Ap Statistics Chapter 9 Test Form B: Fill & Download for Free

Short AnswerI am going to take a different approach to some other answers.The British did a lot of analysis of the threat posed by the IS-3 tank. I am going to use this analysis, albeit in a ‘back of a fag packet’ approach. It won’t be all that accurate, but its better than nothing and I don’t have time at the moment to do anything better!ResultAssuming the Tiger II has defect-free armour and carried tungsten-cored APCR ammunition, then the Tiger II and IS-3 are about equal.If the Tiger II is limited to APCBCHE ammunition, then 8.5 IS-3 tanks can take on ten Tiger IIs. Edge to IS-3.This is counter-intuitive because in a game of Top Trumps, the IS-3 is clearly superior, especially in protection from side attack. However, more detailed modelling gives the Tiger II a few advantages.Long Answer1. IntroductionThese two leviathans possibly illustrate the adage “the best is the enemy of the good” insofar the designers seem to have tried to devise the most powerful tank they could, whereas the aims of the designers of the contemporary Pershing and Centurion were more modest. The latter two vehicles were successful giving decades of service with successive upgrades, whereas the former two (apart from making impressive museum exhibits) are rather in tank history’s scrapheap.Both IS-3 and Tiger II had production problems which led to serious issues. Most readers of this will be familiar with the automotive shortcomings and armour quality defects of the Tiger II, however fewer will know what a gash-heap the IS-3 turned out to be. Early versions were plagued with engine, gearbox and hull armour problems and had to be rebuilt. [Ref 1] It was a useful vehicle to launderette owners in Western garrison towns, but its combat utility was very low. This is attested by its lamentable performance in the 1967 Six-Day War where the IS-3 was shown hard to knock out, but achieved next to nothing. Some of the poor performance may be down to the skill and morale of its Egyptian operators, however, it will be noted that the Israelis used captured examples as pill-boxes on the Bar-Lev line guarding Sinai rather than as tanks see Refs 2 and 3. Some of these tanks are rumoured to have died of shame! (One Russian commentator drily observed about IS-3 pillboxes in Russia that “they were more mobile in that role than any other!”)2. The IS-3Now on paper the IS-3 is a very tough customer indeed. Designated Object 703 and was designed such that of hits from the PzGr 39 round from a KwK 43 would only have a ~40% chance of knocking it out.[Ref 4] Its thick and well-sloped armour give it excellent protection and from an all-round approach it is much better than the Tiger II because its turret side is much stronger and the upper hull armour is heavily sloped inwards. This can be seen in the armour diagrams at Annex A.Figure 1 below taken from Ref 5 shows the vulnerable areas of the IS-3 to British 17 pdr APCBC and 20 pdr APDS Mk 1 at 1000 yards. As can be seen, the IS-3 is invulnerable to hits on the frontal armour from the 17 pdr and even the potent 20 pdr APDS only gets 5 square feet of vulnerable area (about 18% of presented area). At the same range, the vulnerable area of the Centurion III to the 122 mm round was nearly 32 square feet. The IS- side armour is superior to the Centurion front armour in many aspects!Figure 1. Vulnerable Area of IS-3 as a Function of Angle at 1000 yardsThe IS-3 was also very compact, making it a small target- albeit this is a double-edged sword; one man’s (the designer’s) compact tank is another man’s (the crew-member’s) hell-hole. The IS-3 is poor ergonomically, which would lead to low rates of fire and a capability that would fall with fatigue. It is obviously hard to model these effects. If you see then Chieftain’s hatch video, on the IS-3it is telling that you do not see inside the tank! I suspect that if Nick Moran had got in he would still be there!Here is a photo from inside showing ammunition racks around the turret and some less than Rolls-Royce standard machining of the hull -presumably to give clearance for the gun as it rotates.The IS-3’s 122 mm gun has less-than-stellar anti-tank performance, perhaps unsurprising as it is optimised for firing a heavy and effective HE shell. The IS-3 normally carried 28 rounds of ammunition of which only 8 