Pilnmēness nogurdinātie - Par to cik tālu mēs varam aiziet lietās, kas mūs amuzē

But that equation makes no sense: one cannot compute the time-to-full-recoil-recovery by just solving the 'time' out of that equation because the 'time' variable does not denote _time_ per se.

Recoil decrease is a differential equation. If the left-hand side (that remained implicit in the original equation) was written out, the equation would be:

dR/dT = -kt^2,

where R = recoil, T = time, k = Gun_recoil_decrease_constant * Scale_constant, and t = time_since_last_shot. Note that 1. T /= t, 2. t is the only variable, and 3. the equation is not a proper rate equation without R itself in there.

Anyway, now that T is discrete and corresponds to frames at 30 Hz, you can rewrite this into deltas:

delta_R / delta_T = delta_R / 0.033 s = -kt^2
<=>
delta_R = -jt^2,

were for simplicity the constants are again wrapped into j = 0.033*k

This delta_R has to be calculated at each frame and subtracted from the current value of R if R > 0. To get the time-to-zero-recoil, one needs to integrate (sum) these 'delta_R' with t increasing from 60/RoF in steps of 0.033 until Sum{delta_R} >= R and then look into how many frames it took.

Finally,

@Veritable

note that the 0.1 scale and recoil decrease during the firing cycle are totally irrelevant in magnitude (look at this) already because t^2 for small t is so very small. Having the scale = 0.1 there on top of that is an overkill. So for any practical calculations, the 0.1 scale regime can be ignored and one can start considering recoil decrease after the firing cycle of the burst's last shot has ended.

Thank You for clarification.

Last time when I was solving a differential equation... it was almost 20 years ago (yes... I an old man ) when I was studying Acoustics at Technical University, but since this time I have been working mainly in music industry as producer and mixing, mastering engineer so I forget a lot about math:(((

if it is like dR/dT = -kt^2 which I did not known from the first post, my equation have no sense at all, but the problem is...

I've checked empirically in Test Range RPMs which were solutions of my equation (95 RPM for no recoil and 135 RPM for no H recoil) and it seem to work perfectly.