"Technique for computing compound angles of armor???" Topic

All of you tankers know the problem with attempting to compute compound angles (vertical slope and lateral angle) in a game. It's too much of a hassle even if you'd like to use it.

Last night I found a paper from the Aberdeen Proving Grounds Test and Evaluation Command that has a Compound Armor Nomograph.

Link: tinyurl.com/k4qwuoa

Take a straight edge and put one end on the Horizontal Oblique Angle (lateral angle) to the target and align it with the Vertical Oblique Angle (armor slope) on the right side. The middle Compound Oblique Angle will read in the center ruler.

Next go to the armor strength chart on the right. This is from a spreadsheet I programmed to give the true armor thickness based on slope. In the example the target is at a 55 degree angle to the firing unit and the target surface being hit is 75mm sloped at 35 degrees. This equals a 62 degree compound angle. This gives a reading of 195mm of armor (actually about 220mm if not rounding off).

I did this all late last night and I need some people more knowledgeable than me to check it out.

Thanks
Wolfhag

Are we going to assume lasers or shells with trajectories. In which case you have a parabolic angle to calculate for true normal to be derived.

[ ducks ]

Full marks for trying but I think even with these tools to help it's more trouble than it would be worth.

I tend to find in my games there are few really close calls – either it's an easy kill or a very unlikely one. Then we have the random factor to cover all our inevitable fudgery.

But I am curious how you get on with this. It could maybe be worth it in a single tank game where a player commands only one AFV.

Are we going to assume lasers or shells with trajectories. In which case you have a parabolic angle to calculate for true normal to be derived.

You have to start somewhere.

Wolfhag it does work. Tried 2x45 degrees and 2x60 degrees. By induction all angles work. :)

Tractics had a chart like this included in it to calculate armor thickness for penetration consideration.

You also need to include shells angle to the horizon (which is based on the shell's ballistics and is something you could calculate).

IMO, not worth the effort to check because your effective angle will also vary based on how level the bloody tank is.

A tank coming down a hill effectively reduces the slope of the glacis.

Look, a 12" difference between left and right tracks of a Sherman is roughly a 7 degree change in side armor slope (German tanks are a bit wider, so that's a lesser change for them).

It's a 4-variable angle problem, which would require 3 nomograms.

At a bare minimum, you'd need to reference 2 nomograms. First is the one you linked, then there's the incoming shell angle versus armor compound angle nomogram. I figure dice could account for the impossible-to-know tank level/lack thereof.

And this still doesn't account for the tendency for rounds smaller than the armor thickness to skip off, or for more modern rounds to 'turn into' the armor.

For modern rounds, armour slope makes very little difference as the Swedes discovered when they test fired modern AP ammo at their S tanks. Something to do with the relative mass, velocity and surface area or something.

Mobius, Thanks for the feedback.

Martin, you're right but I'm only doing WWII.

Sundance, I'm not familiar with the Tractics chart but one of our guys was using some of the Tractics type rules and techniques and the one he uses for compound armor angles is very different from the one from the Aberdeen Proving Grounds.

Lion, you're completely right about the different nuances of vertical and horizontal angles being generated by the target above, below you or at the same level going down a slope, etc. The possibilities are almost endless. For most high velocity rounds the angle of impact will be less than 5 degrees (IIRC) so it could be just rounding down to the nearest 5 degrees on all shots to accommodate that or 10 degrees for lobbing in lower velocity HE rounds. Then you get into the mess of did the round hit a vertical or horizontal surface. You've got to draw the line somewhere. I'm thinking of rounding down the spreadsheet armor figures to 5mm increments.

I'm more interested in simulating the lateral/horizontal angle as I feel that has a bigger impact, especially when the mostly vertical side armor is being hit at a 50-70 degree angle as from the spreadsheet I did that pretty much effectively doubles the armor. At 50 degrees a 35mm armor increases to 66mm and at 60 degrees increases to 91mm.

