88mm flak fuze timing is unrealistically precise and guns are thus too accurate in ranging their burst

[icuham]

Historical fuze timing variance for 88m is detailed in a report available here: https://apps.dtic.mil/dtic/tr/fulltext/u2/a953461.pdf

 

This report details a chart in Fig. 1A which gives tested variance between fuze setting and burst delay.  A fuze setting near 0s yields an error of near 0s, but a fuze setting of 26s yields a variance in burst delay of >5s.  After the shell has traveled 26s it's velocity will still be hundreds of meters per second dependent on angle of fire (say ~550m/s as an example calculated on a ~60* firing angle, with 2760ft/s initial velocity) . Thus, the placement of the burst could be anywhere along the line of trajectory within a range of 550m*5s = 2750m. 

 

We can establish a test of fuze timing accuracy in DCS.... At a distance of about 5.5-6km (3km altitude and 5km distance varying as the target flies) from the gun and an angle of ~30* the shell will take 7-8s to reach the target.  it will be traveling 800m/s and it will have a fuze variance of (presumably) 2-3s depending on which initial shell velocity is modeled in DCS (less error for 2600ft/s and more for 2760ft/s from the report Fig 1A). That means, based on the report, we should see a range variance of 800m*2.5s or 2000m. 

 

Instead, in game we see the shell hit a highly predictable spot with a nearly exactly repeatable fuze delay shell after shell.  The cadence of explosion is exactly the same, it seems, as the cadence of fire (a frequency of 1 explosion every 3s with error attributed to firing delay, not fuzing).  This suggests there's no variance whatsoever in the shell's fuze and this seems to be an issue in the model which results in much higher longitudinal precision than a real world 88mm gun would have achieved.

 

Attached are a few tracks representing this test.  Upon replay most detonations follow the target high at the 9:00 or 8:00 position, predictably enough that you just need to turn your head left and look up to view most impacts.  In reality, about half should explode before reaching the aircraft, half after, randomly. And the fuze variance should result in shells exploding at any distance from 1000m short to 1000m long, but almost all hit in a highly predictable & repeatable spot with what appears to be <100m in variance.  We can conclude that the model likely doesn't factor in fuze variance at all, or that if it is modeled it is much too precise compared with the real world data presented.

flaktest.trk flaktest2.trk flaktest3.trk flaktest4.trk

[Yo-Yo]

Thank you for your observation and for the article. I agree that now the fuse  time has lack of deviation.
Anyway, your numbers seem to be a bit strange. At 3000 height and 5000 horisontal distance the shell will have about 340 m/s and the travel time will be about 12 seconds.
Standard deviation for the series of tests is about 0.8 seconds, so you can expect +-3 sigma or +- 2.4 s full range. So, full variance is about +-820m with the 50% of bursts within +-205 m.

UPD: the time of flight and velocity is for HE with time fuse. Sorry for the typo for 50%.

[icuham]

I'm using this calculator for the trajectory: https://amesweb.info/Physics/Projectile-Motion-Calculator.aspx

 

Trusting it's math... I used 2760 ft/s Vo (841m/s), 30* launch angle (based on this solution: https://www.calculator.net/triangle-calculator.html?vc=&vx=3000&vy=&va=90&vz=5000&vb=&angleunits=d&x=47&y=7), 0m initial altitude, 3000m final altitude, earths gravity.

 

This results in a final velocity of 805m/s.  (A vertical vector of 342m/s and a horizontal vector of 728m/s.) Flight time of 7.8s. If drag is slowing the shell further (considerably further) that may account for an discrepancy in both the velocity and time of flight, so while the range error is decreased the fuze accuracy is also decreased and a different calculation needs to account for drag induced deceleration to adjust my calculation.

 

So I generally agree with the assessment, but I believe the shell velocity you should use is closer to 805m/s, not 420m/s, for this example (granting this may be affected by drag).  I agree with the full range timing at 2.4 so this means the full variance should be +-805*2.4s = 1932m ( I used round numbers above to illustrate it more simply and arrived at 2000m).  We can probably assume a normal distribution from there, so the final 50% value will also be wider, maybe closer to 200m on either side of the aircraft, but I'll leave that final detail to you Yo-Yo... It seems in principle we are in agreement.

Edited January 25, 2021 by icuham
math values

[Yo-Yo]

I can not trust this math.... It's ridiculous.

It seems to me that it's a super simplificated air-free calculation

Let's perform a small check:

Full energy for 9 kg shell at the nozzle at H=0 and 841 m/s is  E_kin_0 = 3182765 J

If the shell elevates to 3000 m without any drag losses it will have potential energy E_pot_3000 = 264600 J
So, as it preserves the same energy E_kin_3000m = E_kin_0 - E_pot_3000, thus E_kin_3000 = 2918165 J and the velocity is 805 m/s. Bingo...

And, by the way,  the speed for 9 kg HE will be 340 m/s. Sorry, the previous 420 was for AP shell.
So, the 50% of bursts will be within +-205 m, see the corrections in my previous post.
 

 

My sources are firing table for this shell and our model.

[icuham]

Yeah, so with drag factored it looks like that's getting much more realistic than the current model.