Max Hit Probability

[jasoncawley@ameritech.net]

"must include some out-and-out mistakes"

Excess out and out mistakes at short range? That is easy. Not pausing to level the bubbles.

A tank's gun is laid on the target by dialing in the proper range and elevation settings into the sight (while looking at the target of course, through the sight). So far so good. After that is done, the gunner has to move the barrel itself to match the direction his sight is pointing. The way that is done is by elevating and deflection screws or hydraulics, depending on the tank. Again, simple enough.

But the way the match up between barrel and sight is measured as exact, is there are bubbles in tubes, like on a carpenter's level. When the bubble goes too far to one side, you move the barrel back the other way, and vice versa, until both bubbles, for deflection and elevation, are simultaneously centered in view in the center (marked) part of the tubes.

But this is a time consuming and relatively tedious process. It is easy to see when the barrel is more or less aligned, as when you've dialed up the elevation enough that the bubble slides from one "side out" to the other "side out". Now, it seems to me with an enemy tank at 500 yards, this is the sort of thing a gunner would do in rather a bit of a hurry. Just a little, there.

He is effectively counting on not needing to point so straight, and trading that for a few seconds on the speed of the shot.

It is also a common error to align the sight, and think that doing so has put the gun on the target, or to adjust only the elevation or the deflection on the gun, after adjusting both on the sight.

When I say "common error", I mean even today under training conditions with plenty of time and no threat. The commander catches such things, sometimes with a checklist or with a sign-song back and forth of orders given and responses called out when a task is finished and the next can begin. In training he does, most of the time, that is.

At 500 meters, live or die by who fires next? I'd bet not leveling the bubbles was more common than leveling them.

[medlinke]

Wow...I'm impressed by the level of discussion going on in this thread, it actually makes me enjoy physics...(I'm an English Major with a History Minor in Secondary Education at Michigan State)

I think that the spirit of Charles post is being overlooked. It's not that mathematically a round couldn't hit and penetrate at a particular range close to 100% of the time. It's the intangibles involved in the situation.

Any game can only be close approximation, and it can only be a game. In real life terms, dust storms, and million to 1 things that can happen are just impossible to model. Although the physc of the battlefield certainly is interesting, it seems to me that quantifying it in any other way than is in the game isn't "fair," because it makes too many assumptions...and remember the rule about assuming....You make an ___ outta you and me!

In game terms, close to 100% hit at 500 would be boring to me. In the 1.1 patch for instance, this leaves the game down to a mere modeling of paper, rock, scissors in terms of turret / hull rotation speeds. That Sherman that can get it's turret to bear before the Hetzer wins because of technology alone? Certainly there is evidence of this in real life, but in game terms, I enjoy the occasional ping as the round ricochets off the Hetzer's armor.

In the ASL community there is a lot of complaining about which combat results table to use. Those who are familiar...feel free to groan. But I think it all boils down to 1 thing.

Does the current system uphold the spirit and feel of combat in an interesting / fun way? I believe the 1.1 patch does, and that's good enough for now.... Think of the alternative in game terms... Predictability would kill the spirit of CM in my opinion.

Keith

[Monte99]

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

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

-tom w<HR></BLOCKQUOTE>

I was referring to rex's continuing use of the royal "we." But never mind. It's not germane to the thread...

(edited to remove coordinates to secret treasure)

[This message has been edited by Monte99 (edited 01-14-2001).]

[jasoncawley@ameritech.net]

Reply to Jeff's interesting post -

It is interesting that the 8 rounds to kill figure is smack in the middle of the range I got by an entirely different estimation process, based almost exclusively on doctrines used, and cross checked with nothing more than some crude unit history report estimates on the back of an envelope.

I also used a hits per kill range of 1.2 to 2.0 based on nothing more than my sense of such things from the unit histories, and you give British figures from detailed studies that have the Pz IV at the low end of that, the Sherman smack in the middle of it, and the Panther slightly above it. Not bad for the back of an envelope and some reasoning from doctrine, it seems to me.

