Max Hit Probability

[rexford]

Following up on previous post, what would be a reasonable maximum limit on accuracy for ace, average and poor crews at:

1000m

500m

250m

100m

Our spreadsheet allows close to 100% accuracy inside 500m and this may be too superhuman, based on previous posts. We would like your opinions so we can finish the sheet. Placing a max accuracy may also model less than optimum rate of fire, duds, rounds that hit and break (Germans admitted that quality control allowed a small % of ammo to go out that would penetrate almost nothing), jammed guns, etc.

If 90% max accuracy for ace crews at ranges inside 500m, then 10% of hit tries would be automatic misses regardless of where the computer says the shot landed.

We would really like to hear your suggestions on this.

Thanks.

[Jarmo]

It kinda depends.

What weapons are you talking about?

[rexford]

75L48, 75L70, 88's, 76 U.S., even 75L40 has close to 100% at close range against stationary target.

[JoePrivate]

The highest hit percentage I have seen was 99%. The situation was a M4A1(76) firing down against the side of a Panther at 40-50m. IIRC the Sherman had already fired one shot.

[Jarmo]

IIRC, the hit probabilities you get with the LOS tool, are not the ones

actually used. The tool just gives a rough idea of the hit chance.

[Guest Big Time Software]

rexford,

This is always a tough question because human factors which are difficult to measure tend to outweigh the more easily-measured mechanical issues.

That said, I think near-100% accuracy out to 500m is too generous. Let's take the German 75mm KwK40 L/48 gun for example (from the PzIV tank). Muzzle velocity is 750 m/s.

I'm just doing these calculations with my hand calculator, so this isn't precise, but will make my point nonetheless. Consider a PzIV aiming to take a shot at an enemy tank 500m away.

The biggest threat to accuracy is range estimation error, especially in the heat of battle where severely limited time and human error problems weigh heavily.

Let's say the gunner mistakenly estimates the range to target at 400m, when in reality it's 500m. We can make a rough calculation of the 'drop' of the shell due to gravity, and see that it would be a clear miss.

Very rough calculations here but... it takes the 75mm shell about 0.56 seconds to travel 400m. Gravity drop in that time is about 3m. It takes the 75mm shell about 0.71 seconds to travel 500m, and gravity drop in that time is about 5m. That's a 2m difference in gravity drop between the two ranges.

So if the gunner is aiming at the tank believing it to be at 400m range, he'll elevate the gun accordingly, and the shell will end up being a full 2m too low once it travels the actual distance of 500m. In fact it will plow into the earth short of the target.

I haven't even talked about other human errors, wind, miscalibrated sights, gunbarrel wear, uneven-quality ammo, etc.

Just the problem of range estimation alone - even a 100m error at 500m - is enough to produce a clear miss. And altough I think gunners would usually do a better job than that, I think near-100% accuracy is definitely too generous.

Just my opinion.

Charles

[Jeff Duquette]

I think you need to recheck your figures…its ½ gh^2…not gh^2. In addition your frame of reference assumes no initial height. Typical axis for the main gun will be somewhere around 2 to 2.5 meters above the ground at the start of the trajectory. So your example would result in a slam dunk hit on the target in question.

[Jeff Duquette]

In addition the position function for projectile motion typically assumes parabolic trajectory and constant velocity. This is obviously not the case unless firing occurs in a vacuum. Flight time vs. range is pretty darned close to linier, and therefore fairly easy to derive velocity as a function of time equation…velocity degradation vs. range as a function of time.

For the projectile position equation…instead of velocity being constant you replace it with a function of velocity relative to flight time. Position Function for a projectile:

r(t) = (Vo cos (theta))ti + {h + (Vo sin (theta)t - ½ gt^2}j

r = position at time t

theta = superelevation angle…gun lay

h = initial starting height of projectile

g = gravitational constant

So instead of muzzle velocity Vo being inserted as a constant…velocity as a function of flight time is inserted.

This a graphical derived from original gun test data provided by Rexford on an earlier thread on the topic of main gun accuracy.

