How did that happen?

What can your camera do to helicopter rotor blades

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with articles on technical aspects of photography.

It is recommended that before reading this article you read through another one, on focal-plane shutters, unless you are already familiar with the geometric distortion they cause.

A month after that article was published, a Reader from Switzerland found what seemed as a great example of the geometric distortion caused by focal-plane shutters, a picture of a flying helicopter (published on the Canadian SOS Levasseur Coalition site; original link no longer working). Here I am reproducing a small fragment of the original.

Have a look. What's wrong with the rotor blades? Not only are they bent (two significantly, the third one, partly hidden, less so), but they don't seem to be spaced evenly!

We could try to explain it with a focal-plane shutter, traveling from left to right (in the picture orientation as shown) — but the numbers seem to contradict that hypothesis. Still, let us assume it for a while, and see what happens.

The left blade tip has been exposed first; as the shutter slit moved to the spindle, the rotor turned clockwise by more than 30° this is why the blade seems to bent by that angle. Before the shutter reached the tip of the right blade, another 30° rotation occurred — that's why that tip points in the direction of rotation.

All that can also be explained by the blade turning anti-clockwise and the shutter traveling right to left, but this does not change anything.

(Thanks to Sape Mullender for catching my logic error in the original version of this paragraph. Gee, I have to watch what I'm writing, some people actually read this stuff!)

The red lines I've added to the picture show the blade orientation at the moment when the shutter slit is at the rotor spindle.

I'm not a helicopter expert, but I believe the rotor's turning rate in most types is 600 RPM (rotations per minute) or less. Assuming that, let us estimate the shutter travel time necessary to provide the observed distortion.

The full frame, oriented vertically, was reproduced as 960×1280 pixels; (I'm not showing it, as this might no longer constitute a "fair use"). The horizontal distance between blade tips is about 240 pixels; 1/4 of the shorter frame dimension. If the rotor blades travel 60° in 1/4 of the shutter travel time, this makes 240° or 2/3 of a full rotation within that time. 2/3 of a rotation at 600 RPM (one revolution in 1/10 s) corresponds to 1/15 s. Such shutter travel time would be needed for the focal plane shutter hypothesis to work. (Most helicopter rotors spin more slowly; this would only make the required shutter travel time even longer.)

The digital SLRs have a shutter travel time of 1/200 s or less; even 50-year old film ones go down only to 1/30 s, not longer. The focal plane shutter hypothesis seems to be out.

On the other hand, some P&S digital cameras may show a similar effect: the signal is picked up from the sensor one pixel row after another while the image is being exposed, and that would introduce a similar distortion! What these cameras effectively have is an equivalent of a focal-plane shutter, with the slit just one pixel wide (this also may explain why the rotor blades are not blurred).

If such a camera has a readout cycle of 1/15 s, this would perfectly fit the magnitude of the distortion we see in our picture. The cycle of 1/30 s is quite common, so 1/15 s is also thinkable, at least not outrageously unrealistic.

Therefore my bet would be on a digital camera with a sequential live image readout. Correct me if you have a better idea, with better numbers.

Well, next time you see some picture, any picture, have a close look and have a calculator handy. You may discover some strange and wonderful things.

Back to the Nitty-Gritty section,
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Posted 2007/03/23; last updated 2009/02/24 Copyright © 2007 by J. Andrzej Wrotniak