As for the Panther's excess, that is obviously its front armor superiority to the short 75, and in covered terrain, down narrow roads, etc. There weren't all that many Tigers in Normandy, but there certainly were some, and the higher number of hits to kill them is testimony to their superior side armor. Those ~2-3 hits on the dead Panthers were probably 1-2 front and one lethal one from the side. With the Tigers, obviously the side hits didn't get them so easily, even at such short ranges. (Flat side hits, it should have been possible even for the non-Fireflies that close, but at any angle to the side, tougher).

As for the idea that the hits per kill probably went up after Normandy, I am not so sure about that. Yes, the engagement ranges certainly increased (although they also tended to the low in the Bulge, for woods - but not hedgerow low. The Brits were exactly in the hedgerows around Caen, though, either - but those are quibbles). But there are countervailing tendencies - 76 Shermans, improve TDs, and much more experienced U.S. tankers. That ought to have meant more flank shots and fewer frontal bounces from the heavier German makes. The hits to kill each Sherman or Pz. IV I doubt changed all that much. What longer ranges would do more readily, is reduce the hits per round.

If the shots in the Normandy fighting were above average chance to hit for the war, which seems likely, then those may have seen 4 shots per kill rather than 8. That would mean roughly 30-50% hit chances really achieved. Considering some longer range shots, shooting through hedgerows, and above all cases of moving shooter and moving target, that does not seem at all absurd to me.

On repeated firing into a tank to brew it up, I do not doubt it was done, but disagree entirely with the suggested motive. The tankers weren't trying to put the tank out of the war for good, in glorious fufillment of the 5 year plan from the great patriotic motherland. They were trying to make sure the bastard was dead, so it was not going to kill them, which they could not easily tell unless it was burning.

But within limits. If they had other targets, they would not bother. And they'd rather recover the wrecks than burn them. They just didn't have time to worry about those sorts of things in combat. "Is it dead? Not sure, shoot it. Sure? You are sure it is dead?" "Yes I am bleeding well sure goddammit, now let's get the hell out of here!"

But those rounds certainly got counted by the Brits in their hit to kill survey. They were not taking after action reports on when tank A ceased firing, but looking at the number of scars or holes in the wrecks. Incidentally, that is probably part of the reason the Shermans have more than 1 1/2 holes in them on average. I doubt the non-kill penetrations were any more common for the Shermans than the Pz IVs, considering the guns that were hitting them.

I find the 8 rounds per kill figure highly plausible for all sorts of reasons. And I think it means the hit probability of most of the shots actually taken was in the range of 15-25%. In Normandy the hit chances were higher because the shot were closer, undoubtedly.

Your comments were quite useful by the way, thanks for them.

[Jeff Duquette]

Monte:

Rexford's use of "we" refers to a group of armor enthusiasts that he is a member of. They have apparently been collecting data on the topic at hand for many, many, moons. So the use of “we” is Rexford giving credit to the group…rather “I” did this trajectory model, or “I” came up with such and such a conclusion.

[rexford]

Even if ideal trajectory due to range estimation error is 0.1m below the hull bottom, random up and down errors (dispersion) will bring some shots back onto the target. Some shots will have more powder than others, some less, some will weight slightly less, etc.

Who is "we"? Agree that my responses sound like something out of X-Files.

The work quoted in "my" posts is based on the efforts of a group of folks over a long period. I did most of the math but "we" developed the stuff through contributions and it seems right to use "we" instead of "I".

Just a manner of speaking. Sorry if it bothers folks.

[Jeff Duquette]

<BLOCKQUOTE>quote:</font><HR>medlinke said:

In game terms, close to 100% hit at 500 would be boring to me. In the 1.1 patch for instance, this leaves the game down to a mere modeling of paper, rock, scissors in terms of turret / hull rotation speeds. That Sherman that can get it's turret to bear before the Hetzer wins because of technology alone? Certainly there is evidence of this in real life, but in game terms, I enjoy the occasional ping as the round ricochets off the Hetzer's armor.<HR></BLOCKQUOTE>

Hello medlinke. This just goes to prove that English Majors are people too (kidding man).