[LuckyStrike]

Bump

[Jeff Duquette]

Some pertinent info from “The Tigerfibel”. I suspect this type of thing established the foundation for modern battle-sight gunnery concepts. Yes Range estimation is very important…to an extent. Close range fire (i.e. fire at ranges of less than 1000 meters) is far less susceptible to misses due purely to range estimation errors for high velocity, flat trajectory rounds. This is the whole reason Battlesight gunnery works.

[rexford]

If a target is at 500m and the 75L48 sets the gun for 400m and aims at target center, the simplified trajectory equation is:

-0.00001025 x (target distance)squared + 0.00410 x (Target distance).

For 500m target distance and 400m gun setting for 75L48, shot passes target

0.513m below aim point, this is a hit on most targets. Even with double vertical and lateral dispersion cranked in, being off by 25% against 400m target still plows most shots into target, and buys close to 100% accuracy.

If target was at 400m, simplified trajectory equation predicts 0.0m error from aim point.

Previous analysis using gravity considerations may not have considered that gun is aimed above target point to counterbalance gravity effect, with range settings set for projectile trajectory and gravity.

Target at 400m, aim at 500m is a hit with most WW II tank guns if one limits themselves to pure mechanics. My question had to do with how often do people just mess up and set the gun for 800m instead of 500m, and what is a reasonable max for hit accuracy.

Battlesight aim is one answer to minimizing human error, although some people might use 600m instead of 900m in the heat of battle.

[jasoncawley@ameritech.net]

Gravity and range estimate is one source of error that gets progressively tougher with range. Another issue is target motion. In the examples given, the guns has a flight time to the 500m target of .56 to .71 seconds, right? Well, if the target is moving laterally 6m/sec, that is a 10-13 foot miss (3-4 meters) - turrets are smaller than that, but it is a hull-down issue probably. Or if the gunner leads that much and the tank stops.

At 2 kilometers, the flight time may be 2 seconds, and the distance the target covers during the flight of the projectile will typically be greater than its length. In addition, at distances over 1 mile, target motion usually is often not evident (think of highways and you will see this is true - optics help but the speeds are also lower than cars on a highway).

Next there is the error in the dialed in deflection and range. Those will often be off by a "mil", sometimes by two. That matters more for artillery dispersion - the distances covered by direct fire weapons is short enough that the pointing problem is not all that hard. An error term of a few meters will nevertheless creep in here.

In addition, there will be small alignment errors, the optical sights not being perfectly aligned with the tube (especially after many shots and the accompanying recoils, or long travel cross country, etc). Again a few meters.

Then there is the dispersion of shot from the gun itself, just from its ballistics. That varies from gun to gun, obviously. Last, there is the tendency to fire rapidly rather than to calmly ensure the gun is fully laid on the target before firing, a "heat of battle" effect that will result in shots with the gunner thinking the range or deflection is "close enough" rather than perfect.

I think 90% at 500 meters as a maximum accuracy for a crack crew would be quite generous. Regulars at 1000 meters, I think more like 50% is a better ballpark to be in.

Here is another way to think about it. The rival combatants built and deployed 50,000 (German) to 200,000 AFVs (roughly 1/2 Russian and 1/2 American-made), loaded them with 30-50 AP shot apiece in a single combat load, then smashed them against each other repeatedly and in the process expended several times the combat load of each tank in ammo. And the victors had tens of thousands of AFVs left intact (or recovered, to be sure) at the end.

That implies an enourmous portion of the AP rounds fired, were fired at ranges (or other battlefield conditions - smoke, concealment, etc) producing a hit probability in single digits, or the low double digits at most. Otherwise none of the tanks would have driven off the field, or the basic ammo loads would have lasted the whole war.

Another item - in a 3 month period in Russia, the Germans confirmed around 5000 tank kills. Only about 500 of these were scored with the infantry weapons of all types, most of those infantry kills by Panzerfaust. But the Germans deployed 7.4 million Panzerfausts against a total of around 200,000 Allied tanks and tank destroyers. Most of them obviously were not fired at tanks - probably were not fired at all - many of those that were fired were probably fired at houses or bunkers, despite being relatively unsuited to it.

