The underlying assumption in this analysis is that the constant is 1.
Maybe I should have clarified that in the thread.. Thank you for pointing it out!
Maybe I should have clarified that in the thread.. Thank you for pointing it out!
By the way with your data it looks like you get a better fit if you assume your first image is not at 50ms but rather 38 ms. A line fit between t and r^(5.2) gives a slope of 1.6 10^13. This gives 4 kt if you use the lower estimate of 1 kg/m^3 for the density of air.
I do worry you may have overestimated the distance slightly, as these numbers are frankly ridiculous, and with a power of 5 even small errors grow quickly.