A tank with a glacis sloped at 56 degrees (like some Shermans) from the vertical with 51mm of armor is effectively 111mm of armor if shot at from head on (rounding both figures down to nearest 5 degree increment). If shot at from 45 degrees the chart from Aberdeen shows a compound angle of 65 degrees increases armor to 165mm or rounding down to 60 degrees it is 130mm. That's almost a 30% to 50% increase if I'm reading and doing this right. Using the nomo and pre-calculated armor figures printed on opposite sides on one sheet makes it fairly easy and no math, odds, die roll, etc. I think rounding down the armor value and compound angle to the lower 5 degrees increments can include some of the nuances. I do have a variable armor penetration routine that can account for many of the other and unknown factors, which are many and impossible to simulate in a playable game. It's never going to be perfect but for us it's a step in the right direction.

Right now I'm not so concerned about playability and if people will like it or not. I want to make sure I'm on the right track and numbers/calculations are correct.

Wolfhag

More precision doesn't translate to more accuracy. Given the time-frame of a turn the tank could have many different angles within that time. It is moving up and down over terrain that increases or decreases the armor angle from second to second. It may change its orientation to the firer several times within the turn. So you should perceive the angle as a window bounded by limits. If your armor calculation gets the number somewhere in that window then that is enough. In Panzer War I try to also add a random factor to spread the possible outcomes around (the variable penetration table) but still stay within the limits of the window.

Presumably if you had two rounds of equal mass but one was long and thin and the other short and fat, the first round would be more likely to defeat sloped armour?

I ask this because when either round strikes a sloped glacis, it will tend to want to rebound off at the same angle at which it arrived. The longer the round, however, the greater the moment of inertia acting through the rear end of the round; holding it "down" on its incoming trajectory.

By analogy (yeah, I know), if you shove a pool ball from point A somewhere on a pool table to point B somewhere on the side cushion; and if you shove a pool cue of the same weight as the ball from A to B – the ball will bounce off and roll away but the cue will not.

Consequently, a long thin round fired at sloping armour will defeat it more frequently, ceteris paribus, than a short fat one.

Does this explain how to defeat the armour of an S tank?

Mobius,
I completely agree about the accuracy and time frame. That's a good point. We are using 10 second turns. Most tanks are going to make just one turn in that amount of time unless maneuvering through/around obstacles at low speed. I guess we could put an artificial rule restriction on turning movement for that. Even then it can be a big swing. Most rounds have a MV of about 800m/second which means anywhere from .5 to 3 seconds to hit a target that may be moving after or during the shot is taken. If you fired at a static tank that starts a brake turn he could rotate his hull up to 90 degrees in 3 seconds. At least that's what I've seen of videos of other WWII tanks under ideal conditions. I'm not attempting to come up with some exact formula. I'll have to think about how that "window" would be formed.

Cuirassier: The AT rounds in WWII behave differently than long rod penetrators. I think most WWII AT rounds will bounce on 70+ degree slopes.

Thanks,
Wolfhag

Wolfhag, you aren't going to have infantry in your game? Because at 10 second turns their typical turn movement would be about 12-15m.

Presumably if you had two rounds of equal mass but one was long and thin and the other short and fat, the first round would be more likely to defeat sloped armour?

Not always. You have a T/D (thickness over diameter) factor to take into account. If hitting at an obtuse angle the short fat projectile will turn into the plate and reduce its effective thickness i.e. normalize the angle. But the velocity and nose complicates things. If the nose is hard and blunt it will try to normalize the angle better. If it is ogive shaped it will tend to glance off.

For example I ran a 14lb ogive round of 3" and 1.5" diameters at 2000 ft/s vs 1" plate. I change the angle of the 1" plate from 0° to 75° in Nathan Okun's M79APCLC formula. The 1.5" diameter shell penetration beats the 3" up to about 40° then the 3" penetrates more.

It certainly doesn't help that modern long-rod penetrators are pushing 1700m/s muzzle velocity, either. Very flat trajectory when compared to a PAK43, nevermind an M3 75mm tank gun!

Mobius,
Infantry? Absolutely! I was in Marine infantry in the early 1970's. That's US Marines for our British Blokes. I did spend some time with the Royal Marines at Lands End and FFL 2nd Para on Corsica. I also spent the night as a guest on the HMS Hermes when she was at Port Everglades, FL. I took the ships Rugby team out on the town and they took me back to the carrier to share their grog rations (canned beer if I remember right) and I had breakfast on the ship in the morning with a terrible hangover.

