where x apparent  and y apparent  are the apparent positions in inches, x actual and y actual are the actual positions in  the spacecraft’s plane of the fall, and 81 is the distanc e in inches from camera to the plane of fall.  

To determine the spin rate for each deploy, two photo targets were chosen on the spacecraft such that  each was visible during the entire fall of the spacecraft. The positions of these two targets were found at 8  ms intervals beginning just after the XY and XYZ mechanisms released the spacecraft until just before it  was caught by the cables roughly 200 ms later. The two target positions gave an angle of the spacecraft  at every time. Then the spin rate could be found by  taking the change in this angle divided by the elapsed  time between the frames where the spacecraft angl es occurred. 26 angles for each deploy determined  the average spin rate of the spacecraft.  

To determine the zero-g spin rate for each deploy, t he average spin rates from the six spring-and-gravity  deploys were compared to the average spin rates from the two gravity-only trials. From equation (3), it  can be shown that the gravity-only spin rate s quared equals the spring-and-gravity spin rate squared  minus the gravity-only spin rate squared.     Spin Rate Res ults  The primary goal for the qualification deployment testing was to show that the measured spin rate in zerog was within 10% of the desired value. While the spin rate values were fairly consistent for all  temperatures and flip types, the data showed that the six zero-gravity spin rates were an average of 13%  less than the 3.4 rad/s (32.4 rpm) spin rate predicted by the analytical models. 

To explain this discrepancy, the possible error sources were lumped into five categories:   1) Deployment stand flexib ility (Stand recoiled on deploy)   2) Modeling error (Imperfect values for x 1, m sc, Ig.sc, Lhing.cg and h cg)   3) Friction and losses due to non-flight interfaces (Catching cables)   4) Measurement error (Imperfect pixel picking)   5) Friction and losses due to flight inte rfaces (Pusher and XY and XYZ mechanisms)  These possible error sources were then exam ined and quantified to determine how much each  contributed to the 13% difference between the measur ement and the model, keeping in mind that the first  four were caused by imperfect techniques and that t he first and fifth would likely be present on flight.  

The first error source, energy loss due to stand recoil,  was a major contributor to the discrepancy. From  the video files, it was determined that the stand deflected roughly 3.0 mm (0.12 in) as the spacecraft  deployed. A separate test to rev ealed that a 356 N (80 lbf) tug on the stand caused a 2.0 mm (0.08 in)  deflection, which meant that t he stand had a lateral stiffness of roughly 175 N/mm (1000 lbf/in). The  following equation gave the percentage of the spring’s potential energy that was lost due to this recoil:  1005.5.100 % s2 sstand2 stand⋅ = ⋅ = pringpring totallost kk PEPEEnergyLostδδ (6) where k stand and δstand where the measured stiffness and deflection of the stand and k spring and δspring were  the known properties of the spring. Completing this calculation showed that stand recoil caused a loss of  about 7% of the spring’s energy and result ed in a 3.7% loss of spin rate.      The second error source, modeling error, was also significant. A large bundle of thermocouple cables  hung from the spacecraft to the chamber wall, adding roughly 0.45 kg (1 lbm) to its mass and about 0.118  kg-m2 (400 lbm-in2) to its inertia. Incorporating these additi ons into the model reduced the predicted spin  rate prediction by another 3.4%.  

The third error source, non-flight interface friction, had a very small contributi on to the discrepancy. About  0.25% of the spin rate was lost due to the ca tching cables wrapped around spools on the spacecraft. The  final testing-induced error source, measurement erro r, was principally due to imperfect pixel picking and  did not contribute to the discrepancy.  Measurement error did cause a 3 σ uncertainty bound of about 0.6%  69