Experiment: "von Braun space station" top with and without fairings*
Test top: High-AMI, low-CM spoked flywheel top with 2 easily removed rigid (HDPE?) disk fairings of negligible thickness
Base: Concave lens, modest curvature, lubed with skin oil. Taken at the horizontal flywheel's lower outer edge, the top has 22 mm of ground clearance on the lens and 12 mm on a flat surface.
Measurements: Best spin time of 3+ runs from 1,010±10 RPM and 0° tilt to first audible scrape.
Top A. Bare top, short test stem, no fairings
Top B. Top A + single 17.2 g fairing
below flywheel (bore sealed from below)
Top C. Top A + single 11.6 g fairing
above spokes (bore not entirely sealed from above)
Top D. Top A + both of the fairings above
Variables1. Total mass (
M): 137 - 165 g
2. CM-contact distance (
H): 24 - 26 mm
3. Total AMI (
I3): 7.1e-4 - 8.2e-4 kg m²
4. Total TMI at tip (
I1t): 4.5e-4 - 5.2e-4 kg m²
5. Critical speed (
ωC): 10.8 - 11.4 rad/s (103-109 RPM)
6. Scrape angle (
θmax): 15° on lens, 8° on flat surface
Controlled parameters (reasonably constant from top to top)1. Flywheel, spoke, and core assemblies, max radius 84 mm
2. Release speed (
ω0): 106 rad/s (1,010±10 RPM)
Best spin timesTop A (no fairings, on lens) .................. 185 s
Top B (lower fairing only, on lens) ......... 188 s
Top C (upper fairing only, on lens) ......... 203 s
Top D (both fairings,
on lens) ................ 333 s
Top D (both fairings,
off lens) ................ 290 s
Can lightweight fairings improve a spoked flywheel top's spin time? You bet! Fair the flywheel and spokes both above and below, and you get a whopping 64% gain in spin time over the better 1-fairing case (Top C) and an 80% gain over the 0-fairing case (Top A).
With just the lower fairing, Top B stayed up only 2% longer than Top A. But with just the upper, Top C consistently stayed up 10% longer than Top A — and that with an 8 mm air gap still present between the upper fairing and flywheel.
Fairings vs. mass properties: The simple shapes and the few internal air voids involved allowed me to calculate mass properties with decent accuracy. Turns out, the fairings had little impact on CM height: In mm, Top A = Top D = 25, Top B = 24, and Top C = 26.
The moments felt the fairings more. When both were present (Top D), they accounted for ~17% of the top's total mass, ~12% of its total AMI, and ~13% of its total TMI about the tip. However, all 4 tops ended up with nearly identical TMI/AMI ratios at the tip (where it counts).
Fairings vs. critical speed: Estimated critical speed combines all of a top's key mass properties into a single figure of merit with a big impact on spin time. In RPM, Top A = 104, Top B = 103, Top C = 109, and Top D = 107.
So for all the differences in mass properties, little change in critical speed. No good explanation for Top D's dramatic success there, so it must have been aerodynamic.
Ground effect? Most of the 43 s lost when Top D came off the lens must have been lost to air resistance. Why? Well, Tops A-D were already in their death spirals at the 8° scrape angle available
off the lens. Takes at most another 5 s to reach the 15° scrape angle available
on the lens. The rest of that 43 s had to be aerodynamic, cuz nothing else changed.
With Top D off the lens, there was still a 12 mm air gap beneath the lower fairing. Would a narrower gap have reversed the trend? Hard to say, but it would definitely have made the top harder to twirl on a flat surface.
Suppressing a top's centrifugal pumping action may still be a good thing to try, but top aerodynamics are clearly way more complicated than that.
Play value: I really enjoy this space station top. Plan to hang on to the fairings, but prefer the top without them. It's big and bold, loves to sleep, and stays up 130 s with a single twirl without fairings. When I want more spin time, I'd rather go to a fun starter instead.
* Acknowledgments: Thanks to
Iacopo for pushing me to do this experiment. Sorry it took so long. Also thanks to
ortwin for pointing out that von Braun beat me to this top's basic design
70 years ago. (And some Russians long before him.) Not sayin' Werner had it easy, but no gravity or air resistance to contend with in orbit.
https://youtu.be/5JJL8CUfF-o
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Topic: Flywheels and fairings and spokes, oh my! (Read 23761 times)