Why is a rotor not opaque?

Question

Helicopter rotors spin at around 300 rpm. Now for the naked eye they look like transparent, like if the rotors were not even there.

https://www.quora.com/Why-do-we-see-individual-helicopter-rotor-blades-when-they-are-spinning-so-fast

This is said to be because the rotor spins so fast, that our eyes cant catch up to the angular velocity of the rotor.

So this way the rotor becomes invisible for our eyes, and the whole area where the rotors spin becomes transparent.

But light is much faster then the rotors, so basically for light, the rotors are relatively slow, like 0.00001 c, and therefore if we use a camera that can catch up to 300 rpm speeds, the video we would record would show the rotors simply spinning fast, and the same way if our eyes could catch up to 300 rpm speeds, we could simply see the rotor spin fast.

But if the rotor spins so fast, and our eyes can't catch up to that speed, then shouldn't the rotor area be opaque, a full opaque circle, like if there was rotors all around?

Our eyes should see photons coming from the rotor at all angles, and since our eyes are so slow, they should catch all frames of the rotor being at all angles at the same time. This way the rotor would seem to be a full circle opaque.

Question:

1. Why do we see helicopter rotors to be transparent?

2. Why do we not see a full circle (since it spins so fast compared to our eyes capabilities) of the rotor being opaque?

Answer 1

The image on your retina is basically the sum of all the light sources that reach your eyes from a particular direction over a short period of time.

If we imagine looking at a point through the rotor disc, then some light will be coming from sources beyond the disc (perhaps a bright sky), and some light will be coming from reflections off the rotor.

If it's daytime, then most of the light reaching your eye from this point will be from the bright sky. The rotor will probably not be as bright, and it will only be present for a small fraction of time. The overall contribution is swamped.

Now, if it's nighttime and you have some lights shining on the helicopter, the situation is quite different. In this case almost all the light that reaches your eye is reflecting from the rotor. There's nothing else to swamp it out and it will be clearly seen as a disc.

This situation is very similar to how "one-way mirrors" work. There the situation is manipulated so that most of the light is on one side of the mirror. Then the image in either direction is of the lit side. It's not that the darker side is invisible, it's that the small amount of light from there is lost in the much greater signal from the bright side.

Answer 2

I think your over thinking this. If you look at a fan, you will actually see that it DOES look a little opaque just as you describe. Our eyes see at about 32 frames per sec or 31ms, so at any "moment" in time our eyes "see" the rotor here, then there then there, etc. The overall effect to our brain IS to spread that rotor out and the sky will look a little opaque as we look up through the rotor space.

Answer 3

When we look at a spinning helicopter rotor on the background of the sky, we see the average brightness/color, which will depend on the brightness/color of the blades and the sky and on the percentage of time (duty cycle) we see each at any given location.

Assuming the the blades are darker than the sky and have uniform width, a spinning rotor would look darker close to the center of rotation and lighter close to the tips of the blades, because the "duty cycle" associated with the blades decreases as we move from the center of rotation out toward the tips.