I just wanted to say that it is not being suggested that 100% accuracy at 500meters is a realistic number. The idea here is to suggest what is behind the mechanics of gunnery…remove human error from equation and look at how tank gunnery is supposed to work. Ultimate gunnery…pure gunnery Why a range estimation that is off by 200 meters will still result in a hit...is it magic? Establish a "pure" gunnery model as your foundation. Than look at the model and figure out how humans might ****-up the equation (excuse my French). That’s pretty fundamental engineering. Figure out what the theoretical way in which stuff works and try to make it as idiot proof as possible.

Now consider Joe Concrete truck driver that dumps 15 gallons of water into his mix between the batch plant and the construction site. He wants to keep his mud wet becuase theres an accident on the freeway and its taking him more time to get to the construction site than he thought.

Once on site Frank Forman wants his mix a little more workable to get his mud around his rebar and form work…boom he adds another 10 more gallons of h2o into the mix.

So a mix that was supposed to have a theortical strength of say 4500 psi is now at 4000psi or 3500psi. That’s why engineers include factors of safety to accommodate these little things from resulting in our bridges and buildings falling over (some still occasionally tumble inspite of our efforts). We (we = the community of civil engineers) know the theoretical strength is 4500psi…but we also conclude that when all is said and done we should probably only count on a strength of 3500psi in our design.

No offense intended to any contractors out there…if we relied on engineers to build ****…nothing would ever get built. Design-build..a symbiotic relationship I hope that wasn’t to vague an analogy.

[:USERNAME:]

I would love for someone to explain to me what they think dispersion is and what accuracy means to them.

As an engineer I have to admit that people here use terms incorrectly but they seem to be in some agreement as to these words.

Hey. What do you think you are talking about? I want to know.

Lewis

[Jeff Duquette]

If a number of rounds of ammunition of the same caliber, lot, and charge are fired from the same position with identical settings used for deflection and elevation, the rounds will not all impact on a single point but will fall in a scattered pattern.

The points of impact of the projectiles will be scattered both in deflection and in range. Dispersion is caused by inherent (systemic) errors. It should never be confused with round-to-round variations caused by either human or constant errors. Human errors can be minimized through training and supervision. Corrections to compensate for the effects of constant errors can be determined from tabular firing tables.

[Guest Big Time Software]

jasoncawley,

Thanks for the well-thought-out post. I agree with most of what you said, and would like to add just one thing. I think that AP ammo loads also consider one extra thing which is supply, or rather the possible lack of it. A tank is often expected to be able to operate behind enemy lines, temporarily cut off from supply, which makes it wise to carry around extra AP ammunition. In other words, that ammo is supposed to last through more than one battle. But that's a minor point; I agree with your basic logic. AP ammo loads typically in the 25-45 range implies that the majority of them are expected to miss the target.

---

rexford,

Let me try that again with some simplified numbers. Let's take a shell traveling at a fixed velocity of 700 m/s (to keep this simple I'm not correcting for deceleration, but over short ranges it's not a big issue).

Shot drop at range 350m (time = 0.50sec) is 1.23m.

Shot drop at range 500m (time = 0.71sec) is 2.5m.

So the gunner who thinks the range is 350m when it's really 500m, will undershoot by 2.5m - 1.23m = 1.27m.

A T-34 is 2.4m high. Aiming at the vertical center means that there's a margin of error up or down of 1.2m.

Since the gunner shot too low by 1.27m, he has exceeded the 1.2m margin for error, and the shot misses. It comes close enough to make the T-34 guys wet their pants, probably but it's still a miss. My numbers here are totally simplified and I'm not trying to examine a particular gun or target tank down to the centimeter (i.e. the issue is not whether random gun dispersion can occasionally correct 10cm) but rather to make the general point that a sizeable but still rather modest mistake in estimating the range often equates to a miss, even at the relatively short range of just 500m. And of course this does not even begin to account for the various physical inconsistencies in gunnery (which you have mentioned) as well as the many other human factors and foibles that have been mentioned in this thread, and which would degrade accuracy even further.

