dumb bomb dispersion modelling problem (Full Version)

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DracheTek -> dumb bomb dispersion modelling problem (7/16/2020 12:56:51 PM)

I noticed that some fellow players are complaining about dumb bombs not hitting target, and I did a test using F-15E and LDGP bombs, which should be fairly accurate and effective in real life with the aid of advanced laser sighting and CCRP calculator, and the result is below. "CEILING" is the ceiling of each dispersion group, and "FREQUENCY" is frequency. Number equals to the CEILING is counted inside the group.

a total of 783 bombs are disposed.

CEILING FREQUENCY
61 97
122 84
183 137
244 127
305 106
366 144
427 64
488 23

Note that the peak appears at the middle of dispersion RADIUS instead of ZERO, which means that most bombs dropped about 250m off the target.

In case I am wrong, I will later post a result with some 10k bombs. Hope my computer safe.

In case someone would like to do some math, I included the source data of my third test here.



DracheTek -> RE: dumb bomb dispersion modelling problem (7/16/2020 1:28:44 PM)

Here is the result for 4932 working bombs (malfunction entries are removed). Bombs are released from 36000ft.
CEILING FREQ
10 38
50 397
100 569
150 529
200 587
250 498
300 464
350 484
400 327
450 229
500 162
550 129
600 74
650 58
700 56
750 54
800 44
850 45
900 38
950 67
1150 57
1300 26


For some reason, the dispersion center is near 200m instead of 0.



DracheTek -> RE: dumb bomb dispersion modelling problem (7/16/2020 2:07:08 PM)

And here is the result of 4966 working bombs released from 1000ft.

CEIL FREQ
0 52
5 162
10 385
15 551
20 599
25 607
30 551
35 532
40 475
45 385
50 295
55 163
60 104
65 70
70 23
75 9
80 2
85 1

Maximum distribution is reduced by ten folds, but distribution peak is still near 20%~30% of maximum distribution (20~30m off target).

Keep in mind that the standard bomb target is a 5*5 target. If attacking structures with larger dimensions, some "OFF" result will turn "HIT". Or to put simple, dumb bombs are best suit engaging structures larger than 20*20m, which ensures around 30% total accuracy. If intend to attack critical component or target that is much smaller than that, it is better off going for "expensive" precision guided munition, which will save a lot of flight time, and greatly reduces losses due to close in bombing, which in turn may lower cost.



thewood1 -> RE: dumb bomb dispersion modelling problem (7/16/2020 3:39:49 PM)

"If intend to attack critical component or target that is much smaller than that, it is better off going for "expensive" precision guided munition, which will save a lot of flight time, and greatly reduces losses due to close in bombing, which in turn may lower cost."

Is this the final conclusion of your testing? I didn't read through it all. Because if it is, I think we knew that already. Its why PGMs were developed in Vietnam to begin with.



DracheTek -> RE: dumb bomb dispersion modelling problem (7/16/2020 10:46:03 PM)

I was posting at 23:07 GMT8+, and was just trying to stuff something that looks wise at the end of my post and go to bed.

quote:

Keep in mind that the standard bomb target is a 5*5 target. If attacking structures with larger dimensions, some "OFF" result will turn "HIT". Or to put simple, dumb bombs are best suit engaging structures larger than 20*20m, which ensures around 30% total accuracy.


This may be what I was trying to emphasize, I wanted to limit the result of the test more gameplay-wise.



SeaQueen -> RE: dumb bomb dispersion modelling problem (7/17/2020 11:35:15 AM)

quote:

ORIGINAL: DracheTek
Note that the peak appears at the middle of dispersion RADIUS instead of ZERO, which means that most bombs dropped about 250m off the target.


Thanks for testing that! I'd been meaning to look at that too. Originally the distribution of bomb hits was uniform, which made for too many far misses. Now it's more Gaussian, which is better, but it's peaked in the wrong spot. It looks like D needs to shift it over so that the peak is at zero. Now it doesn't overestimate miss distances QUITE as bad as it used to, but it's still a little high.



DracheTek -> RE: dumb bomb dispersion modelling problem (7/18/2020 12:25:20 AM)

Now that I have a hell lot of free time, I decided to do the same for artillery and basically anything else not precision guided.
This time I tested 10000 rounds of 155mm howitzer shells at max range. The outcome is in the attachment.

Note that the distribution of shell forms a distinct shape: At stage 1 (0~70m dispersion) it separates into two distinct lines as if it has two distinct mean values(60 and 120 ). at stage 2 (70~140m) it distributes uniformly (~75 round per one meter ring, stdev = 11), stage 3 has a uniform distribution with ~10 rounds per meter ring and stdev = 8.



