The wagon-wheel effect (alternatively called stagecoach-wheel effect or 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 rotating object will show it, such as helicopter rotors, aircraft propellers, and car commercials. In these recorded media, the effect is a result of temporal aliasing. 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: 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.
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. An analog movie camera that records images on filmstock typically operates at 24 frames per second while digital movie cameras operate at 25 frames per second (PAL; European Standards), or at 29.97 frames per second (NTSC; North American Standards). 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 currents, 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 100 times per second on a 50-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 cases, 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 backward. 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, albeit 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 the 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 movement, but their argument has not troubled the consensus.