Rockets are powerful stuff, and satellites and astronauts experience tremendous G-forces pushing down on them during launch. For picosatellite work, it is necessary that your design be able to withstand forces equivalent to perhaps 10 times Earth gravity-- 10Gs. To test this, the easiest way is to build a centrifuge.

Think of the spinning bucket gimmick. If you tie a bucket to a rope and fill it with water, you can make the bucket swing in a loop-the-loop over your head and not spill, as long as it is spinning fast enough. You need enough spin to counteract the 1G of the Earth's pull, so you need a spinning centrifuge of at least >1G.

Most homebuilt centrifuges are used by mad scientists doing medical or chemical studies that require they separate a fluid by density. For satellite building, we can use a far simpler design. Yes, you can actually just spin your satellite in a bucket at the end of a rope-- or build a 10G spinning rig using an ordinary electric drill.

What we'll first tackle is just how fast do you need to spin to pull 10Gs? This is our rotational problem.

We want a 10-gravity centrifuge, that
is, a spinning apparatus that produces a centripetal force equal to
10 Earth gravities, or 10 * 9.8 m/s^{2}.

A typical 1/4" electric drill can spin from 300 to 1600 rpm (rotations per minute), providing a torque (or spinning power) of 500-100 Newton meters, i.e. at 300 rpm you get 500 Nm, at 1600 rpm you get 100 Nm. Often drills say they can only get half their usual rpm under a heavy load, but we'll temporarily ignore that for now.

F_{c} = m v^{2} / r =
F_{10G} = m a_{10G} = m * (9.8 m/s^{2} * 10)

v = w r

A drill rpm / 60sec/min = rps, convert this to radians/second given 1 rotation = 2 pi.

Torque: T = F l = (for this case) F * r

KE = 0.5 m v^{2} (as usual),
and potential energy U = m g h for a falling object.

Solve for 1 of these cases, as assigned. If needed, assume a 1 kg payload is being spun (though you'll find the mass drops out of all the equations except torque). The term 'equivalent falling height' means that, given the centrifuge payload's kinetic energy, this is the equivalent of having the same object dropped onto your head from what height 'h'?

**You solve it!**

Centrifuge with an 'r'-length lever arm:

r = ________

rotational speed w in radians second =

rps needed =

torque required =

linear velocity of payload in m/s =

kinetic energy of payload =

equivalent falling height =

**Solution**

This actually makes a handy lab for a physics class. For the simple case of a 1-meter rotational arm trying to reach 10 G, if you approximate 1 G as 10 m/s^{2} (instead of the more accurate 9.8 m/s^{2} ) and with 2 pi (1 rotation) as 'a little more than 6', you end up with w^{2} = 100 or an angular velocity of 10 radians/sec or 1.5 rotations per second, under 100 RPM. Torque is more key-- do you have enough twisting power to spin it? Given torque = 10 G * r and we're using a lever arm of r=1m, you need to be able to pull 100 N*m of torque-- again within most electric drills.

Oh, and the kinetic energy equivalent as in "if the object were to go flying off the centrifuge and hit you, that's the equivalent of it falling from what static height" is basically 0.5 m w^{2} r^{2} = m g h, again the mass drops out and (assuming r=1m) you get 0.5 * 100 = 10 h, or it's the equivalent of a falling mass dropping from 5 meters (16 feet), or about the same as dropping it out of a 2nd story window. You can also calculate its momentum. It's basically a 1kg weight traveling at the speed of a shotput. So be careful.

Conclusion: you can build a picosatellite 10G test rig using an ordinary electric drill and some parts.

A writeup at the Aquatic Pathobiology Laboratory suggests plotting a nonogram of RPMs versus G-forces needed as a visual comparison of G-force (maximum relative centrifugal force) to RPMs (rotations per minute).

For those curious about the difference between centrifugal force and centripetal force, we'll let XKCD explain.

Until next week,

Alex

music" href="http://projectCalliope.com">Project Calliope, ionosphere->music

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