art by zenniefox

the pedantic one among us was curious of how fast zennie (the fox rushing) would be going if the color change observed was redshift, so here are her calculations (with a little help of course from a couple others, and equations pulled from the internet :D)

math

given the guard is alive, i will make the educated assumption that zennie only gains such significant speed after this fun interaction. the fur color prior will be the “baseline”.

using the sRGB color profile, the hue of the fur is 17.1 degrees at baseline, and zero degrees at speed, corresponding to (per this tool) wavelengths of about 586 nm and 611 nm respectively.

assuming a lower velocity (relative to the speed of light) the approximation z = v / c would hold true enough. v is velocity, and z is the amount of redshift. solving for velocity we get v = zc.

z is also equal to the change in wavelength or frequency divided by the baseline wavelength/frequency. that is, z = ( observed wavelength - emitted wavelength) / emitted wavelength

as such, v = ( 611 nm - 586 nm ) / 586 nm • c

solving this out yields around thirteen million meters per second. that’s approximately:

  • 1/20th the speed of light
  • forty-six million kilometers per hour
  • thirty million miles per hour
  • thirty-eight thousand times the speed of sound in air (in standard conditions)
  • ten to fifteen thousand times the speed of a 223 round

so uh its safe to say zennie here is FLUSTERED :3c