# Howto find out the distance travelled by a point on a rotating ceiling fan?

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### Accepted Answer

Walter Roberson
on 4 Nov 2013

You do not need to calculate linear distance traveled in order to calculate rpm. You only need to find angular velocity.

In your set-up is it allowed to mark the center of the fan as well as the point? If so then for any one frame, you find the coordinates of the mark and the coordinates of the center, find the difference in x coordinates and the difference in y coordinates relative to the center, and convert that to polar coordinates to get an angle. Next frame gives you an updated angle. Difference in angle together with time difference between frames gives you angular velocity -- provided, that is, that the fan did not turn one or more complete turns as well as the angle difference you measure. Also, if you do not know the direction the fan is rotating then an angle change of more than Pi radians in one direction will have the same change in the picture as an angle change of less than Pi radians in the opposite direction of rotation.

As you track through multiple frames, you can improve the accuracy of the angular velocity; you track complete revolutions and then for the K'th frame you find the difference in angle between the first frame and that frame, and calculate (2*Pi*Complete_Revolutions + angle_change)/K to get the average velocity per frame. And hope you have a really consistent frame rate!

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### More Answers (1)

ES
on 4 Nov 2013

Edited: ES
on 4 Nov 2013

between two continuous frames, find the distance(d). You ll know the frame rate. 's' in seconds will be the time between frames(t). And v=rw where v is the velocity=distance divided by time(d/t), r will be the distance between the center of the fan and your point. w will give you the rps. convert to rpm.

Checks: 1. Frame rate of your imaging device must be sufficiently good. That is your device should make at least 2 pictures before your fan completes one rotation.

2. v should be distance/time. But you will most probably end up calculating displacement/time.

3. rpm and rps conversions

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