I can relate to the WWII equipment because that's pretty much what we had back then. Same equipment, pack, helmet and web gear, M-14 (basically a modified M1), 3.5" rocket launcher, WWII model flame throwers and 60mm mortars. We did have M1919 LMG's in training but M60's when we deployed. We had the M-48A3 tank with the same WWII 90mm gun. The PRC-25 was a smaller version of the SCR-300. We still had a few WWII Okinawa and Iwo vets at Regiment level. I like tanks but am still a Grunt at heart.

Yes, ten second turns are a bitch with infantry. My thoughts are they would basically keep their heads down until able to engage with HHAT weapons or ambush. Defensively not much moving while enemy tanks are advancing. Definitely AT guns too. The tanks would also advance at walking pace with the infantry (Americans using Walking Fire) and the Russians could ride on them. For a straight infantry game I'd have 30-60 second turns. The reason I'm trying 10 second turns is that pretty much corresponds to the ROF of most tanks 5-6 rounds/minute and you don't need to go into a lot of the Opportunity or Cover fire. With the ten second turns a tank can get 3-4 kills in one minute without much abstraction. Especially if engaging them all at the same range. I'm working on a spotting/reaction system too. It's turning out a little like the Nuts! game as there is the suspense of spotting an enemy vehicle and trying to get your gun on him but I'm not going to be activating every member in the crew. I'm not trying to make things real complicated (really) as right now I'm getting everything together and then when I see what I've got and the options I'll start streamlining. It was a real mess last year but the more I talk to other people the further along I get. This is a great forum for that and the stuff you and Salt have has really helped.

Thanks,
Wolfhag

Wolfhag, I can see how a 10 second turn would be pretty good for a tank to tank gun fight, however for other things it's not ideal.
Think about the orders or command decision cycle. Getting new orders or changing orders to units on a 10 second basis is pretty unrealistic. You might have to resort to some clunky step by step system to slow the delivery of orders.

Even the typical 60 second or Panzer war's 75 second turns for evaluation of situation and change of orders is pretty quick.

Mobius,
When I got started on this stuff it was not really my intention of creating a combined arms game. I wanted to model a gunnery sequence using the info from Bird & Livingston's book using an aiming point with a randomized round dispersion rather than a To Hit # with die roll modifiers. Sort of a gunnery simulation. I'm looking at different sequences of play including things like orders, artillery, etc. The clunky step by step system to include other aspects I'm not that interested in. My interpretation is that most tank-tank engagements were fairly short term with a battle involving a number of these short term duals/engagements. A two minute dual/engagement would involve 12 ten second turns. Not bad for a game.

I never played Panzer War but my son and I spent hours playing WWI Sea War. I liked the difference in FC systems and the salvo differences. Why did you pick 75 second turns for Panzer War?

Wolfhag

Why did you pick 75 second turns for Panzer War?

That goes back a long way. It's likely to have something to do with scale.
Each turn you have to touch each unit that is moving. I wanted the infantry to move an appreciable amount of distance. Walking infantry averages about 3 miles an hour or ~4800m/hour. 75 seconds is 1/48 of an hour. So infantry moves 100m a turn or 50mm @ 1:2000 in PW scale.

Mobius,
This is an alternative method I've looked at. To get infantry moving at 50m/turn I'd need 30 seconds turns. That's the equivalent of three 10 second turns. That could be done by having vehicles three chances to perform an "action" in a 30 second turn. One action could be spotting, acquiring or firing, etc. Any firing would use a "To Hit & DRM" technique with firing being rolled on a binomial table to determine the number of hits based on the ROF. So if you did have a ROF of 3 at a moving target and the binomial table showed one hit the first two shots would be assumed to be misses and the third one hits. However, if the third segment of the targets movement took him out of the LOS the third shot would also be a miss.

At the start of each turn (Orders Phase) the player would stack three action chits for each unit, in order that they are to be performed. Each of the three phases of a turn (10 seconds) the order is flipped and seen how it interacts with the target.

Interaction Example: A vehicle has fire, move, move orders. An enemy unit that spotted that vehicle last turn has acquire, fire, fire. The second unit would have acquired the target when it was static but fired at it as a moving target.

This would be pretty much simultaneous movement, no activation and good FOW as you don't know what the enemy is going to do next. This is more playable with larger sized units and infantry but you could not use the targeting overlay and detailed firing sequence. Can't satisfy everyone. If I've thought of this I'm sure someone has tried it before.

Wolfhag