What Tiger Vets Say About Range Estimation

[rexford]

JasonC's point about aim variations is on the mark with regard to battlesight aim, the major problem is trying to guess how large the factor would be. The high accuracies that are predicted with perfect aim at target bottom would be lowered if the aim point were allowed to vary about the bottom of the target, which would be expected in real life.

On another subject and this is the last time I will say it, the Germans were aware (published ballistic tables) that if they aimed the 88L56 at the bottom of a 2m tall target and set the range to 900m, they would have a good chance of hitting the target at all ranges from 0m to just under 900m. Battlesight aim in everything but name.

[Mr. Tittles]

It is worth noting that you dial in 1000m range and then point at the target bottom. If you point at the target bottom and THEN dial in 1000m, then you will be off.

[rexford]

Originally posted by Mr. Tittles:

It is worth noting that you dial in 1000m range and then point at the target bottom. If you point at the target bottom and THEN dial in 1000m, then you will be off.

Battlesight aim works by aiming at the target bottom and then elevating for an 800m to 1000m shot, which is how my calculations went earlier in this thread.

If one elevated the gun for an 800m to 1000m shot and then pointed at the target bottom they would probably end up with the same situation as doing it in the reverse fashion. One is basically adding the angle from gun to target bottom to the elevation needed for an 800m to 1000m shot, and it would seem that the order would not be important.

[Jeff Duquette]

“Lorrin Said: No, the height of the Tiger gun above the ground is not a factor as long as it doesn't become radical (like on top of a 20 story building).”

I just wanted to clarify something on this thread. Lorrin is quite right in his above assessments in that there is very little effect on shot placement relative to the gun height. The angle between the line of sight and muzzle superelevation is quite tiny (that is unless the target or firer are at vastly different elevations, or the target is at extremely short range).

But this all assumes that the tank commanders range estimation to his target is perfect. The significance of barrel height does come into play when range estimation errors are incorporated into the problem. So while the trajectory between a gun firing from a hull down position is basically the same in shape as the trajectory fired from level ground, the trajectory is not originating from the same height above the ground. In other words ranging errors will come into play when trying to hit a target dependent upon the height of the firer and the height of the target.

Example:

For the purposes of developing trajectory plots, my bullet is: (although any bullet will suffice for this example):

Springfield 30-06 Norma Full Jacket (17651)

Diameter = 0.308-inch

Weight = 146-grains

BC = 0.422-lbs/sq.-inch

G1 Drag Function

Muzzle Velocity = 2772-fps

Standard Metro Atmospherics

This example focuses upon bullet trajectory and the ability to hit a rather large target at long rifle range from either a prone or standing position even if I am not estimating my range to the target correctly. Hypothetically speaking, lets say I have a rather large piece of plywood that I am using as my target. The plywood target is say 76-inches in height. It’s just a big rectangular piece of wood that extends from ground level to 76-inches high. It's also wide enough such that any inherent lateral bullet dispersion will still strike the plywood target.

Let’s also say that my aim point is 72-inches above the ground. For my range estimation error lets say my large piece of plywood is set 400-yards away from my firing position. However, I guess that the range to the target is actually 500-yards and line up my sights accordingly. I now fire from both a prone position and from standing position.

The Prone Position. You will find that I will still hit the big piece of plywood if I am firing from a prone position even if I overestimate the actual range to the target. Moreover the maximum height of the bullet trajectory still passes through the "footprint" of the large plywood target.

The Standing Position. If I am aiming at the exact same spot as I did from the prone position (i.e. my aim point is still a bullseye placed 72-inches above the ground on my sheet of plywood) and I have the same range estimation error, my bullet trajectory will not pass through the footprint of my sheet of plywood. The bullet actually sails over the top of my plywood by about 10 or 11-inches.

Sooo…with that same 500 yard sight zero, and actual target distance of 400 yards the bullet height at 400yrds is about:

prone: 74"

standing: 87"

My target height is 76” in height. So I’ll still schwack the plywood if I am prone, but will not hit the plywood if I am firing from a standing position.

Sorry – normally I would post the trajectory plot to better demonstrate my point, but that is not so simple for this web site. If someone wants to examine the trajectory plots I will be happy to email them along.

[Mr. Tittles]

German AT fire was leveled at the bottom of the target. So this must be taken into account.

I know sights had level bubbles but there must be a way to rectify the height difference. It clearly makes a difference. My simple example of two firers at 0,5m and 2m firing level (0 degrees) clearly demonstrates that it does make a difference.

[lorrin]

Originally posted by Jeff Duquette:

“Lorrin Said: No, the height of the Tiger gun above the ground is not a factor as long as it doesn't become radical (like on top of a 20 story building).”

