore, the period of oscillation is constant. Since no perfect system exists, a new method is presented here which compensates for losses and gives an accurate value for the period of oscillation. In turn, from the oscillation value, an accurate value for the moment of inertia of the oscillated object can be determined. This approach to moment of inertia determination has been applied to a torsional air-bearing table. The air-bearing table provides an easy and rapid method for determining moments of inertia of variously shaped objects and lends itself readily to automation. %B 24th Annual Conference, Denver, Colorado, May 17-19 %I Society of Allied Weight Engineers, Inc. %C Denver, Colorado %P 30 %8 5/17/65 %G eng %U https://www.sawe.org/papers/0504/buy %9 6. INERTIA MEASUREMENTS %M 0504 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0504 %0 Conference Paper %B 24th Annual Conference, Denver, Colorado, May 17-19 %D 1965 %T 505. An Approach to an Automated System for Determination of Mass Moments of Inertia %A Bridges, C S %A Carpenter, G T %K 06. Inertia Measurements %X The objective of this paper is to illustrate the feasibility of the design of a specialized digital system for determination of the moment of inertia of space-oriented objects. The feasibility was illustrated through the use of an analog computer and associated interface equipment that was developed in NASA's Mass Metrology Laboratory. Existing mechanical and electronic units were employed, where possible, in an attempt to expedite the feasibility study. It was required that determination of the moment of inertia be obtained to 85% accuracy. The developed prototype system greatly exceeded this accuracy, thus concluding the feasibility of the development of a more elaborate and accurate system. Limitations were found in the analog computer accuracy of 'solution, specifically in regard to the solution of non-linear functions. These limitations can be avoided, in many instances, by variation of computer scaling. In general, the analog computer was found adaptable as an in-line computational device for the subject feasibility study. This may be attributed to the fact that the frequencies encountered are compatible to analog solution and that the versatility of the computer, mathematically, is unmatched for the time-limited feasibility study program %B 24th Annual Conference, Denver, Colorado, May 17-19 %I Society of Allied Weight Engineers, Inc. %C Denver, Colorado %P 21 %8 5/17/65 %G eng %U https://www.sawe.org/papers/0505/buy %9 6. INERTIA MEASUREMENTS %M 0505 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0505 %0 Conference Paper %B 23rd National Conference / Sheraton, Dallas Hotel, Southland Center, Dallas, Texas May 18-21 %D 1964 %T 424. A Bifilar Moment of Inertia Facility %A Jones, G H %K 06. Inertia Measurements %X Most mass measurement facilities perform single functions. However, a facility for performing multiple mass properties measurements of rigid bodies, such as spacecraft components and/or assemblies weighing up to 1,000 pounds, is in operation at the NASA - Goddard Space Flight Center. It provides measurements of weight, center of gravity, moment of inertia, and product of inertia in a completely self-contained facility. Weight measurement is provided by a calibrated load cell mounted in the support system; center of gravity, by load cells’ arranged to determine the mechanical moment required to balance the weight moment of the test item: moment of inertia, through application of the bifilar pendulum; and product of inertia, by means of dynamic recording of force moments developed in torsional oscillation. A view into the background of spacecraft mass measurements at Goddard Space Flight Center is discussed. The advent of the second generation or observatory type scientific spacecraft pointed to the need for larger capacity and more accurate mass measurement facilities.. This need led to consideration of a multiple mass measuring facility instead of individual facilities for the separate operations. The development history of the facility is discussed, including problems encountered and their solutions. The historical treatment begins with the design specification and runs through the proposal, contractor's development, installation, modifications, acceptance, and operational experience. A description of the facility is given with a functional discussion of the major components and assemblies. Built-in handling and maintenance aids are described. A test sequence for a typical sample spacecraft is described. Use of data sheets for recording test measurements is described, and the derivation of constants used in the data