No strobe needed for "Wagon Wheel" Reverse Rotation effect

I've seen the same effect....

Strobe effects might be caused by observer vibration.

Probably has to do with the small movements of your eyes that you don't notice. The eyes are always jittering to allow the chemicals in the vision receptiors to rejuvinate.

No, that doesn't work. Visual saccades are aperiodic. They can cause random flickering effects, but they don't create the type of smooth continuous virtual motion seen in the truck wheels.

And besides, we don't need wild speculations about the cause when such a straighforwarded explanation exists. If you don't believe it, just get a handful of large hex nuts and position them on an old record player turntable. I can see the diagram of rotating lug-nuts in my head, and describe it in words, but I guess nobody else will see the whole phenomenon unless I create an animated GIF.

(((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))) William J. Beaty

They might be... but they're not! Once you've seen the lugnuts-wagonwheel effect, the cause is totally obvoious. Well, obvious if you know some simple optics. I strongly suggest that you give a serious try at reading the message to which you responded.

Hey. HEY! Another brainstorm!

I'd been wondering how the garage mechanics could stumble across this weird optics effect. Perhaps they hire out-of-work physics PhDs who get bored and start pulling Feynman-esque tricks with spatial beat patterns? It only takes one person to discover the trick, and from then on it spreads from garage to garage. But even so, the pattern of adjustment would be a bit complicated. I doubt the trick would spread far. But maybe it's been spreading for many decades?

Here's the brainstorm: what happens if we adjust the lug nuts so one flat facet of each nut is parallel to the ground? That's gotta be it! In this case the slowly drifting "stroboscopic" pattern will still be there, but it will move two notches ahead per revoltion of the wheel: twice as fast as the optimized pattern I described in the first message.

The hub-facing facet of each successive hex nut would then be off by an angle of 360*(1/12 - 1/10) degrees, like so:

Lug nut position Angle deviation (numbered CW) (degrees) 0 0 1 - 6 2 - 12 3 - 18 4 - 24 5 0 6 - 6 7 - 12 8 - 18 9 - 24 10 0

So the bright pattern of periodic "highlights" will drift in *reverse* direction relative to wheel rotation.

So... communicating the trick really doesn't take any effort. Just tell other mechanics to tighten the lug nuts so they're parallel to the road, and everyone else will start arguing about impossible strobe light effects; effects which occur in direct sunlight.

(((((((((((((((((( ( ( ( ( (O) ) ) ) ) ))))))))))))))))))) William J. Beaty

I guess I'm unusual (surprise, surprise!) but I have no trouble at all visualizing that from your description, even the ones with the nuts at incremental angles, which, it turns out, does make a pretty cool visual (at least in my headbone. ;-) ).

Cheers! Rich

I can see it without, er, seeing it. I guess it's a spatial perception/imagination thing.

And yeah, it's pretty cool!

Mark L. Fergerson

Sounds a bit dangerous, in that the nuts are clearly not tightened to the proper torque. If they had used some kind of decorative nut cover, perhaps...

I've seen the effect with wheels having recessed lug nuts, so I have concluded that a strobed light source was not a factor for my observation.

Or maybe they were over-tightened? To set up the parallel-facet pattern, you can either turn them tighter by between 0 turns and 1/6th turn... or tighten/loosen them by plus or minus 1/12th turn. On the other hand, if truck wheel structure has more "give" than car wheels (so the force changes less per turn,) then the fancy pattern on truck lug nuts would be less dangerous than a similar pattern on a car wheel. Also note that many (all?) large truck wheels have ten lugs.

((((((((((((((((((((((( ( ( (o) ) ) ))))))))))))))))))))))) William J. Beaty Research Engineer snipped-for-privacy@chem.washington.edu UW Chem Dept, Bagley Hall RM74 snipped-for-privacy@eskimo.com Box 351700, Seattle, WA 98195-1700 ph425-222-5066 http//staff.washington.edu/wbeaty/

I didn't say they were looser than they should be, I just said not correct.

I've always found this interesting as well. I've read things relating this effect to the framerates of our eyes but I wasn't impressed. The lugnuts here ARE the strobe with a frequency of however many times they're aligning just right with the sun to relfect at your eye. Lots of mag type wheels will produce this effect as well because of the huge difference in reflection between the mettallic spokes and the dark voids in between them. As far as the backwards effect, I'm guessing that is caused by differences between the rate of reflection and the angular velocity of the wheel, almost like a beat frequency. If that doesn't make much sense, think of a wheel spinning at 120rpm with one mirror on it compared to a wheel spinning at 120rpm with two mirrors on it. If the speed of the wheel changes just a tiny bit, that changes everything. Any takers?:)

-Doc

Bill Beaty wrote:

I would guess the mechanics are not doing this on purpose but rather is a reuslt of the torque wrench or some other aspect of the way the nuts are tightnened.

Intreesting...thanks

Mark

Exactly. That provides the first frequency.

Yes and no. If all the similar reflectors are aligned to the same angle relative to a radial line passing through the hub... then they will always flash at the same wheel angle, and the flashing spot of light will seem to remain still as the wheel rotates. (In other words, a small flat mirror mounted on a spinning wheel will sweep out a reflection and act somewhat like an unmoving cylindrical mirror.)

