Corrected Aim with Burst on Target

[rexford]

The “burst on target” method is presented in several different gunnery manuals from WW II as an effective means of correcting for first shot misses. To use the method, the gunner observed the fall of shot in front of the target and immediately elevated and rotated the gun to place the target on the point where the ground hit was observed.

While the method provides a good means of correcting for first shot misses it has limitations:

1. High shots are not as easy to correct for, as one must deduce the height of the round as it passes over the target which would appear to be very difficult.

Graphical review of the ground hit locations from high misses suggests that even if they were observed, such as on wide shots, the perceived ground placement of a high miss would not result in effective aim adjustments.

U.S. Field Manual FM 17-12 does not discuss how one uses Burst on Target with high shots.

2. U.S. Armored Force Field Manual FM 17-12 notes that “Only where impact is on dry, open terrain can the strike of AP projectile on the ground be sensed.” The manual also notes that “Frequently the gunner will be unable to observe consecutive rounds; that is, he will see one round clearly but the next will be obscured by dust or smoke.”

3. U.S. Field Manual FM 17-12 notes that the burst on target method is effective out to 1,000 yards when visibility is good, with bracketing used beyond that range (200 yard changes after the first miss at 1500 yards or less, and 400 yard changes beyond 1500 yards). The German Fibels for Panther and Tiger crews advise them to use “fire for effect” out to 1200m, and bracketing beyond that range (200 range changes after first miss out to 2000m, and 400 changes beyond that distance).

4. Random scatter can disguise and distort the true adjustment, where some misses may have the correct range but the shot fell short due to scatter.

5. Variations could take place in placing the target on the burst point due to human error.

To test the applicability of the Burst on Target method with different guns, a computer simulation was prepared where a firing tank missed on the first shot with a given target range and aim setting, and the second shot was adjusted using Burst on Target. The stationary target was taken as 2m high by 2.5m wide, all terrain was level at the same elevation and the first shot was assumed to follow the theoretical trajectory without scatter, which simplified the mathematics.

The simulation results suggest that Burst on Target works best with higher velocity rounds and at short to medium range, and as the flight time to target increases (lower muzzle velocity) the curvature of the trajectory reduces the second shot hit percentage. Burst on Target is still an effective method to home in on a target for third and follow-up rounds from lower velocity guns but will take time.

The computer results follow, where double dispersion was applied to the follow-up shot trajectory:

SECOND SHOT HIT PROBABILITY USING BURST ON TARGET CORRECTION

1. Target at 1000m, Initial Aim at 700m (30% first shot range estimate error)

75L24 at 385 m/s, 0%

75L40 at 619 m/s, 0%

75L48 at 750 m/s, 19%

88L71 at 1000 m/s, 73%

Note: Muzzle velocities listed after gun, where all projectiles are capped steel AP.

2. Target at 1000m, Initial Aim at 800m (20% first shot range estimate error)

75L24 at 385 m/s, 0%

75L40 at 619 m/s, 11%

75L48 at 750 m/s, 42%

88L71 at 1000 m/s, 81%

3. Target at 1000m, Initial Aim at 900m (10% first shot range estimate error)

75L24 at 385 m/s, 1%

75L40 at 619 m/s, 71%

75L48 at 750 m/s, 73%

Note: Burst on Target correction accuracy significantly increases as initial round gets closer to target for medium velocity projectiles., but does not help low velocity 75L24 shots very much.

4. Target at 700m, Initial Aim at 490m (30% first shot range estimate error)

75L24 at 385 m/s, 0%

75L40 at 619 m/s, 89%

75L48 at 750 m/s, 84%

Note: Reducing the range from 1000m to 700m with a 30% error on the initial range setting significantly improves Burst on Target hit probabilities. for medium velocity guns

5. Target at 700m, Initial Aim at 560m (20% first shot range estimate error)

75L24 at 385 m/s, 0%

75L40 at 619 m/s, 95%

75L48 at 750 m/s, 93%

Note: Reducing the range from 1000m to 700m with a 20% error on the initial range setting significantly improves Burst on Target hit probabilities. for medium velocity guns

6. Target at 700m, Initial Aim at 350m (50% first shot range estimate error)

88L71 at 1000m/s, 93%

Note: Burst on Target is very effective in obtaining second shot hits with the high velocity, flat trajectory 88L71 even with a 50% first shot range error as long as the range is.

7. Target at 500m, Initial Aim at 250m (50% first shot range estimate error)

75L40 at 619 m/s, 67%

Note: Short range shots result in a flatter trajectory, even with the 75L40 gun, so Burst on Target is very effective even with a 50% range error on the first shot.

8. Target at 500m, Initial Aim at 350m (30% first shot range estimate error)

75L40 at 619 m/s, 97%

The second shot accuracy with Burst on Target correction improves with muzzle velocity at a given range, and increases as the accuracy of the initial shot is improved which can occur through decreased initial range estimate errors at a given range or a shorter range with the same percent range estimate error.

The above analysis assumed that the first shot was not impacted by random scatter. During real combat half of the first shot misses would be closer to the target than the simulation assumed (resulting in a higher second hit rate in many cases), and a share of the Burst on Target corrections would be higher or lower than ideal raising or lowering the second round accuracy as the burst placement error required.

It should also be noted that Burst on Target is most or primarily effective for short misses where the ground strike can be observed by the gunner, which would make up less than half the misses as a general rule.