DracheTek -> RE: dumb bomb dispersion modelling problem (7/18/2020 4:25:29 AM)

TEST 5

Another with 10000 rounds of 155 shells is done. This time ranged at 2nm.
Result is close to the TEST 4, but dispersion upper limit is down to 33m. even distribution cutoff at 22m(2/3 of max dist range), mean value is 400 rounds per meter ring within 22m and 50 rounds per meter ring within 22~33m ring. which is consistent with the result of test 4.



DracheTek -> RE: dumb bomb dispersion modelling problem (7/18/2020 5:39:22 AM)

TEST 6
A/G strafing was extremely accurate in the game. It has achieved a 585/614 (~95%) hit rate against 5*5m target.

FINAL CONCLUSION
With all results combined, there is some problem in unguided bombing math modelling that causes even the newest multitask aircraft equipped with advanced ground search/measuring apparatus and CCIP computers to have some unreasonably low efficiency against armored target. Judging from the dispersion, their aims are always 20% off the target instead of right on spot (does not apply to air to ground gun strafe though). It can technically be justified by the following: Novice pilots tries to put the center of aiming reticle (think of the WWII-pre cold war reflective/gyro sight), forgetting to adjust for parabolic trajectory of bombs/rockets, and the actual fall points will be off.
If move the mean value to zero (or at least do it for those newer aircrafts and give them an attribute like "CCIP aid" in database), and keep variance unchanged (15 for bombs, 10 for rockets, 2 for cannons), the accuracy of bombs/rockets will be increased to around 8% each bomb, or 64% that one sortie of strike eagle or A-10C hitting at least one tank sized target. That result may be more realistic and historically accurate.



Rory Noonan -> RE: dumb bomb dispersion modelling problem (7/24/2020 7:13:32 AM)

Hi all,

After seeing this thread we did some analysis of our own.

Method
The test case was 1152 Mk82 bombs (48 aircraft each with 24 bombs) dropped from 800ft on a target marker with a size of 5x5m. The test was conducted in two series.

Series 1 used default WRA settings of 'all weapons' being allocated per salvo, with the modification of selecting '4 units' to fill salvo quantity (aircraft were organised into flights of 4).

Series 2 used WRA settings of '1 round' and '1 aircraft' to ensure single drops.

Results
The results from series 1 showed 6 direct impacts, 23 malfunctions and 1123 misses ranging from 2.74m to 704.40m. The standard deviation for misses was 137.78m, and the CEP for all bombs (minus malfunctions) was 52.43m.

On a histogram (image 1) the distribution of impacts around the target shows an annular pattern, with a relatively low number of impacts in the 0-5m bucket and peak incidence in the 40-45m bucket.

[image]https://i.imgur.com/qyk5M8J.jpg[/image]Image 1

When the results for individual bombs from series 1 were organised into their sticks of 24, the reason for this annular distribution became more apparent. The V-shaped distribution of impacts for weapons in sticks that contained a hit (image 2) shows that hits occur in the middle of sticks, with other weapons in the same stick spread across the CEP in a fairly uniform distribution. Interestingly you can actually see the difference in miss distance for sequential bombs being released from the left and right side of the aircraft in the graph.

[image]https://i.imgur.com/zsxZBfv.jpg[/image]Image 2

The results from series 2 showed 34 impacts, 23 malfunctions and 1095 misses ranging from 2.74m to 287.73m. The standard deviation for misses was 33.14m, and the CEP for all bombs (minus malfunctions) was 44.50m.

On a histogram (image 3) it is apparent that the peak impact incidence was in the 0-5m bucket, with a similar annular distribution of misses grouped around a secondary peak at 35-40m.

[image]https://i.imgur.com/qN2I4oN.jpg[/image]Image 3

Discussion
The above results demonstrate the difference in results between stick bombing and individual bomb release. Stick bombing sacrifices accuracy of individual weapons in exchange for low time over target (ToT). Because of the linear nature of stick bombing even sticks that contain a hit still contain misses, and the magnitude of misses can be magnified.

Single-drop bombing is more efficient in terms of obtaining the most hits on target for the least expenditure of weapons, however it comes at the cost of increased time over target. In order to achieve 24 individual weapon drops, the aircraft delivering weapons had to make 24 separate runs over the target.

