rexford

I have Hollow Legions and West of Alamein and will sell you the scenario's for whatever you feel is reasonable since I don't use their scenario's.

Another way of looking at sloped armor multipliers is that a round that can penetrate 179mm @ 0° on half the hits can also penetrate 3.52" at 47° using the same criteria.

Glacis 4" thick but two plates in contact, so use 88% of thickness as effective, for 3.52" rolled single plate equivalent. T/D ratio of 100/88 (to be conservative) results in 2.00 slope multiplier. So, 3.52" x 25.4mm per inch x 2.00 slope effect = 179mm at 0° equivalent resistance. 3.52" at 47° has the same penetration resistance as 179mm at 0°. Slope effect is multiplier that converts sloped armor to equivalent resistance at 0° that can be compared to 0° penetration. If we didn't convert sloped armor to 0° equivalent we would need tables of penetration at every angle for every gun to determine if penetrations occur. By converting to 0° resistance, we only need one penetration table at 0°. Jumbo Sherman glacis resistance is same as a single 179mm plate at 0° slope. 88L71 penetrates about 175mm 0° plate at around 2000m.

Sherman Jumbo front armor is: Mantlet 3.5" rolled over 3.875" cast Glacis 1.5" plate over 2.5" glacis at 47° Assume two plates in contact resist like one plate with 88% effective thickness. 3.875" cast vs. 88 equivalent to 3.62" rolled. Mantlet resistance => 159mm rolled Glacis resistance => 179mm @ 0° 88L71 APCBC should be able to penetrate Jumbo glacis at 2000m. Slope effect when 88 hits 100mm at 47° is 2.00 (we used full thickness in T/D ratio to beon conservative side). We can write short things too.

German projectile data, doubled 50% dispersion and flight time to range, dispersion rounded to nearest 0.1m in many cases. Divide 50% dispersion by .675 to obtain standard deviation (68.3%). 50L60 APC 100m:.03m vert and .03 lat .12 sec 500m: .15m vert anc .15 lat .65 sec 1000m: .33m vert and .30m lat 1.43 sec 1500m: .58m vert and .50m lat 2.35 sec 75L48 APCBC 100m: .1m vert and 0.04m lat .13 sec 500m: .3m vert and .2m lat .68 sec 1000m: .6m vert and .5m lat 1.44 sec 1500m: 1.0m vert and 0.9m lat 2.27 sec 2000m: 1.6m vert and 1.3m lat 3.16 sec 2500m: 2.4m vert and 1.8m lat 4.12 sec 3000m: 3.3m vert and 2.3m lat 5.20 sec 76.2L51.5 APCBC 100m: .1m vert and .1m lat .14 sec 500m: .4m vert and .3m lat .73 sec 1000m: .8m vert and .6m lat 1.52 sec 1500m: 1.3m vert and 1.om lat 2.38 sec 2000m: 1.8m vert and 1.4m lat 3.32 sec 2500m: 2.5m vert and 1.9m lat 4.33 sec 3000m: 3.3m vert and 2.4m lat 5.43 sec 88L56 APCBC 100m: .1m vert and .1m lat .13 sec 500m: .2m vert and .2m lat .65 sec 1000m: .4m vert and .2m lat 1.35 sec 1500m: .6m vert and .3m lat 2.09 sec 2000m: .9m vert and .5m lat 2.91 sec 2500m: 1.0m vert and .5m lat 3.08 sec 3000m: 1.3m vert and .8m lat 4.66 sec 88L71 APCBC 100m: .1m vert and .04m lat .10 sec 500m: .2m vert and .2m lat .50 sec 1000m: .5m vert and .3m lat 1.04 sec 1500m: .7m vert and .5m lat 1.60 sec 2000m: .9m vert and .7m lat 2.20 sec 2500m: 1.1m vert and .9m lat 2.83 sec 3000m: 1.4m vert and 1.0m lat 3.50 sec 3500m: 1.6m vert and 1.2m lat 4.21 sec 4000m: 1.8m vert and 1.4m lat 4.96 sec 75L70 APCBC No dispersion data available. Comparison of listed dispersion hit %'s in tables from various sources suggests using 50L60 APC up to and including 1000m, 88L56 after that. Panther flight time estimated at: 100m: .11 sec 500m: .56 sec 1000m: 1.17 sec 1500m: 1.82 sec 2000m: 2.52 sec 2500m: 3.27 sec 3000m: 4.06 sec For 88L56 vs. 2m high x 2.5m wide at 2000m, 50% dispersion is .9m vert and .5m lat. This corresponds to 68.3% dispersion of 1.33m vert and .74m lat (68.3% of dispersions will be within stated distance from center of box). 1m/1.33 = .75 standard deviations = 55% For lat dispersion, 1.25m/.74m = 1.69 standard deviations = 91% Lat % x Vert % = .91 x .55 = .50 listed in table for 88L56 at 2000m.

We have had access to original WW II documents through National Technical Information Service, Bovington Museum, Canadian sources and some data from Germany. At one point we had many WW II reports from U.S. Navy regarding 76mm APCBC penetration, and shatter gap. Analysis of data was accomplished over a 20 year period. We also collected articles from alot of different mags, including naval journals. 88L71 was very close to failure area during German tests, due to excessive stresses on projectile. BIOS report not only goes into armor but presents penetration data from tests. Germans used very best rounds during penetration tests and admitted that service rounds used in battle were inferior. German penetration data gives two curves, best quality and service. Uncapped German 50mm AP shatter failed in tests.

