Max Hit Probability

[Iron Duke]

Great post guys. I'd like to add my .02$ here. What I want to point out is what is actually seen in CM rather than the theoretical and hard physics of the real world.

Test:

3000m

1 Elite Nashorn

1 Elite M8

Level ground, no obstacles, both stationary

The units are really not that special for what I want to bring out.

At this range, the Nashorn starts with a 2% chance to hit the M8, while the M8 gets a 1% chance.

Now, to quote above:

<BLOCKQUOTE>quote:</font><HR>This is a lot better than a WW II tank (German tanks included) that usually needed 8 rounds or so to get a kill.<HR></BLOCKQUOTE>

So if we are in agreement that this ratio of 8 rounds for 1 hit is correct, then can we say that on round #8, the Nashorns to hit probability should be in the neighborhood of 90+ %?? Or at least, since the crew is Elite, 80% (With all other detrimental factors weighed in?) I would say yes. But what we see in Combat Mission is that, bracketing does not apply on a round by round basis or if it does, it only raises to a set number and goes no further.

In the above test this is what happened. (Aside from the occasional kill because of a lucky shot)

Turn 1:

Nashorn 2% to hit prob: fired 8 rounds no hits

Greyhound 1% to hit: fired 13 rounds no hits

Turn 2:

Nashorn 10% to hit: fired 8 more rounds no hits

Greyhound 3% to hit: fired 14 rounds no hits

Turn 3:

Nashorn 10% to hit: fired 7 rounds no hits

Greyhound 3% to hit: fired 14 rounds no hits

Turn 4:

Nashorn 10% to hit: fired 7 rounds no hits

Greyhound 3% to hit: fired 15 rounds no hits

Turn 4:

Nashorn KO's M8 with 1 more round @ 10% to hit. Lucky shot

I repeated this test quite a few times, and yes there where a number of times that the battle did not last longer than 2 turns, but that is not the point. The point is that, BRACKETING is the root for all the gunnery problems seen.

Take this example:

The crew of the Nashorn, using learned techniques, could say estimate the range to 2000 meters for the first shot. They then see that it is way low, so they add 500meters for the 2nd shot. Still low, add 500 more, now they see that they are in the "ballpark". So, at this point, IMO the bracketing figure should be somewhere in the vicinity of 30 to 35% to hit with the next round. Then say the next round is fired but this time it is a bit too high and sails over the M8, that miss would STILL ADD to the to hit probability for the next round because that is how bracketing works. So for the next shot, they should have a 40 to 50% chance to hit, and so on, until they reach the 8 to 1 ratio. Where at round #8, they should have hit the M8.

I think this would cure most of the long range accuracy problems SEEN in CM.

I do not think the underlying physics are incorrect for accuracy, but I do think that the follow on shots (especially at a stationary target) are not getting a bracketing bonus, as seen in play.

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One shot...One Kill

[This message has been edited by Iron Duke (edited 01-16-2001).]

[This message has been edited by Iron Duke (edited 01-16-2001).]

[This message has been edited by Iron Duke (edited 01-16-2001).]

[rexford]

Long range accuracy should hardly ever reach 90% at long range due to dispersion effects.

It is possible to hit on a first shot and have a bad range estimate because a large dispersion pulled the shot onto the target.

So the tank in the above situation would assume that first shot was range accurate and follow-up, but since dispersion changes from round to round the next shot might miss low after the first hit high.

The following will explain what "eye" mean (as opposed to what "oui" mean):

At 2000m, 88L71 vertical dispersion for 50% of shots is 0.9m on first ****s, so 50% of shots will be within 0.9m of aim point, 68% will be within 1.33m of aim point and 95.5% will be within 2.66m of aim point.

Say the Nashorn estimated 2000m, target is at 2000m and aim point is the center of a 2m high target, then 45% of the shots miss a 2m high target due to variations from shot to shot!!!!!!!! Dispersion is the scatter that occurs due to variations from shot to shot (projectile weight varies, powder charge varies, barrel recoil changes, tank inertia, etc.).

