Unstable Motion

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fig.  39 - Chopper 5 Velocity Study – Stabilized and Raw
fig. 39 - Chopper 5 Velocity Study – Stabilized and Raw

Link to my original Chopper 5 velocity study.

A real plane flying through the air has very stable motion. Any changes in speed are very, very gradual. Video cameras scan images at an extremely consistent rate, 1 every 1/59.94 second. Therefore, a real plane on a stable video will move the same distance in every frame.

Noise Factors

While the actual motion of an airplane is perfectly steady, certain random noise factors can affect the apparent motion of an airplane on video. I have exploited the presence of these noise factors to provide a scientific proof that the motion of the plane in Chopper 5 is too unstable to be real.

The noise factors that can influence the apparent motion of a moving airplane on video are:

  • Atmospherics
  • Video Resolution
  • Camera Motion
  • Measurement Error

If the air was perfectly transparent (which it isn’t), and if video had infinite resolution (which it doesn’t) and the camera was perfectly still (which it wasn’t) and if position measurements could be made with infinite precision (which they can’t), then the motion of the airplane would appear perfectly stable. Such perfect stability would be represented by a perfectly straight line on a graph of velocity over time.

In reality, the atmosphere can distort the apparent position of a plane a tiny bit, video resolution is only so good, the camera in Chopper 5 was moving, and there will be small errors in trying plot the exact position of the airplane in each frame.

All 4 of these are random errors. Each type of error adds to the deviation from perfect stability. These are as likely to be errant left as right, up as down. Such random errors tend to accumulate. They add up. Each error type will add to the total error, that is increase the deviation away from perfect stability. Each will make the graph line more jagged.

Method

Therefore, if we can find a way to eliminate one source of error, while holding the other 3 sources of error perfectly constant, then we would expect to see the total error decrease. We would expect to see the graph line become less jagged. I have devised a method to do just that.[#_ftn10 [10]]

• Stabilize the video to subpixel accuracy.

• Catalog the distance each frame was moved in the stabilization process.

• Place a wireframe around the plane image frame by frame, going for best overall fit.

• Measure the change in airplane position (velocity) per frame.

• Graph these position changes as “∆X Stabilized”.

• Calculate the “Raw” (un-stabilized) data by subtracting the distance each frame wasmoved from the velocity measurement of that frame.

• Graph these position changes as “∆X Raw”.

• Compare “Raw” graph line to the “Stabilized” graph line.

By doing this, we have subtracted the camera motion from the total error, while holding the other three error types perfectly constant. Any measurement error was held perfectly constant because the measurements were only made once. In a legitimate video, the stabilized graph line must be straighter, with less deviation from the norm, than the raw graph line.

Conclusion

Given sufficient time, a video compositor can correct motion problems. But Chopper 5 was shown live. There wasn’t time. The 9/11 perpetrators had to show us news helicopter shots, because if they didn’t, everyone would wonder where the news helicopters were. With the gyroscopically stabilized camera mounts, they were hoping the drifting helicopter shots would be steady enough so as to make the motion problems undetectable. Chopper 5 was almost that steady. But not quite.

Thus, airplane motion data are consistent with the compositing hypothesis, and not with the real plane hypothesis.


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