88L71 APCBC penetration has been subject of much past discussion and here is another angle. DeMarre equation allows penetration to be estimated from a reference, and works very well if ammo quality is consistent (also allows 57mm ACPCBC penetration to be estimated very well from 90mm APCBC< or vice versa). For 88L71 APCBC we'll treat U.S. 75mm APCBC as DeMarre reference, with 91mm penetration at 2030 fps for 75mm M61 U.S.: 88L71 pen = 91 x (velocity/2030)1.428 power x (88/75)1.07143 power x ((10.16kg x 2.2lbs/88 cubed)/(15 lbs/75 cubed))raised to 0.7143 power. Here is 88L71 velocity vs. range data from German booklet on ammunition: 0m-3247 fps 500m-3123 1000m-2972 1500m-2821 2000m-2673 2500m-2532 3000m-2391 3500m-2257 4000m-2125 Plugging velocity into DeMarre equation yields following 0° penetration if 88L71 APCBC ammo were same quality as U.S. 75mm: 0m-199mm 500m-189mm 1000m-176mm 1500m-163mm 2000m-151mm 2500m-140mm 3000m-129mm 3500m-119mm 4000m-109mm We have seen British data where 30° test penetration of Panther and Tiger guns is much higher than German data, which British attribute to harder German test plate (harder to penetrate?). Americans fired German 75L46 APCBC at same velocity as U.S. 75mm at U.S. plate and "German penetration was somewhat higher". If British reports during WW II of Panther 30° are converted to 0° using T/D multipliers the result is 190mm penetration for Panther at 0m and 0°. Since Germans list Panther penetration as about 168mm at 0m/0° (estimated from 30° test penetration using assumed slope effect), this suggests that German test plate was "harder to penetrate" and German rounds outpenetrated U.S. due to greater nose hardness (60.7 average Rockwell C hardness on German rounds analyzed by Brits as opposed to 56 Rockwell C hardness for U.S. ammo). If we do a DeMarre for Panther 75mm at 3068 fps from U.S. 75mm we obtain 164mm at 0m/0°, suggesting German ammo outpenetrates U.S. by 190/164, or 1.158 ratio. Multiplying previous DeMarre estimates for 88L71 by assumed German quality advantage (1.158)leads to: 0m-230 500m-219 1000m-204 1500m-189 2000m-175 2500m-162 3000m-149 3500m-138 4000m-126 This would be the penetration against U.S. best quality test plate with 240 Brinell Hardness Number, corresponds to good U.S. armor without flaws after October 1943 when quality control and quenching practices improved. ------------------------------------------- There is another way to look at German penetration data based on 30° slope multipliers. British BIOS report data on German penetration lists 30° figures, so where did Germans get those 0° figures? They probably calculated them using assumed figures: Look at the slope effects for 88L71 that result from published data: 100m (202@0°)/(177@30°)=1.14 slope effect 2000m (132@0°)/(121@30°)=1.09 slope effect We have studied slope effects for U.S. APCBC and above figures look bogus. If U.S. 90mm APCBC hits a 180mm thick plate at 30°, the slope effect is about 1.32. Why would 88L71 be 1.14? Lets convert German 30° penetration figures to 0° using U.S. slope effects: 100m-177mm@30° x 1.32 = 234mm @ 0° 500m-165mm@30° x 1.32 = 218mm @ 0° 1000m-151mm@30°x 1.31 = 198mm @ 0° 2000m-121mm@30°x 1.30 = 157mm @ 0° ---------------------------------------- Panther Fibel lists slope effects for Panther 75mm APCBC, with 3.00x slope multiplier at 60° and 2.00x at 45°. If Panther gun penetrates 190mm at 0m/0° than slope effect of 3.00x results in 63mm penetration at 60°. U.S. slope effect for T/D=0.84 (63/75) and 60° is 3.10, which also is very close to Panther Fibel. If Panther slope multiplier is 2.00 at 45° with 190mm penetration at 0°, 45° penetration is 95mm and T/D = 1.27. U.S. slope effect at 45° and T/D = 1.27 is 1.85, very close to Panther Fibel result of 2.00. This, of course, is based on premise that Germans tested Panther gun against armor quality close to U.S. and British and reported actual slope effects they found. If memory serves me, Panther Fibel presents different slope effect data than Tiger Fibel and we assume that Panther Fibel is the real thing, and alot of other German slope effects are assumed figures that disregard T/D effects. Above exercise suggests that Panther Fibel slope effects are based on 190mm penetration at 0° against Allied quality armor plate. It is possible that Germans tested Panther gun againt recreated Allied armor because Germans reproduced hard T34 armor and shot their 37mm and 50mm ammo against it, we have report. -------------------------------------------- We use DeMarre from U.S. 75mm M61 times 1.158 for German APCBC penetration data, which results in 88L71 penetration of 219mm at 500m and 175mm at 2000m. -------------------------------------------- When two homogeneous armor plates are placed in contact, naval test data suggests that the effective thickness of the two plates is less than the combined thickness. Material in outer plate around hole can be pushed out of way in radial direction without much resistance from inner plate, other than some friction. This may decrease Sherman jumbo armor resistance if it consists of two plates in contact. Two face-hardened plates in contact resist like a greater thickness of face-hardened, which may be due to thicker total face-hardened layer in two plates than one single. PzKpfw IIIH front hull gained by having two 30mm face-hardened in contact. Crusader matched regular and hard armor in contact, which added to overall resistance. If someone will provide Sherman jumbo glacis and turret front armor we will examine whether 88L71 could penetrate and at what range, based on DeMarre estimate times 1.158.

We have math models that predict second and follow-up shot range estimation errors and dispersion decreases. Also have math models for velocity vs range for all rounds so computer can calculate flight times. Dispersion data is also converted to math models vs. range. Made one little goof in previous message, used dispersion at 900m instead of target range of 700m. Lower dispersion increases 25% avg range error hit prob. and lowers 35% avg range error prob. 88L56 with 25% average range est. error gets 75% hit probability, and 35% avg error actually goes up because we quadruple basic dispersion for poor crews (35% avg range error), which lowers % when trajectory is on target but increases hit % when trajectory misses target: big dispersion brings more rounds down on target when trajectory is high, raises half of shots when trajectory is low. We compared the results of the simplified trajectory model with a complicated BASIC ballistic computer program for naval ammunition (great accuracy to 10 miles range, I guess), and our model was always within about 0.1m of the time consuming result for typical tank battle ranges. If anyone wants it we can post German dispersion data on this site, say every 500m for lateral and vertical dispersion and convert 50% data to 68.3% (one standard deviation coverage). Can also post flight time data and max trajectory height info.

