Finding a Formula for indirect damage to units?

[x3kj 1247]

I'm currently trying to configure my artillery and tank HE rounds with the standard damage system. Both Formulas i found (biki, bisim) for indirect damage at a specific range do not match the experimental data i aquired from a couple of controlled tests. Does somebody have more info how indirect damage is calculate, or does somebody have an idea what formula it could be using?

 

First, let me explain what is known currently: The following Ammunition tokens are relevant for indirect damage

indirectHit - determines damage value

indirectHitRange - determines the explosive radius where the projectile deals maximum damage

explosive - (nonlinear) multiplier for indirectHit damage. For the purpose of this test i used eplosivevalue >= 1 only (pure chemical damage, no kinetic component)

 

Within a radius of indirectHitRange, the shell/grenade will deal a damage with the value of indirectHit. When the distance from epicenter to target is > indirectHitRange, but < 4*indirectHitRange, the damage dealt to the target is a fraction of indirectHitRange, depending on the distance. At distances >4*indirectHitRange, no damage will be dealt.

 

Here is the experimental falloff of the damage (0% Loss = full damage, 100% Loss = no damage)

the anomalies at the transition points is due the slight imprecision of the units placement and explosion epicenter. The relative indirectHitRange and Damage Falloff does not change, irregardless of the ammunition stats used. So it has to be a formula where only the relative indirectHitRange and the relative Range to the target (respective to indirectHitRange.) are involved. Here is the tabledata for the most detailed experiment graph

indirectHitRange    10%    20%    30%    40%    50%    60%    70%    80%    90%    100%    110%    120%    130%    140%    150%    160%    170%    180%    190%    200%    210%    220%    230%    240%    250%    260%    270%    280%    290%    300%    310%    320%    330%    340%    350%    360%    370%    380%    390%    400%    410%    420%
Damage Loss    0.00%    0.00%    0.00%    0.00%    0.00%    0.00%    0.00%    0.00%    0.00%    0.11%    31.89%    52.11%    65.00%    74.00%    80.22%    84.78%    88.00%    90.56%    92.33%    93.78%    94.86%    95.78%    96.43%    96.99%    97.44%    97.81%    98.12%    98.37%    98.59%    98.77%    98.91%    99.04%    99.16%    99.25%    99.33%    99.40%    99.46%    99.52%    99.57%    99.61%    99.65%    100.00%

The problem is that i can't find formula that could reproduce this graph. It's not a root function, that's for sure (the curve is too "round"). I somewhat got close with an exponential function, but it match the experimental data universally.

I had tried

damage = indirectHit * Explosive* C1^(C2 * (indirectHitRange - Range to target))

whereas C1 and C2 are constants i varied to try and fit the graph.

[ceeeb 147]

Damage = 1 / (IHR ^4)

(so long as 1 <= IHR <= 4.1)

[x3kj 1247]

aand we've got a winner :)

I've added it to the A3 damage description