I just wanted to clarify something on this thread. Lorrin is quite right in his above assessments in that there is very little effect on shot placement relative to the gun height. The angle between the line of sight and muzzle superelevation is quite tiny (that is unless the target or firer are at vastly different elevations, or the target is at extremely short range).

But this all assumes that the tank commanders range estimation to his target is perfect. The significance of barrel height does come into play when range estimation errors are incorporated into the problem.

With all due respect to Jeff, something about his analysis does not seem correct.

We're talking about battlesight aim where the Tiger doesn't care what the range to target is as long as it is less than the gun setting of 800m to 1000m.

I've posted several examples on this thread where a Tiger aimed at the bottom of a target at 200m and elevated the gun for a 1000m shot, and the round reached the target at the same height above target bottom whether the Tiger gun was 2m above target bottom or 0.5m below.

Let's do a simple example for the doubting Thomas's out there, and we'll use a simple trigonometric model that doesn't require access to complex ballistic programs (there will be a small error in the details but the overall conclusions stll hold).

CASE 1

Tiger gun is 2m above bottom of T34, T34 is at 550m from Tiger and Tiger commander couldn't care less what the actual range is.

Aim at bottom of T34, so gun is depressed -0.208 degrees,

Set gun for 1000m shot, so gun is elevated 0.50 degrees above initial aim at target bottom.

End result, gun is elevated 0.292 degrees above horizon.

What is height of round at target?

2m (gun height) + 550m x tangent (0.292) - 0.5 x 9.81 x 0.72 squared or 2.26m above target bottom.

CASE 2

Tiger gun is -1m below bottom of T34, T34 is at 550m from Tiger and Tiger commander couldn't care less what the actual range is.

Aim at bottom of T34, so gun is elevated +0.104 degrees,

Set gun for 1000m shot, so gun is elevated 0.50 degrees above initial aim at target bottom.

End result, gun is elevated 0.604 degrees above horizon.

What is height of round at target?

-1m (gun height) + 550m x tangent (0.604) - 0.5 x 9.81 x 0.72 squared or 2.26m above target bottom.

CONCLUSION

For battlesight aim, height of gun relative to target bottom doesn't make a hill of beans of difference as long as the initial aim is at target bottom and the subsequent elevation rise fo range setting is the same.

The real trajectory will be a little lower since air resistance resists the initial upward motion and then resists the downward motion.

[Jeff Duquette]

Remember that battlesight assumes no real focus on range estimation by the TC or gunner, so range errors are inherent with the technique.

Now my example was not focused on battlesight per say. I am simply quantifying the effects of initial barrel height and its effect on range estimation errors. I totally agree with your previous explanation – assuming no range error is thrown into the mix. The location of the two particular trajectories in my above example do not plot right over the top of each other -- that is unless I rotate one or the others axis as well as shift the vertical axis up or down. If I rotate and do a vertical shift, than the two trajectories exactly parallel each other. But the real path to get to my aiming point is different (this concept is I suspect easy for you, but will doubtless create some confusion for a few – no offense intended to anyone). The real paths can’t be the same for obvious reasons (I’ll post something at Yahoo so you can better see what the heck I’m talking about).

In my example, one trajectory starts at 6 or 8 inches above the ground, and the other starts about 60 or 70-inches above the ground, depending upon how tall you happen to be. I’m pretty tall so I’m at even more of a disadvantage. Both bullets have to get to the same aim point set at 72-inches above the ground at a range of 500-yrds. So the trajectory of my standing position bullet increases in elevation to a point and than drops back down to hit my aim point at 500-yrds. Conversely from the prone position my trajectory is rising during just about its entire flight before hitting that exact same aim point at 500-yrds. So you are right that there is no noticable effect in my zero range setting wheather I shoot from the prone or from standing. The angle is just to small to matter. But I'm speaking of the effect of a target range that is different from my zero range.

Now back to battlesight – like I said at the start, let’s remember that battlesight assumes no real focus on range estimation by the TC or gunner. Thus we should conclude that range errors are a defacto part of the game. Battlesight is simply what sort of range setting I need to ensure a high first round hit probability against a surprise target. I cut my engagement time down considerably if I’m not trying to figure range. It’s a preset range used for snap shot engagements. There are a number of assumptions involved with the particular flavor of your optimum battlesight range setting. Such as; the most likely target you will encounter given the tactical situation; visibility; and the local terrain. If I'm expecting infantry and antitank guns I will likely have HE/spgr up the spout and will probably use a different preset range than if I’m expecting to encounter armor.

But the effects are the same regardless. If I engage with battlesight with a preset range of 800m and my target is only at 600m (or whatever), the likely hood of hitting my target with my first round will be directly effected by the barrel height (and thus my maximum trajectory height) and the target height -- that is if we assume the gunner employs the same initial aim point in both cases -- i.e. aim center of visible mass or whatever a particular tank gunnery doctrine suggests to use for the aim point. It's simply a function of trajectory height at any given point relative to target height and initial barrel height.

