rexford

Ooops! Tiger Fibel shows 1000m aim with over 2m height at 500m. Our analysis is consistent with Tiger Fibel.

A. Physics allows one to analyze a falling shot by freezing the frame and using that as time zero. When the round reaches 350m it is pointed downward due to gravity. Freeze time at 350m and start from there. Round has no vertical speed but is pointed downward. Calculate gravity drop from 350m to 500m by using time it takes to go that far. Incorporate previous effect of gravity by using 350m descent angle to see how far it falls in 150m to 500m. And this method yields the same result as the simplified trajectory equation. If a stone is dropped and I want to know how far it drops from 1 second of fall to 2 seconds of fall, one valid equation is: (velocity at 1 second) x time (from 1 to 2 sec) + 0.5 x 32.2 x (2-1) squared. velocity after 1 second is 32.2 fps. So answer from freezing time at 1 second and going to 2 seconds is: 32.2 x 1 second + 0.5 x 32.2 x 1squared, or 48.3' Now lets use another approach: The answer from 0.5 x 32.2 x 2squared is 64.4' in 2 seconds, 16.1' in 1 second, 48.3' from 1 to 2 seconds. You are not familiar with the methods I am using, which accounts for some of the problem. I minored in plasma physics in college, and have analyzed alot of moving particles besides tank gun rounds. B. I stated that the StuG III gun was at the same height as the target center, and my equations used an elevation angle on the gun. If the Stug IIIG 75 is aimed at the center of a target at 350m the round at 350m will be at the gun elevation, 0m above gun. At 500m the round aimed at the middle of a target at 350m will be about -0.73m below the gun elevation and below the center of the target at 500m. So it hits with a 150m range estimate error when aimed at 350m, and 2m high target is at 500m. Make a drawing that follows the above logic and you'll see what I am getting at, and that my analysis is correct. C. The trajectory elevation equation for height above gun barrel is: range x sine (gun elevation) - 0.5 x 9.82 x (flight time) squared, for results in meters. 350m aim x sine (0.2°) - 0.5 x 9.82 x 0.5squared (for 700 m/s constant velocity) = 0m. Shoot a 700 m/s constant speed round with 0.2° elevation and it is at gun barrel elevation at 350m. If target center is at gun barrel height, above equation meets our criteria (aim puts shot at height equal to gun barrel at 350m). Now how high is the shot at 500m relative to gun barrel and target center? 500m x sine (0.2°) - 0.5 x 9.82 x (.71) squared, or -0.73m. A hit! This is basic trajectory physics, and is consistent with the simplified trajectory equation. D. The simplified trajectory equation not only matches the Tiger Fibel case very well, and agrees with the above example, but it disclosed an error in the Tiger Fibel!!!! Since the max trajectory height to 1000m range is over 2m, based on my trajectory equation and German ballistics data, the shot goes over the woman's head at 500m although Tiger Fibel says it hits. Tiger Fibel made a mistake that "weeeeeeeeee" caught.

Long range accuracy should hardly ever reach 90% at long range due to dispersion effects. It is possible to hit on a first shot and have a bad range estimate because a large dispersion pulled the shot onto the target. So the tank in the above situation would assume that first shot was range accurate and follow-up, but since dispersion changes from round to round the next shot might miss low after the first hit high. The following will explain what "eye" mean (as opposed to what "oui" mean): At 2000m, 88L71 vertical dispersion for 50% of shots is 0.9m on first ****s, so 50% of shots will be within 0.9m of aim point, 68% will be within 1.33m of aim point and 95.5% will be within 2.66m of aim point. Say the Nashorn estimated 2000m, target is at 2000m and aim point is the center of a 2m high target, then 45% of the shots miss a 2m high target due to variations from shot to shot!!!!!!!! Dispersion is the scatter that occurs due to variations from shot to shot (projectile weight varies, powder charge varies, barrel recoil changes, tank inertia, etc.). While dispersions might be corrected for, bracketing can almost never attain 90% or 95% accuracy on long range shots due to random scatter. Our spreadsheet for tank fire uses an equation that corrects range estimation for bracketing the target, but dispersion limits how good one can get. The story where an M18 hit four panzers at 2000 yards with four shots, and some were low StuG III, can occur but certainly is not the commonplace. Due to dispersion, one may see a high shot and correct it downward when it was a low shot that scattered high. The farther the shot, the larger the dispersion.