While dispersions might be corrected for, bracketing can almost never attain 90% or 95% accuracy on long range shots due to random scatter.

Our spreadsheet for tank fire uses an equation that corrects range estimation for bracketing the target, but dispersion limits how good one can get. The story where an M18 hit four panzers at 2000 yards with four shots, and some were low StuG III, can occur but certainly is not the commonplace.

Due to dispersion, one may see a high shot and correct it downward when it was a low shot that scattered high. The farther the shot, the larger the dispersion.

[Iron Duke]

Rexford,

that is all fine and dandy, but still does not address the fact that the bracketing bonus in CM during gameplay will not rise above 10% for this vehicle. That's why I also said that perhaps it should be 80% and not 90+%...hell, even 70% would be infinitely better than the 10% we see now.

I hope I am explaining my self clearly here. I am NOT after what each shot can do in terms of dispersement etc...but what I AM after is that a stationary Nashorn firing at a stationary M8, should have more than 10% chance to hit the M8 after firing off 8 frik'n shots!! Or better, after firing off 24 AP rounds.

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One shot...One Kill

[Jeff Heidman]

Duke,

Those eight rounds you cited was an average for ALL ranges. Since most engagements happened at far less than the ranges you are talking about, I would guess that the average for 3000m is much, much greater.

As far as the pop-gun 37mm goes, I would not be surprised to never see that thing hit at that range.

I am not saying that the 10% chance is correct, but given that CM does not adjust for the optics in the Nashorn, it would not surprise me if that number is closer to reality than you might expect.

Jeff Heidman

[rexford]

A. Physics allows one to analyze a falling shot by freezing the frame and using that as time zero. When the round reaches 350m it is pointed downward due to gravity.

Freeze time at 350m and start from there.

Round has no vertical speed but is pointed downward. Calculate gravity drop from 350m to 500m by using time it takes to go that far.

Incorporate previous effect of gravity by using 350m descent angle to see how far it falls in 150m to 500m.

And this method yields the same result as the simplified trajectory equation.

If a stone is dropped and I want to know how far it drops from 1 second of fall to 2 seconds of fall, one valid equation is: (velocity at 1 second) x time (from 1 to 2 sec) + 0.5 x 32.2 x (2-1) squared. velocity after 1 second is 32.2 fps. So answer from freezing time at 1 second and going to 2 seconds is:

32.2 x 1 second + 0.5 x 32.2 x 1squared, or 48.3'

Now lets use another approach:

The answer from 0.5 x 32.2 x 2squared is 64.4' in 2 seconds, 16.1' in 1 second, 48.3' from 1 to 2 seconds.

You are not familiar with the methods I am using, which accounts for some of the problem. I minored in plasma physics in college, and have analyzed alot of moving particles besides tank gun rounds.

B. I stated that the StuG III gun was at the same height as the target center, and my equations used an elevation angle on the gun.

If the Stug IIIG 75 is aimed at the center of a target at 350m the round at 350m will be at the gun elevation, 0m above gun.

At 500m the round aimed at the middle of a target at 350m will be about -0.73m below the gun elevation and below the center of the target at 500m. So it hits with a 150m range estimate error when aimed at 350m, and 2m high target is at 500m.

Make a drawing that follows the above logic and you'll see what I am getting at, and that my analysis is correct.

C. The trajectory elevation equation for height above gun barrel is:

range x sine (gun elevation) - 0.5 x 9.82 x (flight time) squared,

for results in meters.

350m aim x sine (0.2°) - 0.5 x 9.82 x 0.5squared (for 700 m/s constant velocity)

= 0m.

Shoot a 700 m/s constant speed round with 0.2° elevation and it is at gun barrel elevation at 350m. If target center is at gun barrel height, above equation meets our criteria (aim puts shot at height equal to gun barrel at 350m).

Now how high is the shot at 500m relative to gun barrel and target center?

500m x sine (0.2°) - 0.5 x 9.82 x (.71) squared, or -0.73m.

A hit!

This is basic trajectory physics, and is consistent with the simplified trajectory equation.

D. The simplified trajectory equation not only matches the Tiger Fibel case very well, and agrees with the above example, but it disclosed an error in the Tiger Fibel!!!!

