SAWE Technical Papers

@inproceedings{3775,

title = {3775. Influence of the Inertia Parameters on a Dynamic Driving Simulator Performances},

author = {Giorgio Previati and Gianpiero Mastinu and Massimiliano Gobbi},

url = {https://www.sawe.org/product/paper-3775},

year  = {2022},

date = {2022-05-21},

urldate = {2022-05-21},

booktitle = {81st Annual Conference, Savannah, Georgia},

pages = {14},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Savannah, Georgia},

abstract = {This paper deals with the analysis of the effects of inaccuracies in the knowledge of the inertia properties of a dynamic driving simulator on the performances of its motion control. Dynamic motion simulators aim to reproduce the motion of a vehicle with a high degree of fidelity. The simulators are moved by actuators up to relatively high frequencies. Special algorithms are used to scale the motion of the actual vehicle in order to comply with the travel allowed by the simulator while maintaining the more significant motion characteristics. Such algorithms are fine tuned to reproduce the feeling of each vehicle and suit the expectations of each user. Therefore, the motion controllers of the driving simulators must be able to accomplish the desired motion. Errors in the knowledge of the inertia parameters of the driving simulator can reduce the performances of the controller and increase the tracking error with respect to the desired trajectory.},

keywords = {05. Inertia Calculations, 31. Weight Engineering - Surface Transportation},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3761,

title = {3761. Estimating Mass Moments of Inertia – A Quick Check Method},

author = {Damian P. Yañez},

url = {https://www.sawe.org/product/paper-3761},

year  = {2022},

date = {2022-05-21},

urldate = {2022-05-21},

booktitle = {81st Annual Conference, Savannah, Georgia},

pages = {14},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Savannah, Georgia},

abstract = {Mass Moments of Inertia (MOI) are important and often critical components of the mass properties of a vehicle, but many Mass Properties Engineers tend to focus only on weight and center of gravity (CG), and have limited exposure to these other, rotational properties. In this paper, I present a brief overview of MOI, why they are important, and a method for quickly estimating the MOI of a part, subassembly, or assembly. This method is particularly useful when reviewing CAD calculations or a supplier’s mass properties reports in which you don’t have visibility into the details to ensure that the results are reasonable. You can also use this technique to make a quick MOI estimate for trade studies. While there are some limitations to this method which are described in this paper, this technique will get you in the ballpark and increase your confidence that the rotational properties of your vehicle are properly represented.},

keywords = {05. Inertia Calculations, 25. Weight Engineering - System Estimation},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3728,

title = {3728. Investigation on the Mass Properties of Cars},

author = {Giorgio Previati},

url = {https://www.sawe.org/product/paper-3728},

year  = {2019},

date = {2019-05-01},

booktitle = {78th Annual Conference, Norfolk, VA},

pages = {14},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Norfolk, Virginia},

abstract = {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.},

keywords = {05. Inertia Calculations, 06. Inertia Measurements},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3612,

title = {3612. Measurement of the Inertia Tensor - A Review},

author = {Giorgio Previati and M. Gobbi and G. Mastinu},

url = {https://www.sawe.org/product/paper-3612},

year  = {2014},

date = {2014-05-01},

booktitle = {73rd Annual Conference, Long Beach, California},

pages = {23},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Long Beach, California},

abstract = {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.},

keywords = {05. Inertia Calculations, 06. Inertia Measurements, 32. Product of Inertia Measurement},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3620,

title = {3620. Inertia Uncertainty Coordinate Transformation},

author = {Adam M. Tahir and J H Nakai},

url = {https://www.sawe.org/product/paper-3620},

year  = {2014},

date = {2014-05-01},

booktitle = {73rd Annual Conference, Long Beach California},

pages = {18},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Long Beach, California},