In terms of the "pure" gunnery that Jeff mentions, in his entirely reasonable intent to separate the physical factors from the human ones before analyzing each and then combining them, I'd say that the near-100% accuracy at 500m or less, which you use in your spreadsheet (?), is probably correct. I'm sure you could verify that just by looking at published dispersion patterns for various guns on firing ranges (and you probably have, which is cool and I'd like to talk to you more about that when I have some time). But of course that's performance "in the laboratory" and doesn't equate directly to real-world combat. (Though it's a good place to start, followed by adding in the human factors, etc.)

---

Jeff,

Very good bit about the 8:1 shots-to-kill ratio in WW2. That surely implies a lot of misses!

---

I just want to say... damn you guys! Damn you all for putting these ideas into my head for future CM games! How am I supposed to sleep tonight?

Charles

[rexford]

0.21 seconds go by from 350m to 500m, so shot drops 0.22m in that distance due to gravity.

If constant velocity at 700 m/s, flight time to 350m aim range is 0.5 seconds.

Trajectory equation is:

-0.00001154 (target range)squared

+0.0040 (target range)

Descent angle at 350 meters is 4 mils, or 0.229°. Projectile drop from 350m to 500m if gravity stopped at 350m range is 150m x tangent 0.229°, or 0.60m.

Add 350m to 500m drop due to gravity (0.22m) to drop due to descent angle at 350m extended to 500m (0.60m), and round drops below aim point by -0.82m between 350m and 500m.

Trajectory equation predicts -0.90m below aim point at 500m.

Your analysis may not include gun barrel elevation factor, which is not a constant from 350m to 500m, as you may have assumed.

Trajectory equation with constant velocity probably should have a factor along the lines of "tangent(gun elevation) x range", which is the same as "tangent(gun elevation) x constant average velocity x flight time" and considers the vertical velocity given to the round by virtue of weapon elevation.

Above analysis assumed barrel is at same elevation as aim point on target, which might be true for StuG III or if firing tank is on slightly lower ground than target. This simplifies the math.

[rexford]

Regarding leveling the gun and the guide bubbles:

if a Tiger turret is aligned with the hull and is facing a Sherman, and the ground under the Tiger slopes at -1° from left to right track, does the gunner have to adjust the gun so it is level and will not fire at a skewed angle?

When tanks are on sloping ground and fire across the slope, the trajectory would seem to be impacted, may include a sideways error and this may contribute to short range misses as noted in a previous message.

Pitch, roll and yaw of the tank then becomes an issue. Our analysis considers everyone is on level ground, nice flat terrain, which is certainly not the case.

A 1° ground slope with unadjusted gun would result in quite a sideways error at 500m, if the err is based on distance times sine of angle.

If gunners have to adjust for ground slope, this would also decrease rate of fire.

[rexford]

Trajectory equation predicts that 700 m/s constant velocity will result in shot falling -0.9m below aim point with 350m against target at 500m. Did analysis consider term for distance x tangent (barrel elevation)?

Round loses 0.2m due to gravity from 350m to 500m, and loses 0.6m due to continuation of 350m descent angle. 0.8m total drop below aim point from 350m to 500m.

[Jeff Heidman]

What about the gunner just missing the target?

Are we assuming that the gunner always manages to even get the X on the center of mass to begin with? In combat conditions? While people are shooting at him? At a likely moving target?

Anyone ever play Counter-Strike? Bad analogy, granted, but bear with me. If you use a sniper (AWP) rifle, and get the center dot onto your target when you pull the trigger, you kill the guy every single time.

In theory, this is extremely easy. Had I never had to actually play the game against live opponents, I would think that it is a near 100% surety that I can kill a moving target as long as I could get a bead on him.

But you know, once you actually play, it gets kind of hard. Your adrenaline starts going, that guy is shooting back at you, he isn't moving in a consistent or predictable manner, and it seems like half the time I actually pull the trigger, I know even before I see the round hit that I missed. Why? Because I know that when I pulled the trigger that damn little dot WASN'T on the target. So why did I shoot to begin with? Good question, not really sure. I guess I thought it was, or maybe I was just hoping that it would be. Frustration? Nerves? Who knows?

