monitor distance Problem with my Derived Monitor Distance Formula

[Tsing]

Hi guys,

Sorry for the continued questions but I'm trying to derive the formulas for monitor distance and viewspeed myself (there will probably be a few more questions yet before I get there!).

I have derived the following formula for matching monitor distance at coefficient m from original FOV theta_1 to new FOV theta_2:

and the following for coefficient 0:

I have checked the results these formulas give me for CS:GO against the sensitivity calculator and they are correct for 4:3 aspect ratio. For example, I obtain the following zoom sensitivity ratios for the first awp zoom for 0% and 50%:

0%=0.818933...

50%=0.873581...

However, as soon as I recalculate for 16:9 I get incorrect results, even when I adjust my FOVs for 16:9:

0%=0.737720..., correct is 0.818933...

50%=0.823462..., correct is 0.910887...

75%=0.907653..., correct is 1

Can anyway tell me what is wrong with my formulas and how I should modify them so that they work for all aspect ratios? If more details of my derivation are needed I can always provide.

Thanks a lot for the help!

Edited June 5, 2020 by Tsing