# How to measure speed of a ceiling fan?

I thought for fun I might measure how my ceiling fan slows down when turned off, and maybe find out what forces act on it when it slows down. My problem is that for that I need to measure its rotational speed when it's turned on. When it's in the lowest speeds it's easy because you can see it rotate, but for higher speeds that's not an option.

I thought one way would be to use a strobe light and try to match up the frequency, but I don't have one of those. Can you think of any DIY way to measure the speed of a very fast ceiling fan?

## 9 Answers

If you have a smart phone with a flash, you probably have a strobe feature at your disposal.

You can put a drinking straw into it and record the sound it makes, and measure the frequency in sound-editing software. Imagine the fun explaining this to paramedics.

Similarly, a laser-pointer, a mirror, and a photo-diode cleverly hooked up to your computer's sound card can be coaxed into doing science.

Finally, a laser pointer, two mirrors and knowledge of the speed of light in your room can be used to to determine the rotational speed of the fan, provided your room is big enough, and the fan is moving fast enough. If this is going to work, it will probably be the least accurate but most fun.

• A computer sound card is one of the best, most accurate scientific recording instruments easily available. I abuse my sound card all the time. – Brandon Enright Nov 15 '13 at 0:39
• Hopefully, paramedics won't have to be called. – Kaz Nov 15 '13 at 6:16
• I think the problem with the straw is that you actually add extra resistance to the fan and slow it down faster, leading to less correct results. – Cruncher Nov 15 '13 at 14:05
• @Cruncher That's Heisenberg's Fan-Straw Uncertainty Corollary! – tom Nov 15 '13 at 14:41
• Replace the straw with an eyelash, if you wish :) – lionelbrits Nov 15 '13 at 15:18

Another simple DIY method might be to attatch a string with a weight at the end of one of the blades (possibly another one on the other side if the fan gets too unbalanced). By looking at the angle the string makes you should be able to determine the rotational speed of the fan: $$\omega=\sqrt{\frac{g\tan{\theta}}{r+l\sin{\theta}}},$$ where $\theta$ is the angle of the string with the vertical, $r$ is the radius at which you connect the string to the blade, $l$ is the length of the string and $g$ is the acceleration due to gravity.
Measuring $\theta$ accuratly will be another thing. Best bet might be taking a photo with a long exposure time to make sure that you view the string from the 'side'.

• however this will influence the startup and slow down of the fan which is what he wanted to measure – ratchet freak Nov 15 '13 at 10:58
• @ratchetfreak in the question Javier Badia said that he wanted to know the speed when the fan is on, so this influence should not matter. It will probably also influence the max speed of the fan slightly, but when using a thin string and a small weight it will probably be negligible. A way you can check this is my mounting the string to the blade at lower radii, since this reduces its speed and moment of inertia. However the error propagation of $\theta$ into $\omega$ will be the smallest when $\theta\approx30°$ when $r>l$, so changing this can also improve your accuracy. – fibonatic Nov 15 '13 at 11:51
• Measuring the angle of the weight, will likely prove to be a harder task than the original – Cruncher Nov 15 '13 at 14:47
• @fibonatic Actually, I've found that even small weights can affect the speed of rotation perceivably! Once we were decorating for a party, so we attached streamers to the end of each blade. You could notice the difference in speed looking at it. – mikhailcazi Jan 20 '14 at 11:06
• @mikhailcazi but this is not due to their weight, but due to their air resistance. – fibonatic Jan 20 '14 at 11:32

I don't know if you would classify this as cheating but you might be able to affix a bicycle speedometer to one of the blades.

You can pick them up quite cheaply, it would be quite easy to affix and it would give you a fairly accurate reading. • Sounds as by far the easiest of options! – Michiel Nov 15 '13 at 13:38

Adding to the sound-card theme, you could fasten a small, light, constant frequency sound generator on the end of a blade. Then use the size of the Doppler shift for linear velocity, or more simply, the period of the frequency oscillations for rotation period (Again, there is a good possibility of EMS explanations to be made.)

• woohoo, +1 for doppler shift – Cruncher Nov 15 '13 at 14:07

Having first measured the width of the blade, the period of time during which line-of-sight to a light-source or marker on the ceiling is occluded is a measurement of the average (linear) speed of the blade at the time. Combine with the radius at which that measurement was made to get angular velocity.

A webcam can be utilized for this purpose (though data reduction by hand will be boring) or a photodiode driving the sound card. As others have noted the audio-in port on your sound card is a surprisingly versatile (though sensitive and limited) data acquisition port.

Just an idea not a fully fledged proposition:

You can place a pencil in such a way it gets struck by the blades of the fan, and makes a noise every time a blade passes it (I remember seeing a video of some one on youtube making music with it but now I can't find it).

Then you could record the sound it makes a analyse it with an audio editor (To see how fast its hitting the fan)

You can record a video of your fan rotation and calculate the fan rotation frequency based on the frame rate, using, e.g., Microsoft Movie Maker software. I did something like that some time ago.

Ok other methods described here are awesome like

Inserting a straw into it and measure the number of clicks ( the clicks can be recorded and time difference between the clicks can be measured using a audio editing software )

Tie something to the end of it and measure the angle it makes with the vertical and measure the velocity by using the relation $$(\omega)^2= g*tan(\theta)/r$$

My method may look far-fetched but in theory it should work ,It uses Probability to measure the speed it is basically a Monte Carlo experiment where you calculate the probability of an object hitting the fan both theoretically and and practically by actually throwing lots of shots.

A fan has 3 wings each of them has an arc length of say 20 deg if we assume the fan to be stopped (at random places ) then the probability of hitting it will be 60/360 but if the fan is moving say with speed of ω and object remains in the plane of the fan (the vertical position in which object can hit the fan ) for time T seconds we know that $$\omega= d\theta / T$$ now the fan will behave as if each of its wings are having an arc length of
= 20 + dθ hence making a total wing area of
$$AREA = (20+d\theta)*3$$ probability of hitting the fan becomes
$$3*(20+dθ)/360$$

where dθ=ω*T

$$p(hitting)=3(20+ω*T)/360$$

solving it for ω $$ω=(120*p(hitting)-20 )/T$$

where p(hitting) can be calculated by actual throwing for example if 30 times you hit out of total 100 throws p(hitting) becomes 3/10 . Though you will need to make those throws coherent and do a reasonable approximation for T .

I have described the method here

It's quite simply really: A tachometer is used for measuring rotational speed, allowing us to measure what you're interested in.

## protected by Qmechanic♦Apr 23 '14 at 18:14

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