abstract = {The nominal values and uncertainties of inertia tensor elements (moments and products of inertia) are dependent on the coordinate frame in which they are described. In many mass properties applications, there is a need to perform coordinate transformations in order to describe moments and products of inertia and their uncertainties in different coordinate frames. Coordinate transformation methods and algorithms for nominal moments and products of inertia are well known, but to date there are no agreed-upon procedures and algorithms to perform coordinate transformations on inertia uncertainties. This paper proposes a method to consistently express inertia uncertainties in different coordinate frames. This method addresses the problem as a linear optimization problem. The method's accuracy is being tested using a probabilistic model. Early results look promising.},

note = {Mike Hackney Best Paper Award},

keywords = {05. Inertia Calculations, Mike Hackney Best Paper Award},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3628,

title = {3628. Control Surfaces - Mass Properties under Control},

author = {Jesùs San Pedro Pérez and Radoslaw Zawadzki},

url = {https://www.sawe.org/product/paper-3628},

year  = {2014},

date = {2014-05-01},

booktitle = {73rd Annual Conference, Long Beach California},

pages = {25},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Long Beach, California},

abstract = {The mass modeling process is part of the A/C development process, creating mass distribution data as input for loads and aeroelastics. The mass properties derivations is a key milestone in building aircraft dynamic and flutter analyses and further more for dimensioning of primary structure. 

This paper gives an overview about A/C control surfaces and discusses the results of appropriate mass properties as input variable for flutter investigations. A simple example illustrates the evolution of mass properties on the process throughout the different maturities during development. 

Furthermore impact of uncertainties related to estimated mass and finally the validation of mass properties is taking into account as a key aspect in terms of certification requirements.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3561,

title = {3561. The Importance Of Inertia Properties Measurement For Road Accident Reconstruction},

author = {Massimiliano Gobbi and Giorgio Previati},

url = {https://www.sawe.org/product/paper-3561},

year  = {2012},

date = {2012-05-01},

booktitle = {71st Annual Conference, Bad Gögging, Germany},

pages = {17},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Bad Gögging, Germany},

abstract = {The paper refers to the accurate reconstruction of road accidents which often requires the proper computation of the motion of vehicles before and after crash. A sensitivity analysis is performed for quantifying the effects of the main mass properties on accurate accident reconstruction. In particular the respective uncertainties of the location of the centre of gravity and of the moment of inertia around the vertical axis of crashed vehicles are considered. The final aim of such a theoretical investigation is assessing and prescribing the measurement accuracy of both the centre of gravity location and the inertia tensor components of crashed vehicles. An existing test rig for measuring the c.g. location and the inertia tensor of crashed vehicles (pre- and post- impact), meeting the accuracy determined on the basis of the theoretical study, is presented. The theoretical analysis shows that an accurate accident reconstruction needs accurate measurements of both the centre of gravity location and the inertia tensor of crashed automobiles.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3502,

title = {3502. Development of Inertia Model for 787 Flight Simulator},

author = {F. Allan Balliett and M. Patrick Mitchell},

url = {https://www.sawe.org/product/paper-3502},

year  = {2010},

date = {2010-05-01},

booktitle = {69th Annual Conference, Virginia Beach, Virginia},

pages = {20},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Virginia Beach, Virginia},

abstract = {The computation of airplane-level inertia data is discussed. Inertia envelopes are 

developed that show maxima and minima and typical values as a function of airplane 

weight. These envelopes along with gross weight versus CG envelopes are used in the 

flight simulator. They provide boundaries for calculated mass properties data. An interior 

arrangement is shown of the typical 787 used in the plots. Airlines may request 

operational empty weight mass properties data reflecting their unique interior layouts for 

their flight simulators. Some general comments about inertia data are made. It will be 

shown that generating airplane-level inertia data is an important part of airplane design, 

simulation and operation.},

keywords = {05. Inertia Calculations, 11. Weight Engineering - Aircraft Estimation},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3504,

title = {3504. Method for Finding Min and Max Values of Error Range for Calculation of Moment of Inertia},

author = {Runar Aasen and Bruce Hays},

url = {https://www.sawe.org/product/paper-3504},

year  = {2010},

date = {2010-05-01},

booktitle = {69th Annual Conference, Virginia Beach, Virginia},

pages = {26},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Virginia Beach, Virginia},