After a 75L24 misses the first two shots at a target with Burst on Target after the first miss, the following hit probabilities would apply to the second attempt using Burst on Target (double dispersion):

75L24 ACCURACY FOR SECOND BURST ON TARGET ATTEMPT

1000m target, 700m range estimate on first shot (30% error): 0%

1000m target, 800m range estimate on first shot (20% error): 0%

1000m target, 900m range estimate on first shot (10% error): 16%

700m target, 490m range estimate on first shot (30% error): 0%

700m target, 560m range estimate on first shot (20% error): 29%

The above data suggests that the low velocity 75L24 might be better used with bracketing on long range shots or with a large error on the first shot at any range, where the poor performance with Burst on Target is probably due to the extremely curved trajectory and relatively long time of flight

[JasonC]

Problem - as Deming famously demonstrated in his "funnel" experiments, correcting a random scatter just widens the scatter pattern.

Everything depends on the diagnosis of the miss. If it is due to pointing in the wrong direction, then continuing to fire at the same aim point will consistently miss. If, on the other hand, the aim is fine but the shot missed due to the ordinary dispersion of the shots around the aim point, then trying to compensate by such offset procedures will widen the scatter pattern, by an order of magnitude - especially if repeated in shot after shot (because the size of the correction used tends to increase to the largest random error encountered in the series so far).

One can debate whether a wider scatter pattern is worth it to eliminate a pointing mistake initially. But attempting to correct for a gun out of "true", that "throws" a little low or right etc, is famously a way to wreck the accuracy the gun is actually capable of. The best procedure is to boresight the gun as accurately as possible long before action, train the gunner to always aim center of mass regardless of observed fall of shot, and then trust the gun. That gives the smallest shot to shot dispersion pattern in the long run.

The problem is, gunners in combat don't care about the long run because they can die if they don't get the short run right. So they adopt such heuristic correction procedures, suggested to them by "common sense". When they are based on a misdiagnosis of the original cause of the error, however, they make the problem dramatically worse rather than better. But for understandable reasons, accepting that shots will always display some random dispersion is difficult for people to accept, especially when lives are on the line.

[Mr. Tittles]

Rexford claims the dispersion actually follows a bell shaped curve. Its not random in that there is no prediction to it, he claims the germans took data on where 50% of the rounds would impact and that statistical methods can then be used to predict where the other 50% will impact.

Please review the the APCR thread for more on this. i am sure people would like to hear your opinion.

http://www.battlefront.com/discuss/ultimatebb.php?ubb=get_topic;f=23;t=010029

[ August 29, 2004, 12:27 PM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

What method to use is not always range dependant.

Yesterday while driving, I entered a long stretch of road once I came over a slight rise. In front of me the road stretched about half a mile down a gentle slope and then up another slope.

It occured to me that if I was firing rounds and they flew over the cars ahead of me that were going up the slope ahead of me, I would be able to see where they landed quite clearly and judge the amount short or long they were. This being because the cars ahead of me were on the forward slope and long rounds would still strike ground that was in my LOS. On very flat terrain, it is very difficult to judge long rounds simply because the target is in the way of viewing where they land.

The road had electric power poles every 100 yards and I was quite sure of the range. I was just using my naked eyes but having any binos would have made it even easier.

But Jason brings up a good point about 'tweaking'. Its a human reaction to fiddle with things because the mind wants to correct a situation once any data is presented.

In the APCR thread, I was not happy with the area spread that rexford is claiming for shot (single) dispersion. I was not buying some of the double dispersion spreads either.

Hitting targets (which are basically characterized by area lxw) would require a certain level of precision (which is also a area function). If the spread of shots is greater than the area size of the target (or even very close), then corrections can not be made without firing quite a few rounds to first 'zone in' the shot spread. You are actually trying to move this shot spread area onto the target area.

As Jason points out, if your life is on the line, then you do not want to hang around and be a target area yourself.

I would venture a guess that if using bracketing, shorts are more valuable and range estimation should go for the conservative initial guess.

[ August 29, 2004, 12:44 PM: Message edited by: Mr. Tittles ]

[Akula2]

*whew!

I thought I was the only one on earth that terrain considerations came into mind while driving.

I don't need to add that sh.t to my mental health folder, that's for sure.

This discussion is silly.

The factors involved make it so.

[JasonC]

I don't see anything wrong with Rexford's assumption of bell random distributions or using 50% regions. Both are standard idealizations and techniques.

But if people have the impression that gun accuracy is shot accuracy then there is a problem, certainly. It isn't.

Start with the dispersion pattern of the gun itself. Now, pick a pair of randomized half mil error (plus zero or minus, side to side and on range independently chosen, two errors). This isn't for the shot it is for the zeroing.

Now, simulate 10 randomized shots at the slightly off aim point. Pick the 4 shots that happen to land closest to each other, regardless of where the rest of the pattern lands. Draw a cross through those 4 shots, and note the location of the intersection. Record the "actual" (laser light) crosshair and this location's offset from it. Call that "zeroing error".

Now simulate an engagement, in which the target is located *perfectly* (no errors in estimated position or range, no motion on either end, no elevation difference). Again pick randomized pointing errors, this time up to 1 mil each in deflection and quadrant. (Again, this is for a perfect estimate of the range - just pointing error). Add the zeroing offset. That is your new "real pointing location". Now fire just one round at that location, with random scatter according to the gun's dispersion, around this offset aim point.