Another factor to consider is the salvo success rate. Series 1 comprised of 48 salvos (of 24 weapons each) for a total of 6 hits; so the chance that a salvo would hit its target was 1 in 8. In series 2, there were 1152 salvos for 34 hits--the chance of a salvo hitting its target was approximately 1 in 34.

Real world operations commonly use stick-bombing for unguided weapons, willingly trading a higher volume of dropped ordinance for a higher per-salvo hit rate and the increased survivability that comes with a reduced time on target.

Summary
[image]https://u0v052dm9wl3gxo0y3lx0u44wz-wpengine.netdna-ssl.com/wp-content/uploads/2016/01/Black-Buck-I-Recce.jpg[/image]Image 4
[image]https://i.pinimg.com/564x/2f/41/27/2f4127d2cb9481e5a7d391a30a70fb2c.jpg[/image]Image 5

The annular distribution of weapon impacts in stick bombing is a tradeoff for the benefits of low ToT and increased per-salvo accuracy. The more efficient single-drop bombing method is balanced by markedly increased time over target and decreased per-salvo accuracy.

For most practical cases the optimum delivery method is stick bombing, as the increased ordinance use is offset by the increased chance of survival of aircraft delivering weapons (see the results of the Black Buck raids in image 4). In cases where there is no opposition and insignificant fuel and time constraints, it is possible to reduce total munitions expenditure by using single-drop bombing.

In Command you are able to enforce stick sizes using the WRA doctrine settings. Experimenting with these settings (e.g. limiting stick size to 4) will determine the optimum stick size for the mission and target at hand.




decaf -> RE: dumb bomb dispersion modelling problem (7/24/2020 5:53:59 PM)

Outstanding analysis, apache85!

What's really impressive is how CMANO/CMO uses different modeling
between the stick bombing and the individual bomb drops.

Now I understand the really large outliers with LDGP. Those are
the tails of the stick. Way realistic!



boogabooga -> RE: dumb bomb dispersion modelling problem (7/25/2020 2:13:48 AM)

Interesting. So while dumb bombs are touted as "cheap," if you are forced to drop a stick of 24 to hit anything, you are really looking at ballpark $50,000; more accurate GBUs start to become cost-competitive.

What do you count as "direct impacts"? A 2.74m "miss" is actually about the length of the bomb, and I would expect even 10m or so to devastate a soft target.



Dimitris -> RE: dumb bomb dispersion modelling problem (7/25/2020 5:39:08 AM)

We do track damage inflicted by blast (and shrapnel/frag, and other effects depending on warhead type and detonation altitude).

So the 2-meter near-miss you see on the log can be more accurately described as "just missed a direct impact on intended target, but anything soft in the vicinity (incl. the intended target itself, if applicable) is having a McClane-level bad day".

This is why artillery (and Arc Light-style bomb drops like the one shown above) don't need to be super-precise in order to wreak havoc against most mobile unit types.



SeaQueen -> RE: dumb bomb dispersion modelling problem (7/26/2020 1:42:53 PM)

The single bomb drop distribution pattern ought not be annular. The peak of the normal distribution ought to be at 0. Essentially, what that distribution is saying is that the most likely place for the bomb to land is somewhere a ring of radius 40-45m away from where he points the pipper! That suggests one's bomb sight is little bit off.



DracheTek -> RE: dumb bomb dispersion modelling problem (7/26/2020 3:10:22 PM)

I see what is going on, but I really think this behavior should not apply to unguided rockets. Rockets are fired in a more straight path and should be centered around target no matter how many is pulled off.



boogabooga -> RE: dumb bomb dispersion modelling problem (7/26/2020 3:22:18 PM)

quote:

ORIGINAL: SeaQueen

The single bomb drop distribution pattern ought not be annular. The peak of the normal distribution ought to be at 0. Essentially, what that distribution is saying is that the most likely place for the bomb to land is somewhere a ring of radius 40-45m away from where he points the pipper! That suggests one's bomb sight is little bit off.



You need to read that post again and pay more attention to "series 2".



RoryAndersonCDT -> RE: dumb bomb dispersion modelling problem (7/27/2020 4:45:04 PM)

quote:

ORIGINAL: SeaQueen

The single bomb drop distribution pattern ought not be annular. The peak of the normal distribution ought to be at 0. Essentially, what that distribution is saying is that the most likely place for the bomb to land is somewhere a ring of radius 40-45m away from where he points the pipper! That suggests one's bomb sight is little bit off.



[image]https://i.imgur.com/45l7uRk.png[/image]
The teal area is larger than the orange area, thus we get the annular histogram. The mean of the distribution remains at 0,0.