sheets is shown. %B 23rd National Conference / Sheraton, Dallas Hotel, Southland Center, Dallas, Texas May 18-21 %I Society of Allied Weight Engineers, Inc. %C Dallas, Texas %P 25 %8 5/18/64 %G eng %U https://www.sawe.org/papers/0424/buy %9 6. INERTIA MEASUREMENTS %M 0424 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0424 %0 Conference Paper %B 23rd National Conference / Sheraton, Dallas Hotel, Southland Center, Dallas, Texas May 18-21 %D 1964 %T 442. Determination of Parameters for Mechanical Mass Measuring Devices, With Discussion of Readouts, Mechanical and Electronic %A Trebilcock, J L %K 06. Inertia Measurements %B 23rd National Conference / Sheraton, Dallas Hotel, Southland Center, Dallas, Texas May 18-21 %I Society of Allied Weight Engineers, Inc. %C Dallas, Texas %P 25 %8 5/18/64 %G eng %U https://www.sawe.org/papers/0442/buy %9 6. INERTIA MEASUREMENTS %M 0442 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0442 %0 Conference Paper %B 23rd National Conference / Sheraton, Dallas Hotel, Southland Center, Dallas, Texas May 18-21 %D 1964 %T 448. Inertia Measurements of Aerospace Equipment %A Rogers, N %K 06. Inertia Measurements %X Measured inertia data submittal of Aerospace equipment is needed for determining expected performance characteristics of a vehicle. Procuring agencies are beginning to request such information from equipment suppliers. This paper recommends the torsional pendulum as one method for obtaining experimental inertia values and presents formula derivation, equipment calibration, and measurement procedures. %B 23rd National Conference / Sheraton, Dallas Hotel, Southland Center, Dallas, Texas May 18-21 %I Society of Allied Weight Engineers, Inc. %C Dallas, Texas %P 15 %8 5/18/64 %G eng %U https://www.sawe.org/papers/0448/buy %9 6. INERTIA MEASUREMENTS %M 0448 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0448 %0 Conference Paper %B 23rd National Conference / Sheraton, Dallas Hotel, Southland Center, Dallas, Texas May 18-21 %D 1964 %T 455. The Avco Rad Moment of Inertia Measurement Machine %A Hollenbeck, L G %A Dispensa, M T %A Mykytyn, R J %A Bloch, D B %K 06. Inertia Measurements %X The method and machine for performing actual tests of mass moment of inertia upon various types of hardware, as discussed in this paper, were developed by the Research and Advanced Development Division of Avco Corporation. In its present configuration, the machine is extremely accurate and relatively simple to operate. Basically the machine consists of a turntable which supports a test article, rotary motion is imparted to the turntable by means of a falling weight attached to a cable which is wrapped around the turntable perimeter. Acceleration of the turntable, including test article, is measured when the weight is falling and deceleration is measured during the coast down which occurs after the weight has disengaged. These measured values are instantaneously fed into an integrating digital voltmeter and printer. The read-out, in radians per second squared, is converted to moment of inertia by means of a modified form of the equation for torque ( T = I a ). To calibrate the system, a standard was obtained by constructing a slug consisting of a simple geometric shape whose mass and moment of inertia could be accurately measured and calculated, During a preliminary calibration run on the late test version of the moment of inertia machine, accuracies of 0. 04 percent were obtained. The system could be conservatively rated at 0. 20 percent. The fact that the new machine will give this accuracy with a single run represents a significant improvement. With the older machines, it is necessary to take the average of several runs to approach this accuracy. 'The missile and space industry should find many applications for a moment of inertia machine of this indicated accuracy. %B 23rd National Conference / Sheraton, Dallas Hotel, Southland Center, Dallas, Texas May 18-21 %I Society of Allied Weight Engineers, Inc. %C Dallas, Texas %P 19 %8 5/18/64 %G eng %U https://www.sawe.org/papers/0455/buy %9 6. INERTIA MEASUREMENTS %M 0455 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0455 %0 Conference Paper %B 22nd National Conference, St. Louis, Missouri, April 29 - May 2 %D 1963 %T 369. A Simplified Technique for Measurement of Product of Inertia %A Codr, J J %A Harris, E C %K 06. Inertia Measurements %X This paper was presented at the Twenty-second Annual National Conference of the Society of Aeronautical Weight Engineers at St. Louis, Missouri, April 29-May 1, 1963. This paper presents a technique developed by Douglas Aircraft Company, INC. for measurement of POI (product of inertia). The