abstract = {Modern ship design practices require knowledge of a vessel s mass Moment of Inertia (MOI) for various aspects of performance analysis. To find an accurate MOI value of an object, one needs to know the object s actual shape and density to be able to calculate the MOI through integration. Determining the exact MOI for a complete vessel, comprised of thousands of items, is not practical. Instead, engineers simplify the parts of the vessel to point objects or to standard shapes like a box or a cylinder, and calculate an approximation of the MOI. The accuracy of this approximation is dependent on the number of parts the vessel is divided into and how well the shape, orientation and density of each of the simplified items resembles the real objects. The quantification of the inaccuracy involved is seldom addressed. This paper describes a method to find the absolute error range for this simplified MOI calculation by finding the extreme values the MOI approximation can generate, and quantifies the effect that an error in MOI can have on the results of various types of performance analysis.},

keywords = {05. Inertia Calculations, 13. Weight Engineering - Marine},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3476,

title = {3476. A Step by Step Procedure for Determining Product of Inertia Using the Moment of Inertia Method},

author = {William Middelaer and Brandon Rathbun and Kurt Wiener},

url = {https://www.sawe.org/product/paper-3476},

year  = {2009},

date = {2009-05-01},

booktitle = {68th Annual Conference, Wichita, Kansas},

pages = {28},

address = {Wichita, Kansas},

abstract = {This paper builds on the generic relationship between Product of Inertia (POI) and Moment of Inertia (MOI) as presented in SAWE paper 1473 (Jodry & Boynton) to develop a step by step procedure, using six MOI measurements to calculate three POI values and the uncertainty in the results, for a given coordinate system. Since the uncertainty varies as a function of the MOI measurements, the method is most suitable where relatively large POI exists, and is least suitable for balancing applications where the desired POI is zero. The method and results are also referenced to Mohr's Circle. This tool clearly shows the relationship between the MOI measurements, the calculated POI, and its uncertainty. Mohr's circle may be used to identify the Principal Axes or Moments and Products of Inertia for any orthogonal two-axis coordinate system in the reference coordinate plane for which two MOIs and a POI or 3 MOIs are known. The paper further describes how to populate the Inertia Tensor with MOI and POI values to achieve the standard sign conventions for the tensor so the MOI and POI can be derived for any coordinate system. The equations used to solve for the moments and products of inertia required to generate Mohr's circle from three Moments of Inertia about non-orthogonal axes are derived.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3417,

title = {3417. On the Influence of the Inertia Properties on the Vibrations of a Car Engine},

author = {Luis Muñoz and Claudio Scalmana and Stefano Troccoli},

url = {https://www.sawe.org/product/paper-3417},

year  = {2007},

date = {2007-05-01},

booktitle = {66th Annual Conference, Madrid, Spain},

pages = {21},

publisher = {Society of Allied Weight Engineers},

address = {Madrid, Spain},

organization = {Society of Allied Weight Engineers},

abstract = {The paper presents a study about the influence of the inertia properties on the dynamic behavior of a vehicle powertrain (in our specific case we considered a system composed of the engine and the gearbox of a front wheel drive car). The dynamic performance of such a powertrain was studied both theoretically and experimentally by means of proper sensitivity analyses. The information provided by the measurements was used for the validation of two mathematical models of the powertrain. Both the experimental and the theoretical simulations confirmed that the powertrain vibrations in the range 10 ? 15 Hz are particularly sensitive to slight variations of the inertia properties. According to the common knowledge referring to the dynamic behavior of cars, at relatively high speed, the vibrations of the powertrain in the range 10-15 Hz can seriously decrease comfort and even affect safety. The conclusions derived from the analysis of the examined particular case can be extended easily to a broad class of road vehicles.},

note = {Student Paper},

keywords = {05. Inertia Calculations, 31. Weight Engineering - Surface Transportation},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3435,

