Archive for History

Applying N-squared to internet tank debates

Posted in History, musings with tags , , , , on 30/03/2014 by sangomasmith

One of my hobbies (I have many, as can be seen by the scatter-shot nature of my posts) is going onto history forums and debating things. As I play World of Tanks (which has a fairly active historical armour forum), this sort of thing then tends to leads into ruminations on what I tend to think of as technical history. A perennial favourite, of course, is the idea that technically superior equipment will trump a numerically superior opponent. This is especially the case when Nazi wunderwaffe (which seem to have entire industries devoted to proclaiming their advantages) are compared to Allied equipment of the same era.


A common victim of this process are the T-34 and M4 medium tanks; which seem to be doomed in popular culture to throwing themselves endlessly against impervious Nazi super tanks (various myths listed here). Now, obviously this is a fallacy: Tiger, Tiger II, Ferdinand and all the rest never made up a substantial part of the German tank park. And even if they had, their high maintenance requirements and long logistical tails meant that they would have been actively detrimental to the German war effort.  Which begs the question of what the best setup for German production would have been.


In an effort to resolve this (and because I’m a giant geek when it comes to models and gaming things), I decided to apply something like Lanchester’s model to tank-vs-tank battles. See this page for reference, while this article gives a pretty good overview of the concept and then applies it to battleships.


First, the assumptions:

  1. Terrain is not a factor
  2. Other arms are not used
  3. All penetrating hits are fatal
  4. Relative amounts of vehicles are based on weight of steel (unless otherwise noted)
  5. Rate of fire and accuracy for vehicles are the same (unless otherwise noted)


Obviously these are pretty big limits (especially 1 and 2), so be advised that this is a rough model. For all scenarios, I used a hit model based on an exponential approximation of this data (the hit percentage working out to roughly 31*e^-0.0016x where x = distance in metres; coefficient of determination = 0.54). To work out when hits would penetrate, I used this post and this website. Because I am a simple soul, the model was pretty granular: each round saw the opposing vehicles fire, then move a set distance closer for the next round. Hits were rounded up, so a hit score of 1.5 became 2 hits.


For scenario one, I took the Tiger (56.9 tonnes) and T-34/76 (26.5 tonnes). This means that, for every Tiger tank produced, an equivalent amount of resources could have produced 2.15 T-34s. Tiger gets to penetrate T-34 at all ranges, while T-34 only gets to penetrate when the range is 500m or less. Here are the results:

Tigers Remaining T-34s Remaining Distance (m)
10 21 1000
10 20 900
10 19 800
10 18 700
10 17 600
10 16 500
8 15 400
6 14 300
3 13 200
0 12 100


This doesn’t look very good for Tiger, though the assumptions going in were about as generous as possible. Even when greater engagement ranges are used (up to 2000m), the low hit probabilities mean that combat goes to the more numerous T-34. So, given that longer kill range and better armour don’t help, the question becomes: what would?

Here are a few ways to ‘win’ that this model suggests:

  1. Have greater numbers of vehicles.
  2. Fire faster than your opponent
  3. Fire  more accurately than your opponent
  4. Be invincible


The first point has been tested, while point four is a bit problematic from the standpoint of mobility/logistics (Tiger was at the margin of what automotive technologies of the time could deal with).  Consequently, it is points two and three that we shall investigate next.


In terms of the model, both concepts (faster fire rate and increased accuracy) result in the same mechanistic end. As there are known historical limitations on fire rate (the loader’s ability to, well, load the gun), the more productive of the two options is to concentrate on accuracy. Accuracy in a tank-on-tank combat revolves around range-finding; with higher gun velocities and better rangefinding equipment simplifying the task. In the case of dedicated tank hunters, a specialised weapon, specifically-trained crew and appropriate tactics can make a massive difference.


For scenario two, tanks and tank hunters face off against each other in similar numbers to the Tiger/T-34 example above. The tank hunters have no advantage over the tanks beyond their accuracy, which allows them to engage targets with a 100% better chance of hitting. The results are, again, not encouraging: by 400m all the tank hunters are dead. If, however, a combination of better accuracy and better staying power is achieved (the ‘Desert Storm’ scenario), then things change dramatically:

Tigers (+100% better accuracy) T-34s Distance (m)
10 21 1000
10 20 900
10 19 800
10 17 700
10 15 600
10 13 500
8 11 400
6 8 300
4 6 200
3 4 100


What this shows, in the end, is that Lanchester’s square law holds. It takes exponentially better equipment to defeat superior numbers in a head-on fight; a fact that is especially true given the technological parity of the major WWII combatants. In the end, this means that the best approach is always to maximise the amount of forces available for a given amount of logistical support rather than trying to achieve one-on-one superiority for any given system.


The fixation on German superweapons, then, obscures the fact that they were tactically and strategically the wrong choice to make.



Posted in media, News-related, rant with tags , , , , , , on 23/03/2010 by sangomasmith

I was recently reading a Time magazine article on the (sadly all-too-real) phenomenon of white minority fears. For those of you still in touch with sanity, it’s this idea that white folk are going to become minorities in their ‘own’ countries. The assumption is that, ten seconds or so later, they will all be herded into a camp and shot. Also, their jobs will be taken by non-white people. And the trains will all explode.

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Cracked wins twice

Posted in economics, History, media with tags , , on 12/02/2010 by sangomasmith

I was going to say something profound today, but cracked already beat me to it. Way to go, guys.

Swords and Stockholm syndrome

Posted in History, media, pedantry, rant with tags , , , , on 24/08/2009 by sangomasmith

The new rash of historical revisionism is killing historical understanding

I was recently watching a history-themed show by National Geographic called ‘Samurai bow’ and was enjoying myself immensely until they got to the inevitable ‘comparison with X’ section of such shows. In this case, the comparison was between a Japanese longbow (or Yumi) and an English longbow of equal draw weight. Which is where I start to have problems.

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