method is used to dynamically balance missile control fins. Derivation of equations, discussion of hardware design and general test procedures are included. The POI of an object is a mass distribution property which can be measured only when the object has angular motion. Any system used in measuring this property must produce angular acceleration and/or velocity on the test body. The angular motion, in this case, is caused by rotation of the test body as a pendulum. A bifilar pendulum system was selected to provide the angular motion because of the necessary restraints provided by the supporting linkage. Harmonic motion occurs as the bifilar pendulum oscillates. Thus, the angular accelerations and velocities vary sinusoid ally according to the natural frequency of the pendulum. Turning moments are induced about each of two horizontal axes because of the angular velocity, angular acceleration, and the POI of the test body. These turning moments cause pertabations in the pendulum motion. Adjustable counterweights added to the system induce turning moments opposite to those caused by the test body. The resulting pertabation in the motion of the pendulum system is visually observed and the counterweights are adjusted until the pertabations no longer occur. The system, therefore, is dynamically balanced; the POI of the counterweights is equal and opposite to that of the test body. The POI of the test body can be readily calculated from the mass and geometry of the counterweights. This technique is advantageous because: A. POI of the test object may be measured with essentially the same test apparatus that is used in locating cg (center of gravity) and measuring moment of inertia. B. Measuring instrumentation for POI test is not required. C. A simple test procedure permits unskilled personnel to conduct the testing. This approach may be used as a relatively simple and inexpensive method for dynamically balancing test objects if a high degree of precision is not required. It is concluded that there are many useful applications of this technique for measurement of POI. %B 22nd National Conference, St. Louis, Missouri, April 29 - May 2 %I Society of Allied Weight Engineers, Inc. %C St. Louis, Missouri %P 28 %8 5/29/63 %G eng %U https://www.sawe.org/papers/0369/buy %9 6. INERTIA MEASUREMENTS %M 0369 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0369 %0 Conference Paper %B 22nd National Conference, St. Louis, Missouri, April 29 - May 2 %D 1963 %T 380. Measurement of the Moment of Inertia of the Orbiting Astronomical Observatory %A Dolan, F J %K 06. Inertia Measurements %X This paper was presented at the Twenty-second Annual National Conference of the Society of Aeronautical Weight Engineers at St. Louis, Missouri, April 29-May 1, 1963. The precise stabilization and control requirements of the Orbiting Astronomical Observatory (OAO) require an exact knowledge of the spacecraft’s mass moments of inertia. In addition to the normal calculations, a carefully conducted test program was taken to measure these moments of inertia. After a literature survey to investigate the measurement available, the bifilar torsion pendulum was chosen as simplest and most exact. The design of the bifilar hardware and test instrumentation is presented in detail. The three axes mass property measurements (weight, center of gravity, and moment of inertia) made on the OAO are described. Particular attention is given to the measurement of tare inertia. This tare inertia arises primarily from the adapters necessary to affix the OAO to the suspension filaments, and also from the additional apparent mass effect caused by air drag of the spacecraft’s large solar paddles. Both effects were measured directly by the bifilar pendulum. The adapters were swung as a unit, without the OAO, and their combined weight, c.g., and moment of inertia were recorded. The drag effect of the air on the oscillating paddles was determined by swinging two large open frameworks of the same size and shape as the actual OAO paddles. These frameworks were then covered with lightweight mylar and re-swung. The difference between the two measured inertias was the additional mass effect caused by paddle air drag. The bifilar facility proved to be readily adaptable to other vehicles associated with the OAO development. %B 22nd National Conference, St. Louis, Missouri, April 29 - May 2 %I Society of Allied Weight Engineers, Inc. %C St. Louis, Missouri %P 26 %8 5/29/63 %G eng %U https://www.sawe.org/papers/0380/buy %9 6. INERTIA MEASUREMENTS %M 0380 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0380 %0 Conference Paper %B 21st National Conference, Seattle, Washington, May 