It was certainly not the case that each deployed Panzerfaust translated into even a 3% chance of a dead enemy tank, or there wouldn't have been any Allied tanks left. The proper percentage was probably about 0.2%. Some of that will reflect use on other targets, perhaps enough to raise it into the 0.5%-1% range. And a large portion will reflect Fausts that just never got close enough to be fired. But the hit chances for the shots that were taken were probably in the 5-10% range, not the 50% range.

There is a general tendency in wargames to model weapon lethality based on abstract ideas of physical effectiveness. In practice, one sees that lethality is far lower, and is puzzled as to why. In some cases, it will reflect people not using their weapons at all (as Marshall famously found).

But in most, the cause is probably that men in combat are far less willing to expose themselves to extreme danger than wargame designers - or generals for that matter - expect them to be. And that means many more shots are taken at extreme ranges, in low probability situations. The participants seek safety in many low probability shots themselves, to disable an enemy long before they themselves are exposed to a high probability of a return "kill" from a single shot.

Otherwise put, the historical participants did not mash themselves together as aggressively as we do. And they missed a lot more than we sometimes think, in part because it it. The proof is in the ammo expended vs. the targets it was expended at, many of which came through unscathed.

[rexford]

Here is verification of the simplified trajectory estimate when 75L48 fires at a 500m target with 400m range setting.

At 400m, shot is even with aim point on target, by definition. Descent angle is 4 mils or 0.229°, from German stats. Shot still has 100m to go to reach target.

Multiply 100m x tangent 0.229° for continuation at 400m descent angle, equals 0.400m drop from 400m to 500m.

Gravity effect is 0.5 x 9.82 meters/second squared x (100m/697 m/s average speed from 400m to 500m)squared, or 0.100m.

So shot drops 0.5m from 400m to 500m, and will be 0.50m below aim point on target when it reaches 500m. Simplified trajectory equation predicted 0.51m below aim point.

[M. Bates]

Out of interest, who is 'our' and 'we'?

Just wondering.

[Jeff Duquette]

jasoncawley@ameritech.net…can I call you Jason Great post. Your obviously well informed. I would not argue any of your points...yet. However, I think the fundamentals need to be nailed down prior to spinning off into sources of human error and battlefield psychology. I would not start the problem from the human error perspective and subsequently work my way back toward systematic error. I would reverse my approach.

I understand Rexford’s attempt here is to quantify “human error” and battlefield psych into basic accuracy formulas. His post assumes a common frame of reference amongst the viewing audience regarding exterior ballistics. In my mind the example above in which a MkIV firing and missing due only to a 100 meter range estimation error needs to be addressed prior to spinning off into a discussion on “cool-gunners” or “nervous-gunners”.

In addition we can always come back to hand waiving about bore-sighting, play in carriage mechanisms, variations in the arrangement of the propellant grains, Air temperature or whatever. But just to clarify; if you look closely at Rexford’s calc’s above, typical lateral and vertical dispersion from systematic deviation away from an MPI on the target's visble center of mass was included. I also think he was employing a very conservative doubled dispersion…and still came up with a hit.

[Guest Big Time Software]

Jeff,

Whoops you are right about the 1/2T^2. That'll teach me to do the off-the-cuff stuff.

So change what I said to, say, a 150m mistake on 500m - a mistaken estimate of 350m instead of the true 500m, and you'd have a miss.

As I said, most gunners would do better than that most of the time, but not 100%, or close to it, in my opinion. Combat conditions are highly stressful and everyone is in a huge hurry, and that's when mistakes of all sorts are made. It's really hard to put a number on human error though.

Charles

[:USERNAME:]

Woh..

Hey Chas if you need help, let me know, I am a motion control engineer right? (I noticed you never responded to my downward sloping post regarding the lower hull of the panther).

A thing to keep in mind is the ground the firers vehicle is on. Pitch, roll and yaw might not have been that easy to correct for and would play a role in accuracy.]