title = {3435. Providing The Inertia Properties of Vehicles and Their Subsystems for Virtual Reality and Mechatronics Applications},

author = {Peter Eberhard and Christoph Henninger and Massimiliano Gobbi and Giampiero Mastinu and Luis Muoz and Werner Schiehlen},

url = {https://www.sawe.org/product/paper-3435},

year  = {2007},

date = {2007-05-01},

booktitle = {66th Annual Conference, Madrid, Spain},

pages = {18},

publisher = {Society of Allied Weight Engineers},

address = {Madrid, Spain},

organization = {Society of Allied Weight Engineers},

abstract = {There are many methods available to measure (and/or compute) the inertia properties of vehicles and their subsystems. But no standards are presently available defining the appropriate measurement tolerances that are needed for engineering activities. This paper addresses this problem by means of both experimental and theoretical investigations. Two different validated mathematical models were used, one for the entire vehicle and the other for the powertrain. A sensitivity analysis over a selected set of performance indices was performed by using the two models. After defining reasonable tolerances on the performance indices defining the dynamic behavior of the vehicle and its powertrain, the proper tolerances on the inertia properties were obtained. Relatively small variations of the inertia properties may produce significant variation in the considered dynamic performances of a vehicle and its subsystem.},

keywords = {05. Inertia Calculations, 31. Weight Engineering - Surface Transportation},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{3237,

title = {3237. Obtaining Optimal Results with Filar Pendulums for Moment of Inertia Measurements},

author = {David P. Lyons},

url = {https://www.sawe.org/product/paper-3237},

year  = {2002},

date = {2002-05-01},

booktitle = {61st Annual Conference, Virginia Beach, Virginia, May 18-22},

pages = {29},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Virginia Beach, Virginia},

abstract = {A common experimental problem in engineering is determining the mass moment of inertia (MOI) of a non-homogeneous rigid body with complicated geometry, which does not lend itself to analytical methods. In recent years the labs at Lockheed Martin Aeronautics Company-Marietta (LMAC-M) have developed improved methods for MOI testing. Initially, a quadrifilar pendulum was built. This apparatus produced quick MOI test results with accuracies as good as 1-2% for objects with large MOI, but only 5-7% accuracy for objects with a small MOI. A requirement for improved accuracy on a recent program provided the incentive to ensure better-than-1% accuracies. Initially, it was believed the existing ?simple? theory on filar pendulums, available in the engineering texts, was inadequate to produce the desired results. A higher order solution was developed. Hardware improvements were made. The existing simple theory was reviewed rigorously, and an exhaustive investigation of alternative analytical methodologies was conducted. Finally, refinements to the measurement process were implemented. In the process of identifying a superior solution, the existing textbook simple theory was validated, based on a certain criterion. A concept for treating viscous damping analytically, and hence windage effects, was developed, but not proven. The latest generation MOI test capabilities developed at LMAC-M, which guarantee better than 1% accuracy, are the filar pendulums. Testing with these pendulums is done with little to no fixturing, enabling high accuracy, low cost, quick turnarounds. These pendulums are designed for a class of test objects with not-to-exceed weights and dimensions that do not produce significant windage effects. Though this project utilized the trifilar design, these refinements could also be used for bifilar and quadrifilar configurations.},

note = {L. R. 'Mike' Hackney Award},

keywords = {05. Inertia Calculations, Mike Hackney Best Paper Award},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{1880,

title = {1880. The Effect of Entrapped Air on Moment of Inertia Measurements},

author = {G Jones},

url = {https://www.sawe.org/product/paper-1880},

year  = {1989},

date = {1989-05-01},

booktitle = {48th Annual Conference, Alexandria, Virginia, May 22-24},

pages = {46},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Alexandria, Virginia},