With battlesight aim, aim at hull bottom and set gun for 900m with Tiger I. Would terrain grades effect shot? Never thought of it, and we hadn't even considered including battlesight until a few messages ago. Trajectory height is estimated with regard to bottom of target, shooting down a slope would still result in same trajectory shape relative to line between firer and target, so grades might not substantially impact distances. So if target tank is on higher or lower ground than firer it may not significantly change results. We'll look into this further. Good question. See message on trajectory model for more on how things work and the assumptions that were made. Trajectory model developed about 13 years ago and we forgot most of what went into it. Good questions from readers made us open up the old yellow notepads and try to decipher cryptic scribblings. Somewhere in our storage shed we have a curve for armor resistance to HEAT versus target hardness. Reason why bazooka failed to penetrate Tiger I and T34/85 in Korea was because hard armor increases resistance to HEAT and HEAT must over-penetrate by about 20mm or so to do real damage. But HEAT hits can scare heck out of crews and make them abandon vehicles. First use of bazooka against panzers (North Africa?) caused hull hatches on PzKpfw IV to blow open but crew and tank interior undamaged. Crews thought bazooka gases were poisonous so they bailed, but later got back in and continued when fellows left behind were not dead. Side skirts may increase HEAT effectiveness by providing stand-off distance that allows HEAT jet to get organized. Some modern HEAT anti-tank ammo uses pole on end to promote stand-off distance, at least that is what Guard buddies told me.

The following analysis is in response to a question regarding what equations were used to calculate hit % using range estimation and battlesight aim: We have detailed info for German projectiles, flight time vs range, max trajectory height, firing and final descent angles, 50% dispersion (vert and lat), etc. Max trajectory height = 1.336 (Flight time) raised to 1.919 power. Max trajectory height occurs at following distance from gun: 0.4443 (range setting)raised to 1.0224 power. Above two equations determined from regression equations through alot of data points for every German gun listing, and correlation R squared is over 0.99. We have found that these equations work very well with 105mm APDS and 50mmL42 APC. They don't work especially well with slow rounds, like 75L24. But we're mostly interested in 88 and 76 anti-tank types, for most part. And slow rounds will have low hit % anyway. We used above two equations to fit an equation thru trajectory and found that following equation predicts max trajectory height, point of max height and descent angle reasonably well and is fairly easy to use on spreadsheet, it is a good and quick and dirty shortcut to complex trajectory analysis: Trajectory height at given range equals: A x (distance to target)squared plus B x (distance to target) A = flight time to gun range setting divided by (C - D) C = .4443squared times gun range setting raised to 2.0448 power D = .4443 times gun range setting raised to 2.0224 power B = A times -1 times gun range setting For 88L56 aimed at 900m (battlesight range), equation results in following trajectory equation: traj. height = -.00000952 x (target distance)squared + .000857 x (target distance) This equation will closely predict max height of trajectory, location of max height and final descent angle, so should be good estimate for trajectory along path. Estimated descent slope at 900m when 88L56 aims at 900m is 0.049° or .00857 radians or 8.57 mils. German charts list 9 mils as 88L56 fall winkel when gun is aimed at 900m. Doing similar analysis for other guns aimed at 900m battlesight range results in following comparisons: 50L60 APCR Trajectory equation predicts 9.26 mils descent, chart lists 10 mils 75L48 APCBC Equation predicts 9.55 mils descent, chart lists 10 mils 88L71 APCBC Equation predicts 7 mils descent for 1200m range setting, chart lists 7 mils 76.2L51.5 APCBC Equation predicts 10.7 mils descent at 900m, chart lists 11 mils 75L70 APCBC Equation predicts 7.7 mil descent when gun is aimed at 1100m, we don't have German data for this ammo So above equation is reasonable model for wargame analysis, it may be off by close to 7% at times in predicted trajectory height, but to hit a target trajectory has to be very close to target and dispersion data might vary in field anyway (things start to loosen in field, or warp and bend under stress and bouncing), and guns wear so that muzzle velocity decreases with time which reduces accuracy. What occurs in the field is not exactly what happens on a nice day in the firing range with carefully kept-up guns and ammo that has been proofed under non-stress and ideal conditions. So we can accept some slack in the trajectory model. We'll use the model to predict battlesight accuracy when target is at 700m and is 2.2m high and 2.2m wide, fired at by 88L56 using 900m range setting with aim at bottom of hull. Target is 2.2m high at 700m. Equation predicts that average trajectory height will be 1.33m above bottom of hull. This puts round right on the turret/hull meeting point on my 1/72 scale M4A1 Sherman. So trajectory is 1.33m above bottom and 0.87m from top. At 900m, doubled 50% dispersion of 88L56 equals 0.3m vertical and 0.2m lateral. Convert to 68.3% dispersion by dividing by .675, for .44m vert and 0.30m lat. Trajectory breaks Sherman hull into 1.33m above and 0.87 below vertical aim point. Now we use bell shaped curve data for percentage vs # of standard deviations (1 standard deviation contains 68.3% of data points, 2 standard deviations contain 95.5%, etc.). 1.33m from trajectory to bottom contains 3 standard deviations, so 100% of dispersions fit into 1.33m. All of dispersions below trajectory hit target vertically although we still have to check lateral spread. 0.87m from trajectory to top of tank, which contains 1.98 standard deviations and contains about 95% of dispersion spread. 100% of dispersions above trajectory hit, 95% below hit, 97% of all dispersions hit target. Lateral spread check. Tank is 1.1m from center to outside, lateral standard deviation is 0.3m, over 3 standard deviations from center to outside width equals 100% of dispersions within 2.2m lateral box dimension. So when Tiger I uses battlesight aim at 700m Sherman target, 97% hit probability against fully exposed front hull. What if Tiger uses range estimation vs. 700m target and average error is 35%. Standard deviation for 35% avg. error is about 28.6%. 700m times 28.6% is 200m, which represents standard deviation for range estimation error. 700m + 200m is 900m aim for 35% average error. Standard deviation for Tiger I aim error is associated with 900m aim, target is at 700m. 2m is standard deviation for range error impact, which places trajectory 2m above or below aim point at center of Sherman (for discussion purposes we'll ignore aim at turret/hull point). 2m above target center is 0.90m above turret top. 0.90m divided by 0.44m vert error standard deviation equals just over 2 standard deviations, so about 96% of high dispersions miss target and 4% hit. Same thing for low dispersions. All shots are within lateral dimension as previously determined. So 35% average range estimation error against 700m Sherman target results in 4% hit chance. For 35% range estimation error we normally assume poor crews and increase dispersion, so hit % even lower. Equation for trajectory height with 840m aim is -.00000959 (target range)squared plus 0.00805 times target range. With 25% average estimating error, trajectory above aim point is 0.94m above aim point, which places trajectory on target. % of hits is found by dividing distances above and below trajectory by standard deviation of vertical dispersion and then checking to see that all lateral dispersion is within width. 0.26 meters from trajectory to top of tank divided by 0.44m standard deviation for vert dispersion yields 0.59 standard deviations, or 44% of high dispersions hit target. There is 0.94m from aim point to center of target, which equals 2.14 standard deviations of vert dispersion or 97%. So average % of dispersions on target is (97 +44)/2, or 70%. Battlesight increases hit % over range estimation by average crew from 70% to 97% against 2.2m high target. This can be placed on a computer and math can be automated. Our spreadsheet goes thru the above steps with a few shortcuts but uses the same logic. We model dispersion with curves of best fit and randomly choose a range estimation error for each shot based on curve for crew quality, lateral and vertical error from aim is determined for each shot and we measure error on model to see where shot falls. With above models and dispersion data one can calculate hit %'s. We had used ballistic analysis program in BASIC language but wanted something that would quickly predict trajectory with reasonable error. For Battlefield aim the trajectory equation predicts a height that is about 0.1m above maximum trajectory height, our spreadsheet reduces estimates near or above max height but it is okay to use it unrevised to model gun barrel wear or misaligned sights or whatever. Accuracy never improves with weapon age. Regarding Clint Eastwood's advice on how to pick targets, he was asked how he could take on ten men at once and get them all. Luck, and knowing who was likely to aim and who would just pull the trigger. Regarding limitations, it is early in the morning and I tried to be careful but some minor errors may have crept into the analysis. The equations were checked several times. A man has got to know his limitations.