If the gunner does not correct, repeat only the shot dispersion roll. If he re-aims center of mass, "roll" new pointing errors then repeat. If the gunner tries to correct, then offset by whatever the previous offset was, and then reroll a new pointing error and apply it too. Then reroll a new dispersion and place a new shot.

All of this is for perfect range estimates. Which you won't have. In fact, you will be lucky to get within 400m on the range. At short range this won't much matter, because the shot line is practically flat and you are "bowling" rather than "golfing". But at 2 second flight time and beyond, it is a significant additional source of misses.

Gunners would sometimes miss if they were shooting at each other with lasers. Because they dial in pointing errors of half a mil even in training, and up to a mil in action. The errors during zeroing would still be there. But it would all stay pretty small and probably under the size of typical targets at modest ranges like 1 km.

But they aren't shooting with lasers. They are trying to zero guns that produce random scatter on their own, by looking at where a limited number of rounds actually go. But where they go with their pointing errors and those random round dispersions, not where they want to point.

And then they fight each other with guns slightly out of "true", with errors in their pointing again, and random dispersion from the gun itself. If these overlapping causes all stay small enough they will hit what they point at a fair amount of the time. If, on the other hand, the gunners pretend they are shooting lasers and expect every shot to tell them deterministically where they ought to point, then they will overcorrect, amplify the random scatter that can't be removed, and (as in Deming's funnel tests) produce a wider, oscillating smear of results instead of a relatively tight ball around their aim point.

The best thing is to zero the gun as carefully as possible before action, then consistently aim center of mass and trust the gun. Even then you can miss, but that is the way to minimize the pattern dispersion for all your tanks. But plenty of gunners do not do this.

This is the kind of thing Rexford's double dispersion rule of thumb is meant to account for. Whether it does is anybody's guess. One can code up a simulation of the steps easily enough, and see what typical results it gives, empirically. You'd find, I'll wager, that correcting shot to shot based not on re-aiming at center of mass, but looking at where the last one went (even if you could tell perfectly, which you can't) is a bad idea.

[Mr. Tittles]

I wonder if a tank would have to reaim after each round when zeroing. That is, would the gun be repeatable enough in returning to its firing position? So just aim center of mass and fire a shot group without constant sight adjustment?

I read of how M48 tanks zeroed. They adjusted the sight to the shot group. They aimed at a center of the target and the middle of the actual shot group was then where the sight was adjusted to point. Then they aimed for the center again and fired a new shot group to verify adjustment of the sight.

"The Tank Commanders Guide"

compiled and edited by

William L. Warnick, Lt. Col. John G. Cook, USA Ret.,and Dr Robert A. Baker

of

The United States Army Armour

Human Ressearch unit

Fort Knox, Kentucky

Military Service Division

and I quote;

"Zeroing is firing the gun to ascertain the point of projectile impact, then all instrument crosshairs should be aligned with the center of the shot group on the target."

"The gun is said to zeroed if the check round hits within 2 feet of the aiming point at 1500 meters" (for the M41 90mm gun)

[Mr. Tittles]

The Germans had test requirements for tank gunners that were based on correcting fire. They had to hit targets at unkown ranges with so many rounds. They werent being tested for luck but for skill.

The Germans trained 100s of thousands of gunners for ATG, Panzer and Assault guns. They certainly had a reputation for accuracy. I dont buy Jasons trust the gun and damn the corrections. Even he says that you usually dont know the range, so aiming and eventually correcting must be done.

I think he overstates this supposed zeroing error also. Zeroing targets typically have a easily identified center area and the magnification of the sight would allow the gunner to put his 'cross-hairs' acceptably close. Once the gun is zeroed, than any pointing errors are a function of the human not the gun. It isn't built into the gun.

[ August 29, 2004, 09:48 PM: Message edited by: Mr. Tittles ]

[Joachim]

Tigerfibel suggests corrections using fork (bracketing shorts and longs when area behind target can be observed) or knife (consecutive shorts converging into the target when area behind target can't be observed) at ranges beyond 1200m.

So German gunnery training included correction of shoot.

The trouble without correction:

If your guessed range is wrong, the chance to hit the target is rather limited. You need a lucky shot to hit. The bigger your estimation error, the bigger the necessary luck.

The trouble with correction:

If your guessed range is correct and the miss is solely due to the gun scatter, you will correct the gun scatter. Always correcting for gun scatter might result in the aim point wandering off - but this is rather unlikely. After a few shots the sum of gun scatter will effectively converge to zero. So gun scatter will affect measurement, but only with an additive error term.

Is this noise enough to completely throw off measurement? Considering that eyeball mk1 has usually more scatter than a somewhat decent gun/sight combo, I'd go for correcting shoots.

Trusting the gun might be a good idea with a freshly boresighted gun that has not moved since boresighting. After a few bumps in the terrain I would not trust a gun.

Another point:

Once a gunner sees 3 rounds falling in the same point off target - I bet he will change aim no matter what training says. So you will better behave strategically and teach him a method that works with his intuition. Even if that method is slightly inferior in theory - in practice it will work better. So training manuals might not show the best way to hit a target. They will show the best way to hit a target considering human errors.