Since the max trajectory height to 1000m range is over 2m, based on my trajectory equation and German ballistics data, the shot goes over the woman's head at 500m although Tiger Fibel says it hits.

Tiger Fibel made a mistake that "weeeeeeeeee" caught.

[Jeff Heidman]

Every time I read one of rexfords posts, I get dizzy.

Jeff Heidman

[rexford]

Ooops!

Tiger Fibel shows 1000m aim with over 2m height at 500m. Our analysis is consistent with Tiger Fibel.

[rexford]

These are the max hit %'s that "wea" allow the 88L71 to have against a 2m high target, usually attainable on 6th or 7th round:

AVERAGE CREW

1000m-90%

1500m-75%

2000m-60%

2500m-45%

3000m-35%

ACE CREW (better maintained guns and sights so lower dispersion, and better able to home gun in on target)

1000m-95%

1500m-90%

2000m-80%

2500m-70%

3000m-55%

The limitation on max accuracy is due to dispersion, which not only scatters rounds but presents misleading shot results (high miss with low range estimate, etc.).

[rexford]

Since most targets in real world are higher than 2m from hull bottom to turret top, max hit % for 88L71 against Sherman or T34/85 will be greater than listed in previous post.

Sorry for "dizzying" posts. A few people are interested in details, most are not. Skim over the stuff and ignore the baloney if you are so inclined. "AYE" do when "EYE" go thru other peoples' stuff.

[Iron Duke]

Rexford,

I am not doubting your prowess in physics here! Good job, kudos, here is a metal!

I am simply making an observation within the game: No matter how many times that Elite Nashorn fires, even with the crew supposedly being able to adjust fire, its to hit percentage never rises above 10%. Now, we have to ask how in the world the Nashorn was able to routinely hit and destroy targets at 3000 to 4500 meters on the Russian front? It seems that those Nashorns of old should have NEVER of hit those targets, so are we to say that they all got lucky? Like your M18's you noted before? I doubt that.

Jeff:

As I noted in my test...the vehicles do not matter, they could have been a Panzer V vs an Easy Eight...the results would have been the same. Each of those vehicles, no matter how many times they fired, would have never had gotten a higher to hit percentage than 10%, which to me, having fired tank guns using standard optics, is just not right. I'll give you that todays weapons and optics are a far cry from WWII BUT, the methods and results of bracketing a target are no different. Anyway...I guess I am not making my self clear here.

Physics...good

Bracketing...bad

Better?

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One shot...One Kill

[rexford]

Here are the figures we use for average crew 88L71 firing at stationary 2m high x 2m wide target at 2000m:

1st shot

7%

2nd shot

21%

3rd shot

30%

4th shot

36%

5th shot

40%

6th shot

40%

7th shot

44%

8th shot and thereafter

48%

Results differ from previous numbers cause we're using a 2m wide target on this post

ACE crew at 2000m vs 2m x 2m target

1st shot

20%

2nd shot

46%

3rd shot

59%

4th shot

65%

5th shot

70%

6th shot

70%

7th shot

70%

8th shot

75%

Above results consider effect that dispersion has on accurate gun corrections.

[Iron Duke]

Rexford,

are you getting these figures from a book or are you calculating them out?

I think they are great and I would LOVE to see them IN THE GAME. But the sad fact is that it doesn't work that way IN Combat Mission.

Do a 3000 meter test IN the game for yourself and see that the to hit percentage does not reflect what you are saying...although I wish it did!

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One shot...One Kill

[rexford]

10% max limit on elite Nashorn accuracy at 2000m seems too low.

Hit scores at 500m often seem too low.

Our stuff is based on trajectory equation analysis using assumed bracketting range estimates and corrections after first shot.

Elite Tiger crews supposed to be within 10% on first shot, so long by 200m on shot #1, on average.

Shot two is maybe 100m short. Correct by adding about 150m for 50m long (although there will be errors in estimating how much over or under).

Good chance for a hit here on shot three, even if estimate is bad dispersion may bring shot onto target.