A good friend of mines father was a police officer in Harlem fro almost 30 years. he generally refused to discuss specifics, but he had been in a fire-fight before, and certainly had known several fellow officers who had been in fire-fights. The thing he often stressed when he took us hand gun shooting is that you would be surprised how often people miss at ranges that it would seem to be literally impossible to miss. I think every single time we went shooting he stressed that the winner of a gun fight is almost always the guy who remains the calmest, not the guy who gets off the first shot. Because the guy who remains calm will fire his weapon the way he has been trained, and will take the time to do all those things that seem like they are so simple they can be skipped, especially at a range of several feet, like breathing and getting a good sight picture, etc. The other guy might be spraying bullets everywhere, but it only takes one hit to end the fight.

I am not trying to say that firing a tanks main gun is anything like playing Counter-Strike, or being in a short ranged pistol fire-fight, but I am saying that irrespective of range estimation errors, gun alignment errors, etc., that sometimes the gunner is just plain going to freaking miss. Even at 500m, which is basically point blank, sometime he is just plain going to miss. For whatever reason, when he pulls the trigger, the gun is not going to be pointed at the bad guy, and he is going to miss.

Jeff Heidman

[This message has been edited by Jeff Heidman (edited 01-15-2001).]

[Jarmo]

Some rough, but almost correct figures to help consider the drop.

These are the same for all weapons.

During the first half second the projectile drop is about 1,25 meters.

During the first second, the projectile drops 5 meters.

During 2 seconds, the drop is 20 meters.

[rexford]

The trajectory drop equations also include barrel angle effects, which may have been neglected in some results.

If StuG IIIg round maintains 700 m/s to a 500m target center point level with StuG gun, but is aimed at 350m target center, the initial barrel elevation is about 0.20°.

The physics equation for trajectory elevation as a function of distance and time is:

elevation = distance x tan (0.2°)-0.5 x 9.82 x (flight time) squared.

elevation at 350m is 0m, elevation at 500m is -0.72m below target center.

A hit with 150m range estimation error!

The simplified trajectory equation predicts -0.8m below aim point at 500m when gun is set for 350m range.

Previous calculations may need to incorporate gun barrel elevation into computations.

[Theron]

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

0.21 seconds go by from 350m to 500m, so shot drops 0.22m in that distance due to gravity.<HR></BLOCKQUOTE>

This is only true if the round has no vertical velocity after it was fired. We know that most likely the round has some vertical velocity after traveling 350m. I believe that Charles is assuming a zero gun inclination angle.

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

If constant velocity at 700 m/s, flight time to 350m aim range is 0.5 seconds.

Trajectory equation is:

-0.00001154 (target range)squared

+0.0040 (target range)

Descent angle at 350 meters is 4 mils, or 0.229°. Projectile drop from 350m to 500m if gravity stopped at 350m range is 150m x tangent 0.229°, or 0.60m.

Add 350m to 500m drop due to gravity (0.22m) to drop due to descent angle at 350m extended to 500m (0.60m), and round drops below aim point by -0.82m between 350m and 500m.

Trajectory equation predicts -0.90m below aim point at 500m.

<HR></BLOCKQUOTE>

I haven't figured out where you went wrong in the equations above, but I sincerely believe that you have made a mistake. Using a gun angle of zero you should get the same numbers as Charles did earlier. Not a 0.8m or 0.9m drop.

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

Your analysis may not include gun barrel elevation factor, which is not a constant from 350m to 500m, as you may have assumed.

Trajectory equation with constant velocity probably should have a factor along the lines of "tangent(gun elevation) x range", which is the same as "tangent(gun elevation) x constant average velocity x flight time" and considers the vertical velocity given to the round by virtue of weapon elevation.

<HR></BLOCKQUOTE>

The trajectory equation as you call it is

round height= tan (gun angle) * range -

1/2 * 9.82m/s^2 * deltaT^2

It is not the same as or derived how you describe it (unless the constant average velocity refers to the velocity in the x direction, but I don't think that this is clear). It comes from the following

(1) How the round moves in the y direction

round height= sin (gun angle) * gun_velocity *deltaT

- 1/2* 9.82m/s^2 * deltaT^2

(kinematic motion with constant acceleration, i.e. gravity)

(2) How the round moves in the x direction

range= cos (gun angle)* gun_velocity *deltaT

(kinematic motion with constant velocity, i.e. no air friction)

substitute for gun_velocity * deltaT in equation one using equation two and you get the trajectory equation.