Obviously if the initial round sails over the target, and either the TC or gunner actually sense their tracer flying over their target they will make an elevation adjustment -- assuming they survive long enough. Think about it in terms of a guy sitting in a hull down overwatch position relative to his track mate that's not hull down.

[lorrin]

Jeff,

Regardless of barrel height, aim at target bottom with the same range setting on the gun results in the same trajectory height at the target.

The example I presented shows this.

Now, let's go one step further and look at the case where a Tiger sees a 4 mil high T34 and aims the gun for a 750m shot based on the perceived height, but the actual range is 500m. The T34 is only 2m above ground due to dips and folds and looks 4 mils high, so a 750m range estimate results.

CASE 1

Tiger gun is 2m above T34 bottom.

Tiger aims gun at target bottom, angle is -0.229 degrees.

Tiger sets gun elevation for a shot of 750m + 4 x 1/2 x 100m or 950m. Elevation angle is 0.465 degrees.

Final angle = 0.465 - 0.229 = 0.236 degrees

Trajectory height at 500m T34 equals:

2m + 500m x tangent (0.236) - 0.5 x 9.81 x 0.66squared = 1.92m above target bottom

CASE 2

Tiger gun is -2m below T34 bottom.

Tiger aims gun at target bottom, angle is +0.229 degrees.

Tiger sets gun elevation for a shot of 750m + 4 x 1/2 x 100m or 950m. Elevation angle is 0.465 degrees.

Final angle = 0.465 + 0.229 = 0.694 degrees

Trajectory height at 500m T34 equals:

-2m + 500m x tangent (0.694) - 0.5 x 9.81 x 0.66squared = 1.92m above target bottom

So there we have it, regardless of what type of aim (Battlesight or aim at bottom with adjusted range estimate), and regardless of how high or low the Tiger is with regard to the T34, THE ROUND REACHES THE T34 AT THE SAME TRAJECTORY HEIGHT ABOVE TARGET BOTTOM.

Because we are discussing the effects of Tiger gun elevation upon the accuracy of the rounds, and meaning no insult, let me state that I am not interested in examples with rifles and will not really look very closely at the results.

If someone else will run a trajectory program for the above examples and present the results here it would be good for comparison purposes; I already did the computer runs and the results support the conclusions in this and my preceding post on this thread.

[ September 12, 2004, 02:39 PM: Message edited by: lorrin ]

[lorrin]

Now let's look at things from the Allied perpective for a change, and we'll stick with tank guns since that is what is under study.

Also using the same simple trigonometric model.

Example Details

===============

A 17 pdr armed Firefly is getting ready to fire off an APCBC round at a PzKpfw IVH that is 600m away but the Firefly crew thinks it is 800m distant. Only 2m of the panzer height is visible.

0.70 seconds to 600m

0.95 seconds to 800m

CASE 1

Firefly gun is 2m above panzer aim point (3m above bottom and 1m above top).

0.317 degree setting for 800m shot using simple trig model.

Angle from Firefly to center of panzer is -0.191 degrees.

Trajectory height at panzer equals:

2m + 600m x tangent (0.317 - 0.191) - 0.5 x 9.81 x 0.70squared, or 0.92m above target center.

CASE 2

Firefly gun is -2m below panzer aim point (1m below bottom and 3m below top).

0.317 degree setting for 800m shot.

Angle from Firefly to center of panzer is +0.191 degrees.

Trajectory height at panzer equals:

-2m + 600m x tangent (0.317 + 0.191) - 0.5 x 9.81 x 0.70squared, or 0.92m above target center.

Son of a gun, same result whether 17 pdr is 2m above or 2m below the aim point. Just as I been saying, makes no difference if gun is a few meters this way or that.

As an aside, the math model we use to predict the impact of range estimate errors predicts that 17 pdr APCBC fired at 800m against a 600m target will reach the target 0.85m over the aim point regardless of relative height (gun vs aim point). As stated in the last post, the impact of upward and downward air resistance is not considered in the simple model I used and actual trajectories will be a tad lower (0.85m vs 0.92m).

[Jeff Duquette]

Lorrin Said: Regardless of barrel height, aim at target bottom with the same range setting on the gun results in the same trajectory height at the target."

Absolutely right. As I said I have no argument with you on that point.

But I'm throwing in the additional caveat of range estimation error and its effect on shot placement relative to barrel height and target height. It makes no difference whether we are talking about rifles or tanks. My rifle bullet example is something alot of folks here can probably better relate to. But ballistics are ballistics.

The main point to remember is that – like I said – battlesight is by its very nature a shooting method that ignores range estimation and therefore will more often than not include an MPI that is offset from the point of aim as a result of the ranging error. But that is why we are trained to shoot center of visible mass.