10% max is way too low for elite Nashorn at 2000m, compared to "hour" average crews.

The trajectory model used to estimate hit % may be too drastic in assessing how estimate errors influence fall of shot. This is why "i" spent the time discussing and clarifying accurate models.

The simplified trajectory equations have been compared to German ballistic data and are comparable, the equations match the Tiger Fibel, and maybe they should be used to re-examine the hit %'s in CM.

Just a suggestion.

[rexford]

If Nashorn range estimate is off by 50m against a 2000m target, the trajectory will be about 0.62m from target center (average shot with 50m error will be on target, with some scatter about center).

A 100m range estimation error results in a 1.28m error from target center (average shot is just over or under).

A 200m range estimation error (the average for elite crews) will be 2.67m over or under.

First shot +200m estimate error, say a miss.

Second shot -300m estimate error, say a miss.

Third shot within 50m of true range, average shot trajectory on target.

Once the average shot trajectory is on target, misses will still occur but range may eventually be closed even more (when gunner aims at exact range, hit % peaks).

Our figures for elite crews look high, but average crew seems okay. Any comments?

[rexford]

My results are calculated.

The simplified trajectory equations are on "migh" hand calculator and allow the effect of range estimation errors to be computed using flight time to estimated range, estimated range and actual target range.

To simplify things, "oui" assume that gun is at target center range. For game purposes this is adequate.

Like trajectory analysis, "hour" results seem to vary alot from CM.

[Iron Duke]

Yes,

the thing that stands out is the "thereafter" after the 8th shot. The to hit bonus should continue to rise shouldn't it? Just because it is the X number shot shouldn't mean the gunner just gives up on improving his lay.

Rexford,

could you make a couple of charts for Reg and Elites at 3000 meters? I would be very interested to see those.

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One shot...One Kill

[Jeff Duquette]

Iron Duke:

Thanks for the test case. It is my understanding that the 1:8 figure was apparently derived from studies by TN Depuy. This ratio and similar ratios were bated around at length about a year ago on a deceased forum focusing on armor and armored warfare. My understanding of the gist of this discussion is that 1:8 needs to be taken with a large grain of salt. The numbers were apparently derived from ordnance reports on monthly or weekly divisional ammunition take-offs. 3rd AD draws 5,000 rounds AP for the month of August 1944…or the like. The numbers were being assessed for logistical studies…what kind of munitions stocks are required to maintain an armored division in combat for X number of days. The intent was not originally conducted, as an attempt to quantify number of rounds fired per KO'd tank. Apparently the munitions take-offs were inclusive of replacement tank uploads and munitions lost during combat…tank brews-up…boom…50 rounds up in smoke. This skews accuracy statistics onto the conservative side. This is why you occasionally come across figures as high as 1:20 KO's/round. This number is not in and off itself an indication of ordnance expended in actual combat firing...i.e. 1 hit for every 8 rounds fired. It is analogous to the numbers I used to see on the news regarding how much money or how many tons of TNT was required to achieve one enemy KIA in Vietnam. What do these numbers really mean?

You are correct in that bracketing does not follow a logical course of execution in CM. But as has been explained by either Steve of Charles…the CM gunnery model was never intended to tackle this. Rather (and I am guessing here) the model employs some sort of "to hit" function, with all kinds of input stimuli that could potentially effect accuracy. One input parameter is apparently "subsequent rounds fired on the same target"…some sort of acquisition bonus. Unfortunately this bonus seems to be a simple boost in the "to hit probability". So even in an ideal situation where a gunner is zeroed in on a stationary target…he has gotten a hit…this does not mean that there is a real good chance of a 2nd hit occurring. So even though a real world gunner has the range down pat from the previous hit…the next round could easily go 200 meters over and 150 meters wide of the target.

[DraGoon]

Rexford, Before you run out of options you are hereafter excused of having to find different ways to say "WEE", "EYE" "UZ" Et flippin cetera.

Anybody,

Before I go making a fool of myself by challenging this "8 round per kill" factor, where does this come from? What research substantiates these figures?

I agree with Iron Duke on his comments on bracketing procedure.

