Fake Banner
    Build Your Own G-Force Test Rig
    By Project Calliope | May 18th 2012 10:24 AM | 6 comments | Print | E-mail | Track Comments
    About Project

    Alex "Sandy" Antunes is the mastermind behind 'Project Calliope', a pico-satellite funded by Science 2.0 and being launched in 2011 by a mad scientist...

    View Project's Profile

    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/s2.

    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.

    Fc = m v2 / r = F10G = m a10G = m * (9.8 m/s2 * 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 v2 (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/s2 (instead of the more accurate 9.8 m/s2 ) and with 2 pi (1 rotation) as 'a little more than 6', you end up with w2 = 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 w2 r2 = 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).

    Nonagram from UMD.

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

    Centripetal vs Centrifugal

    Until next week,

    Alex

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


    Comments

    rholley
    This reminds me of an Eagle Annual.  One of the heroes was jet skiing (more or less) when the boat was suddenly stopped.  However, the hero continued forward

    under the impetus of the centrifugal force

    and caught up with the villains, whereupon his ski-rope wrapped itself round them and bound them tightly.

    Which is where I first learned those words, over half a century ago.

    What a way to acquire scientific vocabulary! 
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Hank
    under the impetus of the centrifugal force
    Did you correct them mentally and say 'centripetal'?
    rholley
    Didn’t think of that.

    Could we assemble some sort of quantum correlation device with spacetime non-locality so that I did?
     
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Hank
    Sure, we just have to find a theoretical physicist. An aerospace engineer will just make goat noises at us and walk away.
    BDOA
    Got a Dr theorectical physicist here, but i'm busy at the Majorana Demonstrator project at area 51. Its nice to live in area 51, the rest of my live i living in the capital city of a nuclear power. I went to school just north of target roundabout by the airbase. My house had a anderson shelter just big enough for me to huddle with blanket with a bbq and a tins of hotdogs, some small protection against a blitz, but no conform from a nuclear blast. Is the axial force vertex public domain information next or is MI5 going to crufixie me.
    BDOA Adams, Axitronics
    BDOA
    What will the Mad Mullah in Terhan do under if he was told of neutrino particle accelector and resonant frequency of the U-235 and PU-239 nuclides. Would his mind shrivel under the weight of the knowledge or would he trust in god and dis-believe in physics. The critical mass is highlly variable due to this information being a miltary secret, lie i've never met any miltary. But at the quantum level it varies with the intensity of the axial force bombardment. If you've never been to CERN how much can you believe in what the have there. The woman should have one at greenham common. Now our own weopens can be turned against us.
    BDOA Adams, Axitronics