Stand on a tilted board and aim a rifle at a target by raising it at an angle instead of staight up and down, won't this generate lateral errors?

Original post assumed 700 m/s velocity to any range, so 0.5 second flight time to 350m and 0.71 seconds to 500m.

If a Stug IIIG fires on a target at 500m but sets the gun for 350m, and the shot has a constant velocity to any range, the physics equation of motion is: tangent (0.2°) x distance - 0.5 x 9.8 x (flight time) squared = elevation above gun (assumed to equal target center of mass in this case to simplify math) Above equation yields 0m from aim point at 350m, and -0.72m below aim point at 500m. "My" trajectory equations predicts -0.8m below aim point. So a hit still occurs with 350m aim and 500m target if there is no dispersion, which is due to relatively flat trajectory of round. One can be off by 30% in range estimate at 500m and still hit on most of shots, if not practically all if range estimation errors are the only errors that occur.

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.

Good reasoning, and a decent alternative to blindly using data that has often proved to be bogus. Shoeburyness tests in England during May '44 are consistent with TM-9-1907 U.S. penetration curves, although 76 APCBC outperforms published data (penetrates 100mm at 30° and 500 yards). Then 76mm gets to France and can't pierce Tiger front beyond 50 yards (Faint Praise). This suggests large variations possible in field, which your discussion describes. Would you support penetration data for U.S. projectiles that exceeds published data?

One of the posts in the max accuracy thread discussed leveling tank guns using bubble levels. We assume that this was required when hull was on sloping terrain to avoid skewed trajectory. "I" would appreciate additional details on this as it appears that failing to level the gun when it fires across a -1° slope might lead to short range misses. Thanks from me.

Jentz report on British tests vs. Tiger show 6 pdr APCBC shattering on a 30° hit when it should have penetrated, and British are quoted as being disappointed. They expected caps to prevent shatter. Tiger tank in those tests have 250-285 Brinell Hardness armor, so wasn't that much different from U.S. and British penetration test plate. 6 pdr APCBC is solid shot vs. U.S. 57mm with HE burster, so there is about an 8% to 10% penetration advantage to 6 pdr right there. Where does that come from? 75mm solid shot AP penetrates about 113mm at 0m/0°, 75mm APCBC with HE burster cavity penetrates about 91mm at same range/angle. That's a 24% increase due to differences in nose, burster and caps. We compared data for 37 AP and APCBC and figured that caps cost about 10% of penetration, bursters from 8% to 10%. Exact analysis buried in "my" storage shed somewehere (this clarifies that "I" do not live in a commune where everything is shared, including thoughts). Projectile shatter is related to striking velocity and penetration/resistance ratio. Faint Praise indicates that 76mm APCBC didn't penetrate Tiger front hull beyond 50 yards. Rounds shatter because they are too soft and pushing material out of the way at high speed creates stresses that the round can't handle. U.S. tests on nose hardness showed this, harden nose to German level (61 Rockwell C) and shatter failure disappears on hits that should penetrate. Lowering penetration in CM may be a compromise solution, indepth analysis would have to compare striking velocity to shatter failure ranges and compute ratio of penetration/resistance to see if it fell into the apparent range for shatter gap failure, 1.05 to 1.25. Should 17 pounder APDS use 76 HVAP slope effects? "I" have never seen a curve for 17 pounder that answers this question, so it is not resolved. Bovington may have something that can answer this. 90mm HVAP appears to have lower slope effects than 76mm, but this doesn't resolve APDS issue.

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.

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.

