Posting this has been on the back of my mind for a long time (obviously, since the thread has been dead for almost 10 months).
Carlo, a friend of mine, developed a tool for calculating the speed of vehicles from videos using the
cross-ratio equation and a known dimension on the vehicle as reference (usually, vehicle length or wheelbase - axle spacing). The tool is available on his GitHub, only available in Brazilian Portuguese, at
https://github.com/demusis/fotogrametria
When this thread first popped up, so about a year ago, we had been discussing this tool, and I showed him the thread. At the time, he was creating material for a short course where he would teach other forensic professionals about photogrammetry, including how to use the tool he had developed and he actually included this thread as an example in the course just for fun.
Our object here seems to be rotating, so it fails one of the assumptions for cross-ratio, but it does so for a very small angle, so we just take that into consideration, meaning our error bars are increased.
At the time, since I was still learning the tool, I didn't feel very comfortable discussing it here. But now I have used it several times, so I have no excuse to keep procrastinating this (and do this to procrastinate other stuff I have to do, instead).
So, the tool requires knowledge of the framerate of the video and a known dimension.
In a post on this thread,
@Mick West said it looks like 8x slow-mo, or 240 fps.
The length of a blade of grass is very much variable, so we can run the test for 10 cm and 15 cm.
I'm not going to get into the nittygritty of it, but the tool allows us to load the video into it, select two frames, create a composite that overlays the two frames with the chosen object visible in both positions, correct camera distortion if needed, apply one of several image filters if needed. And then comes the actual estimation part.
We choose two points on the moving object for which we know the distance - say the wheels on a car -, and we just click the composite image on their locations, one at a time "A, B, C, D" ("C" is point "A" after it moved, same for D and B) and we do that a dozen or a couple dozen times to create an estimate of the actual position of these points in the image. Then the tool does a
Monte Carlo simulation to calculate a probability distribution of the distance that the object travelled between the two frames, and of the speed, by dividing the distance by the time between frames, and it also calculates a confidence interval (usually a 95% CI, but in forensics a 99% CI is common).
Doing this to our video, using two frames that are 10 frames apart, and running the calculations for 10 cm, we get an estimated speed of 42.5 km/h (39.7 --- 45.8, 95% CI), which is 26.4mph.
And doing the same for 15 cm, the result is 63.9 km/h (59.6 --- 68.8, 95% CI) which is nearly 40mph.
Assuming I used the correct frame rate, if wind speeds are 10-15 mph (16-24 km/h) with gusts over 20 mph (>32km/h), since anything carried by the wind wouldn't be moving faster than the wind itself (this isn't the funny sailbike from Veritasium), so it's unlikely to be anything much larger than 10 cm.
So it could be a small blade of grass, around 10 cm, traveling at ~26 mph at a gusty moment when wind speeds are slightly above that. Or a smaller piece, more likely.
I hope this makes sense.