The battlesight hit %'s are based on a gun aimed at Sherman hull bottom and range set at 900m for most guns, 1100m for Panther. The percentages would apply to all shots taken without changing range or aim spot. Second shots that adjust for misses would increase hit probability. We put a 2.2m high Sherman (hull bottom to turret top) at 600m, calculated the "no dispersion" trajectory of the gun at 600m when it was set for 900m and then used dispersion to calculate % of shots that fall onto Sherman. Alot of turret hits. If Sherman height is changed to 2.1m, the scale height of a 1/72 M4A1, the hit percentages drop by quite a bit. Battlesight works best against tanks that are fairly high from hull bottom to turret top. A 2m high T34 would result in 50% accuracy at max trajectory height against most guns, except Tiger I. We have detailed dispersion data for 75L48, 50L60, 88L71 and 88L56, among others. Hit percentages for single dispersion are for shots aimed at center of target, no range estimation error. Double dispersion shots take into account battlefield impacts on aim but shots are still bunched around center of box. Since second shots usually contain some degree of range estimation error, the double dispersion hit % would be too high since it is based on an average aim at center of target. Shots can still hit if range estimation is long, since dispersion can act to bring high shots down to tank level: If a Tiger I estimates 2000m range and shoots at a Sherman at 1900m, the shot flies over the aim point by 2m without dispersion. Say the target is a 2.1m high Sherman and aim is at vertical center. Shot flies over top of Sherman by 2m from aim point minus 1.05m from aim point to turret top, or 0.95m. Since dispersion adds to and subtracts from average trajectory height, we have to consider dispersion. Vertical Tiger I dispersion at 1900m is 50% of shots within 0.9m from average trajectory, or 68.3% within 1.33m. 50% of dispersions will be lower than average trajectory, and dispersion standard deviation is 1.33m (standard deviation represents 68.3% of distribution). 0.95m above turret divided by 1.33m results in 52% of low dispersions missing tank and 48% hitting. With 5% range estimation error against 1900m target, 24% of shots will hit even though average trajectory is above target. Dispersions can bring bad range estimate shots back onto target or turn a good estimate into a miss at long range. Tiger I gun has 50% dispersion of 0.9m at 2000m, which corresponds to a standard deviation of 1.33m. If range estimation is perfect and average aim is at center of 2m high target, we have 2m high target divided by 1.33m standard deviation for 1.5 standard deviations. 1.5 standard deviations is equal to 87% vertical accuracy, which is the figure published for 88L56 at 2000m with single dispersion (100% of lateral shots are within 2.5m distance). If we double the 2000m dispersions, we have 2m vertical distance divided by 2.67m standard deviation, for 0.75 standard deviations within the vertical distance. This corresponds to 55% of vertical dispersion within 2m high distance, lateral % is 91%. 55% vertical spread in box times 91% lateral dispersion results in the 50% overall figure for shots within 2m x 2.5m box when average aim is at box center and shots are subject to dispersion. Range estimate errors lower percentages by quite a bit, 25% average range error (bell shaped distribution curve) at 2000m results in 5% hit chance against 2m x 2.5m, down from 50% with perfect average aim at center of box. Tanks with really great gun sights, like 10x Jagd Panther, don't make gunners squint to see where they should be aiming on 2000m shots, which increases hit %. The further one aims from the center of mass, the lower the percentage of hits when range estimation errors are considered. 10x scopes yield a real good view. Tanks with 1.0x sights suffer compared to 2.5x scopes in terms of increased eye strain, greater variations in aim point, less ability to pick up on fall of shot, etc. Tanks with 2.5x scopes might represent a standard in CM, which would then suggest accuracy bonus' for 5x, 6x and 10x and penalties for the 1.9x and 1.0x scopes. The less powerful the sight, the smaller the perceived target and the more difficult it is to aim at the center, or at the bottom if one is using battlesight aim. In our rules, elite or battle hardened vets that take care of their instruments and gun alignment may qualify to use 1.25 times test dispersion for their first shots along with decreased range estimation errors, while average folks use double dispersion and 25% average errors. Good vets in Jagd Panther with 10x scope would certainly qualify for our bonus', while green troops might not know how to take advantage of tank instruments and wouldn't get the same results. Based on The Desert Fox' Panther site presentation of hit probabilities when average aim is at center of 2m x 2.5m box, Panther 75mm has less dispersion than 88L56 and slightly less than 50L60. When 50mm Pak entered North African theater it immediately increased engagement range due to less dispersion than other guns, better optics and a greater magnification gun sight than 2 pounder (3.0x magnification for 50mm Pak, 1.9x for 2 pounder, 1.0x for U.S. 37mm). 50mm Pak round to round dispersion at 900m is about 60% less than German 76.2 L51.5 and 40% less than 75L48 APCBC. If one can''t aim properly at a long range target or has a gun with large dispersion it makes sense that one won't hit it as often, and 50mm Pak clearly was a superior weapon with regard to accuracy. The ability to hit is tied into many factors such as distance estimations, gun sight optics and magnification, weapon alignment and fine adjustment, and if everything else was equal 50mm Pak would probably have a higher hit % than 2 pounder based on gun sight advantages.

