Wagon-wheel effect
The wagon-wheel effect is an optical illusion
Optical illusion
An optical illusion is characterized by visually perceived images that differ from objective reality. The information gathered by the eye is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source...

 in which a spoke
A spoke is one of some number of rods radiating from the center of a wheel , connecting the hub with the round traction surface....

d wheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...

 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
A film, also called a movie or motion picture, is a series of still or moving images. It is produced by recording photographic images with cameras, or by creating images using animation techniques or visual effects...

 or television
Television is a telecommunication medium for transmitting and receiving moving images that can be monochrome or colored, with accompanying sound...

 depictions of stagecoaches or wagons in Western movies, although recordings of any regularly spoked wheel will show it, such as helicopter
A helicopter is a type of rotorcraft in which lift and thrust are supplied by one or more engine-driven rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forwards, backwards, and laterally...

 rotors and aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...

A propeller is a type of fan that transmits power by converting rotational motion into thrust. A pressure difference is produced between the forward and rear surfaces of the airfoil-shaped blade, and a fluid is accelerated behind the blade. Propeller dynamics can be modeled by both Bernoulli's...

s. In these recorded mediums, the effect is a result of temporal aliasing
Temporal aliasing
The stroboscopic effect is a visual phenomenon caused by aliasing that occurs when continuous motion is represented by a series of short or instantaneous samples. It occurs when the view of a moving object is represented by a series of short samples as distinct from a continuous view, and the...

 . It can also commonly be seen when a rotating wheel is illuminated by flickering light. These forms of the effect are known as stroboscopic
A stroboscope, also known as a strobe, is an instrument used to make a cyclically moving object appear to be slow-moving, or stationary. The principle is used for the study of rotating, reciprocating, oscillating or vibrating objects...

 effects: 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 (NTSC; North American Standards), at 25 frames per second (PAL; European Standards), or at 29.97 frames per second. A standard television operates at 59.94 or at 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
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

, such as gas discharge lamps (including neon
Neon is the chemical element that has the symbol Ne and an atomic number of 10. Although a very common element in the universe, it is rare on Earth. A colorless, inert noble gas under standard conditions, neon gives a distinct reddish-orange glow when used in either low-voltage neon glow lamps or...

, mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

 vapor, sodium
Sodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...

 vapor and fluorescent tubes), flicker at twice the frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 of the power line (for example 100 times per second on a 50 cycle line). In each cycle of current the power peaks twice (once with positive voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

 and once with negative voltage) and twice goes to zero, and the light output varies accordingly. In all of these cases, a person sees a rotating wheel under stroboscopic conditions.

Imagine that the true rotation of a four-spoke wheel is clockwise
Circular motion can occur in two possible directions. A clockwise motion is one that proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back to the top...

. 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
Motion perception
Motion perception is the process of inferring the speed and direction of elements in a scene based on visual, vestibular and proprioceptive inputs...

 property called beta movement
Beta movement
The Beta movement is an optical illusion, first described by Max Wertheimer in 1912. Its illusion is that fixed images seem to move, even though of course the image does not change. It might be considered similar to the effects of animation...

: 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 or on propellers under continuous illumination, although often there are other explanations.

Other physical explanations

Some cars have special wheel hubs called spinner
Spinner (wheel)
A spinner is a type of hubcap that spins independently inside of a wheel itself when the vehicle is in motion, and continues to spin once the vehicle has come to a stop. Being an attachment to the car's wheel, spinners operate by using one or more roller bearings to isolate the spinner from the...

s; these can truly rotate backwards. With conventional wheels or propellers, 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 wheel (or even another wheel on the same car if it has a slightly different diameter) or from a nearby propeller that is rotating at a slightly different rate from that of the observed wheel or propeller. It is even possible to produce stroboscopic illumination intentionally 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 1/6 rotation as the wheel rotates once.

Effective stroboscopic presentation by vibrating the eyes

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.

Truly continuous illumination

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.

There are two broad theories for the wagon-wheel effect under truly continuous illumination. The first is that human visual perception
Visual perception
Visual perception is the ability to interpret information and surroundings from the effects of visible light reaching the eye. The resulting perception is also known as eyesight, sight, or vision...

 takes a series of still frames of the visual scene and that movement is perceived much like a movie. The second is Schouten's theory: that moving images are processed by visual detectors sensitive to the true motion and also by detectors sensitive to opposite motion from temporal aliasing. There is evidence for both theories; as of 2011, the debate is not completely settled although the weight of evidence favours the latter.

Discrete frames theory

Purves, Paydarfar, and Andrews (1996) proposed the discrete-frames theory. One piece of evidence for this theory comes from Dubois and VanRullen (2011). They reviewed experiences of users of LSD
Lysergic acid diethylamide, abbreviated LSD or LSD-25, also known as lysergide and colloquially as acid, is a semisynthetic psychedelic drug of the ergoline family, well known for its psychological effects which can include altered thinking processes, closed and open eye visuals, synaesthesia, an...

 who often report that under the influence of the drug a moving object is seen trailing a series of still images behind it. They asked such users to match their drug experiences with movies simulating such trailing images viewed when not under the drug. They found that users selected movies around 15–20 Hz. This is between Schouten's alpha and beta rates.

Other evidence for the theory is reviewed next.

Temporal aliasing theory

Kline, Holcombe, and Eagleman
David Eagleman
David Eagleman is a neuroscientist at Baylor College of Medicine, where he directs the Laboratory for Perception and Action and the Initiative on Neuroscience and Law. He is best known for his work on time perception, synesthesia, and neurolaw...

 (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
David Eagleman
David Eagleman is a neuroscientist at Baylor College of Medicine, where he directs the Laboratory for Perception and Action and the Initiative on Neuroscience and Law. He is best known for his work on time perception, synesthesia, and neurolaw...

 (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. 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
Multistable perception
Multistable perceptual phenomena are a form of perceptual phenomena in which there are unpredictable sequences of spontaneous subjective changes...

. The long time required to see the reverse rotation suggests that neural adaptation
Neural adaptation
Neural adaptation or sensory adaptation is a change over time in the responsiveness of the sensory system to a constant stimulus. It is usually experienced as a change in the stimulus. For example, if one rests one's hand on a table, one immediately feels the table's surface on one's skin. Within a...

of the detectors responding to the true rotation has to occur before the weakly stimulated reverse-rotation detectors can contribute to perception.

Some small doubts about the results of Kline et al. (2004) 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).

In 2008, Kline and Eagleman demonstrated that illusory reversals of two spatially overlapping motions could be perceived separately, providing further evidence that illusory motion reversal is not caused by temporal sampling. They also showed that illusory motion reversal occurs with non-uniform and non-periodic stimuli (for example, a spinning belt of sandpaper), which also cannot be compatible with discrete sampling. Kline and Eagleman proposed instead that the effect results from a "motion during-effect," meaning that a motion after-effect becomes superimposed on the real motion.

External links

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