14-17 %D 1962 %T 304. Simulation of Mass Properties for Test Vehicles Using the Inertia Component Method %A Denney, L M %A Durrington, V L %K 06. Inertia Measurements %X This paper was presented at the Twenty-First National Conference of the Society of Aeronautical Weight Engineers at Seattle, Washington, May 14 – 17, 1962. The mass properties of aerospace vehicles and their components have become of ever increasing significance and must be simulated for testing in the various design stages. This is required not only for preliminary wind tunnel testing, but also for full scale models used in ground vibration tests, drop tests, etc. This paper discusses the mass balancing of a test vehicle to meet required weight, center of gravity, and moments of inertia about three axes. The design and construction peculiar to the test vehicle complicate the mass balance problem considerably. The inertia component concept is developed into a procedure for analyzing a mass balance problem and for calculating ballast weights to meet moment of inertia requirements. This inertia component mass balance procedure replaces the often used trial and error technique with a precise method of calculation. An exact weight installation is achieved by resolving the pitch, roll, and yaw required and actual test inertias about three axes into components along lines parallel to the three axes --- any one of which can be changed or considered without affecting the other two. %B 21st National Conference, Seattle, Washington, May 14-17 %I Society of Allied Weight Engineers, Inc. %C Seattle, Washington %P 17 %8 5/14/62 %G eng %U https://www.sawe.org/papers/0304/buy %9 6. INERTIA MEASUREMENTS %M 0304 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0304 %0 Conference Paper %B 21st National Conference, Seattle, Washington, May 14-17 %D 1962 %T 312. A Simplified Technique for Precision Measurement of Moment of Inertia %A Robertson, R L %A Harris, E C %K 06. Inertia Measurements %X This paper was presented at the Twenty-first Annual National Conference of the Society of Aeronautical Weight Engineers at Seattle, Washington, May 14-17, 1962. The method for determining the mass MOI (moment of inertia) discussed in this paper was developed by the Missile and Space Systems Division of Douglas Aircraft Co., Inc., for use on the Skybolt weapon system. The attractiveness of this method lies in its simplicity and accuracy. a. Simplified equations allow determination of the vehicle mass MOI about the axis of rotation without the measurement of either its mass or its center of gravity. The only variable in the equation is time. b. The technique minimizes ground handling problems by permitting measurements of the vehicle and its major components in their normal (horizontal) handling position. c. An accurate MOI about the center of gravity can be determined because of the small MOI transfer term inherent in this system. %B 21st National Conference, Seattle, Washington, May 14-17 %I Society of Allied Weight Engineers, Inc. %C Seattle, Washington %P 25 %8 5/14/62 %G eng %U https://www.sawe.org/papers/0312/buy %9 6. INERTIA MEASUREMENTS %M 0312 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0312 %0 Conference Paper %B 21st National Conference, Seattle, Washington, May 14-17 %D 1962 %T 316. An Arbitrary Axis Inertia Measuring System %A Woodward, W R %K 06. Inertia Measurements %X This paper was presented at the Twenty-first Annual National Conference of the Society of Aeronautical Weight Engineers at Seattle, Washington, May 14-17, 1962. This is a case history of a successful application of purely analytical instrument design. In consideration of the problems in aligning and leveling large packages, and in consideration of the availability of modern computing equipment, a more basic approach is made to the measurement of all inertial properties. Arbitrary suspension axes are used to minimize the mass and inertia of support structure. Thus the errors commensurate with large tares are required. The technician simply measures two reference heights (or angles) on the specimen and one period of oscillation for each suspension. After several suspensions sufficient data are accumulated for the computer to solve for all inertial properties. Because of the arbitrary nature of the suspension, the human bias factor is eliminated from the recording of the specimen position. Better accuracy of inertial determination has been demonstrated. The system lends itself to a statistical approach which yields an appraisal of the reliability as well as the mean value of results. Computation time is 30 seconds for all inertial properties expressed in three of the more common