Gruß

Joachim

[ August 30, 2004, 06:19 AM: Message edited by: Joachim ]

[JasonC]

Yes you fire a shot group to zero the gun. But you aren't firing a shot group from a laser. The center of the shot group (a random sample by definition) is not exactly where the gun is pointing. It is just reasonably close. Within half a standard deviation of the actual aim point, you won't be able to tell the difference. The test round within 2 feet at 1500m is saying something similar. A half mil error at that range would produce of miss of .75 meters or about 30 inches. So if the test round is within a little under half a mil of the aim point, they consider the gun "zero'ed".

When I speak of trusting the gun I mean not trying to correct dynamically for it perhaps being out of "true". You don't aim a little to the right of the target because you saw the last one hit a little to the left. You aim at the center of the target. Then you aim the next one at the center of the target. Each time you aim, you are centering your sight and effectively "rerolling" your pointing error. Eventually you will get a pointing error that is small.

You can still miss because the rounds aren't laser light and do not go exactly where you are pointing. They go somewhere in the vicinity. But you won't add their random scatter to your random pointing error in a linked driven oscillator (which is what causes wider smearing if you overcorrect). Instead you overlay the two random distributions, and that means on average they will cancel each other out almost as often as they reinforce, and the sum of the two goes up about as the largest plus square root of the smaller. (You can get a more accurate estimate of the composed probability distribution by programming it and running enough samples).

As to range corrections, yes you have to correct for range once the distance is long enough that you aren't "bowling". At 1 km the shell is dropping about 3m in flight. You are aiming 2m above the apparent top of the target. When one says the gun is "zero'ed for 1000m", that is what it means.

At 500m the flight time is half, the falling time is half, and the distance the shell falls is only a quarter or less than 1m. You can easily miss with an "over" half the time if you mistakenly think the range is still 1000m. At 500m, to move the aim point down 2 full meters would require a 4 mil correction in the quadrant. That is quite large, and certainly noticable.

If in practice the gunner drops 2 mils and checks the next round, sometimes he will hit immediately (perhaps top half of the target, perhaps a "low" "roll" for the dispersion or his quadrant pointing error or both).

Go up to 1500m and the flight time is 50% longer and the drop can be as much as 10m. If you think it is 1000m because of range estimation error, you will be pointing 2m above the top of a target, that you'd have to be pointing more like 9m above the top of, to hit in the center, and 8m above to hit at all. 6m difference at 1.5 km is again a 4 mil difference in the quadrant.

See, the dispersion from the gun and from pointing error alone are about as large as the target, already, at typical ranges. That means you have to be pointing at exactly the right spot for the dispersion pattern to still mostly be on the target rather than off of it. The hit probability is high, even with this scatter, if and only if the true aim point is actually directed at the center of mass of the target. If instead it is directed at the top of the target, you are only going to hit about half the time, for that pointer-position.

You certainly do need to correct for the range. You need to get the range correct to within about 200m or the pointing in the height dimension is going to be off by more than 2 mils. Unlike the deflection, you can't just read the correct quadrant off the sight by pointing correctly. You have to include a reasonably accurate range estimate - typically based on the apparent target size in the sight.

Now, being off by 2 mils in the height when the range is 500m is not a disaster. The gun will be pointing at a spot that is 1m away from where it ought to be. That will let some of the random scatter cone fall off the target area, and lower the hit chance. But some of that cone will stay covering the target, because the target is bigger than 1m. But make the same 2 mil pointing error at 1.5 km, and now the gun is pointing 3m away from the target's center. And the target isn't that big. Morever, the random dispersion from the gun is only about a meter, so essentially the whole distribution will be moved off of the target.

In other words, 200m range estimation error at short range might cut your hit chance in half, but the same error at 1500m can drop it to zero.

Range is the only thing worth correcting for from shot to shot. The pointing should just be center of mass. When you see an over you can drop 2 mils and try again, and the reverse for an under. But there is a definite problem with this procedure. It means the random part of the error is going to be smeared out and made worse (driven overcorrection style). The only reason this is acceptable is that range estimation error is so bad that it can be worse than an increased gun-given dispersion.

To see this, imagine you are pointing correctly, but the round fired happens to "roll" a "long" dispersion and goes over the top of the target. You will correct downward 2 mils. The next round is practically certain to be a short, as a result. Then you will think you have him bracketed. Your next will be up 1 mil. But still a mil too low, in reality. The first miss, which by hypothesis was due to gun error only (and would probably have gone away with the next shot, if you hadn't corrected) will be turned into two successive misses plus a 50% reduction in hit chance on the third shot.

The cause of the problem in that case is that the hypothesis about the source of the miss is wrong. The correction procedure assumes that a miss is caused by an error in the range estimate. If that guess is correct, then the procedure helps and improves things. But if that guess is wrong - the cause for that particular round was actually gun dispersion - then the procedure overcorrects and makes things worse. Whether the procedure helps or hurts in any given case depends on the cause of the actual miss on the previous shot. Which the gunner cannot know.

It is always a bad idea to "guess" that the cause of the error is the gun being out of true. That leads to systematic overcorrection. The reason not to guess that way is not that there is no zeroing error. There is, though it will typically be small on average (though an outlier tank can have a bad zeroing error "wired in"). But trying to make up for it in action by watching where the rounds go will make things worse, because there are too many other things that make the rounds go to different places. You can't correct for a cause that isn't isolated from other error causes, effectively. Hence my previous point.

