# Q&A: Bicycle Wheel Illusion

Question: When we were kids in Nebraska, we loved riding our bikes at night (when it was cooler). The high-pressure sodium lamps were at 60 Hz, and if we rode at just the right speed, it looked like our bicycle wheels were spinning backward. I’m pretty sure I understand how the strobe effect does that, but was wondering if you could explain it using some easy-to-understand graphic or animation? Thanks. KS — Cascabel, AZ

Answer: No problem. Things are always easier to understand something when you get multiple explanations. First watch the animation above. For simplicity it’s only four spokes, and I left out the rim. True rotation is clockwise, as you can see during the gradual startup. The RPM increases continuously over 30 seconds.

It runs at 60 fps, so that’s the primary strobe frequency. But overlaid on that will be the refresh rate of the display on whatever device you’re using to watch it. That creates a visual beat frequency effect. The result is some pretty bizarre apparent motion. Nonetheless, you will see the rotation “reverse” on multiple occasions.

Of course, the reversals are an optical illusion caused by the strobe effect. The following graphic shows how this happens. Again, we’re keeping things simple with only four spokes and no rim:

So if any of the four spokes can rotate to the red position in one frame (or flicker from the streetlamps), the spoke will appear to have moved “backwards” from its previous position. The eye-brain interprets this as a counter-clockwise rotation. If the spoke makes it to the green position, the wheel will be seen as rotating clockwise — though not at its actual RPM.

I watched a lot of westerns as a child, and saw wagon wheels doing this all the time. Between the film’s frame rate and the scan rate of the analog TV, you get the same illusion you saw in my animation. I asked about it but my parents couldn’t really explain. It wasn’t until my high school physics teacher showed us what a strobe lamp could do to a the blades of a spinning fan that it all made sense.

Here’s a YouTube video that shows what I saw in that physics class, along with some other interesting effects. RT = 2:59. Definitely worth a look:

I’ve been having fun with these rotation animations. So next week we’ll take a look at an amazing, and not yet fully understood, visual illusion called Fechner colors. When certain black and white designs are printed on a disc, and that disc is spun fast enough, somehow colors appear!

Next Week in Sky Lights ⇒ Benham Discs