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22 August 2019 04:29

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Subject: Calculation of pitch Stabilising gyroscopic effect
Question: All of the maths I've seen on gyros give methods of calculating the precession force from a given roll rate. I would like to know how to calculate the resistance to roll moment of a gyro so that I can use it as a tilt stabilising device.
i.e. If a given rotor has an angular velocity of zero, no gyroscopic forces are present, so the angular acceleration of the rotor (around any axis) can be calculated from the applied moment and the ritational inertia of the body around the axis of rotation.
This can be easily demonstrated with a (stationary) pushbike wheel. If you hold the wheel in space by supporting each end of it's spindle, then remove one of the supports, you have effectively applied a moment to the assembly (weight x 1/2 spindle length) which causes the wheel to rotate around the remaining support. The angular acceleration can thus be both measured and calculated without any gyro maths.

Now take the same wheel, this time with some angular velocity about it's spindle axis. When the support is removed as above, the same moment (due to gravity) exists trying to accelerate the wheel about the remaining support, but the rotor resists this moment and precesses about the vertical axis.

The next step is to imaging the second support as a horizontal pin joint, only allowing rotation of the spindle in the vertical plane at 90 degrees to the spin axis. In this way, the wheel is prevented from precessing around the vertical axis. My question then is: How can I calculate the acceleration of the assembly around the pivot pin axis for a given applied moment?
Date: 23 November 2004
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