All of the stuff I spoke of in previous posts (before this one) explained how you can miss even with zero range estimation error. But for most ranges, range estimation error is going to be the leading cause of misses. Because it creates a +/- 4 mil pointing error, potentially, while gun dispersion and zeroing error are on the order of half a mil, and pointing error in action is on the order of a half a mil for good gunners and 1 mil for average ones.

Range error is therefore the first order term for hits and misses. But the presence of all the other kinds in addition, means it is harder to deal with this first order error by "mere empiricism" - just watching where the last round went. Because where the last round went has a significant random component coming from other causes besides the range error one is attempting to correct. (Pointing error, zeroing error, round dispersion). And a miss caused by one of those, can be misdiagnosed as a range estimation error, and overcorrected.

I hope this helps.

[ August 30, 2004, 06:15 AM: Message edited by: JasonC ]

[Mr. Tittles]

I think Jason makes the point that range errors (for any weapon system without a means of actually measuring range to +/- 50m lets say), is the greatest cause loss of accuracy. It is itself range dependant in that longer ranges make larger errors.

But gun scatter is much larger than this pointing error he brings up. To give an example, a 75mmL48 has about 1.0m by 0.9m 50% zone at 1500m. This means that typically 5 out of 10 rounds will fall within an area of 0.9 sq m. The next 5 will fall within 7.6 sq m. Most of the 10 will be within the size of a typical tank target in late WWII. The pointing error he claims is smaller than this area and a neccessary component of adjusting for range. So the relative size of each and its function needs to be taken into account.

I would 'trust' the gun only for 2-3 shots and then make corrections at long ranges. The precsion of the gun at shorter ranges would enable the gunner to make corrections after one shot. The Germans certainly thought so and the British certainly changed their style to the Germans during the war.

Its like trying to throw a ball through a tire. A hard baseball or a still larger softball might not be that much different given a short range and a 16 inch rim type tire. Trying to throw a basketball through it gets much harder.

If the precision of the shot scatter is small in relation to the size of the target, then precision can be achieved. Lets say we are firing a Tiger I at a Pershing at 100m. The shot scatter is actually so small that the offset of the gun in relation to the sight is larger.

[Mr. Tittles]

Range estimation is almost certainly the TC's call at greater than 1000m or so. He is the one that has the best ability to do this when he is using any binoculars (with reticles). The gunner has a monocular sight.

He is also the one to call corrections. His stereoscopic perception is increased with binoculars and many gunners can not sense the tracer or depth with a monocular sight.

German sights had a means of estimating range directly by the gunner but this would be best used for short to medium ranges and have a component of guestimation also. Since firing at these ranges is somewhat forgiving, it wasn't a bad system. But at longer ranges, the task was best accomplished by the TC and his experience and the quality of his binoculars would have a direct bearing. having to face an enemy that conveniently had a homogenous tank mix (like the Russian T34), certainly helps.

[Mr. Tittles]

"Zeroing is firing the gun to ascertain the point of projectile impact, then all instrument crosshairs should be aligned with the center of the shot group on the target."

"The gun is said to zeroed if the check round hits within 2 feet of the aiming point at 1500 meters" (for the M41 90mm gun)

The major flaw here is that a check ROUND (singular) is used as a final check. It would have to be a shot group of rounds really. One round does not tell much unless the target is very close.

I strongly suggest that reading the APCR thread would help in understanding the concepts here.

The fact is that gun scatter, if modeled according to a normal distribution, will place many rounds with acceptable precision but quite a few rounds with marginal precision. 1 out of 20 will be wild in all but the closest ranges. So correcting aim based on observed shots needs to take that into account.

[ August 30, 2004, 08:40 AM: Message edited by: Mr. Tittles ]

[JasonC]

Look, if you want to really understand this I can just send you a Mathematica notebook that lays it all out. It is easy to simulate the zeroing process. You get a distribution of leftover errors, not one average. The worst few guns will have 1 SD errors left in where they point, 60% have small errors under 0.5 SD on both axes. Not zero. You can't get zero error from taking a few random shots and trying to guess where the actual center of the distribution is.

As for pointing error, it is independent of range estimation or zeroing, and also independent of the gun. It reflects gunner skill more than anything else. It is going to be an error with something like half a mil SD (thus, 95% within 1 mil). That is still going to mean 0.5 to 1m errors at the target, on top of zeroing error and shot distribution.

Then you get range estimation error. You can write code for this easily enough. You use the velocity and calculate the drop of the shot as a function of range (half the time spent descending from apex, to first order, etc). You assume the gun is zeroed for 1000m, which means it is pointing about 2m too high at point blank and 3m too low at 1500m, 6m too low at 2000m, (rough - using 750m/s as a typical velocity).

So then you assume a 20% SD range estimate of the range, and convert that into the mils dialed in. You get an error from the proper aim point again in mils, and convert that back to meters off at the target. So you get a function of range that spits back how many meters off the shot is in the height dimension, from range estimation error alone.

At 500m it is small but present - the size of the other error sources or similar. The errors in the range are on the order of 100m and the pointing change that makes is a fraction of a mil. A fraction of a mil at 400-600m is half a fraction of a meter at the target - something like a foot.

At 1500m it is not small. The range estimates are spread between 1200m and 1800m, leading to mil dispersions up to 2 mils, which at that range turn into errors in the height of on the order of 3 meters. Enough to clearly miss, even if all the other factors go well.

