For WTC 1 the tilting is probably not significant from the standpoint of making vertical measurements. For example, a tilt of one degree of arc of the top block means that the antenna tower has descended about 0.55 meters. So measuring the descent can be used to determine the tilt angle for at least the first 0.8 seconds, before the north wall breaks.
The notion of a t_0 is artificial, albeit useful. What is
interesting is the descent (tilt) starting at the time that floors 98 and 97 expressed smoke and actual flames. This occurs about two seconds before NIST's t_0, and measuring this descent for that time and, say, the following two seconds would provide some useful data regarding collapse initiation hypotheses.
I see what you're saying, and I'm going to attend to things in a different order because you may not need the level of detail I'll eventually have.
As I mentioned, there are three types of methods I'm using to extract numeric data, each with an associated resolution and applicable timeline range. They could loosely be categorized as fine, medium and coarse measurements:
- Slow transition of pixel-sized features across single pixel distances (earliest motion)
- Faster transition of pixel-sized features across several pixels (first obvious vertical motion on video - the elbow of the curve)
- Manual digitizing of multi-pixel features from frame sequences and einsteen images (entire sequence)
The third method, while weak in the early timeline, may be sufficient for what you describe. Rotation doesn't enter in to making
that measurement. I can produce several datasets of that type from at least 3 videos in a day or two; no need for you to wait for other stuff to be complete. The bigger effort, in that case, is obtaining reliable scaling factors for the conversion from pixels to meters. The data will be in pixels and I'll provide the best conversion numbers I can get get at this time - you take responsibility for converting to meters!
Now a long-winded explanation of the problem of rotation.
Rotation is an impediment for the first two methods, especially the first which attempts to map the motion of a feature through pairs of adjacent pixels. This method could yield position resolution of 0.05 meters (not that I'm claiming or guaranteeing that). A tilt of one degree in this context is a whale flopping in a minnow pond.
When lateral translation occurs concurrently with vertical translation of a similar order, the problem becomes 2D in the (x,y) plane. This is a minor hassle but can't be ignored. If lateral motion (x) can be independently measured first - and in this case it can - a linear correction can be calculated and the vertical motion can then be processed in 1D as opposed to simultaneously solving both dimensions in a discrete space with a 3x3 mesh
But the biggest problem with rotation is how small amounts can radically change the appearance of a feature compared to translation. Simple and extreme example: take a hand mirror outside, hold it at arm's length and adjust the orientation so the sun is reflected directly into your eye. Lower the mirror a couple of millimeters while preserving the orientation; chances are your retina is still on fire. Now tilt it so one edge drops the same amount, the intensity drops off substantially.
The antenna is a 3D object with components having different surface properties and appendages. That can be a good thing; the tiny white 'orbs' show up in one video as gray-brown crosshairs, two on each side. Generally, however, a small rotation can change pixel brightness quite a bit without (hypothetically) any accompanying translation. The distribution of smoke in the scene influences the incident light (ambient and diffuse) and the irregular antenna surface, with its specular properties, could be expected to exhibit unpredictable variations of reflectivity under rotation. Not so with translation.
The tapering of the antenna alone is enough to drive me nuts! Then there's the deviation of the frame from true vertical, but at least that's static over time and changes insignificantly over small pixel regions.