Lewis

[jasoncawley@ameritech.net]

If the "we" question was asked of me, I meant by it we gamers, we modern armchair tacticians, we designers, historians, modern vets wondering what the old days were like before guidance systems, and the whole sick crew.

As for the other fellow's comments on saving crew stuff for later, I do not look at it that way at all. We know the misses occurred, as an absolute fact. The entire detective story is what caused them, and the reason to pin that down is to get right things like how accuracy decreases with range as opposed to crew quality or environmental conditions, etc. The analysis many of you are focused on basically starts from physics and perfection and goes forward. I mentioned a number of the factors involved there in my last.

But my overall approach is not to speculate on crew psychology, but to establish the historical benchmark of fact from other known facts (besides physics) and from doctrine. I think I can get pretty good estimates for overall accuracies and even break them down by ranges that way, roughly. I will illustrate the matter more below. But the point is that it is not necessary to isolate the particular physical factors that caused each miss, if one has a decent estimate of the overall rate of them from all causes.

I start from the simple observation of the ammo loads the sides bothered to supply to their tanks. 30 to 50 AP rounds was standard. Why? Not because they expected each tank to despatch 30 to 50 of the enemy, certainly.

They would plan for "runs", of luck or skill or positioning, certainly. Imagine extremely crudely that which tank wins a duel is a coin toss. Then 1/8 can be expected to win 3 duels in a row, and so on. Beyond 4 or 5 such "heads", the chances are so small that it will have little impact on how well the whole army does, what happens in those cases. Similarly, doctrinal tank platoon sizes are an obvious ammo-load "target" level, again 4-5 tanks. If a well situated tank of yours can despatch an entire platoon of the enemy's if it gets lucky, that is "enough".

So, it is reasonable to assume that 30-50 rounds were expected to be able to destroy 4-5 tanks. That puts the number of shots expected per kill at 6-12, it being understood that a quite optimistic case of the lucky tank winning its duels is involved. Then there should be a correction factor for the expected number of hits to knock a vehicle out. An upper bound on that is probably 2 hits, and a lower bound might expect 1/5 hits to be non-lethal. Then 3-10 shots are expected per hit.

Thus, we can derive as a best case or upper bound of what the historical participants expected or planned for, that hit probabilities for individual shots would usually, or in good cases, be in the 10-33% range. At what distance? The maximum effective range the Germans expected from their tanks was about 2.5 kilometers, and in the early war and the Allies, often expected ranges in the 1-1.5 kilometer range.

From these bounds, it is relatively easy to guess that a typical regular crew would average about 33% hit probability at 1000 yards, with 10-15% typical for 2000 yards (in the case of guns meant for that range). 20-25% might be expected at ~1500 yards.

Between 1000 yards and 500, the hit probability would certainly rise - it might double. Between 500 and point blank, it would rise sharply to almost 100%. These higher lethality ranges would be comparatively rare, expect in environmental conditions that depress the accuracies again (fog, night), precisely because the men would not relish the greater danger involved.

That is going to be about the right answer, in terms of the level of lethality of the weapons. It would apply for a non-moving shooter, a non-moving target, a regular crew not in any panic or shocked state, unbuttoned, average tank-sized target, with an averagely accurate gun.

Gun improvements would raise the figures perhaps 5-10%, not more, because gun ballistics are probably not the cause of most of the misses. Poor guns would detract by equal amounts, perhaps a bit more, especially at ranges that are far for the gun in question.

Target motion would cut the figures in half. Firing motion would eliminate the hit chances altogether beyond 500 yards without gyros, and beyond 1000 yards even with them, and cut them in half in the remaining cases.

Hull down would reduce the hit chances 1/3 to 1/2, and the target size would affect it roughly proportional to the target cross section.

Crew states would halve the figures or eliminate fire altogether, except perhaps under 500 meters at a threat. Being buttoned would have a modest effect, 5-10% (its real effect is on spotting in the first place). Crew qualities would have fixed size 5-10% effects, with the result that they would make a large proportional difference in range shots while making relatively little (proportional) difference in short range ones. Crew quality would also effect rate of fire, obviously.

