When does the wagon-wheel effect occur?

Sometimes you see a video of a fan or a propeller spinning very fast, and the apparent rotation is distorted. The fan can appear to be moving in the opposite direction of rotation, or even stationary. This optical illusion is known as the wagon-wheel effect. If I understand correctly, this occurs because the camera framerate is slower than the frequency at which the fan makes one rev, so stroboscopic effects should be expected.

Does the wagon-wheel effect occur only in videos, or can we observe it just with the eye?

There are three frequencies here, two frequencies $f_1,f_2$ are nearby to each other and the third human eye capability frequency $f_E$. Stroboscopic effects occur is when $|f_1-f_2| < f_E$. Thus if they are spinning at 5000 Hz and 5002 Hz when human eye cannot detect more than say 30 Hz,stroboscopic wagon wheel effects are still seen.

• What do $f_1$ and $f_2$ represent in the context of a single spinning wheel? – Ehryk Dec 30 '14 at 18:55
• There should be two spinning wheels for strobe effect.The second wheel can be also substituted by a stroboscope with frequency adjustable near about $f_1$ – Narasimham Dec 30 '14 at 19:30
• The effect being described in the question does not necessitate two wheels or a strobing light source, it can be observed with a single wheel and continuous light source. – Ehryk Dec 30 '14 at 19:32
• You do not answer the question. As I said, the effect can be observed with one wheel, or one spinning blade. – Joshua Benabou Dec 31 '14 at 5:11

The simple answer is yes, you can see it with the naked eye. It requires only that the light source is showing significant, periodic variations in intensity, and preferably with a frequency greater than the fusion frequency of the human eye (20 - 30 Hz). The greater the intensity variation, and the shorter the "on" duration, the more pronounced the effect will be. Under some circumstances you can even use fluorescent lighting.

It used to be a common technique to use a strobe light to analyze rotating machinery, although I expect that video cameras are more common these days. If you're actually interested in messing around with this, you can go on eBay and get a working Strobotac for less than \$100. This produces a beam of flashing light, with the flash frequency variable to suit the object you're looking at. Shining this on any rotating object can produce interesting results. Or, if you're handy with electronics, you can save some money and make a driver for some high-power LEDs (not white) and get useful results, although strobe tubes give higher peak light levels and so are easier to use.

• Also a mobile can let you play with strobo. Physics suite is one of many apps. – Alchimista Feb 4 at 12:04
• Note that indoor fluorescent lighting and outdoor street lighting frequently has intensity fluctuations at the power-line frequency (50 Hz in Europe, 60 Hz in USA). This means that it's possible to see stroboscopic effects by accident indoors, or outdoors at night, but to have those effects disappear if the lighting source is full sunlight. – rob Feb 5 at 20:51

From my experience it also occurs when objects spin at a faster rate than our eyes can perceive them to. I see it all the time on wheels of vehicles on highways and all, and also for fans, of course.

• I don't understand, because the eyes are not like a camera. The eyes don't have a frame rate and in any case I would expect the frame rate of the human eye to be much faster than the rev/s of a car wheel. – Joshua Benabou Dec 31 '14 at 5:13
• I think there is some max fps upto which an eye can process information and then tends to get all stroboscop-ish. This is why we can't distinguish individual colours when we rotate a multicolored disk at a very fast rate. Instead, we see white. I love the counter-intuitive nature of nature! – Hritik Narayan Dec 31 '14 at 5:18
• You do often see this effect but I believe it is always when there is artificial lighting involved: many lighting technologies make light that throbs at the AC mains frequency. It is especially evident at night, but even in the daytime, a fan with an artificial, AC powered light nearby can be strobed. Machine shops must use three-phase lighting - three phase delivers a time-steady power to the light source and there is no throbbing. Many serious accidents happen in non-three-phase lit shops when workers have tried to change bits and blades of strobed rotating machinery. – WetSavannaAnimal Mar 19 '15 at 12:32