Wagon-wheel effect

The wagon-wheel effect, (alternatively, waggon-wheel effect, stagecoach-wheel effect, stroboscopic effect) is an optical illusion in which a spoked wheel appears to rotate differently from its true rotation. The wheel can appear to rotate more slowly than the true rotation, it can appear stationary, or it can appear to rotate in the opposite direction from the true rotation. This last form of the effect is sometimes called the reverse rotation effect.

The wagon-wheel effect is most often seen in film or television depictions of stagecoaches or wagons in Western movies, although recordings of any regularly spoked wheel will show it, such as helicopter rotors and aircraft propellers. It can also commonly be seen when a rotating wheel is illuminated by flickering light. These forms of the effect are known as stroboscopic effects and they arise from temporal aliasing: the original smooth rotation of the wheel is visible only intermittently. A version of the wagon-wheel effect can also be seen under continuous illumination.

Wagon-wheel effect under stroboscopic conditions
Stroboscopic conditions ensure that the visibility of a rotating wheel is broken into a series of brief episodes in which its motion is either absent (in the case of movie cameras) or minimal (in the case of stroboscopes), interrupted by longer episodes of invisibility. It is customary to call the former episodes frames. A movie camera typically operates at 24 frames per second, and standard television operates at 59.94 or 50 images per second (a video frame is two separate images; see interlace.) A stroboscope can typically have its frequency set to any value. Artificial lighting that is temporally modulated when powered by alternating current, such as gas discharge lamps (including neon, mercury vapor, sodium vapor and fluorescent tubes), flicker at twice the frequency of the power line (for example 120 times per second on a 60 cycle line). In each cycle of current the power peaks twice (once with positive voltage and once with negative voltage) and twice goes to zero, and the light output varies accordingly. In all of these case, a person sees a rotating wheel under stroboscopic conditions.

Imagine that the true rotation of a four-spoke wheel is clockwise. The first instance of visibility of the wheel may occur when one spoke is at 12 o'clock. If by the time the next instance of visibility occurs, the spoke previously at 9-o'clock has moved into the 12-o'clock position, then a viewer will perceive the wheel to be stationary. If at the second instance of visibility, the next spoke has moved to the 11:30 position, then a viewer will perceive the wheel to be rotating backwards. If at the second instance of visibility, the next spoke has moved to the 12:30 position, then a viewer will perceive the wheel to be rotating forwards, however more slowly than the wheel is actually rotating. The effect relies on a motion perception property called beta movement: motion is seen between two objects in different positions in the visual field at different times providing the objects are similar (which is true of spoked wheels — each spoke is essentially identical to the others) and providing the objects are close (which is true of the originally 9-o'clock spoke in the second instant — it is closer to 12 o'clock than the originally 12-o'clock spoke).

The wagon-wheel effect is exploited in some engineering tasks, such as adjusting the timing of an engine. This same effect can make some rotating machines, such as lathes, dangerous to operate under artificial lighting because at certain speeds the machines will falsely appear to be stopped or to be moving slowly.

Finlay, Dodwell, and Caelli (1984 ) and Finlay and Dodwell (1987 ) studied perception of rotating wheels under stroboscopic illumination when the duration of each frame was long enough for observers to see the real rotation. Despite this, the rotation direction was dominated by the wagon-wheel effect. Finlay and Dodwell (1987) argued that there are some critical differences between the wagon-wheel effect and Beta motion, but their argument has not troubled the consensus.

Wagon-wheel effect under continuous illumination
Many people report seeing the wagon-wheel effect on car wheels under continuous illumination. The effect can be produced with a special pattern of lug nut orientation, but often there are other explanations. Some cars have special mag wheels called spinners; these can truly rotate backwards. With conventional wheels, there's always the possibility of stroboscopic illumination. At night, it can come from artificial light sources. During the day, it can come from reflections from another car's wheels that are rotating at a slightly different rate from that of the observed wheel, or even from another wheel of the observed car if its diameter is not exactly the same as that of the observed wheel. The same caution needs to be exercised for propellors if other propellors are spinning nearby.

