Odd visual effect - spinning wheel nuts

Factual Questions
1

While traveling on the interstate yesterday I was slowly passed by a semi truck. Its front wheels had very long (like 4-5") decorative nuts on the studs, something like what can be seen here. As it pulled past, I noticed a strange optical effect that I can’t figure out. The geometry is tricky to explain:

When the wheel of the truck was directly in line with my shoulder, I saw the ring of spinning nuts as a blurred circle that was transparent; I felt like I could see the wheel through the blur of fast-moving nuts.

As the truck pulled forward a bit, the circle foreshortened to a vertical oval or ellipse, similar to the photo at the above link. Again, the leading and trailing spinning walls of nuts were indistinct blurs that were transparent, or at least translucent, with the top and bottom edges being opaque where the nuts overlapped visually. You couldn’t see the wheel through the nuts at the top or bottom.

As the truck pulled farther forward, that leading wall and trailing wall started to overlap visually, and that’s when the effect appeared: opaque horizontal bands appeared in the area of overlap. There were maybe 4 or 5 bands with ‘clear’ spaces in between - ‘clear’ in that I could see the tire and bright road surface through the spaces, but not through the dark bands. ISTM that the dark bands were slowly moving upward, but I can’t be sure of that memory. As the truck receded, the dark bands shrunk in size proportionally. The effect was only clearly visible for four or five seconds.

This was in daylight, so no strobing illumination. It was also on the shaded side of the truck, so I doubt that it was the effect of reflection off of faceted surfaces, and there weren’t any bright highlights at any point. The bands did not appear where there was only one ‘layer’ of nuts to look through; it was where you had to look through both the leading and trailing nuts. It is possible that I was wearing polarized sunglasses at the time; I was also looking through car windows.

TLDR: a line of horizontal rods, rapidly moving up, is smoothly see-through. A separate line of rods, moving down, is also smoothly see-through. Overlap them, though, and dark bands appear that are opaque. What could cause this? Intereference fringes somehow? Brain frame-rate? Is it similar to the fan effect in this thread?

2

In that thread, Rat Avatar posted a link to a Wikipedia article on the wagon-wheel effect. (I’m not sure why it hasn’t been merged with Wikipedia’s article on the stroboscopic effect).

The wagon-wheel article mentions that the stroboscopic effect can happen under continuous illumination, which was news to me. It also seems to account for what you observed. Apparently, this can happen due to eye vibration from humming (per the article) but road vibration might have a similar effect.

That wagon-wheel article also suggests that this aliasing can be an artifact of the way the human retina and its components register motion. The article also suggests that a cognitive “frame rate” might be responsible, but favors the motion-registration explanation.

3

A couple of other points:

You say that the geometry of what you observed is tricky to explain, and I agree. FWIW, I found your description unusually clear and unambiguous. Well played!

It makes sense to me that the top and bottom boundaries were opaque. When you project circular motion onto a plane parallel to the axis of rotation, the motion is sinusoidal. So the apparent speed of the nuts is zero at the top and bottom, minimizing motion blur and making the nuts opaque at those extremes. This is the same thing as saying that an engine’s pistons come to a complete stop for an instant at TDC and BDC (top/bottom dead center).

Yep—this sounds exactly like what I’d expect to see when experiencing the stroboscopic effect under continuous illumination. I think that’s what you saw.

Well, both interference fringes and the stroboscopic effect are both examples of aliasing, so it’s not much of a reach to say that they’re essentially the same thing. I suppose it’s possible that some weird effect was creating stroboscopic light under the conditions you describe, but I’ve been told that the simplest explanation is most often the right explanation.

In this case, continuous-illumination stroboscopic aliasing seems like the simplest explanation, even though I wasn’t aware of that explanation until yesterday. :slight_smile:

4

What strikes me as the most peculiar is that whatever strobe or brain-perceptual effect it was only applied to the area where the nuts were crossing one another.

5

I think it’s aliasing between the cylinders (nut covers) on the near side and the far side. You are looking through both at the same time. They are all on the same wheel, so they are synchronized. As they move together, there are certain spots that are always blocked by one or the other.

6

I think that this makes sense to me, but I’m going to have to do some pencil-and-paper work to really understand it. It seems like this would depend upon the relative sizes of the nuts and gaps, and how much of a given gap is blocked by the nut farther away. So if they were narrow like pencils there might be no dark bands, or if they were much wider like Pringles cans there would be no clear bands, or if the wheel was huge such that the far nuts didn’t visually fill the gaps significantly…

It seems like the conditions must have been juuust right for me to see this at all!

7

It’s like a zoetrope - imagine there’s a solid bar where the horse is, and an opening in between. When the slit on the near side is aligned with your eye, there’s always a horse (bar) behind it.

8

Definitely. Also, I was wondering, were the nuts shiny chrome like in your example? Were they cylinders or prisms (circular cross sections or hexagonal)? Facets and reflected light could add to a stroboscopic effect.