dunmunro wrote: ↑Wed Jan 19, 2022 2:38 am
wmh829386 wrote: ↑Wed Jan 19, 2022 12:10 am
We know in practice, automatic mode in Mk37 is faster than rate control. We even have test data on its the probabilities for TTB in automaic mode using VT ammo.
You are exaggerating to say that manuvers always defeat the FC solution of by Mk37. With gun crew with good dead time discipline, we can scale the kill probability of the test results.
OK, please do.
Let's do a rough estimate by using fuse time error of 0.15s and dead time error of 0.5s. Take the plane speed of 140knots=238 ft per second.
Assumptions: In the test, TTB are determined by burst within 100ft of the target, with over 95% within 80ft. If we replace VT fuse with MT fuse, for all the projectiles that could be triggered, only a fraction will burst within the radius.
In a simplified geometry, the MT fuse need to have a range error of less than 80ft.
Furthermore, (because I am lazy), uniform distribution will be use for dead time error (which is fine) and fuse time error (I should use normal distribution, but I am too lazy to make assumptions about the SD).
Since the target use is relatively low angle, I will take the projectile velocity from Okun's armour penetration table for common shell. (yes the higher elevation reduces MV)
Let's consider 3000yrds: projectile speed = 1697 ft per second.
One more assumption, the FC do not have a significant range rate error
if the projectile can be bring close enough to trigger VT fuse and with radar range rate in use as manuvers will produce more changes to deflection than range rate.
So,
Rnage error due to DT = 238*0.5 = 119 ft
Range error due to fuse time = 1697*0.15 ~255ft
Two errors are independent, so how to calculate this?
Consider if a shell has no DT error, what is the probability of it bursting with range error less than 80ft: simple, 160/(255*2)=0.314. *long and short included
How about if a shell has the maximum DT error?
So, DT error of 119ft long. For a shell to burst within 80ft of target, the fuse time error is between -39ft and -199ft.
So probability is still 160/(255*2)=0.314
That means the DT error is irrelevant because the fuse time error is much larger. The scaling factor at 3000 yard is
80/255=0.314
The math becomes more complicated if we use normal distribution for fuse time. But the idea remains the same: with a well trained crew, most of the error comes from fuse time. OTOH, if the gun crews have poor dead time discipline, and let say 1.5s of DT error, the reverses with even lower hit probability.