I posted some comments in another recent thread and include a link to it.

http://www.battlefront.com/discuss/Forum1/HTML/015015.html

The gunnery procedures I list in the thread are ideals and combat factors will definately add to these, but 8 rds per kill would be a problem.

The ready rounds (ammo stored in easy access racks) per vehicle would very quickly run out in this type of scenario, necessitating the withdrawal of the vehicle to rotate the turret to allow access to additional ammo.

This happened but in the accounts I have seen (including many official) this was not common.

Que Rexford to list ready round stowage in WWII vehicles

"We" await.

DG

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Remember:

Always end your lay in elevation.

[Iron Duke]

<BLOCKQUOTE>quote:</font><HR>You are correct in that bracketing does not follow a logical course of execution in CM. But as has been explained by either Steve of Charles…the CM gunnery model was never intended to tackle this. Rather (and I am guessing here) the model employs some sort of "to hit" function, with all kinds of input stimuli that could potentially effect accuracy. One input parameter is apparently "subsequent rounds fired on the same target"…some sort of acquisition bonus. Unfortunately this bonus seems to be a simple boost in the "to hit probability". So even in an ideal situation where a gunner is zeroed in on a stationary target…he has gotten a hit…this does not mean that there is a real good chance of a 2nd hit occurring. So even though a real world gunner has the range down pat from the previous hit…the next round could easily go 200 meters over and 150 meters wide of the target<HR></BLOCKQUOTE>

Hmmm...this is sad news. I have been dreaming of the tank battles to come in the next CM...I hope they can figure something out by then. Hell, I wish they could do something with this CM.

BTS...could we get some input on this bracketing issue?

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One shot...One Kill

[Dittohead]

Lots of good info here http://www.britwar.co.uk/salts/salt6.htm

[Iron Duke]

Dittohead,

thank you for that info. Good stuff.

It seems, by those charts, that subsequent rounds tend to increase the chance to hit by 10 to 50%!! This seems about right from my own time on the gunnery range. In game, using my initial Nashorn trials, would have meant that after the Nashorns first shot, it could have had between 20 to 60% chance to hit the M8! (We could call it 15 to 25% because they were an elite crew). So on the third shot, if we say 15% per shot, a 40% chance could have been had...then 55% and so on. This is way better than the observed 10%. (I would say 20-25% for elite crews myself but that's up to BTS)

This would also account for the kills the Nashorn routinely had on the East front.

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One shot...One Kill

[Jeff Duquette]

It is relatively easy to find tank vs. tank combat studies, which emphasize that in tank combat it is typically the tank that spots and fires first that prevails. This should suggest the importance of training and the emphasis on gunnery skills. A 1:8 or 1:20 KO/rounds fired ratio suggests luck is the most important factor in gunnery. That is why I would contend that the 1:8 figure is inconsistent with the findings suggesting first shooter typically wins.

I also agree that more realism in gunnery and bracketing would only add to the immersion level of CM…or CM2.

Regarding the Nashorn…Take a look at “PanzerJager, Tank Hunter” by W.B. Folkestad. He relays a tale of a Nashorn cutting loose on T34’s at a range of 2400 meters and getting 2 kills with 4 rounds. The remaining T34’s quickly scurried under cover. Folkestad indicates the Nashorn Crew was employing an Em70 coincidence type range finder during the engagement (Large handheld range finder employed by Flak 88mm crews). The employment by German tank crews of coincidence or scissors type rangfinders may have been relatively common. Certainly in the case of Assault guns it was SOP.

German Gunnery training stressed accuracy level of at least 1 hit in 3 shots against a tank sized target moving at up to 20 km/hr across its front. Range between 800 meters and 1200 meters. It also indicates that bracketing at ranges below 1200meters is not required…tank crews can immediately fire for effect on point targets. This is a reflection of the large window in range estimation errors, which are possible at these ranges, and still maintain a reasonable chance of obtaining a first round hit. Go back and look at the TigerFibel example I posted on Page 2 to get a feel for what is occurring here.

[This message has been edited by Jeff Duquette (edited 01-16-2001).]