So a standard gun able to hit at 2000 yards - say a Panther's - might have only a 10% hit chance at that range. But a crack crew might make that 15% - a very large relative improvement at that range. At a moving target, though, the hit chance would fall to ~1/13, and some might not be kills. A platoon of Panthers firing at range would still be knocking out approaching T-34s, out of range, every couple of minutes. About right.

Now, that is already a reasonable set of approximate hit chances, which could easily be adapted to every sort of gun with minor changes. Without needing much in the way of physics, just common sense and awareness of doctrine and unit history historical realities, and some familiarity with trying to get guns to hit targets these days.

System design is not about physical engineering. The purpose is not to establish some particular thesis about the cause of missed tank-round shots in WW II. The purpose is to provide accurate enough average hit chances varying correctly with range, to match the known tactical and doctrinal facts of the period, and the real events we know happened.

And in case nobody gets it yet, we know that average crews did not hit almost all of the time in shots at ~1 kilometer range. There would never have been any live tanker vets otherwise, given the number of shells we know they fired at each other.

I hope this is helpful.

[rexford]

Great post, jasoncawley.

Guess one could just set a max for hit % inside 500m, based on what seems right.

Thanks.

[rexford]

Charles,

Your assumed miss with 350m range setting and 500m target may not be so.

If aim is 350m and target is at 500m,

equation for trajectory is:

-0.000009426 x (target range)squared + .00330 x (target range).

For 500m target range, shot passes target at -0.71m relative to aim point, which is a hit against a 2m high target (target extends 1m above and below aim point).

Analyzed another way, extend 3.5 mil descent angle at 350m to 500m and obtain -0.53m. Average velocity from 350m to 500m is 741 m/s, so gravity fall is -0.20m. Shot falls 0.73m below aim point from 350m to 500m.

A hit with a 150m range estimation error against a 500m target.

You assumed this case would result in a miss, and it didn't. Range estimation can be off by amounts that suggest misses at 500m and still result in hits, which is my concern. There is more to close range misses than a 25% or 30% range estimate error, and it must include some out-and-out mistakes (like setting gun at 150m instead of 350m, or aiming at a tree near the target instead of the tank).

[rexford]

Incorrectly used 88L56 data in previous analysis because it was in front of me.

If 75L48 aims at 350m and 2m high target is at 500m, ideal shot trajectory shot falls 0.77m below aim point, which is still on target.

Note that being off by 100m against a 500m target moves aim point -0.51m down, increasing ramge error by 50% moves aim point an additional -0.26m, a 51% increase.

It may take a 200m aim error against a 500m target to miss hitting a 2m high target with the perfect trajectory.

If aim point is -0.77m below center of 2m high target, 75L48 dispersion at 500m results in over 90% accuracy with 150m range error.

[aka_tom_w]

I would like to interject...

Charles and Rexford may appear to be disagreeing here,

BUT the game is now (at least in my opinion) actually balanced with respect to "chance to hit odds" and accuracy probabilities, more towards figures Rexford is talking about.(I think ?)

We still don't know whats in those accuracy algorythms but the latest patch/update read-me had line in it about "short range (point blank ? Whatever that means) accuracy being enchanced so there is a greater chance to hit.

In other threads and posts I have suggested that it is my opinion that ALL chance to hit precentages at ranges less than 500 m have increased, now maeing tank comabt more deadly with more first shot kills.

Charles may be disagreeing here with Rexford but the game seems to be agreeing at least IMHO with Rexford's suggestions and conclusions.

BUT I could be wrong.

BUT jsut play the game with a stationary hull down Crack Vet or elite Panther and see how many times it misses at less than 500 m,

I will bet you will see MANY many more first shot hits than before, the change was made.

-tom w

[This message has been edited by aka_tom_w (edited 01-14-2001).]

[This message has been edited by aka_tom_w (edited 01-14-2001).]

[Monte99]

Before I interject another vapid opinion: Who in the hell do you have there with you that justifies the use of the "we" pronoun?

Perhaps this is a subject for another thread.