But then the glowing spot will just flash twice as fast. But it won't move along.

To make it move, we just have to progressively adjust each mirror angle in sequence. If there are many mirrors equally spaced around a circle on the wheel, and if each one is progressively tilted, then each flash position will advance by that extra angle, and the flashing spot will move along. Unfortunately it will move with sawtooth motion: moving slowly forwards, then suddenly jumping back to the initial position. BUT... but if instead we use faceted nuts as mirrors, in that case there's a magic number for the progressive extra angle we give to each nut, an angle where all the progressive tilting will add up so it tightens the last nut by one entire facet.

Or said another way: the facets of whirling hex nuts produce not one, but *several* bright and rapidly flashing spots, like a dotted line on the wheel circumference, but if we tighten each nut a bit more than the previous one, we can make this dotted line start drifting either forward or back. And if we turn each nut to a particular angle, the row of flashing spots will advance by one entire spot per revolution of the wheel (and so there will be no "sawtooth" motion.) As I said before, for ten hex nuts, one magic angle is quantized 1/60th turn relative to a radially-adjusted pattern. So first adjust the ten nuts to point at the hub, then turn nut #1 by 1/60th turn (6deg,) turn the second nut by 2/60ths (12deg), etc. The last one would turn 10/60ths or 60deg or one facet-space, so don't bother turning it at all.

For ten nuts, another magic angle is 1/10 turn or 36deg. It's doubly magic, since it cause two parallel facets of all nuts be aligned parallel to one line (such as the surface of the earth.) That makes the alignment instructions very easy to remember.

HEY! I wonder if garage mechanics *know* that this happens? Maybe they just align the nuts in a decorative pattern for the hell of it, never realizing that it produces a pattern of backwards-rotating lights?

PS I just saw the moving pattern in some really grubby truck lug nuts. Apparantly we don't require a specular reflector, but just a flat nut-facet surface which changes its apparent brightness as it rotates.

((((((((((((((((((((((( ( ( (o) ) ) ))))))))))))))))))))))) William J. Beaty

Whew! I was afraid that this was yet another instance where my explanation seems perfectly simple to me, yet nobody here has any idea what I'm talking about.

:)

Maybe I can only explain it to other visual thinkers?

Here's another interesting bit: with nuts adjusted with one facet parallel to the ground, the hex nuts must rotate 60deg before they all flash again. But since they're spaced ten nuts per 360deg, or 36deg apart, then when a nut flashes the next time, it has moved amost to the position of a previous flash (which was located at 2x36 or 72deg.) But since the wheel rotated by 60deg between flashes, rather than by 72deg, our brains will perceive the flash as having jumped along by 60deg -

The wheel physically rotated by 72deg each time the flash jumps backwards by 12deg. So the pattern of ten spots of light is rotating backwards at 1/6th the RPM of the wheel! No wonder it's so easily seen. 6x slower.

Now we just have to harness the effect for the benefit of humankind. Like making cheap plastic hubcaps which seem to rotate backwards or forwards (or both,) at quantized speeds of 1/6th, 1/3rd, etc.

((((((((((((((((((((((( ( ( (o) ) ) ))))))))))))))))))))))) William J. Beaty

I think several of us can visualise it quite easily. All the same, it would be really cool is if you could manage to get a video of it actually happening on a truck!

Maybe this thread should be crossposted to a truckers newsgroup. Hmmm, then again maybe not.

All very interesting but I have a hard time believing there's a truck mechanic on the planet that would take the time to arrange the nuts in such a pattern. One that did would be fired for wasteing time.

And the odds of the nuts just working out that way upon being tightened would be millions to one.

Anyhow the angles probably aren't that critical since there will be some reflection from highly polished nut regardless.

How about happening instead on my workbench?

A video will convince no one, since the camera aliasing creates all sorts of drifting patterns. However, when I spin my lugnuts-disk quite fast, I see in the camera viewfinder the same drifting pattern which I see with my unaided eyes.

Apparent reverse motion in truck wheel lug nuts

(Note that I stopped the shutter way down for this video, so the bright pattern would be more easily seen.)

PS

videos on other topics (such as FLIR infrared kitten footage.)

billb videos

((((((((((((((((((((((( ( ( (o) ) ) ))))))))))))))))))))))) William J. Beaty

In the last few days I've already seen two trucks with a very clear "drifting dots" pattern in their spinning lug nuts.

It's perfectly possible that garage mechanics know nothing about this stuff, and the pattern is accidental.

Suppose you use a tire iron rather than an air-driven wrench. Suppose you tighten each nut so the tire iron is parallel to the ground. That creates exactly the arrangement needed to make pseudo-strobelight motion patterns.

Yes, and angle error can be crudely determined: if the hex nut angles are randomized by more than +-30 degrees, there will never be any coherent patterns in the reflections. And for the parallel-facets arrangement, if nuts are randomized by +-18 degrees, their reflections will wiggle around but never overlap with the apparent locations of neighbors' reflections.

So when you're stamping on the tire iron, if you always leave it at the same angle within ~10 degrees, your truck's lug nuts will probably make an easily seen "drifting dots" pattern when on the highway.

((((((((((((((((((((((( ( ( (o) ) ) ))))))))))))))))))))))) William J. Beaty