Rushton (1967 ) observed the wagon-wheel effect under continuous illumination while humming. The humming vibrates the eyes in their sockets, effectively creating stroboscopic conditions within the eye. By humming at a frequency of a multiple of the rotation frequency, he was able to stop the rotation. By humming at slightly higher and lower frequencies, he was able to make the rotation reverse slowly and to make the rotation go slowly in the direction of rotation. A similar stroboscopic effect is now commonly observed by people eating crunchy foods, such as carrots, while watching TV. The crunching vibrates the eyes at a multiple of the frame rate of the TV. Besides vibrations of the eyes, the effect can be produced by observing wheels via a vibrating mirror. Rear-view mirrors in vibrating cars can produce the effect.

The first to observe the wagon-wheel effect under truly continuous illumination (such as from the sun) was Schouten (1967 ). He distinguished three forms of subjective stroboscopy which he called alpha, beta, and gamma: Alpha stroboscopy occurs at 8-12 cycles per second; the wheel appears to become stationary, although "some sectors [spokes] look as though they are performing a hurdle race over the standing ones" (p. 48). Beta stroboscopy occurs at 30-35 cycles per second: "The distinctness of the pattern has all but disappeared. At times a definite counterrotation is seen of a grayish striped pattern" (pp. 48-49). Gamma stroboscopy occurs at 40-100 cycles per second: "The disk appears almost uniform except that at all sector frequencies a standing grayish pattern is seen ... in a quivery sort of standstill" (pp. 49-50). Schouten interpreted beta stroboscopy, reversed rotation, as consistent with there being Reichardt detectors in the human visual system for encoding motion. Because the spoked wheel patterns he used (radial gratings) are regular, they can strongly stimulate detectors for the true rotation, but also weakly stimulate detectors for the reverse rotation.

Purves, Paydarfar, and Andrews (1996 ) also reported reversed rotation of radial gratings. They concluded however, that this was evidence that human visual perception takes a series of still frames of the visual scene and that movement is perceived much like a movie. This can be called the discrete-frame theory.

Kline, Holcombe, and Eagleman (2004 ) confirmed the observation of reversed rotation with regularly spaced dots on a rotating drum. They called this "illusory motion reversal". They showed that these occurred only after a long time of viewing the rotating display (from about 30 seconds to as long as 10 minutes for some observers). They also showed that the incidences of reversed rotation were independent in different parts of the visual field. This is inconsistent with discrete frames covering the entire visual scene. Kline, Holcombe, and Eagleman (2006 ) also showed that reversed rotation of a radial grating in one part of the visual field was independent of superimposed orthogonal motion in the same part of the visual field. The orthogonal motion was of a circular grating contracting so as to have the same temporal frequency as the radial grating. This is inconsistent with discrete frames covering local parts of visual scene. Kline et al. (2004) concluded that the reverse rotations were consistent with Reichardt detectors for the reverse direction of rotation becoming sufficiently active to dominate perception of the true rotation in a form of rivalry. The long time required to see the reverse rotation suggests that neural adaptation of the detectors responding to the true rotation has to occur before the weakly stimulated reverse-rotation detectors can contribute to perception.

As of 2006, there may have been some small doubts about the results of Kline et al. (2004) to sustain adherents of the discrete-frame theory. These doubts include Kline et al.'s finding in some observers more instances of simultaneous reversals from different parts of the visual field than would be expected by chance, and finding in some observers differences in the distribution of the durations of reversals from that expected by a pure rivalry process (Rojas, Carmona-Fontaine, López-Calderón, & Aboitiz, 2006 ). But these doubts would be unlikely to trouble the remainder who would agree that the wagon-wheel effect under continuous illumination does not provide evidence of discrete-frame theory. Rather, it is consistent with rivalry between motion detectors.

Apparent reverse rotation can also be intentionally produced by orienting a wheel's lug nuts (or other reflective objects) so that the facets of each lug nut produce a bright reflection at a sequentially varying position. For example, with hexagonal nuts on a ten-lug wheel on a large truck, all lug nuts can be adjusted with two facets parallel to a single line. When the wheel is then spun, a pattern of slowly moving flashes will be seen, and the location of the flashes will retreat by 1/6th rotation as the wheel rotates once. This pattern of oriented lug nuts may occur accidentally if the nuts were tightened manually using a tire iron.