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.

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.

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.

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).

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

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.

Cutback to rear section of turret side is a benefit that may not have been appreciated by tankers but seems to have interested designers who used the concept again and again. Idea is to minimize target size on popular shot angles, and 30° shots to hull or turret facing were a major concern to tank designers. The post was discussing general benefits whether known to tankers or not. OUr miniatures games use shot placement with measurements on tank models, and many shots have missed Tiger running for cover due to angle of move and rounded back of turret that reduces visible area on alot of shots.

Following web site contains U.S. firing tests for 75, 76 and 90 APCBC during 5/44, just before D-Day, with service rounds (not some high quality test job): http://members.nbci.com/mycenius/weapons/armour4.html Isigny tests against 3 Panthers same site, end with armour6.html During May 44 tests, 75mm with HE burster and with inert filler were both fired at same target, round with HE inside slightly outpenetrated inert filler version. Since HE burster version heavier than inert filler, penetration difference might be due to projectile weight. 75mm penetration against 70mm @ 0° closely matches U.S. test data, suggesting that American data in TM-9-1907 is with service ammo. TM-9-1907 compares to CM data in following manner: 500m CM 89mm TM 82mm 100m CM 97mm TM 90mm U.S. 76mm APCBC in test penetrates 100mm plate at 30° at 500 yards, which exceeds CM prediction by a bit. TM-9-1907 predicts that 76mm APCBC at 500 yards would penetrate 93mm on 50% of hits, so penetrating 100mm/30° on two hits out of two at 500 yards is on the lucky side. 76mm service round in these pre-D-Day tests did not exhibit brittle behavior and exceeded CM and TM predictions. Firing a few rounds on one day does not answer all questions, but does raise a few questions. There is some confusion in the May 1944 report regarding 75mm tests at 30°. Report text says 60mm at 30° in one place, chart shows 70mm at 30°. TM-9-1907 data for penetration range has 64mm at 30°. One other issue is that 75mm APCBC did not "shatter gap" when penetration greatly exceeded 70mm/0° plate, suggesting that shatter failure on overpenetrating hits may be limited to impact velocities above 2000 fps. So "shatter gap" probably would not apply to 75L40 APCBC at most ranges, although it might at 20m or so. This needs more study.

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.

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

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.

Two other benefits from angled approach are decreased hit probability due to movement across line of sight (heading straight towards someone is about the same as shooting at a stationary target), and turret shape. Many, if not most, turrets have a cutback at the rear. Panther does, Tiger II and Tiger I, T34 and T34/85, Sherman. If one holds a T34 Model 1943 figure up and views from front corner to opposite rear corner, you can't see the entire turret side due to the cutback. Very little of the Sherman turret side is visible on corner-to-corner views due to rounding. This minimizes turret hits when the firer is 30° from turret facing, and seems to have designed for that purpose. So when a shot is taken at 45° to tank facing with turret aligned with hull, the turret side is a smaller target than would be presented by a straight plate parallel to turret facing. Approaching at an angle does expose more of the gun barrel, but the center of mass aim point will be well onto the side armor and barrel hits should be relatively infrequent.

Jeff Duquette provided our group with a German tank fire manual that brought up the issue of ricochet HE fire by German crews. When infantry or anti-tank guns were dug in fairly well or hard ot get at, and direct fire might be time-consuming or useless, rounds would be aimed at the ground infront of the target to obtain an air burst over or near the target. Of course the ground would have to be somewhat level, grassy and firm for good ricochet fire, but the power of air bursts was well known and prized. Funny that the Americans seem to have the first to use ground proximity HE detonation for air bursts when the Germans appreciated their usefulness and had tanks use the technique. U.S. tank manuals may have included something on this, too. The manual also briefly treated on battlesight aim as the standard against targets inside 1200m, saying that there was no need for range estimation on many first shots if the flat trajectory of rounds was considered and appropriate aim points were used. German ballistic tables include battlesight aim settings for targets at any range.