Anyway, I don’t really want to argue. Just have a look at what I’ve said and churn it around a bit in that big brain of yours.

Best Regards

Jeff D.

[lorrin]

Originally posted by Jeff Duquette:

Lorrin Said: Regardless of barrel height, aim at target bottom with the same range setting on the gun results in the same trajectory height at the target."

Absolutely right. As I said I have no argument with you on that point.

But I'm throwing in the additional caveat of range estimation error and its effect on shot placement relative to barrel height and target height. Best Regards

Jeff D.

Two of the three examples I provided looked at the effect of barrel height on shots where there were range estimation errors, and barrel height did not influence the result. Your additional caveat has already been addressed.

[lorrin]

Jeff,

Yesterday was a bit hurried and I really should look at the example you provided for a rifle shooter at different heights. You made the effort to look at the topic under discussion and you deserve a fair review of your material.

If you will post the flight times of the bullet to 400 and 500 yards, and the elevation range to fire at a 500 yard target that is even with the gun barrel, the exact situation will be looked at in detail.

During the interim I used some stats for the U.S. 0.30 caliber machine gun bullet:

2775 fps muzzle velocity

1925 fps at 400 yards

1725 fps at 500 yards

Flight times are about 0.511 seconds to 400 yards and 0.667 seconds to 500 yards.

The elevation for a 500 yard shot at a target level with the gun is about 0.274 degrees using the simple model that has been applied in this thread.

PRONE FIRER

Assume gun barrel is 12" above ground.

Angle from barrel to target aim point is 0.238 degrees. Firer elevates gun to 0.238 + 0.274 degrees, for 0.512 degrees.

Height of trajectory at 400 yards is:

1' + 1200' x tangent (0.512 degrees) - 0.5 x 32.2 x 0.511squared or 7.52' (90.23 inches), for a miss by 18.23 inches high.

STANDING FIRER

Gun barrel at 66 inches or 5.5'.

Angle from firer to target aim point is 0.0239 degrees. Add elevation for 500 yard shot to obtain final angle of 0.298 degrees.

Elevation of round at 400 yards is:

5.5' + 1200' x tangent(0.298 degrees) - 0.5 x 32.2 x 0.511squared or 7.54', which equals 90.45 inches. Bullet flies over aim point by 18.45 inches. About the same as prone firer situation.

Based on the above analysis, it appears that standing and prone firers miss the aim point by about the same amount for the same aim point and range estimate.

Lorrin

[lorrin]

I ran Jeff's example on a ballistic computer program using his data for the rifle round and filled in the missing pieces with data from the U.S. 0.30 caliber AP bullet:

bullet diameter=0.308"=7.82mm

bullet weight=146 grains=0.009432 kg

T1 projectile with 0.55 form factor

2775 fps muzzle velocity

1925 fps at 400 yards (U.S. 0.3 caliber AP)

1725 fps at 500 yards (U.S. 0.3 caliber AP)

Elevation angle for 500 yard shot at target with same height as gun = 0.246 degrees

CASE 1

PRONE FIRER, 1' above ground

0.2387 degrees from gun to 6' tall target at 400 yards

0.4847 degree gun elevation for 500 yard shot

Bullet passes 400 yard target range at 2.238m or 7.341' elevation, overflies aim point by 88.09" - 72"=16.09"

CASE 2

STANDING FIRER, 5.5' above ground

0.02387 degrees from gun to 6' tall target at 400 yards

0.2699 degree gun elevation for 500 yard shot

Bullet passes 400 yard target range at 2.234m or 7.328' elevation, overflies aim point by 87.93" - 72"=15.93"

CONCLUSION

If the prone and standing firers both aim at the same point and elevate their guns for a 500 yard shot the rounds from both guns will overfly the target aim point at 400 yards by about the same amount.

[lorrin]

Jeff,

When I ran the rifle example you mentioned on a ballistic trajectory program with prone and standing firers, and both aimed at the same point with the same range error, they both missed the aim point, and the entire board, by about the same amount. See preceding post on this thread.

Could you post your jpeg file on the trajectory to the files or photo section of the Tankers site, and also post up more info on your input variables:

final angle for prone firer shot

final angle for standing firer shot

range for 500 yard shot to same height as gun

height of prone and standing firer guns

form factor used for round

I do not receive posts from the Tankers site automatically, so cannot access the jpeg file you attached to your post. It was stripped from the post when the message was stored.

Thank you.

Lorrin

[jjhays]

quite interesting thread here, It was common (still is) to "battlesight" the main gun at some preset range. There fore it was quite easy to make adjustments with the stadia and your reticle in the gunsight according to the distance to the target. The long range shots also must take into account weather, ammo temp, and the heating up of the gun commonly referd to as gun tube droop in the larger calibers... just my 2 cents in euro.