abstract = {At the 1987 International Conference of the Society of Allied Weight Engineers, the point came up that the effect of ambient air on moment of inertia measurements was an area that needed further study. Since China Lake NWC Environmental Engineering Branch, headed by Steven N. Tanner, owns a large vacuum chamber, I undertook to do some moment of inertia measurements with the effect of ambient air removed. This study led to the derivation of a formula for estimating the effect of ambient air on moment measurements. I also discovered some valuable techniques for performing measurements on low mass density items, test items with very small moments of inertia and test items with moments of inertia larger than the advertised maximum measurement capability of the Space Electronics KGR 300. I will state the most important findings right up front: The formula for estimating the moment of inertia contributed by entrapped ambient air is given by Iea = r/45 (L^3.5)(H^l.5) where the test object is a rectangular plane, r is the density of the ambient air, L is the length of the plane, H is the height of the plane. I call this relationship Spike's rule for determining entrapped air moment of a planar solid.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{1765,

title = {1765. How to Calculate Mass Properties},

author = {Richard Boynton and K Wiener},

url = {https://www.sawe.org/product/paper-1765},

year  = {1987},

date = {1987-05-01},

booktitle = {46th Annual Conference, Seattle, Washington, May 18-20},

pages = {35},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Seattle, Washington},

abstract = {This paper is a tutorial on the calculation of mass properties (moment of inertia, center of gravity, product of inertia). There are numerous textbooks on dynamics which devote a few pages to the theory of these properties. However, these textbooks quickly jump from a very brief description of these quantities to some general mathematical formulas without giving adequate examples or explaining in enough detail how to use these formulas. The purpose of this paper is to provide a detailed procedure for the calculation of mass properties for an engineer who is inexperienced in these calculations. Hopefully this paper will also provide a convenient reference for those who are already familiar with this subject. This paper contains a number of specific examples with emphasis on units of measurement. The examples used are rockets and re-entry vehicles. The paper then describes the techniques for combining the mass properties of sub-assemblies to yield the composite mass properties of the total vehicle. Errors due to misalignment of the stages of a rocket are evaluated numerically. Methods for calculating mass properly corrections are also explained.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{1724,

title = {1724. The Ten Dollar Load Cell},

author = {H A Nielsen},

url = {https://www.sawe.org/product/paper-1724},

year  = {1986},

date = {1986-05-01},

booktitle = {45th Annual Conference, Williamsburg, Virginia, May 12-14},

pages = {12},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Williamsburg, Virginia},

abstract = {Load cells for electronic weighing of any capacity have historically cost hundreds of dollars. Five different low capacity load cells that only cost tens of dollars are described. The criteria necessary to achieve that price are covered. This results in a useful outline of load cell cost factors to get accurate weighing electronically. Performance specifications and physical characteristics of six different types of resistive strain gages are reviewed. Reasons for the etched foil strain gage being the most common in electronic weighing today are given. Prospects of lower cost high capacity load cells are outlined.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{1610,

title = {1610. Error Analysis of System Mass Properties},

author = {J Brayshaw},

url = {https://www.sawe.org/product/paper-1610},

year  = {1984},

date = {1984-05-01},

booktitle = {43rd Annual Conference, Atlanta, Georgia, May 21-23},

pages = {41},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Atlanta, Georgia},

abstract = {Objective of this analysis is to verify the margin of system mass properties over values sufficient for support of other required system capabilities, flight dynamics control, for instance. The system nominal mass properties characteristics are designed (with a tolerance over requirements) using imperfect knowledge of mass and location of its constituent elements. The effect of element errors is to induce net errors in calculated system mass properties. Direct measurement of system mass properties is impractical. 

Approach. Considering both element-internal independent C G errors and element externally dependent alignment errors, a differential analysis calculates effect of net element errors on system mass properties. Then a combination of element effects shows total system error, which quantizes probable loss of system margin. The following information about the whole or portions of the system is provilded: 

1)Standard deviation of the various mass properties parameters of the selected configuration. 

2)Relative system-error contributions of the mass elements (ranked). 

If item (1) shows net system uncertainty values which compromise satisfaction of system mass properties requirements, then item (2) shows which elements are the principal causes of the problems. They are considered cost-effective candidates for more stringent analysis or measurement of local element mass properties. The system error analysis is then rerun with the improved (tighter) element error inputs, and its output determines the best available (hopefully adequate) system mass properties margin. 