What gets you overall is that any combination of these factors can happen to be bad outliers. Unless another one directly counters it, that can be enough to miss. 10-20% of your guns aren't aimed "true". 10-20% of your gunners happen to dial in bad deflection or quadrant by almost a full mil. 10-20% of your TCs get the range estimate wrong by several hundred meters. 10-20% of your shots scatter poorly even when the other things go well. As a result of all of them combined, a shot that gun dispersion and target size alone suggest should be a 90% -er is actually a 40-65% -er instead.

Because shot accuracy is not gun accuracy.

[Mr. Tittles]

In Tankerschool (end 1943) the crews had to fulfill the following:

1st Exercise:

Using HE on a target at unknown range but less than 1200 meters. Own tank stationary target stationary (size of AT-Gun)

Criterion to pass: 1 Hit out of 4 rounds

2nd Exercise:

HE on a target at range greater 1200m, six HE rounds authorized (target the same as in 1)

Criterion to pass: 1 Hit

3rd Exercise:

AT round on a (stationary, frontal) tank target at greater than 1200m. 4 rounds authorized

Criterion to pass: 1 Hit

4th Exercise:

AT round on a moving (ca. 20km/h) tank target across the field of vision at 800 - 1200m. 3 (!!!) rounds authorized

Time: 30 sec. Firing time, target moves 150 m

Criterion to pass: 1 Hit

Notice: No Examination on tanktarget stationary below 1200 m !!

[Mr. Tittles]

http://onwar.com/tanks/ussr/profiles/fpt3476m43.htm

An interesting thing about T34s is that the upper left corner of the drivers hatch is nearly dead center.

If the Germans used the top of the triangle and lined it up on this upper left corner, then they could have a point of reference of repeatability in aiming to reduce this 'pointers-error'.

The greater the magnification/clarity of the sight, the more easily it is to point repeatably at a single point also. I believe it is range dependant but still a small error that may effect the initial shot(s). If the sight is not adjusted during those initial shots AND the gun is repeatable as far as coming back to a common initial starting angle, then it is not scattering but staying constant. Its basically a 'buy-in' error.

In many cases the shot scatter is larger in vertical than lateral. One might then say that immediate corrections to bring the shots in line are worthwhile. Being left or right should be 'fixed' before long or short is what I am saying. Since tanks are generally wider than tall, this further supports 'fixing' the left or right error first. In fact, being left or right is somewhat independant of range estimation errors! This is actually quite important.

Notice that Jasons pointing error is not applicable to adjustments to fire. That is, the firer does not decide to swivel the turret away so that the target needs to be reaquired and a new pointing error created. He could be left of the targets width 1-3mil with the first two shots and adjust the sight to the right 2mil to compensate. This correction would not be subject to his +/-1mil error for 'new' pointing, or does he think it is? Basically he is turning a device to get the effect. He is no longer 'pointing' but rather adjusting. He is no longer striving to get a majical centering on the strangely shaped area target but moving in one plane a percieved amount. There is a difference.

Another related topic is the fine resolution that is needed to make adjustments. It is not infinitely variable. I would imagine the finely geared raising of the gun could be better than the turret traverse used as a method to rotate left and right onto a target. Most tanks appear to have a fixed trunion that the gun can raise and lower about but theres no additional refinement for right and left besides the big gears around the turret.

[ August 30, 2004, 09:45 PM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

88L56 APCBC

100m....0.1m/0.1m

300m....0.2m/0.1m

500m....0.2m/0.2m

800m....0.3m/0.2m

1000m..0.4m/0.2m

Heres a sample of vertical/lateral 50% data for the 88mmL56 APCBC round (TigerI round).

Notice at 1000m the rather narrow spread of lateral rounds. If one were to do the stats, then about 95% of them would fall in a lateral spread of 0.58m. Or about 2 feet right or left.

Jason claims that a pointing error could add up to another 0.5m R or L. But this should be viewed as an initial 'buy-in' type error and not a scattering type error itself.

If firing at a Sherman tank target, the width is approx 3m.

So we could have a pointing error of 0.5m left and another 0.3 m left. This is sort of a worst case but certainly could happen. We are still within the width of a sherman tank at 3m. It would take quite a range error then to bring this round to a 'lateral' miss at a 1000m (I dont care abount being long or short for now). This is due to the simple geometry of the situation.

The vertical sensitivity to range is due to the sensitivity to effects of gravity. Its a square function and the longer the flight time, the greater the drop, the narrower the 'forgiveness' band where the forward moving rapidly dropping projectile will cross the target's area.

The lateral sensitivity to range errors is many times more forgiving. Bringing rounds inline for a 88mL56 at 1000m would take at most one adjustment round (shame on you for missing R or L at this range). Since the so called pointing error is actually larger than the 95% lateral spread, this will be 'nulled-out' by adjusting to the right. Be aware that the rounds are still a scattering variable at this time but the adjustment to the right is not.

Once the next round is fired, it will either be a short, long or a hit. Adjustments will only be in the vertical direction now. If its a miss, and at the same height as the previous round, then odds are that you have a case to adjust the vertical. Lets say the round that went wide to the left was about 3m off the grund. The next adjusted round just missed the top of the sherman by 0.5m (sherman about 2.7m tall). It would certainly be worthwhile to adjust the next shot downward about a 1m. Note that the vertical spread is greater and the vehicle shorter. Here is where you would need to trust the gun since it has already given you two vertical samples while adjusting the lateral spread. The 95% vertical spread will be about 1.164 m. Odds are that those two rounds have 'bracketed' the vertical scatter and a downward correction is advisable. Again, the vertical correction is not subject to this pointing error.