Following is Battlesight accuracy for Panther 75 versus Sherman front, aim at bottom of hull and range set at 1100m: 100m-100% 200m-100% 300m-100% 400m-95% 500m-81% 600m-77% 700m-82% 800m-92% 900m-99% 1000m-94% 1100m-50% Based on dispersion accuracy with gun aimed at center of target, Panther 75L70 is one of the most accurate guns of WW II in terms of small dispersion, being smaller than 88L56 and slightly below 50L60.

When Tiger I uses battlesight method against the front of a Sherman (900m range and aim at hull bottom), it will AVERAGE a very impressive 91% hit probability when target range is 100m to 900m (2.2m high x 2.2m wide): Hit % when target is at indicated range and battlesight method is used: 100m-100% 200m-100% 300m-98% 400m-92% 500m-89% 600m-92% 700m-99% 800m-97% 900m-50% At 900m average trajectory is at bottom of hull and half the random dispersions hit below the hull. Trajectory reaches highest point of 1.8m between 400m and 500m, so most misses occur at this point due to upward dispersion and average trajectory is closest to roof. Above data based on double the test dispersion (doppelte 50% ige streung), so it might be improved upon if crew was very professional and kept things in best order. This sure beats range estimation, and what is even better is that a high percentage of hits strike the turret front and mantlet, which is often much weaker than the hull (Pershing, M4A3E8, IS-2m with 100mm turret front and mantlet, M4A3(76)W and others). 4-for-4 at 2000 yards with an M18 boggles the mind, but Sgt. York did some things with a gun that can only be explained as instinct, training and growing up around guns. The points in the previous message about some people just being plain good is true. The Aussie who hit a German armored car that was beyond the 2 pounder gun sight range marks seems impossible, but it occurred. Regarding short range misses, Clint Eastwood in one of his pics explained that the key to gun fighting was figuring out who would make a move first and who knew what they were doing. The rest would get excited, shoot like heck but wouldn't aim and probably couldn't hit, and this is what occurred in a bar room scene ("The Unforgiven" or "Josie Wales"?). My fathers friend was at Kasserine Pass with other green U.S. troops and when the panzers and nebelwerfers attacked they crouched in the trenches, held their guns above the top and fired blindly. Could this happen to some tankers, unaimed fire under the stress of combat? Street shootings are sometimes like this, alot of shots but few hits because folks don't want to stand still and carefully aim. For 75L48 using Battlesight, 82% average hits from 100m to 900m target range against Sherman front, with low of 69% at 500m: 100m-100% 200m-100% 300m-91% 400m-72% 500m-69% 600m-77% 700m-89% 800m-90% 900m-50% Above figures calculated using trajectory curve for each gun developed from German data and twice the test dispersion. For 75mm L48, Battlesight lowers 400m-500m probability but increases hit probability at longer ranges. If a tank crew does what they are supposed to do and aims according to the book, they should hit close to 93% at 500m. We thought of holding down %'s in miniatures games to model loaders jamming a thumb, grabbing the wrong ammo and having to go back, last minute traverse corrections, etc. Misses can model reduced rate of fire. We just came across Potapov's site on Russian armament, and it has "actual" Soviet test data for AP and APBC penetration, at 20% and 80% penetration probability. Really good details are limited to 76.2mm and 85mm guns plus 122mm. Slope effects look bogus, as T/D increases slope effect goes up instead of down, so data requires close scrutiny before it is held to be dependable. Site address is long, do "search" on potapov and look for Russian Military Zone. Good info on armor thickness and angles for many tanks, although some of the angles and thicknesses seem too low. Does anyone have access to dispersion stats vs. range for Panther APCBC. The Desert Fox has provided hit %'s but we need actual lateral (Breite) and vertical (hohe) dispersion (streung) data.

The 88L56 is close to the 76mm on M18. If target is at 1900m and 88 is set for 2000m, shot will be 2m above aim point prior to random dispersion. Since trajectory is above target and half of dispersion is upward, less than 50% chance to hit a target with a 100m error in range estimation at 1900m. This is why first shot hits at 2000m are very rare, range has to estimated to within plus or minus 50m to get average trajectory onto target.

Very interesting historical info and good insight into actual target lead logic and use. If target was at one mile, 1760 yards, and 76 gun aimed at 2000 yards, 4 hits in 4 shots would be very difficult. One would assume that the range settings would not be changed after the first shot due to continued success. So four straight hits with the same range setting at 2000 yards. Even if the panzers were at 2000 yards, 4-for-4 would still be very rare, but it could happen. Once in a lifetime event? We have 105mm APDS ammo in our spreadsheet for scenario's where Merkava's battle Panthers, and battlesight setting of 1000m for 105mm would probably hit anything inbetween with high accuracy. From what we've read bracketting was a standard method of zeroing in on a target: shoot high aim lower range, too low then aim inbetween original shot and last miss. Battleships use bracketting and so do tanks. Panzers use battlesight. And an occasional range finder.

