Major_tom wrote:How can anyone strap a little rocket engine on a single column that is rotating and not wildly alter the rate of rotation as a result?
One of the many reasons it's a hard pill to swallow. What was it? I try to believe 2π impossible things before breakfast, but only about ei
of them actually stick.
This is like WTC7 to me; a bit weirder, naturally. Why is this event associated with so much crackpot shit? I'm not talking about theories, I'm talking about observations.
Thinking out loud..
1) measurement error (or issues, if you prefer)
3) push from down-rushing air
These are the choices. Did I miss any? Some are faring better than others. #5 hasn't been kicked around; surely that's got to come behind a stray magic oxygen tank as a rational explanation...
#3 I would like, but I think for air to push a column down means the smoke would be going down, too (and faster).
I put measurement problems at the top, along with the related rotation, because this seems most likely to me. We are talking position versus time from video. In this category, included are everything from video distortion to scaling and perspective. femr2 has done an extraordinary job of making a horrendous process seem shrinkwrap smooth on the outside - though it may still be quite a pain we don't hear much about - but there are inherent limitations, and it sounds like this case is not clear cut.
I'm sure I needn't remind you of the all discussions about measurement, interpolation, fitting and so on. My most recent take on it is a simple comparison between the above analysis and the same data with some sinusoidal error thrown in. This doesn't even account for the measurement process itself, since it's all analytical, neither does it treat issues like perspective however amenable they are to analysis.
The first graph shows what happens when you follow the prescription in my 'appendix' above with φ = 0 and angular rotation of 90° per second in a plane perpendicular to the optical axis, the tracking point fixed on the end of a 36 foot section. No air resistance. Blah, blah.
The solid line is position, the dashed is velocity, the (blue) dotted acceleration. The position appears very nearly parabolic. The deviation from a straight line with slope g is evident in the velocity curve. Finally, the acceleration is a large sinusoidal variation about g due to the rotation. The dotted red lines depict g and 1.5g acceleration.
The shaded area is the velocity range of interest in this topic. Notice the rotation causes an over-under g of the expected magnitude. It's obviously a sine wave when you look at the bigger picture, but not at all obvious when considering only the smaller shaded area.
Next, the same function has two sinusoidal components of 'error' added at a peak magnitude of less than 20% of the rotation component, one component at the same frequency in phase, the other twice the frequency out of phase - multiplied - but still very regular and synchronous with the original signal.
Putting them together, you can see that the position curve is very close, velocity a bit different, acceleration wildly different. There is no distortion, scaling, perspective, interpolation - it's all analytical with zero loss or error. This is like putting a recognizable face on error bands; you'll never see anything as regular or identifiable in the real world where there is true uncertainty.And that uncertainty is amplified by taking differences.
The position curves are very, very similar. At the frame sizes, pixel rates, etc, we are talking about, these curves would be within a couple of pixels of each other at all times. Above the shaded area, where the curve is steeper, they appear to lay atop one another. Not to say the measurements aren't better than within a couple of pixels, it's just that a marginal video itself can easily have a couple of pixels worth of funk built into it.