Note that if this stationary sherman decided to move, its best bet is not to move directly backwards but rather at an angle and backwards. This is due to the fact that varying its range at this point does not effect the firer as much as changing its lateral position.

Note how much tighter the vertical 50% zone is at 500m. Since the initial pointing error and range estimates are also reduced (and penetration is up), firing at this close a range at stationary targets is quite deadly.

[Mr. Tittles]

About the pointing error...

Supposedly the Germans aimed at the bottom of the tank with the triangular 'pointer' in their sights.

Aiming at center of mass is different in that you must judge the middle point of two dimensions (Length and Width). It is actually easier to estimate the middle of a line than the middle of an area. The trick with the German 'strich' triangle is to slide it up the bottom length of the tank; ie bring the triangle up so it 'pierces' the bottom line of the tank. When the width of the triangle meets the width of the target, then one bottom of the triangle will touch the outer edge of the target before the other! Then correct right or left, so that the width of the triangle fits neatly between the width of the tank, and you have a very neat way to find the center of the width of the target.

The one drawback of this is that actual aiming at known weak spots means offset aiming.

[ September 01, 2004, 11:17 AM: Message edited by: Mr. Tittles ]

[JasonC]

"adjust the sight to the right 2mil to compensate."

Is it 1 mil, or 2, or 3? How much should he adjust? Is he measuring the distance of the miss with a meter stick and doing a little trig? Is he firing 100 rounds at the old deflection, finding their center of mass, and determining the correct offset to use?

No. He has one round, that missed "some" to the right (if he can even tell - it will probably just look like a "long", since the shot will pass the target, note having reached ground level before its range). But is it wide right because of a random dispersion to the right? Or because he is pointing at the wrong deflection? Suppose he adjusted 2 mils and the next is wide left. Is this because the first was wrong and the second overcompensated? Or because the first was the right deflection but a random scatter round to the right, and the second is a compensation error he added?

He doesn't know, so he splits the difference and readjusts 1 mil back to the right.

He isn't going to get perfect "homing" this way, because each round is scattering randomly by half a mil to a mil to start with. He is going to get some deflection, that won't be the right one, but will be close to the right one. He can get the same looking through his sight. The deflection that looks right in his sight, if he does the sighting right to begin with, will be within 1 mil of correct. But not dead on correct. He will only get dead on correct if he is lucky, not just good.

"This correction would not be subject to his +/-1mil error for 'new' pointing, or does he think it is?"

Sure, of course he is. He is touching the dial. He won't get it perfect. It is like trying to pick up a weak radio station between strong ones. There is only one exact position where you get good reception. Well, you will get some static, most of the time. Adjust it, adjust it again, adjust it again. You will get frustrated, but unless you are lucky you will still have some static.

"Basically he is turning a device to get the effect."

Fine. Is he tuning the positioning of a laser, or of a fire hose? Answer a fire hose. Is he tuning it with a digital computer with infinite precision, or with his right wrist? Answer his right wrist. In practice, a good gunner gets within the right half mil, and any trained gunner can get within the right mil.

A mil is not a lot. It is a small movement of a dial, 1/6400th of a circle, about 3 minutes of arc. The width of your thumb at arm's length is 30 times that (about 2 degrees of arc). Imagine 30 tic-marks across your thumbnail, held out at arm's length. You going to pick not only the exact one that lines up with a distant object, but the right gap between any two? Then you are a good gunner and can get half mil accuracy. But not more.

If the gunner can do this then he can use his sight. And does not need to play games trying to spot his fall of shot to the right or to the left. Because the random error in those dimensions is going to be about as large as his pointing error, he is better off not smearing that pattern out to +/-2 mils with repeated adjustments back and forth across the target, but instead just pointing at the target.

The reason it makes sense to adjust range with overs and unders is the range estimation error can readily be an order of magnitude larger than the pointing or random shot scatter errors. To get it down to the same size, it is worth playing with adjustments - even though those would amplify a random scatter pattern, if the range estimate error was zero.

In the side to side dimension, the only way significant systematic error (more than the half to one mil stuff from shot scatter, zeroing, and pointing) is when the target is moving and the gunner has to give it the right "lead". There he has to estimate the range and the target's speed. This can easily lead to errors as big as range estimation error, in terms of the number of mils off he is likely to be (up to 5 mil errors, not half mil errors).

[ September 02, 2004, 11:42 AM: Message edited by: JasonC ]

[Mr. Tittles]

I think a basic oversight (no pun intended) is that the gunner is watching the fall of shot. Usually he can't. This was brought out in the other thread also.

The TC is the one who observes fall of shot and calls corrections to the gunner. The TC is usually using some form of stereocopic equipment (binoculars or scissorscopes) and has superior depth of percetion that is needed to observe the fall of shot. Carius makes this quite clear (Tiger I) in his book.

Do you really believe that someone with 10X binocs could not observe fall of shot at 1000m? Observation of fall of shot can be related to the width of the target vehicle for shots that go R or L.

There is no recentering when adjusting lateral misses. That is, the adjustment is dialed in and the crosshairs move accordingly. The resolution of the guns traverse sets the amount of adjustment that can be made. There is no smear.