Your use of the trajectory equation is correct, but I think that you miscalculated from Charles's numbers. I believe that Charles is assuming zero gun elevation. Given a gun elevation of zero his numbers are correct i.e. there is a drop of 1.2m not 0.8m or 0.9m when a round moves from 350m to 500m. This is because there is no initial velocity in the y direction with a gun elevation of 0.

If the gun has an elevation of 0.2 degrees you are correct in that the difference in drop is only 0.8m. Therefore the angle of the gun is crucial for how much drop normally occurs. If the gun happened to be slightly depressed by say 0.1 degrees then the drop between 350m and 500m would be larger at 1.84m-3.37m=-1.53m under the target. Therefore even with a more detailed kinematic equation a tank will miss the target if the gunner misjudges range by 150m.

The size of the miss depends on the gun angle as you pointed out before, but it seems to me that on a flat plain the tank would usually miss i.e. the gun angle would be at 0 to -0.? degress. Remember the simulation assumes that you are aiming at the center of mass which is 1.2m above the ground for a T-34 as Charles has pointed out.

Theron

[This message has been edited by Theron (edited 01-15-2001).]

[Guest Big Time Software]

rexford,

<BLOCKQUOTE>quote:</font><HR>0.21 seconds go by from 350m to 500m, so shot drops 0.22m in that distance due to gravity.<HR></BLOCKQUOTE>

This is incorrect. You are assuming that the body drops from rest at 350m, but that is not the case. At the 350m point the shot is already dropping at the rate of 4.9m/s (and still accelerating), so in 0.21 seconds it will actually drop 1.27m as I calculated above.

Charles

[Jeff Duquette]

I guess I missed this during the switching out of problem parameters...what was the starting height of the projectile...Ho?

Vo = 700 m\s

gunners range setting = 350m

target distance = 500m

target height = 2.4m

aim point = targets center of visible mass

[Theron]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Jeff Duquette:

I guess I missed this during the switching out of problem parameters...what was the starting height of the projectile...Ho?

Vo = 700 ms

gunners range setting = 350m

target distance = 500m

target height = 2.4m

aim point = targets center of visible mass<HR></BLOCKQUOTE>

Jeff,

Treat the gun as the reference height i.e. zero meters and calculate the rounds drop versus this height. If you are trying to calculate the gun angle then you need to know

1)the height of the shooter (i.e. gun) relative to some fixed reference

2)the height of the target (center of visible mass) relative to the same fixed reference

3)the estimated range between the two

In Charles' example he treats the gun angle as 0 degrees and measures the amount of drop from in height from the barrel out to 350m and 500m. The difference between these two is the vertical error from improperly ranging the target.

Theron

[Guest Big Time Software]

I've been using a gun angle of zero degrees in my examples which is probably too simplistic. So to cap this off let me offer one more example, fleshed out, to illustrate why near-100% accuracy at 500m is not realistic.

Assume constant projectile speed of 700m/s.

Assume target is at range of 500m.

Assume target is a T-34 tank, which is 2.4m tall to the top of the turret, and 1.6m tall to the top of the hull. Vertical midpoint underneath the turret is therefore 1.2m above the ground, and 0.8m elsewhere. Let's split the difference and assume the gunner aims at a height 1.0m above the ground. And for the sake of simplicity we'll assume the gunner's gun is also 1.0m above the ground and that the ground is flat.

Therefore, if the gunner mistakenly estimates the range at less than 295m or greater than 778m, the shot will be a miss. (I'm skipping the math but if anyone really wants to see it I'll post it).

Further, if the shot is off the turret laterally, which could happen simply from a gust of wind, then it can only hit the (shorter) hull, and in this case the parameters for a miss are even greater. If the gunner overestimates the range at anything above just 617m, the shot will be a miss in this case. That's only a 23% overestimation, which isn't very much at all.

