# 3147. Precise Measurement of Mass

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## Paper

## Abstract

Space vehicle weight is very critical. It is particularly important to have accurate weight if the vehicle weight is near the maximum allowable. Scales with accuracies as good as 0.002% are now available from companies such as Space Electronics. However, unless precaution is taken to correct for local gravity, air buoyancy, and a number of other factors, the high accuracy of the scale is not realized. In fact, considerations which are often overlooked can result in a total error of several percent. Some of the concerns are:

1. Latitude The acceleration of gravity varies from 9.780 m/s2 at the equator to 9.832 m/s2 at the poles (a difference of 0.53%). This is in part due to the centrifugal force resulting from the rotation of the earth, which varies from zero at the north pole to a maximum value at the equator, and in part due to the bulge of the earth at the equator, resulting in a greater distance to the mass center of the earth.

2. Altitude The gravitational mass attraction to the earth at a particular location varies as the square of the distance to the mass center of the earth, resulting in a variation by as much as 0.26% over the surface of the earth.

3. Tidal effects The gravitational mass attraction to the sun and moon at a particular location may exhibit a variation as large as 0.003% of the acceleration of earth gravity at certain dates during the year when the sun and moon align (this means that the scale could indicate a larger weight in the morning than at night).

4. Gravity anomaly Variations in the density of the earth’s crust in the vicinity of an object result in small variations in gravity at different locations. Nearby mountain ranges reduce the force of gravity on the object.

5. Buoyancy The object being measured displaces a volume of air, whose density can vary due to the weather. The resulting upward force is a function of object size. For large low density objects, failure to correct for buoyancy may result in errors of 0.5% or larger.

In addition, errors can be introduced by

6. Moisture condensation or absorption of moisture (evaporates in vacuum of space)

7. Electrostatic attraction to the draft shield surrounding the scale

8. Magnetic attraction to nearby objects and to the earth’s magnetic north

9. Downdrafts or updrafts (due to a temperature difference between object and ambient air)

Variations in the acceleration of gravity result in a change in the weight of an object of about 0.8% over the surface of the earth, and about 0.2% over the contiguous USA!

I put the exclamation point at the end of the sentence because I frequently see specifications for a scale accuracy of 0.03% or better, yet these scales are used at latitudes that are significantly different from the latitude at which the scale was calibrated without any adjustment being made. Air buoyancy can cause a scale to read low by 0.5% or greater. Some of the other factors listed produce errors of 0.1% or more.

This paper discusses several issues:

1. How and when to correct for the acceleration of gravity when measuring mass.

2. How to correct for air buoyancy.

3. A very simple method to correct for both quantities automatically without knowing either the acceleration of gravity or the air density at a particular location.

In addition, this paper outlines the methods for determining local gravity, and summarizes the types of scales which are available and their accuracy. Finally, I have given my opinion on the subject of mass vs. weight, a topic which seems to result in endless confusion and disagreement.