The pointing error is misunderstood by Jason. He may have a case about initial pointing trying to find the center of a target. But he can not apply the same amount of error to any other motion of the gun system after that. The resolution of the gun system traverse and elevation is not a fire hose.

I think the hearrt of the matter is that Jason is making doubts about human perception, confusion about system precision and the actual method of firing a WWII main gun with a 3 man weapon crew (TC, gunner and loader).

[JasonC]

Nope, not basing it on any such misconceptions. The "fire hose" refers to the fact that the round going someplace does not mean the gun is pointed at that exact place, nor that the next round will go to the same place. They aren't lasers. It is pointless to try to adjust *within* the dispersion pattern of the gun itself. In fact, it increases the smear to attempt it (as Deming showed, and as I cited in the my first in this thread).

As for ranging, the actual ranging is usually accomplished by the apparent target size in the sight. Depth perception has basically nothing to do with it. The apparent size of a tank at 1 km is so and so many hash marks wide and the same tank at 1.5 km is only 2/3rds as many hash marks wide. The narrower the target looks in the sight, the more mils high the gunner should dial in. The broader it looks, the closer it is.

I wonder if Tittles has ever actually observed fall of shot. I certainly have, and from lower velocity guns firing larger rounds (SP arty). You can tell an over from an under. Thinking you are going to tell which 50m bracket the round fell in is a fantasy.

Instead you just adopt procedures that will home most of the time from a decent initial estimate. If your error is likely to be 20% of the range or less, then at typical direct fire ranges you will be within a band only about 8 mils wide from top to bottom. Over or under tells you whether you have the right half. From a mid point of that range, 2 mil adjusts will get you a bracket within 3 rounds almost all of the time. Once you have a bracket you can make one more single mil adjustment. Beyond that, there is little point.

Tittles speaks as though the point is to pick which headlight to shine a laser on. It isn't, it is to find the right mil to shoot - which will correspond to the right 1-2m or height at the target. Finer discrimination than that is not only hard, it is essentially pointless for medium range shooting. The only time you'd actually sweat even half mils (and only on range) is for extreme range shooting, and there is no reason to sweat anything more than that. You are trying to hit a multi-meter-sized tank, not a fly in the eye.

Now I will let Tittle return to his scissor telescope triangulation tenth or hundredth of a mil fantasies. I have given him all the reasons he could possibly require - he was the one who asked for my opinion in a discussion he was having with Rexford. That he doesn't like them is his problem. I'm through trying to instruct him.

[Mr. Tittles]

I think you just do not have much experience with precision systems. I am fully aware of the guns scattering and also the Germans expectations of gun crews to pass a course. If anyone has been following the threads at CMBB lately, they would know that.

You are misapplying this pointing error. Perhaps you think its something that needs to be applied every time the guns controls are touched. It is not true. It is only a 'buy-in' first chance factor. It will be nulled out over time.

In the example I used with the 88mm at 1000m, the lateral spread is less than the width of the tank (well 99% will be in 0.6m (thats 0.3m L or R) of where the gun's pointing). Your initial pointing error could be +/- 0.5m Even the worst case of adding them together is less than half the width of the tank (3m width).

The point is that missing laterally IS correctable on the next shot (under these circumstances)! Why? Because the precision of the firing system (as far as lateral is concerned) makes it so! A miss to the left should be corrected by moving the crosshairs to the right. Not 'pointing' the crosshairs but adjusting the crosshairs over by traversing the gun. How much? Depends on the observed offline amount. I think its well within human perception, aided by binocs, to percieve a relationship between the targets width and how much the shot was off laterally.

Wind is not going to make such a large lateral error occur at 1000m. Most likely a out of zero gun would (either through battle damage or road bumps).

The point is that with any system, when trying to use precision, the precision must be within the size of the acceptable limits (width of the tank in this example). Adjustments must have a resolution capability smaller than the 'scatter' of the precision (that is, you should be able to make adjustments that are smaller than the shot spread). Typically 1/10 would be nice. Note that gun elevation and traverse are not firehoses. They can still have repeatable (well backlash..) precision and should have it They are not smearing anything.

I will bring this up with rexford.

[ September 02, 2004, 05:23 PM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

I think you have to stop golfing and start bowling.

[Mr. Tittles]

Heres an experiment. take your cursor and try to point at the middle of the area of this tank. Try to do it 10 times in a row. A training trick is to first move the mouse back and forth along the length, find the middle, then do the same for the vertical.

Depending on your monitor and the German sight, lets say a 5X (later model StuGIIIL48 and other panzers with 5X). You can move your seat or head back and use your thumb at arms length to guage it in (3m width tank at 1000m is 3 mil x 5 =15mil). Use a small diameter tube to look through and move the mouse.

Next, try to point at a particular feature that you can make out. It can be the bow MG or gun travel lock, etc. Inspect your work after each trial by releasing the mouse (without moving it) and moving very close to the screen.

Now point at the bow MG. Try to adjust to the right so that you now are aiming at the right side of the gun travel lock (its that upside down V shaped thing in the front upper hull between the radio operator and driver). Did you adjust that 1 meter interval 1m +/-0.5m? If you did, then you are one lousy gunner!

You should find that while trying to center about an area. You would have a spread or scatter. But while aiming at a point, you would have much less error.

Do you really buy this pointing error?

[ September 03, 2004, 10:29 AM: Message edited by: Mr. Tittles ]