axis systems. Any computer capable of solving a 6 X 6 matrix will perform the computation. Since excellent computing service is as close as convenient as the telephone the cost of a special purpose computer is not justified. %B 21st National Conference, Seattle, Washington, May 14-17 %I Society of Allied Weight Engineers, Inc. %C Seattle, Washington %P 12 %8 5/14/62 %G eng %U https://www.sawe.org/papers/0316/buy %9 6. INERTIA MEASUREMENTS %M 0316 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0316 %0 Conference Paper %B 21st National Conference, Seattle, Washington, May 14-17 %D 1962 %T 319. Method of Predicting Center of Gravity and Mass Moment of Inertia of the Human Body in Any Position %A Siedell, R R %A Guadagnoli, M J %K 06. Inertia Measurements %X This paper was presented at the Twenty-first Annual National Conference of the Society of Aeronautical Weight Engineers at Seattle, Washington, May 14-17, 1962. One of the many problems associated with manned space vehicles confronting the weight control engineer is the predication of center of gravity location and mass moment of inertia about three axes of the human body. In keeping with modern weight accounting methods, an airplane type IBM routine has been adapted for center of gravity and inertial calculations. It was obvious that a human body divided into several parts or segments would yield better results than using the body as one item. This division of the body yielded fourteen segments. The head and neck were left intact. The trunk or torso was separated from the extremities. The extremities were divided into three segments each such as the hand, lower arm and upper arm. Mass, center of gravity location and dimensional data for each segment were derived from existing reports and fed into the IBM routine as weight empty. It is worthwhile to mention the condition of the body when placed in the IBM routine was in an unclad or nude state. Clothing and equipment when decided on could be added as useful load items. As a result of supporting a related study, the body was placed in IBM in seven positions. These seven positions were selected to give the center of gravity “box” of limits along the three axes. Body positions were accomplished by moving only the arms and legs. The head, neck and trunk remained in the same location from the reference planes for all seven positions. Although being unable to experimentally test the moment of inertial data, center of gravity location test for several positions were conducted using subjects within the percentile range of the calculated subject. Tests were conducted by two methods. A simple two scale reaction was used first. The second test was conducted on a very excellent test stand designed to measure center of gravity locations along three axes. %B 21st National Conference, Seattle, Washington, May 14-17 %I Society of Allied Weight Engineers, Inc. %C Seattle, Washington %P 20 %8 5/14/62 %G eng %U https://www.sawe.org/papers/0319/buy %9 6. INERTIA MEASUREMENTS %M 0319 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0319 %0 Conference Paper %B 20th National Conference, Akron, Ohio, May 15-18 %D 1961 %T 290. Tri-Filar Moment of Inertia Apparatus %A Schuelke, R L %K 06. Inertia Measurements %X This paper was presented at the Twentieth National Conference of the Society of Aeronautical Weight Engineers at Akron, Ohio, May 15 – 18, 1961. This paper discusses the approach and problems encountered during the phases that led to the successful completion of an operative trifilar moment of inertia test apparatus. The investigation of three types of pendulums--- torsional, compound, and bifilar--- is discussed and the final selection of a trifilar pendulum is explained. The use of the trifilar allows the weight, centers of gravity, and moments of inertia about one axis to be obtained with one setup, thereby reducing handling. The paper discusses the methods used in the fabrication and assembly of the test equipment as well as its calibration and the calculation of tare values. The paper concludes with the description of operational procedures for performing the desired measurements. %B 20th National Conference, Akron, Ohio, May 15-18 %I Society of Allied Weight Engineers, Inc. %C Akron, Ohio %P 14 %8 5/15/61 %G eng %U https://www.sawe.org/papers/0290/buy %9 6. INERTIA MEASUREMENTS %M 0290 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0290 %0 Conference Paper %B 20th National Conference, Akron, Ohio, May 15-18 %D 1961 %T 296. The Derivation of an Efficiency Factor and Its Application to a Torsional System for Determining Mass Moments of Inertia %A Carpenter, G T %A Meredith, D T %K 06. Inertia Measurements %X This paper was presented at the Twentieth National Conference of the Society of Aeronautical Weight Engineers at Akron, Ohio, May 15 – 18, 1961. This paper explains the derivation, by experimental means, of empirical correction to classical procedures presently used to measure Mass Moments of Inertia by a torsion rod system. The use of an efficiency factor (E) is incorporated in the mathematical equation I = Kt^2 to be I =EKt^2. The relationship between a perfect measuring system (a non-existing absolutely frictionless fixture with no internal or external “drag” forces, capable of producing “perpetual motion”) and a normal measuring system operating in average environment was used to determine the “efficiency factor.” Through intense investigation, it was proven that the decay or dampening experienced with a normal measuring system was directly related to some combination of the system configuration and mass of that object contained within it. This relationship is established and applied to resulting Inertia Measuring methods. %B 20th National Conference, Akron, Ohio, May 15-18 %I Society of Allied Weight Engineers, Inc. %C Akron, Ohio %P 24 %8 5/15/61 %G eng %U https://www.sawe.org/papers/0296/buy %9 6. INERTIA MEASUREMENTS %M 0296 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0296 %0 Conference Paper %B 16th National Conference, Broadview Hotel, Wichita, Kansas, April 29 - May 2 %D 1957 %T 151. Experimental Inertia Tests for Missiles %A Harris, J B %K 06. Inertia Measurements %X The predominance of inertia terms in current missile stability control studies emphasizes the need for precise moment of inertia data. These data may be determined experimentally, quickly and accurately, utilizing simple apparatus and procedure, by either Pendulum or Spring Restrained Oscillation methods. Both of these method types have been used successfully to measure moments of inertia for full scale aircraft and missiles. The purpose of this paper is to present a bibliography of reports and papers which describe apparatus and procedures which have been utilized for such tests, to present an introduction to both the standard pendulum and the spring restrained oscillation methods, and to describe an application of the spring restrained oscillation method for experimental measurement of moment of inertia data for a full scale missile. The presentation is planned to set forth the basic principles involved, to explain what considerations led to the selection of the spring restrained oscillation method for actual tests, and to describe the tests as they were conducted by the Weight Methods Group of Temco Aircraft Corporation. %B 16th National Conference, Broadview Hotel, Wichita, Kansas, April 29 - May 2 %I Society of Allied Weight Engineers, Inc. %C Wichita, Kansas %P 26 %8 5/29/57 %G eng %U https://www.sawe.org/papers/0151/buy %9 6. INERTIA MEASUREMENTS %M 0151 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0151 %0 Conference Paper %B 14th National Conference, Hilton Hotel, Fort Worth, Texas, May 2-5 %D 1955 %T 119. Experimental Inertia Determination %A Kleinhans, R G %K 06. Inertia Measurements %X The Weight Group is in a spectacularly unique position in the aircraft business. No other technical (or non-technical) group receives the complete, over-all aircraft picture while threading their way through the detailed design of each and every component. To rephrase the usual saying “ The weight engineer must see the forest as well as the trees” Of course this unique position since it involves detailed information about all airplane components, results in the allocation of some arduous and onerous duties to the Weight Group. One of these is the computation of the Moment so Inertia of the complete airplane as well as the inertias of some sundry components such as control surfaces, externals stores, and all other items which have an independent motion of their own. The usual chronological steps in arriving at these results are: first, a rough approximation of the total inertia based on the outlines and assumed weight distribution; later an accurate calculation based on finished detailed drawings; and finally (in the case of control surfaces, some store and airplane component ) an experimental determination. It is with this final step this paper is chiefly concerned. %B 14th National Conference, Hilton Hotel, Fort Worth, Texas, May 2-5 %I Society of Allied Weight Engineers, Inc. %C Fort Worth, Texas %P 29 %8 5/2/55 %G eng %U https://www.sawe.org/papers/0119/buy %9 6. INERTIA MEASUREMENTS %M 0119 %1 Non-Member Price: $20.00; Member Price: $10.00 Members: First 10 product downloads are Free. %2 10.00 %3 20 %4 SAWE0119