Consider the PDF of the bivariate normal distribution
[image]https://i.imgur.com/HWKnHcY.png[/image]
[image]https://i.imgur.com/lBt4v9Z.png[/image]

Simplify, let the mean of the distribtuion be 0,0 (Mu1=0,Mu2=0)
Simplify, let the two standard distributions be equal (Sigma1 = Sigma2 = Sigma)
Simplify, let the correlation coffecient be 0. The distribution is uncorrelated on x,y. (Rho=0)

[image]https://i.imgur.com/4gVtp6G.png[/image]

Integrate, change of variables to polar coords

[image]https://i.imgur.com/wnyhGw9.png[/image]

Solve.

[image]https://i.imgur.com/q6e5t36.png[/image]

Plug in some values, choosing Sigma=1.3 to match the earlier graph.

[image]https://i.imgur.com/lqLoLEd.png[/image]


The probability of the annular disk from r=0.5 to r=1 is larger than the probability of the annular disk from r=0 to r=0.5.

Thus bomb drop distribution histogram can show an annular feature.



RoryAndersonCDT -> RE: dumb bomb dispersion modelling problem (7/27/2020 4:47:09 PM)

(I hope I haven't made any mistakes heh.... which I am known to do from time to time [:)])



RoryAndersonCDT -> RE: dumb bomb dispersion modelling problem (7/27/2020 5:01:28 PM)

In part its a quirk of the domain of these histograms, distance from the center. If the 'bins' of the histogram were scaled to the area of the disk they represent this annular feature would go away, I think.



RoryAndersonCDT -> RE: dumb bomb dispersion modelling problem (7/27/2020 8:09:22 PM)

As we drop bombs in sticks, lets see what happens when we crank the total number of bombs up.

The units are in whatever unit scheme we want, could be meters, could be feet for the stickSpacing variable, and the stdDev.

3 bombing runs of 20 bombs each.
[image]https://i.imgur.com/ksQo9NU.png[/image]

100 bombing runs of 20 bombs each.
[image]https://i.imgur.com/qiqOeul.png[/image]


When we crank things up
[image]https://i.imgur.com/ndt1Uv5.png[/image]

And now linebacker III...
[image]https://i.imgur.com/xQYkCKg.png[/image]



decaf -> RE: dumb bomb dispersion modelling problem (7/28/2020 2:21:40 PM)

Very nice work, Rory.

What Rory has derived here is the probability density function (PDF) for the
"Rayleigh distribution". This can be found at wikipedia.org. This is the
PDF for *ranges*, when the underlying distribution is 2-D, independent,
bivariate, normal Gaussian distribution, with zero means in both X and Y.

For the CMO single bomb drop model
X has a zero mean (unbiased), with a dispersion (call it sigma)
Y has a zero mean (unbiased), with the same dispersion
(note that both X and Y can be positive or negative, hence the zero mean)

R is range, R = (X*X + Y*Y)^0.5 (from Pythagorean Theorem)
(note: R is never, ever negative -- so, expect a positive, non-zero mean)

For those who remember their Integral Calculus, the 1-D PDF derived from
the 2-D normal PDF yields the Rayleigh PDF, as seen in the equation and
plots in wikipedia.org.

The peak of the Rayleigh PDF can be gotten by taking the deriviative,
setting it to zero, and solving for the range. Also the wikipedia
provides the mean of the Rayleigh PDF, mu = sigma * (0.5*pi)^0.5
That mean is never zero (unless sigma = 0 --> perfect bombs).

Anyway, Rory, look at the PDF plots in the wikipedia.org. You will
see the "annular" feature will never go away. However, you can get
rid of the "annular" effect if you choose larger bins. Simply choose
a bin size >= the mean of the Rayleigh PDF.

And, I really enjoyed your stick analysis. The bomb error is now
correlated in a stick. (And I sure don't know of any formula)
But, over time we do get an approximate Rayleigh with a different
kind of length scale. Kewl!



SeaQueen -> RE: dumb bomb dispersion modelling problem (7/31/2020 5:23:25 PM)

quote:

ORIGINAL: RoryAndersonWS

(I hope I haven't made any mistakes heh.... which I am known to do from time to time [:)])


Sorry it took me so long to do more than glance at what you did. It looks good to me. It seems that my intuition was off here. Cool stuff! It's interesting that a bivariate normal distribution of bomb hits might give rise to a different distribution for the miss distances. Very cool. It still seems counter intuitive to me, though. I need to think about that one some more, I guess. :-)



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