Mistakes like this were commonplace. I know that may sound crazy but it's true. I remember reading about one tank commander who had the gunner fire his first shot at something like 800m. After about four or five shells they finally got the range. If I remember correctly, it was only 300m! Whoops, 166% too high at first. I was staggered by the degree of initial error. Of course I'm not saying everyone did this badly, but clearly some people did, frequently enough to matter.

It's hard enough to judge range even when people aren't shooting back at you.

And of course there are the dozen or so additional physical and human factors that degrade accuracy which have been mentioned above, which only strengthen my point.

So that's why I say that near-100% accuracy at 500m is far too generous.

Charles

[Simon Fox]

So perhaps all you physics gurus may like to explain why a tank firing uphill is more accurate, especially at long range.

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

Muddying the waters as usual.

[Jarmo]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Simon Fox:

So perhaps all you physics gurus may like to explain why a tank firing uphill is more accurate, especially at long range.

<HR></BLOCKQUOTE>

If I got you right, assuming you're shooting towards a hill.

If you shoot 2 meters too high, firing uphill, the shot explodes right behind the target.

On level ground, 2 meters high goes a long way behind the target.

This leads to easier bracketing.

[Jeff Duquette]

This is a schematic of an M38 gunners sight, commonly found in earlier model Sherman Tanks. For M61 AP, M72 AP and M48 super charged HE the stadia lines with the little 1, 2, and 3 below the lower left side of each line corresponds to range in 1000’s of yards. The dot with the circle around it corresponds to a range of 600 yards (for the metrically challenged conversion is 1ft = 0.3048m).

Now when a WWII gunner engages targets at various ranges (lets forget lead for now) he cranks on his elevating handwheel until the appropriate range line in his sight is on his target. In the first picture (upper left on the image above) the target is at 600 yards. Pretty basic. So as range increases super elevation of the main gun increases…that’s the launch angle. It’s the theta term in the position relationship:

r(t) = (V(t) cos (theta))ti + {h + (V(t) 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

V(t) = velocity (not constant…very important…velocity in our equation above is a function of time)

Now the engineer who has designed and tested the relationship between gun sight and gun, knows typical trajectories of the munitions types fired. He knows the velocity of the M61 AP, M72 AP and M48 HE rounds vs. range, and thus the effects of drag forces on projectiles. How does he know all this stuff…test firing.

Important: Flight path/trajectory is not parabolic. Why? Because velocity is not constant. A projectile has to push air out of its way as it speeds toward its victim. Drag.

The design engineer working on our Sherman also knows that any object that you drop will accelerate towards the earth at 9.8 m/s^2 or 32 ft/s^2.

When GI Gunner lines his sights up for a 600 yard shot on the center of mass of his target, his gun is being elevated into such a way that launch angle considers:

1)Velocity of his munition is not constant

2)The round will fall to the earth…accelerating at 9.8 m/s^2

Is GI Gunner figuring this all out in his nerve racked brain as he aligns his gun on his next target. No. The design of the gun and sight relation accounts for the physics of the problem. Superelevation encompasses shot fall from gravity as well trajectory path.

Cookie question...when firing in a vacum (i.e. no drag, just gravitational effects) what launch angle will result in the longest range being achieved?

All the above factors need to be considered to understand the problem at hand. You can not separate out fall height and explain why gunners miss with a 150 meter range estimation error. Why? Because launch angle will not be zero, and projectile velocity is not constant. Superelevation combines fall of shot from purely gravitational forces along with non-constant projectile velocity, to result in a hit on the intended point of aim.

Consider the 350 meter shot problem once again. If we are relying on purely gravitational forces (1/2gt^2) than I agree…the gunner will miss a target at 500 meters. However in the same example the gunner will not hit his aim point on his 350 meter range intended target either. He will actually get a hit somewhat below the aim point. Why? Because gun alignment relative to the horizontal, even at a target 350 meters away, would not have superelevation = zero. This is fundamental. This is why the initial height of the projectile question was alluded too.

Now consider the following problem from the “Tiger Fibel”. It’s all there, no floating problem parameters. Now, using only r(t)=1/2gt^2 explain why various hits and misses are occurring.

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

[Matthew_Ridgeway]

*punt*