Tank hull and turret ring size limit the gun that can be carried, due to recoil forces. M36 uses Sherman hull which was designed for 76mm gun, Pershing has hull specially designed to carry longer 90mm gun. Rounds for longer gun might have more powder charge and heavier ammo going into gun, but 90mm APCBC projectile came in one size and weight. Panther round that went into gun was longer and heavier than PzKpfw IVH, but both used 15# projectile. My guess is that M36 turret ring and hull limited barrel length and muzzle velocity. If Pershing and M36 used same cartridge and powder charge, Pershing would still have more recoil forces and higher velocity.

90mm gun comes in two muzzle velocities, which are related to barrel length. One at 2650 fps, other at 2800 fps. Different penetration stats for each vs. homogeneous rolled armor: 90mm APCBC at 2650 fps 157mm at 100m 148mm at 500m 136mm at 1000m 90mm APCBC at 2800 fps 173mm at 100m 162mm at 500m 150mm at 1000m Increased muzzle velocity increases accuracy, as general rule. Source is TM 9-1907

A good tank crew would probably assign scan areas to each crew member to cover as much area as possible. Tanks within 50m or 60m of woods probably have to be on alert for infantry attack of some sort. Poor tank crews or vehicles with bad sighting glass, vision block location, etc. might miss fact that shots occurred. How much smoke and blast evidence does bazooka leave behind? If little or none, panzer gunner would have to aim based on instructions from commander. This takes alot of coordination and skill.

Had to close down while wife used phone. The use of the German trick to maximize first shot accuracy by taking advantage of max trajectory height doesn't really assure 100% accuracy between listed ranges, due to dispersion. If target is at 900m and you aim at bottom with gun at 900m, you hit on 50% of hits due to up and down dispersion. Half miss by randomly moving slightly below the hull bottom aim point. But 50% first shot accuracy for 88L71 with target at 1200m is better than estimating range and ending up with 1st shot hits on 35% of tries. If first shot is a tad low and hits the ground, you increase the gun range and you probably end up with a second round hit. If Tiger I aims at 900m and target is at 459m, average trajectory height at target location will be the maximum and equals 1.8m above hull bottom. This puts the average shot trajectory on the Sherman turret and about 0.40m below the turret top and 1.8m above the hull bottom (using some quick calculations on a model tank). Now we'll compute the hit percentage. 78% first shot hit chance if dispersion sends round above average trajectory, and 100% if dispersion is below. So Tiger I aims at bottom of Sherman using 900m gun input, target is at 459m and "88" scores around 89% first round hits. Hit probability will be higher at 230m and 680m since mean trajectory will be closer to middle of target and random dispersion will not put as many shots over or under the target. With this method Tiger crews don't have to be as well versed in range estimation procedures. The fact that German gunnery may have declined at end of war indicates that crews may have forgotten what they learned under the stress of combat, or they didn't catch the importance of the method in the first place. U.S. tank manuals after WW II include the above procedure, and it works really well with 90mm HVAP due to high speed and reasonably small dispersion. 88mmL56 APCR has an average maximum trajectory height of 2m for shots aimed at 1000m range. 88mmL56 HEAT is really slow, 1968 fps muzzle velocity, but would hit a 2m high target from 0m to 700m if the gun aimed at target bottom and range was set at 700m (no dispersion case). With dispersion, the hit % against a target at 500m falls below 100%, but would still be pretty high. Tiger I supposedly used HEAT against T34's carrying infantry, killing tank and HEAT explosion would eliminate infantry. (I also deal with pavements, just asphalt concrete. Presenting a paper this march on pavement response to moving and stationary loads, asphalt concrete stiffness may decrease by 80% or more under stationary load) Our spreadsheet does not currently consider aiming based on max trajectory and target bottom, and we had forgotten about it until we looked in the tables after reading recent messages in this string. If Germans are on defensive, they might also have time to set range markers in grass or measure distances to known landmarks. Then, when enemy moves by landmark, you have range down pat with high chance for first shot hit. Defensive positions may have more advantages than one might think. Mines not only may channel enemy but can force them to follow route that defense has plotted really well for range estimation purposes. If Germans are in woods and trees are alot smaller than usual (different species), enemy may overestimate range since they may estimate range based on perceived size of trees. (Airplane pilots may overestimate perceived distance to runway and aircraft elevation due to pigmy trees). Defense can be good.

