If a spinning object with gaps (like a fan, or helicopter blade) is spun faster and faster, the image will blur, multiply, and become transparent. Is the limit to the transparency merely based upon the size of the gaps vs the size of the blade (e.g. if the gaps are 50% the blades, the image will look 50% darker at best), or some less obvious brain factors (electrical signals across neurons take around a millisecond, so should > 1000Hz rotations have a weird effect), and is the progression of motion illusions over after a certain RPM?
I noticed that helicopter blades spin at a tremendous RPM, and you can still see them, but if I take this little wheel device I have and spin it with just my finger, even with spokes as thick as the gaps, it will create a slightly darkish transparency with no visible after-images of the spokes, even at slow speeds. Something just about size? But using forced perspective changes nothing. I can’t explain this visually/neurologically.
Helicopter blades don’t spin at a tremendous RPM. Around 350 RPM, although it does vary depending on the helicopter. This is only slightly faster than a ceiling fan, which tops out around 250 RPM.
By comparison, airplane propellers spin around 2500 RPM.
The limiting factor on both of these is that shockwaves will form, with various negative consequences, if the tips of the blades approach the speed of sound. Since helicopter blades are much longer than propeller blades, they must turn slower to stay under this limit. Airplane propellers are limited by the need to not hit the ground, otherwise they would be quite large too, since larger, slower blades are more efficient.
With that addressed - my understanding is that the visibility of a rotating object above a certain speed is simply related to what fraction of the object’s area is taken up by the “spokes”, or spoke equivalents. The object blocks X% of the light from reaching your eye. The reason it may not look like the image is X% dimmer is that your perception of brightness is non-linear, and that the spokes themselves are generally still illuminated and may be just as bright as the scene behind them.