Application of this work is to the Galileo space craft system. The system consists of a non-spinning (stator) portion, and a spinning (rotor) portion with long heavy radial appendages. Some of the system mass property design constraints are: retention of CG near the spin axis while matching rotor pitch and yaw moments of inertia; minimizing stator products of inertia; and maintaining margin between rotor spin inertia and overall system yaw inertia. 

Operation of the analysis and of preliminary input processing are performed by computer. Acquisition of local element mass properties and alignment uncertainties, and loading input files turnout to be a significant part of the work. The programs can accommodate changes in mass distribution modeling. 

Conclusion: Operation to date appears consistent, with preliminary inputs.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{1050,

title = {1050. Approximating Inertia Uncertainties for Satellite Flat Spin Analysis},

author = {J D Lagana and J G Lotta},

url = {https://www.sawe.org/product/paper-1050},

year  = {1975},

date = {1975-05-01},

booktitle = {34th Annual Conference, Seattle, Washington, May 5-7},

pages = {20},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Seattle, Washington},

abstract = {Inertia parameters discussed in this paper are the spin to transverse ratio and the 

difference in transverse moments of inertia. Equations derived in this report will yield 

approximate uncertainties for the inertia parameters for flat spin analysis of dual spin 

spacecraft. These uncertainties must have the independent and dependent elements correlated and/or cancelled to be of value. 

The uncertainty of the spin to transverse ratio when applied to the nominal value gives a 

confidence level relative to the critical ratio of 1.00. The uncertainty of the difference 

in transverse moments of inertia when applied to the nominal value and compared to the torque 

that a dual spin spacecraft de-spin motor can supply gives insight as to whether that spacecraft 

can be recovered from a flat spin. 

In the past, both uncertainties were estimated without separation of independent and dependent 

variables, yielding highly inaccurate values in most cases. The generally high inaccuracies imposed 

confining restrictions on the mass properties engineer. This could result in unnecessary ballast 

weight addition or imply that physical measurements are required where calculated values would suffice. 

Therefore, it is of economical importance that these inertia parameters be accurately estimated.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{0965,

title = {965. Inertia Symmetrization of Large Spin-Stabilized Spacecraft},

author = {R W Bocksruker},

url = {https://www.sawe.org/product/paper-0965},

year  = {1973},

date = {1973-06-01},

booktitle = {32nd Annual Conference, London, England, June 25-27},

pages = {22},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {London, England},

abstract = {A need for inertial symmetrization of large spin stabilized spacecraft prompted the development of a universal horizontal axis device for concurrent measurement of center of gravity and transverse moment of inertia of large objects. The resulting equipment and methods have satisfactorily achieved inertia symmetrization to less than one slug foot squared on a large spacecraft with a minimum of handling risks.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{0847,

title = {847. Accuracy of Estimating Principal Axis Orientation by Tangent 2-Theta},

author = {P McGuire},

url = {https://www.sawe.org/product/paper-0847},

year  = {1970},

date = {1970-05-01},

booktitle = {29th Annual Conference, Washington, D. C., May 4-6},

pages = {14},

publisher = {Society of Allied Weight Engineers, Inc.},

address = {Washington, DC},

abstract = {This paper represents the results of a parametric investigation conducted to determine the accuracy of locating principal inertial axes by the relation tan 2(theta)xy = (2Pxy)/(Ix-Iy). Results calculated by the above equation are compared with corresponding angles obtained in an eigenvalue solution. It is shown that for; a) small product of inertia, or b) large values of the term (Ix - Iy), the above provides a good approximation. It is further shown that if either of these conditions are violated, the predicted angle diverges rapidly from the exact solution. The method outlined in the paper is applicable to any configuration, independent of its geometry.},

keywords = {05. Inertia Calculations},

pubstate = {published},

tppubtype = {inproceedings}

}