Maybe it is TM 9-1907. The fellow who gave it to me wrote 9-1900, but it is performance of projectiles. Tigers in Africa had turret top connectors for stadiametric range finder, based on Fletcher's Tiger book. We believe that 88mm FlaK crews may have carried around range finders, those 1/72 scale kits have a guy looking through a long cylinder that looks like a stadiametric range finder. We figure that this may have added to the fierce some rep of the 88 by getting hits faster. Nashorn crews may have used a range finder on occasion. We had a stadiametric range finder that we bought that was used to do range estimation error studies. Go out on the street, estimate range to a distant car, and then check it against the range finder. We were really close alot of times. Bell shaped normal distribution curves resulted, where standard deviation would be about 80% of the average error. 25% average error results in 20% standard deviation, if memory holds. Our spreadsheet developes the bell shaped curve for a crew quality and average ranging estimate error, and then randomly picks a number for the estimation error suffered by a particular shot. Range finder can get one to within average 5% error on first shot instead of 25%, we call this 5% avg. error "super ace" in our system. At 2000m, "super ace" in Tiger I hits Sherman 30% of first shots, 60% on second try. Average shooting tankers in Tiger I get 5% first, 20% second, 25% third. Fletcher's Tiger book may have some hit probability stats for British gunners firing at a target from Tiger I. It may have taken several shots to hit the target. I think the results were close to what our rules predicted. At certain ranges, German crews were also trained that if they aimed at the bottom of the target and set their guns at a certain range, they would almost always hit the target. We have data on this. Something like if you set the range for 900m and aim at the hull bottom with Tiger I, you will ALWAYS hit a target that is so high and so wide. Using the aforementioned method does away with the need to estimate range to within 25%, and assures high accuracy if a target is within 900m. High % of targets are within 900m. There were alot of tricks that tankers could use to maximize hit chances. Here is the data I was looking for. If the Tiger I gun is aimed at the bottom of the Sherman hull and the range is set at 900m, the maximum trajectory height is 1.8m. So a Tiger using the little trick is guaranteed a first shot hit on a Sherman out to 900m. Ha! Think of how much faster Tigers can shoot when they don't have to estimate range but simply set the gun at 900m and hit everything in between!!!!!!!!!!!!!!!!!!! The Germans figured out how to do away with range estimation against fully exposed vehicles and take advantage of trajectory shape. If a target is at 1000m and the 88L56 is set for 1000m. the maximum trajectory height is 2,3m so some shots would clear the top of a 2m high target, but would still hit a Sherman or T34/85. If a Tiger I uses normal, boring, paint-by-the-numbers range estimation with 25% average error against a target at 700m, 60% first shot hits against a 2m high target. Set the gun for 900m and hit it almost every time! Which would you use. The above method is clearly pointed out in several German tank gunnery publications. The Fibels may also go into it. German first shot accuracy climbs pretty fast if CM goes to this for der panzers. Here is some more data from the German tank gunnery statistics: 50L60 APC and 75L48 APCBC: aim at bottom of target with gun set at 900m and hit everything from 0m to 900m that is below 2.0m in height. 88L71 APCBC: aim at bottom of target with gun set at 1200m and hit everything from 0m to 1200m below 2.0m in height. 100% first shot accuracy out to 1200m!!!!!!!!!!!!! If would be really helpful if someone could ask German or American tankers from WW II about their first shot hit probability at 500m and 1000m against stationary vehicles in the open. We have tried to refine our system so it is consistent with reports such as presented by Fletcher and other sources, because there is always one more factor that enters into things. If one can believe the story, British tankers in North Africa were supposed to bail out if the first 88 shot was close, because the second hardly ever missed. This suggests that the 88 Flak crew was cheating and using a range finder.

We have velocity versus range data for most German guns, APCBC, HE and APCR, as well as American data in TM 9-1900. 88mmL56 APCBC velocity from 0m to 2000m changes from 780 m/s to 607 m/s. That's 2580 fps to 1991 fps, for a -23% drop in speed over 2000m. 76mmL52 APCBC goes from 2600 fps at 0m to 1910 fps with M1A1C gun and 1978 fps with M1A2 gun. Small differences, but 88L56 is slightly more accurate if one considers better gun sight and possibly smaller dispersion. We don't have American dispersion data for their APCBC. We do have dispersion for 50mm L60 APC (very small, even smaller than 88L56),50mm APCR, and for 75mmL48 APCBC and APCR. 76.2L51.5 used by Germans has largest round to round dispersion we have ever seen for main ammo, 75L48 is not far behind. U.S. velocity loss with range based on a commonly accepted method of estimating velocity with range called Sciacci's method, using ballistic coefficients. German data for striking velocity at range is probably based on similar estimates. It is very difficult to measure velocity accurately at 2000m. British field test data for lead errors versus moving targets suggests that errors don't improve as number of shots increases. Leading a target is tricky stuff, you move the gun with the target as it moves and then move the gun out in front by the desired lead and quickly pull the trigger. Following is a detailed discussion regarding potential problems with published data. We are constantly re-examining published info and our conclusions. -------------------------------------------- Published Russian penetration data is defined in WW II German documents as DeMarre calculations against "zementen platten" using a penetration constant K, which suggests face-hardened plate. Russian data is similar to German for AP and APBC, main difference is ballistic cap on APBC slows velocity loss so penetration at range is greater. Russian penetration data looks like test data but it probably is calculated, we have American test data for 122mm APBC versus U.S. plate at angles from 0° to 70° and it goes through alot more than 168mm at 0m and 0°, and it has unbelievably low slope effect due to flat nose. 122mm APBC slope multiplier of 1.62 versus Panther glacis at 55°, while U.S. 76mm APCBC has 2.52. We have carefully reviewed alot of German, U.S. and British penetration range listings over a long period of time and most eventually prove to be calculations using available information. British charts even say, on occasion, that about 10% of penetration ranges in a document are based on actual field tests and rest are calculations, but report won't say which is which. Panther and Tiger Fibel contain figures showing how far guns could penetrate enemy armor such as Matilda and T34, and it all appears to be calculated based on (incorrect) assumption that T34 and Sherman armor was same resistance as German penetration test plate. The publishers of penetration ranges sometimes thought they represented field tests, and say they are test results based on a curve of best fit through field results, but ALOT of data out there was computed in an office and is not reliable. Jentz presents alot of penetration range data and it appears to be based on field tests. Like when they shot all sorts of guns and ammo at PzKpfw IIIH front hull in Africa and reported the penetration ranges, this is the real thing (we have original reports, they match and also verify it is a test result). The British often tested ammo at 30° and then used an assumed slope multiplier to convert data to 0°, which overlooked T/D ratio and presents questionable data for 0°. If 17 pounder APCBC penetrates 140mm/30° at a given range, 0° penetration might be listed at 140 x 1.25 = 175mm if 1.25 is assumed multiplier. We have a published set of U.S. penetration data that is all based on one set of slope multipliers for all ammo and all armor thicknesses, so most of the data is suspect. When Soviet data is presented for guns and ammo pen. range versus Tiger II in Jentz, we went through the calculations and the data seems to be real. However, Soviet pen. ranges are often based on calculations from their published data which assumes that AP and APBC penetrate same armor at same velocity, so both have same penetration at 0m: this is unlikely to be true, AP is sharp nose and APBC is flat nose (sounds like Land Before Time). Changes in 122 flat nose penetration with velocity are also different from 122mm AP. That German 50% hit probability by 88L56 against 2.5m x 2m target at 2000m is a calculation based on 0m range estimation error, we reproduced the analysis from original German data sheets. Analysis suggests that 88L56 has 5% accuracy at 2000m vs. 2.5m x 2m when 25% average range estimation error is used with bell shaped distribution curve, based on trajectory and dispersion analysis. British analysis of Panther A armor shows it to be face-hardened on lower front hull and hull side. We have original reports on this. How many books list Panther A hull side armor as face-hardened. Panther D glacis appears to have been face-hardened at first, even though it exceeded 60mm. We play armor miniatures and have graphs that we use to resolve play. Plus the computer spreadsheet that computes everything one might want to know. We are thinking of putting the spreadsheet and supporting documentaion booklet into the public domain when we finish data collection in a month or so. Our group is a loose collection of folks that look at things and present data and speculation. We then try to confirm the speculation. My profession is civil engineering, licensed airport engineer in New York, and mathematical models are a hobby. Tank gunnery makes an excellent subject since it is loaded with odd twists and turns, like shatter gap. Your game seems to be quit excellent and we enjoy the forum.

