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  #1  
Old 02-07-18, 10:54
Alastair Thomas Alastair Thomas is offline
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Default The German tank problem

I thought this may interest forum members. It is heavily based upon the Wikipedia article of the same title. I have read somewhere that a book that includes an equation immediately loses the sale of 10,000 copies. However, never fear, although I have included an equation here, it is simple and can, nevertheless, be skipped over.
Logistics is an important arm of conflict. Napoleon’s army may have marched on its stomach but, nevertheless, resupply from France would be necessary for all manner of things. What resources the enemy has and will have is important information to a commander so considerable effort was expended in WWII to find out. One example of the techniques used was a statistical analysis of the serial numbers of parts of German tanks in order to estimate the rate of production. Of course intelligence was used as well and the two had to be compared to come up with the best guess.
Two mathematical methods were used: Bayesian and Frequentist. The former can be dispensed with quickly as it is not amenable to a simple description. It was invented by a Reverend Bayes in the 18th century. It is based upon estimating the chances of all sorts of things happening in order to arrive at the chance of a particular outcome. A famous example of its use was the finding of Air France 447, which crashed in the Atlantic.
The Frequentist approach is much easier to understand and both methods assume that the enemy has manufactured a series of tanks marked with consecutive whole numbers, beginning with serial number 1.
As captured and damaged tanks became available to the allies, the serial numbers on major items such as the chassis, engine, gearbox and wheels were noted.
What we want to know is “N” the number of tanks manufactured. What we do know is “k” the number of tanks/wheels we have examined and “m” the highest serial number recorded.
The Frequentist solution can be found from:
N (the number of tanks)=m(the highest number recorded)+m/(k(the number examined))-1
As an example, if four tanks were examined (k = 4) and they had serial numbers 19, 40, 42 and 60 (m = 60) then the above equation gives the answer N=74.
Statistical methods do not give exact numbers. They give the likeliest answer and then a spread of values around the answer (this is why statistics gets such a bad name). The fewer the number of samples (k) used, the wider the spread of numbers. It is for this reason that the wheels of the tank are interesting, there being 32 on each Panzer V (a tank of particular interest to the analysts prior to D-Day).
In parallel with the statistical methods, other methods were used. In the case of these wheels, investigation identified how many moulds were being used to cast them. Discussions with UK manufacturers indicated the likely maximum number of wheels that could be cast per month.
These methods arrived at an estimate of 270 tanks produced in February 1944. After the war German records were examined and the true answer was 276.
A comparison was made with the conventional intelligence approach and some results are shown below.

Month | Statistical estimate | Intelligence estimate | German records
June 1940 | 169 | 1,000 | 122
June 1941 | 244 | 1,550 | 271
August 1942 | 327 | 1,550 | 342

This analysis is used by most nations so attempts are made to encrypt the serial numbers. As you would expect great efforts are employed to crack the encryption.
Because all good posts include a picture here is a photo of my Father in a captured Fiat Ansaldo L6-40.
As the narrator of the famous record “Trains” signed off, “Ah well, back to the asylum”.
Alastair
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  #2  
Old 02-07-18, 11:21
Lynn Eades Lynn Eades is offline
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Wow!!!!???????
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Old 03-07-18, 20:30
James P James P is offline
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And I used to think the problems for German tanks where Shermans, Comets, T-34, Typhoons, AT guns.........................
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Old 05-07-18, 16:19
Mike Cecil Mike Cecil is offline
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The Int estimate values are interesting as this intelligence figure is then used to calculate what it would take to counter that Int estimated production - ie how many tanks are we going to need to combat the 'X' tanks produced by the enemy in the last 12 months, minus what we know we have destroyed?

Such a figuring may well have delayed operations pending an Allied build up to a suitable level to ensure success against what the Intelligence people thought the enemy could field (rather than what they could field).

And where on earth did the intelligence boffins think the Germans were hiding all those tanks??

Mike
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Old 05-07-18, 20:15
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Robert Bergeron Robert Bergeron is offline
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Default North american war production

North American war production ( Canada-USA ) is what defeated the German tanks, not the Sherman nor the 6 pdr.

While the Germans had the best tanks, the allies had the most and in overwhelming numbers ( 5 -1 ) .

The Allies had a pipeline going from the artificial ports of Normandy almost right up to the German border while the Germans were running out of gas during the Ardennes counter-offensive ( Dec 44 ) . Hitler wanted his Panzers to push the Allies back into the Atlantic with his tanks running on captured Allied gas... What a workable plan that was !

Anyway, very able and convincing demonstration you have made my friend Alastair !

Cheers.

Bob
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Old 06-07-18, 07:38
maple_leaf_eh maple_leaf_eh is offline
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Quote:
Originally Posted by Mike Cecil View Post
The Int estimate values are interesting as this intelligence figure is then used to calculate what it would take to counter that Int estimated production - ie how many tanks are we going to need to combat the 'X' tanks produced by the enemy in the last 12 months, minus what we know we have destroyed?

Such a figuring may well have delayed operations pending an Allied build up to a suitable level to ensure success against what the Intelligence people thought the enemy could field (rather than what they could field).

And where on earth did the intelligence boffins think the Germans were hiding all those tanks??

Mike
I doubt reality entered some peoples' minds.

One complication to the tank number estimates has to battlefield regeneration of losses. We know that Normandy was fought with tank mostly made in 1942 and 43. The resupply depots were staged to replenish losses after the units were withdrawn. The battles in 1944 and 45 were fought with tanks that survived or were knocked out, recovered, repaired and reissued, and with new builds. The introduction of new designs was resisted because of the bother of retraining and establishing parallel lines, and sustaining the momentum of equipping regiments with Shermans. The following link amply details the business of replenishing combat regiments with Shermans http://scholars.wlu.ca/cgi/viewconte...00&context=cmh.

In the context of German losses, they invariably lost ground in combat after DDay. Any vehicles knocked out were abandoned on the battlefield, which meant their replenishment calculations could scarcely include salvage and returning tanks to front line units. So, their factories had to be very productive to keep up with demand, regardless of availability estimates.
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Old 06-07-18, 08:22
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Hanno Spoelstra Hanno Spoelstra is offline
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Quote:
Originally Posted by maple_leaf_eh View Post
The following link amply details the business of replenishing combat regiments with Shermans http://scholars.wlu.ca/cgi/viewconte...00&context=cmh.
The author, Arthur Gullachsen is a member of MLU. Here is a link to the web page describing his article "No Shortage of Tanks!: The Canadian Army’s System for the Recovery, Repair and Replacement of A and B Vehicles and Major Weapons Systems".

Mr. Gullachsen also wrote Destroying the Panthers: The Effect of Allied Combat Action on I./SS Panzer Regiment 12 in Normandy, 1944. This article argues Allied combat action was responsible for a large percentage of Panthers that were out of action. And like you noted Terry, also the inferior resources of the German tank replacement and repair program were no match for superior Canadian Army practices during 1944.

What also interesting to look at is the cost of manufacturing tanks. Many years ago, I made a web page listing Sherman's 1945 prices, averaging $50,767 across all variants. Recently I came across a chart detailing the WW2 German tank cost: a King Tiger was the equivalent of $320,000, while the most numerous German AFV, the StuG III, cost $33,000.

The Panzer IV was $46,000, which is similar in price and performance to the Sherman tank. So one could argue each combatant got the same "bang for the buck"!

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