# Calculating gyroscope turn regardless of angle

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,509
However, you seemed to ignore the question and so I kept asking it. You eventually said "it is not what you would expect". So what would you expect the output to be?

I have already answered this. Without delving into the mathematics, I would have assumed you would see 141, not 100.

And as I also mentioned, because the result is not what I expect, I'm not going to waste your time. You really have to go back to the maths (that you said you didn't want to) and figure it out for yourself.

I would suggest you look at the rate of rotation in all three axies as you tilt the gyroscope. Maybe you'll get some insight.

#### Tim Brown

Dec 31, 2017
23
Isn't the 'cage' of the gyroscope fixed to the turntable? i.e. the turntable itself is one of the axis? In standard gyroscopes (navigational) this is (I think) the case.....
It is an electronic gyroscope, and wireless, so it can be moved any way you want.

#### Tim Brown

Dec 31, 2017
23
I have already answered this. Without delving into the mathematics, I would have assumed you would see 141, not 100.

And as I also mentioned, because the result is not what I expect, I'm not going to waste your time. You really have to go back to the maths (that you said you didn't want to) and figure it out for yourself.

I would suggest you look at the rate of rotation in all three axies as you tilt the gyroscope. Maybe you'll get some insight.

I see, 0.707 then. I'll check into it some more, maybe my testing was flawed. not wanting to do the math is not the issue, rather not being able to do the math in the time available to me is the issue. Which is why I am on a forum. thanks for your help, i'll look into it further.

Jun 25, 2010
6,039

#### Tim Brown

Dec 31, 2017
23
I have re-tested and 0.707 of the output rate at a 45 degree angle seems correct. So with that confirmation I can now think about it with a different frame of mind and come up with

Assuming a constant rate of rotation on a flat surface and assuming a 45 degree pitch on the X axis

degrees per second = gyroZrate / cos(pitch);

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,509
My faith in mathematics has been restored!

That formula will work as long as the angle doesn't get too large, and there are not simultaneous rotations in another axis.

#### Tim Brown

Dec 31, 2017
23
Great!! Why does the size of the angle matter?

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,509
Because cos θ falls to zero at 90 degrees.

As you get closer and closer to zero it will be harder to correct for the angle.

If you're only going to have relatively small angles that won't be a problem.

#### Tim Brown

Dec 31, 2017
23
I see. A maximum of 45 degrees is my requirement.

Will this formula compensate for roll too. I mean is it as simple as adding them together.

degrees per second = gyroZrate / cos(pitch) + cos(roll);

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