[rexford]

If Nashorn with elite crew in our system can get to within a 50m range estimation error against target at 2000m, not that difficult considering average first estimate will be less than 10% off, or 200m, then trajectory will be on target (0.62m away from center aim point).

With single dispersion for elite crews, everything in really good working order, about 80% of shots will hit at 2000m after gun zeroes in after 5 to 8 shots.

So elite crews could realistically obtain 80% max hit scores at 2000m after so many shots and use of bracketting.

Our hit scores for elite crews can be supported by above logic.

By way, trajectory discussions should be based on an elevated gun that aims at center of target at estimated range, error is then found by checking trajectory height at target. Previous analyses that used zero gun elevation do not test trajectory difference between estimated target range and actual, and result in bogus conclusions.

Mie previous examples fulfilled above scenario.

Real guns don't fire with zero elevation.

[rexford]

Iron Duke,

Against 2m x 2m target at 3000m, average and elite Nashorn crews have following shot by shot progressions:

AVERAGE

1st shot

3%

2nd shot

11%

3rd shot

15%

4th shot

17%

5th shot

20%

6th shot

25%

7th shot

25%

8th shot and thereafter

25%

Dispersion is main limiting factor.

ELITE CREWS

1st shot

7%

2nd shot

25%

3rd shot

30%

4th shot

36%

5th shot

40%

6th shot

40%

7th shot

45%

8th shot and thereafter

45%

Dispersion lower than AVERAGE (half), better at estimating ranges within bracketting procedure.

Based on our statistical studies of what goes on in bracketting, 8th shot is about it for improvements cause dispersion keeps moving rounds around so one can't tell what real range is. The further the range, the less one can tell from a miss about the correction required.

Here is Nashorn using coincidence range finder (5% average error) at 3000m:

1st shot

13%

2nd shot

32%

3rd shot

38%

4th shot

40%

5th shot

44%

6th shot and thereafter

48%

Rangefinder helps get shots close to actual range faster, only boosts max hit score a tad. We have printed hit score sheets for just about every commonplace WW II gun used against tanks, for poor, average, elite and super ace crews (super ace has 5% average range estimate error, or uses a range finder).

Double sided pages allow four crew quality on one page. Page gives chance of landing shot within a 2m vertical height and 2m lateral distance.

We then roll dice using scores to see where shot actually fell on the target tank, and we measure offset from aim point. If you would like to see some typical sheets, e-mail me directly and I'll mail some to you.

We feel that our results are realistic, we checked Tiger 88L56 APCBC against Fletcher story that Tiger crews expected to score hits in 1200-2000m range by such and such a shot, and our results matched up well.

Here's a problem with comparing gravity drop at different ranges and trying to relate it to accuracy.

88L71 APCBC takes 2.20 seconds to get to 2000m, and 1.04 seconds to get to 1000m. Difference in gravity drop when gun is shot without elevation is 18.46 meters. Some people might say that this suggests that difference in shot placement is 18.4 meters (target at 1000m, aim at 2000m).

88L71 trajectory to 2000m has maximum height of 6m, target at 1000m and aim at 2000m max results in an error on target of less than 6m, not 18.4m. Difference is because accuracy analysis must include gun elevation.

[Guest Andrew Hedges]

In many cases -- as I and others have pointed out in other discussions -- it may be the case that the gunners already had a pretty good idea what the range was due to a number of factors. For example, I'm struck in many accounts of long-range accuracy how frequently there was a noticeable feature near where the attack occurred. Sometimes it involves enemy tanks leaving the treeline; other accounts I have read include tanks driving down a road, tanks at a crossroads, or tanks driving near a riverbank. As these features tend to be included on typical topo maps used by the military, I wonder if the tankers in question got an advantage because they knew how far it was to the treeline, the road,the river, etc.

This wouldn't work if the firing tank didn't also know where it was located, but most of the long range accounts with which I'm familiar involve firing tanks that have been stationary for at least tens of minutes.

But even if you had no idea where you were, it would probably be easier to estimate range when you had something else to compare the tank to, be it trees, a road, or whatever.