# How do rate gyros measure yaw, roll and pitch rates?

I need some help in understanding how rate gyros are used for measuring rotation rates about the yaw, roll, and pitch directions.

Suppose a gyro is used for measuring roll rate. How should the spin axis and input axis be oriented to get the rate in output axis.

## 1 Answer In this figure, ζ is the input axis, η is the output axis, and the spin axis is obvious.

If the vehicle is rotated around the axis ζ (the input axis) with an angular velocity ωζ, the frame will rotate around the axis η (the output axis) to an angle β. The dependence of this angle on ωζ is given by the equation β = ωζH/c, where H is the moment of momentum of the gyroscope and c is a coefficient that depends on the stiffness of the spring and on the location of the point where the spring is attached. The values of β are read from the potentiometer; they define the magnitude of ωζ.

So the input axis (when the vehicle is not rotating) should be set up to point along the vehicle axis about which you wish to measure the rotation. For roll rate, it should point along the vehicle's X axis.

Reference

• I'll enjoy reading this and the link today, thanks! – uhoh Apr 19 '17 at 1:55
• I think the link you put in your comment actually has better diagrams. I just didn't want to pirate your research. – Organic Marble Apr 19 '17 at 2:01
• omg please pirate! That's what it's there for :) – uhoh Apr 19 '17 at 3:19
• @Organic Marble and uhoh thanks a lot for answering the question – Soumajit Apr 19 '17 at 17:51
• More goodies here - I'd say consider using some of the se as well. – uhoh Apr 20 '17 at 19:58