If one compares German 88L56 and American 76mmL52 APCBC hit chances while assigning each the same dispersion, which is more accurate? German 88 loses velocity slower than 76mm round so has a flatter trajectory and will have a higher hit probability. We compared German velocity-vs-range data for 88L56 and American data for U.S. 76mm, and Tiger I round will outshoot 76mm at medium and long range with same dispersion. 76mm starts out at 2600 fps, 88L56 at 2558 fps, but 88 catches up and passes after a while. Our spreadsheet considers estimated velocity-vs-range data for each projectile and computes trajectory height over the target aim point, using double dispersion for initial shot. On a related though different topic, 17 pdr APDS appears to lose stability, accuracy and penetration on close to 50% of the shots, based on analysis of many field tests, due to a piece of sabot hanging on longer than the others which unbalances ammo. In U.S. tests at Isigny, 17 pdr accuracy was terrible, and penetration suffered. Will CM give 6 and 17 pdr APDS variable dispersion, where accuracy and penetration may drastically change from tank to tank, or battle to battle? U.S. gunners at Isigny said that 76mm HVAP was most accurate round they had ever fired. British explained that APDS rounds had not been adequately proofed and an earlier test had resulted in clean penetrations of Panther glacis at around 700m or so (lost reference and are using my notes). APDS shots at lesser ranges at Isigny bounced alot. When we analyzed 76mm HVAP with our spreadsheet it did lose velocity faster than 88mm or 76mm APCBC, but it was still more accurate at useful ranges due to large velocity difference. When Soviet T62 fired state-of-the-art APFSDS during 1973 war (APDS with fins that came out of round after it left smooth barrel, which allowed really high velocity), Israeli's reported that T62 shots would occasionally hit the ground at wild angles. New discarding sabot ammo types seem to suffer from teething problems. Our spreadsheet also bases lateral hit probability on motion across line of sight, so targets moving straight at a gun do not lower the hit probability due to motion status. Changes in lateral and vertical hit probability occur because gunner uses incorrect lead or need to estimate lead reduces commander's ability to estimate range (too many irons in the fire at one time). No lead involved when target moves directly at gun. From what you've said in past messages it looks like CM uses a similar system. Just out of curiousity, does 75mm Sherman fire faster and more often than Panther in CM, based on your experiences? Power traverse gets gun on target quick.

Regarding previous e-mail from this writer, it should also be noted that the German estimate of 50% hits for first shot by 88L56 on 2m x 2.5m target at 2000m does not appear to be based on field trials, but appears to be calculated. We did the math, and using twice the listed dispersion reproduces the bracket hit % and represents 0m range estimation error. Many of the calculations and pronouncements in German and other country documents from WW II appear to be based on field tests but are more likely to be calculations from office data. Penetration ranges are often from this type of source.

Thanks for the past message threads which we started to read through and are about 10% through. We would like to add some notes regarding computer models for tank fire that include range estimation and dispersion. We have German dispersion stats and hit probability tables based on perfect range estimation, and built a simple to use computer spreadsheet around that data, which we use to predict hit percentages for first and follow-up shots. The spreadsheet also predicts slope effect based on T/D and ammo type, armor quality modifiers, penetration at range, fall of shot angle, predicts whether round penetrates since % is often between 0% and 100%), and if shatter gap is a possibility. The computer spreadsheet uses an average range estimation error of 10% (ace), 25% (average or 35% (poor), and randomly picks a range estimation error for each shot from a statistical curve for crew rating. At 2000m against a 2m high x 2.5m wide target, an average Tiger I crew will obtain first shot hits on about 5% of the shots. The hit probability given on the German dispersion tables are for perfect range estimation and give hit % for one times and (in brackets) two times the dispersion. The hit % in the German tables for two times the listed dispersion (doppelt 50% ige streung) does not include range estimation errors but is related to errors made in picking the proper aim point, gun misalignment, etc (a friend speaks and reads German and translated for us). With perfect range estimation and double gun dispersion, 88L56 will hit 2m high x 2.5m wide target 50% of time on our copy of German data. With 25% average range estimation error and bell shaped distribution of errors about average, first shot % falls to about 5% (4 hits in 88 tries using our spreadsheet). If Tiger crew can estimate range to within 10% average, hit % rises to 15% on first shot at 2000m. If CM uses 21%, it seems closer to Tiger Vet-Elite status and takes note that Sherman may be larger target than 2m x 2.5m. We realize that adding to old message strings is not always productive or appreciated, and we will try to avoid it. The above explanation seemed appropriate after reading some of the string you kindly brought to our attention.

Regarding Mark IV's last message on open field hit probability, there are stories where green troops in Jagd Panthers missed shots at 400m by aiming very low. It might be helpful if you could play the scenario again and see how the results compare and also keep an eye out for the type of misses. Previous messages complained about alot of easy hits at 400m on first shots, the open field experiment Mark IV completed goes the other way.