were armour piercing. However, 8 rounds would be enough for today’s mission against the Tiger II.The muzzle velocity of the 122 mm gun with AP ammunition is not high, ~790 m/s, meaning range and lead errors are larger than for the German tank’s gun and the rate of fire is about half that for the Tiger II. (The dispersion of the 122 mm, 8.8 cm KwK 43 and 17 pdr with APCBC were similar, by the way).Although the AP round does not have great penetration, the large calibre gives advantages in being less affected by sloped armour as you will see at Annex A. The destructive effect of the AP shell would be high if it exploded inside the target, the filling is 156 g. The larger round would also have more chance of damaging running gear, although this is not included in the model (I did model this in my IS-2 v Tiger II answer, but it took a long time and was based on very limited supporting data).The optics of the IS-3 (x 4) aren’t bad but are rated as inferior to the Tiger II’ s 2.5 x–5 x sights. Gunnery from Egyptian IS-3s in 1967 seems to have been poor, but ow much of this is as a result of crew training is uncertain.The ammunition supply is low, but the 122 mm HE round is of sufficient size to have a useful effect on armoured targets (albeit I find some stories fanciful), I have come across a report of a Tiger abandoned and written off after six 122 mm HE hits from assault guns. If an IS-3 were to hit a stationary Tiger II, it is not unlikely that the crew would be somewhat discombobulated, enabling a second and third round to be sent their way to wreck the tank.3. The Tiger III am not going to write much about this vehicle as it is so well known. See Refs [6, 7 & 8]4. Modelling the Tiger II v IS-3Obviously the British didn’t check out the Tiger II as an opponent in their post war assessment, however, the Figure 1 above may hint at how we can answer the question posed, because the performance of the 88 mm rounds lie between the two British rounds shown in the polar plot.The Tiger II is a very well armoured tank; it rather superior to the British Centurion III in this respect having a glacis nearly twice as thick. But the British also produced the Conqueror, whose armour thicknesses are comparable to the Tiger II- albeit with better shaping. If we took the protection of the Tiger II as being between the Centurion and Conqueror, I don’t think we will end up too wide of the mark.For my answer, I will assume that that both tanks in this Big Daddy v Giant Haystacks tank smackdown are in good fettle with defect free armour. The Tiger II will be allowed PzGr 40 APCR ammunition (although I will consider PzGr 39 APCBCHE ammunition too). The IS-3 is allowed BR471B APCBCHE which was probably unavailable during WWII.The modelling I have used is based on that of Refs 9 & 10, a simplified version of that used in my answers to Which tank was better, the King Tiger or the IS-2? and How would ten Tiger tanks compare with 10 IS-2 tanks in combat effectiveness, assuming all tanks are in good working order?The British study reckoned that a 17 pdr armed Centurion was about equal in tank-on-tank combat effectiveness to an IS-3. This was based upon the rate at which it could gain side penetrations making up for frontal invulnerability of the IS-3. The same report reckoned that ten 20-pdr armed Centurion IIIs would be a match for about a dozen IS-3s.Now, the Centurion with 17 pdr is a bit better ergonomically than the Tiger II -according to the British, at any rate- [Ref 11], but it is less well armoured and its gun is worse in terms of penetration if both guns use tungsten-cored ammunition.We can use this model to build up an answer. I will take a step by step approach to show my reasoning. It’s a bit rough and ready, I admit.Let us consider a Tank ATank A has the ergonomics of a Tiger II, a 17 pdr gun and the armour of a Centurion III.The British reckoned the engagement rate of a Centurion with either gun was about 3 times that of the IS-3 and the Tiger II about twice that of the IS-3. So applying the model gives Tank A about 0.8 the effectiveness of the Centurion.So 10 Tank As would be match for about 8 IS-3sNow “up-gun” Tank A with an 88 mm KwK 43, keeping other factors equal. This is called Tank B. B1 with APCBC, B2 with APCR.Using the PzGr 39 (Tank B1) makes things worse because the PzGr 39 has worse penetration than the 17 pdr