README.md

AlphaPhoenix

https://www.youtube.com/watch?v=YMO9uUsjXaI

input data:

• 140 teeth around the wheel
• total distance = 3.86 miles
• original frame size = 367x367

Inferred speed in the video: mean = 298 Mm/s, 95% CI = [285, 310]

processing

# download part of video
yt-dlp \
  -f 248 -o "AlphaPhoenix-speedoflight-res.%(ext)s" \
  --download-sections "*15:30-15:33" \
  https://www.youtube.com/watch?v=YMO9uUsjXaI

yt-dlp \
  -f 248 -o "AlphaPhoenix-speedoflight-full.%(ext)s" \
  --download-sections "*12:37-12:42" \
  https://www.youtube.com/watch?v=YMO9uUsjXaI

# grab cropped and resized frames
ffmpeg -i AlphaPhoenix-speedoflight-res.webm \
  -vf "crop=958:958:926:46,scale=367:367" \
  -ss 0.6 "frames/res_%03d.png"

ffmpeg -ss 2 -t 3.1 \
  -i AlphaPhoenix-speedoflight-full.webm \
  -vf "crop=1080:1080,scale=360:360:flags=neighbor" \
  "frames/full_%03d.png"

The individual photos appear a couple of times; the first set I noticed started around 15:30 and includes info that they were 367 pixels square. I then noticed full screen versions appearing at 12:37. They are presumably both the same just resampled differently, as they are both stabilised the same.

model.stan

data {
	int<lower=0> N;  // number of frames
	int<lower=0> K;  // number of pixels

	vector[K] angle; // angle of each pixel (in degrees)
	vector[K] dist;  // distance of each pixel away from circle

	vector[N] rpm;
	array[N] vector[K] pixels; // brightness of each pixel for each frame
}
parameters {
	real<lower=-40, upper=-35> alpha; // start angle
	array[N, 3] real<lower=0> mass;
	real<lower=0> scale;

	real<lower=0> sigma;
	real beta; // baseline brightness

	real<lower=0> rpm_mul;
}
model {
	for (n in 1:N) {
		vector[K] mu = rep_vector(beta, K);
		real off = alpha + rpm[n]*rpm_mul;
		for (m in 1:3) {
			mu += mass[n,m] * exp(-scale*square(angle - (off + (m-2) * (360. / 140.))));
		}
		pixels[n] ~ normal(mu, sigma);
		mass[n] ~ normal(0.1, 0.02);
	}
	rpm_mul ~ normal(1e-5, 1e-5);
	alpha ~ normal(-40, 1);
	scale ~ normal(1, 1);
	sigma ~ normal(0, 1);
	beta ~ normal(0.2, 0.1);
}

speed-of-light.ipynb