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The video in the interesting question How did the GoFast 2014 Rocket de-spin? shows a de-spin that went well. An initial very fast spin (for stabilization during propulsion) is almost perfectly de-spun during a maneuver that is so fast that it is hard to imagine it could be anything else but a Yo-Yo de-spin.

The mathematics behind this is summarized in this answer along with links to several original sources. Briefly, $r$ is the ratio of final to initial angular velocity, and will be zero at perfect de-spin but can still be positive or negative for undershoot or overshoot conditions. The remaining terms are described in detail in the link.

$$\frac{m(d+a)^2}{I}=\frac{1-r}{1+r}$$

It's a balance. So if the final angular speed is much much lower than the initial (near perfect cancellation), it suggests that both the initial spin rate and the de-spin were well controlled.

Another example of careful spin and de-spin cancellation (but not with a Yo-Yo) is discussed in this answer and in this answer about NASA's LSDS test.

But what if the initial spin had some uncertainty that could not be controlled?

Question: Has adjustable Yo-Yo de-spin been tested or demonstrated? Reading about a serious but untested proposal would also be interesting.

I can think of all kinds of possible ways to do this, last-second laser trimming of the wires, or just a clever break-away release, vernier yo-yos (say 10kg plus 160g, 80g, 40g, 20g, 10g independently addressable "fine yo-yos") but this kind of complexity really defeats the elegance and reliability of the Yo-Yo technique with fixed mass weights and premeasured wires, so maybe backup thrusters to re-adjust the spin before Yo-Yo would be a better way to stay with known technologies.

Still, have variable Yo-Yo's been tested or demonstrated?

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  • $\begingroup$ The stretch yo-yo despin was devised to account for some uncertainty and successfully tested in 1962. Is that what you are looking for? $\endgroup$ – called2voyage Jun 12 '17 at 13:41
  • $\begingroup$ @called2voyage wow! cool! yes! $\endgroup$ – uhoh Jun 12 '17 at 14:16
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In the 1960s the Goddard Space Flight Center devoted some study to the topic of error in yo-yo de-spin. It was acknowledged that spin-up errors and uncertainty of the spin axis moment of inertia were sources of de-spin error. Since de-spin error can be a source of many problems, which may even impact the success of the mission, the stretch yo-yo concept was devised to reduce de-spin error.

"Analytical Theory of the Stretch Yo-Yo For De-Spin of Satellites" by Joseph V. Fedor explains:

A device that greatly reduces spin-up errors and errors due to variations in spin moment of inertia is the stretch yo-yo (the stretch concept was first suggested by Henry Cornille of Goddard Space Flight Center (Reference 3). It can consist of a weight, a spring, a wire, and end fittings (Figure 1), or simply a weight, spring, and end fittings (Figure 2). The purpose of the spring is to compensate for errors in initial spin-up. For example, in a given stretch yo-yo application there will be a certain amount of stretching or elongation of the spring during normal operation. If the initial spin is greater than the nominal value, the spring will elongate more than normal during operation and reduce the spin to the desired value. If the initial spin is less than the nominal initial spin, the spring will elongate less than normal during functioning and correct for the under spin. The stretch yo-yo is a simple example of an adaptive control system: it senses the spin environment it is in and corrects accordingly. Also, it will be shown that the stretch yo-yo is relatively insensitive to variations (uncertainties) of the spin moment of inertia.

After analysis and design, it was decided that the stretch yo-yo despin should be tested on the Ariel I spacecraft, and in April 1962, it was successfully flown ("Analysis of the Dynamic Tests of the Stretch Yo-Yo De-Spin System" by William R. Mentzer):

Following dynamic analysis and development of design equations for the stretch yo-yo, the decision was made to fabricate and test stretch yo-yos on the Explorer XII (1961 v1) and Ariell (1962 01) type payloads. Three series of tests were conducted beginning with feasibility tests on the two payloads and concluding with flight qualification tests for the Ariel I payload. As a result of these tests, a stretch yo-yo was flown on the successful Ariel I spacecraft in April 1962.

In the record of the experimental results, the effects of the several variables involved in stretch yo-yo design can be readily noted. These variables include optimum spring constant, preload, initial spin rate, spin moment of inertia, and material strength.

You can read the full analysis of the tests in that document, but here's one last brief note on the effectiveness of the stretch yo-yo de-spin:

The Explorer XII type optimum spring scale tests clearly demonstrated the ability of the stretch yo-yo to compensate for errors in initial spin rate. In this series of tests, spin-up errors of +/-20 percent were reduced to within +/-1.5 percent of the design final spin rate.

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  • $\begingroup$ Page 6, Discussion of Test Result: "The Explorer XII type optimum spring scale tests clearly demonstrated the ability of the stretch yo-yo to compensate for errors in initial spin rate. In this series of tests, spin-up errors of +/-20 percent were reduced to within +/-1.5 percent of the design final spin rate." Incredible - thank you for this! $\endgroup$ – uhoh Jun 12 '17 at 14:45
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    $\begingroup$ @uhoh You're welcome! I wrapped that quote into the answer, because it really does show quite clearly how effective the technique is. $\endgroup$ – called2voyage Jun 12 '17 at 14:48

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