APDS. However, with PzGr 40 (Tank B2) ammunition is quite a bit better than the 17 pdr APDS at this range (but inferior to the 20 pdr). Doing some maths gives:10 Tank B1 are equal to 7.5 IS-3 s and10 Tank B2 are equal to about 9 IS-3.Ok. Now let us make Tank C.This is Tank B with but now the armour of a Tiger II.Here we need to bring in the Conqueror tank. Based upon a directional probability variation determined from WWII statistics, the British gave the IS-3 a 66% chance of penetrating Centurion and a 51% chance of penetrating a Conqueror at 1000 yards. In reply, the British reports reckoned a 20 pdr armed Centurion had a 47% chance of penetrating the IS-3 at the same range [Refs 11 & 12], albeit the probability of penetrating from a frontal engagement was only 23%. [Ref 13]The effective thickness of the Centurion glacis against 122 mm ammunition is 190 mm (based on Ref 14), King Tiger 240 mm and Conqueror 400 mm. The side armour of each is not dissimilar. So in terms of protection, Tank C is between Centurion and Conqueror.So for Tank C the probability of a kill if hit would be about 59%Plugging in the maths gives:10 Tank C 1s are equal to 8.5 IS-3s and10 Tank C2s are about equal to the 10 IS-3sBut wait a minute Tank C IS a Tiger II! So we have an answer!5. ConclusionsBased on a simplistic model, in a flat battleground at 1000 yards:Using PzGr 39 APCBCHE ammunition 10 Tiger IIs are needed to fight 8.5 IS-3s. This is because its gun struggles against the IS-3 armour.Using PzGr 40 APCR ammunition, the Tiger II and IS-3 are much of a muchness in tank to tank combat. Although the IS-3 is much better protected, this in cancelled out by the higher engagement rate of the Tiger II.In a tactical situation where the Tiger II were only able to attack the IS-3 frontally, the IS-3 would increase in value.Annex A: Armour ThicknessTiger IIIS-3This is not correct insofar that the outer part of the hull is only sheet metal -it included stowage compartments that can be lifted easily- see Ref 16Centurion IIIAAnnex B: Penetration ValuesNote that the British study considered the Centurion glacis vulnerable to 122 mm fire even, as you can see, it is marginal. The British study generally gave the benefit of the doubt to the Russian tank.Annex C : Frequently asked questionsIs the polar plot at figure 1 similar to the clover diagrams from the Tigerfibel?No, it shows the vulnerable area of the target at 1000 yards as a function of angle, the Tigerfibel clover leaf plots give the ranges at which the Tiger can be penetrated as a function of angle.How does the model work?It assumes attacking tanks are spawned on a circle of 1000 yards radius with the target tank at the centre, The probability of spawning at each angle is given by a directional probability variation see Ref 17 .The model is rather simplistic but was bench-marked against WWII Operational Research data on statistics of tank battles.What are the uncertainties in the model?As well as the simplistic methodology used, the model can only be as accurate as the data input. There are ranges of values given for penetration -see John Salt’s compendium of WW2 data for example. Judgements on engagement rates are subjective-rates of fire and traverse rates are variables not constants and different sources give different values again. The accuracy of the model is therefore no better than plus or minus 1 tank in the “how many to take on ten” approach.If the Tiger II can only penetrate a small area of the frontal armour of the IS-3, why isn’t the IS-3 winning easily?Because the directional probability variation gives about 40% of hits on the frontal armour, giving possible penetrations from the side 60% of the time. Even so, the IS-3 side armour is stopping lots of side hits, hence the APCR ammunition gives a big improvement.Doesn't the APCR round do little damage compared to APHE if it penetrates?There are two parts to my answer:a.APHE which explodes (sometimes, most types had quite high blind rates) it does cause more damage and increase the chance of an internal fire, Ref 18 I however, the British did not think this was worth the lower penetration. Tests of 17 pdr APDS on a T-34 [Ref 19 ] did damage like this :Some commentators think the size of the projectile is important, but I think it is the residual kinetic energy that matters- imagine a tungsten round bouncing inside the IS-3 as