GP-B Post-Flight Analysis—Final Report - Gravity Probe B - Stanford ...

Solution: Create a tetrahedral lapping and polishing machine that brushes the sphere with micro-inch abrasiveslurry in random variations.Result: Each fused quartz sphere deviates less than one micro-inch from peak to valley (25 nm), making themthe roundest objects ever created on Earth.Bonus Fact: In September 2004, GP-B received a certificate from Guinness World Records Limited,acknowledging that the GP-B gyroscope rotors had been entered into the Guinness Database of World Records.The certificate reads as follows: “The most spherical man-made objects are the fused quartz gyroscopic rotorsonboard the Gravity Probe B Spacecraft operated by NASA and Stanford University. Their average departure frommathematically perfect sphericity is only 1.8 x 10 -7 of their diameter.”3.2.3.5 Precisely Measuring Sphericity (Roundness)Figure 3-14. Measuring the roundness of a gyro rotor and mapping the contours on its surfaceChallenge: How to measure the roundness of a sphere at the precision level of 1/10th of one millionth of aninch? The British instrument company, Rank, Taylor, and Hobson, created the Talyrond instrument formeasuring the sphericity or roundness of GP-B gyroscope rotors using a stylus mounted on a round spindle toencircle a gyroscope rotor. However, they could not produce a spindle that was itself perfectly round, and thusthe spindle introduced error into the measurement.Solution: Combine the errors in the spindle’s roundness with the errors in the sphere being measured. Then,rotate the sphere to a new position and repeat the measurement. The measurement errors in the roundness ofthe spindle remain constant, while the measurement errors in the sphere change with each new position. Afterrepeating this process several times, it is possible to separate out the constant spindle error. (The spindleroundness must be checked from time to time, to ensure that it has not changed.)Result: The spindle roundness errors were calculated and stored in a computer, so they could be reused withdifferent spheres. For each rotor, 16 great-circle measurements were made in the perpendicular plane and onefinal measurement was made around its equator, tying all the vertical measurements together. The spindleerrors were subtracted out of the sphericity measurements, and then the sphericity measurements weretranslated into contour maps.84 March 2007 Chapter 3 — Accomplishments & Technology Innovations