------------------

"War does not determine who is right - only who is left."

-Bertrand Russell

[aka_tom_w]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Monte99:

Before I interject another vapid opinion: Who in the hell do you have there with you that justifies the use of the "we" pronoun?

Perhaps this is a subject for another thread.

<HR></BLOCKQUOTE>

To which use of the word "we" are you refering?

-tom w

[Jeff Duquette]

<BLOCKQUOTE>quote:</font><HR>Rexford Said:

There is more to close range misses than a 25% or 30% range estimate error, and it must include some out-and-out mistakes (like setting gun at 150m instead of 350m, or aiming at a tree near the target instead of the tank).<HR></BLOCKQUOTE>

Or leaving your ballistic computer set at SABOT when the loader has HEAT up.

This is what I was alluding to before. Get the basic physical model right first...than dump in fuzzy logic for battlefield psych or stress, or whatever the sexy term for human error is.

Jason:

I like your post again, and I'm not suggesting that human error\sweaty palms do not play a big part in battlefield accuracy or even gunnery range accuracy. However, I am of the opinion that a basic physical model should be in place than "dumb down" the accuracy model from there.

Scott Cunningham (one of the design team members for Steel Beasts) once posted the following info on the old tanknet forum:

<BLOCKQUOTE>quote:</font><HR>"Gun accuracy and lethality has increased remarkably since WWII. We used to say that an M1a1 had 40 stowed kills onboard. Actual RPK is about 1.7 in practice, but the bottom line is that an M1 will hit and kill just about anything that it can see and shoot at out to about 4000m. After that hit and kill percentage drop off drastically.

This goes for both SABOT and HEAT ammo, which are the two primary rounds.

This is a lot better than a WW II tank (German tanks included) that usually needed 8 rounds or so to get a kill. A modern 120mm is probably 5x more powerful than a 88mmL71 (the best of WW II) in penetration, and is far more accurate with modern fire control systems. Gunnery sure has come a long way in 50 years."<HR></BLOCKQUOTE>

My question would be the specifics or context of the 1:8 ratio. Are numerous misses at long range skewing the numbers...or are Ordnance bean counters skewing stats by not distinguishing between rounds lost in brew-ups and rounds actually expended in combat firing?

It's an interesting number to bat around, but the specifics behind the stats may be an even more interesting piece to the puzzle. Perhaps the natural killers ("cool gunners") are getting 1:2...and the remaining shooters are hovering at 1:15? Does this number vary by nationality? Perhaps there is some variation by the gun actually doing the dirty work?

The concept of rounds per kill also encompasses rounds that hit, but don’t kill. Some numbers from British Army Operational Studies conducted during the Normandy Campaign:

Average number of hits to KO a Tank:

MKVI : 4.2 rounds

MK V : 2.55 rounds

MK IV : 1.2 rounds

Sherman : 1.63 rounds

Bear in mind that Normandy battlefield would also skew the above stats toward a lower number of hits per kill. Why? Consider typical engagement ranges in Normandy for tank on tank encounters. Both British Army and US ARMY operational studies concluded that typical engagement ranges in Normandy were very close…less than 400meters for tank battles. No surprise to the avg. grog.

Now consider what these same stats may have been for tank on tank encounters in more open country of eastern France, Belgium (exclude the Ardennes), Holland or the western plains of Germany. Now your looking at typical engagement ranges of 600 to 1200 meters. Big difference in AP round kinetic energy between 400 meters and 1000 meters. Avg. number of hits required for a kill no doubt rose. Again this should no surprise.

One additional thought. Tankers in all armies understood that a tank with merely a hole in it, is a tank that your gonna have face again tomorrow or next week once bad guy ordnance folks hosed off the old crew, and broke out the welding torches, and new paint. Shoot till it burns. Once a tank burns its service life is over. So a tank might be unserviceable for the immediate battle after one hit, but tankers will continue to fire rounds into the carcass till it burns. Two, three, four additional rounds to cook off interior ammo.

Just my opinion on a very interesting topic.

[This message has been edited by Jeff Duquette (edited 01-14-2001).]