shown in the photograph. The chance of it inducing serious trauma in the poor crew members seems very high. See trials data above.Couldn’t the IS-3 blow the Tiger II turret off with HE fire?See my answer to Would the ISU 152 be able to de-turret a modern tank like it did with its WW2 counterparts?I am very doubtful of this. There is a question of whether hits on the turret could collapse the hull roof. This effect was seen in British trials of Malkara missiles on Conqueror and Centurion tanks, albeit Malkara has 4 times the HE payload as a 122 mm shell. Following the Isigny tests in 1944 against captured Panthers the US recommended that a 105 mm HE round could fail the hull roof with a mantlet hit. However, the British assessment of the Tiger II Ref 20 praised the shape of the mantlet in preventing this and the Tiger II armour (40 mm)was much thicker than that of a Panther (17 mm).Would 122 HE be able to knock out the King Tiger with spall?This would depend on armour defects and temperature. For the good armour I have assumed in my model, a 122 mm HE isn’t going to cut the mustard against the glacis- it would trouble a 120 mm HESH round designed to do the job [Ref 21 ]. I am aware of the Kubinka trials, by the way. It will be noted that Ref 20 said the armour quality of that example of a Tiger II was good and there are plenty of photographs of Tiger IIs used as target practice that show no evidence of failed armour. The 1944 Allied trials at Isigny on three Panthers showed one had good armour, one in between and one rubbish armour that cracked easily. It is not unreasonable to assume that a similar situation applied to the Tiger II, and my model did state it assumed “good armour”.On a cold day with dodgy armour, then the Tiger II scores would drop. On the other hand, I don’t have data for IS-3 armour,What would be the effect of real terrain rather than a flat tabletop?It would help the IS-3 somewhat as it is the smaller tank, but overall I think it would favour the Tiger II as the IS-3 suffers from poor gun depression so on a slope it cannot engage in many cases. Players of World of Tanks and War Thunder know about this.Who on Earth were Big Daddy and Giant Haystacks?They were oversized 1970s wrestlers who fought risible bouts on ITV’s World of Sport this programme was screened opposite the BBC’s rather po-faced Grandstand programme. Whilst dire, it beats today’s Saturday afternoon TV offerings in my view and I was happy enough to watch it as a boy. Big Daddy’s real name was Shirley Crabtree, by the way. In the UK, Shirley is a girl’s name. As in “ha ha ha, that man has a girl’s name….er, nice to see you again Mister Crabtree”.ReferencesBaryatinsky M (2006) The IS Tanks Ian Allan p77Ibid p84–87Sewell S (2002) Red Star, White Elephant Armor MagazineBaryatinsky M (2006) The IS Tanks Ian Allan p68–69Eccles RW and Kesteven WL (1951) AORG report 11/51 Effectiveness of British and Russian TanksJentz T L (1998) Germany’s Tiger Tanks Schiffer Military HistoryJentz T & Doyle H (1993) King Tiger Heavy Tank New Vanguard OspreyHiggins D (2011) King Tiger v IS-2 (Duel) OspreyEccles RW and Kesteven WL (1951) AORG report 11/51 Effectiveness of British and Russian TanksBenn E and Shephard R (1952) AORG Report 6/52 Tank Effectiveness, A Comparison of Theoretical Measure with Observed Battle Performance with a Further Note on Rate of FireTunnicliffe C. (1947) WO 291/1003 MORU Report: Motion Studies of German TanksBereford R S and Sturtridge M I (1955) Tank Effectiveness The Heavy Gun Tank No.2 WO291/1341 Table 1Longman A V (1954) Tank Effectiveness, Conqueror, Conway and Charioteer WO 291/1416 Table 1aBereford R S and Sturtridge M I (1955) Tank Effectiveness The Heavy Gun Tank No.2 WO291/1341 Table 2Bird L and Livingston R (2001)World War II Ballistics, Armor and Gunnery Overmatch.Zaloga S (1997) The IS-3 Heavy Tank Military Ordnance Special #20JM Whittaker (1943) in Operational Research Group (W&E) Report 362 Chapter IVIvory W and Rees W (1945) German Steel Armour and Theory of Penetration British Intelligence Objectives Sub Committee)Champion E J (1955) Damage Asssesment Report on Trial of 3.5 Inch Rocket,76 mm HESH & 17 pdr APCBC/APDS versus Russian T34/85 Tank FVRDE AscotWO 194/746 (1944) Armour and Vulnerability of Royal Tiger TankLongman A V (1954) Tank Effectiveness, Conqueror, Conway and Charioteer WO 291/1416 Table 4