# Abstract Confusions

Complexity is not a cause of confusion. It is a result of it.

## A Good Design Can Win You A World War

Often one thinks, “what is it like having a good design?”. What a wonderful design can do to you?. As a matter of fact, history is full of events answering these questions. One such is, Russian designed war tanks versus German designed war tanks during German invasion of Russia, World War II. I saw a documentary on the design of war tanks by German and Russians in Discovery channel. It became evident at the end of war, a good design can win you the world war.

### German Tanks

During World War II Germans designed and deployed a heavy tank named Tiger I. Tiger I was produced after intense research and development. It turned out,

While the Tiger I was feared by many of its opponents, it was over-engineered, expensive and time-consuming to produce. Only 1,347 were built between August 1942 and August 1944. The Tiger was prone to mechanical breakdowns and in 1944, production was phased out in favour of the Tiger II.

Tiger I - German Tank

The main reason for Tiger I failure was often attributed to the fact that it is heavy. This is because, the metal sheets used to cover the hull of the tank were made at a thickness up to 80mm. The thickness is an important armor against bullets fired from machine guns from piercing through it. Often several rounds of machine guns were fired at the tank from the ground level. Providing safety to the crew inside tank is important, without them the tank will not be operable. More thickness means more protection. Along with that the tank was getting heavier. It needed more metal for production too.

### Russian Tanks

On the other hand, Russian’s produced a formidable medium range tank – T-34. T-34’s had only 64 mm armour. But still where able to be more effective then Tiger-I.

Although its armour and armament were surpassed by later tanks of the era, it has been often credited as the most effective, efficient and influential design of World War II. It was the most-produced tank of the war, and the second most-produced tank of all time, after its successor, the T-54/55 series (Harrison 2002). In 1996, the T-34 was still in service with at least twenty-seven countries.

T-34 Russian Tanks

### A Design Flaw?

What made the difference? How come Russian medium sized tanks were able to crush the mighty German tanks? It is because of a design flaw. A design flaw which is so evident and simple, and thus over-looked. The metal sheets used to German tank’s hull are built in a square box shape. All of sheets are fixed perpendicular against Russian tanks armour which is fixed at a tilted angle. This meant, the thickness of sheet is less, but still with the lesser thickness Russian tanks armour resisted the same distance for a gun bullet to pierce through.

Refer to the above picture. A little math and Pythogoras theorem can tell you how this is possible.

Let $T_1$ be the thickness of German tank. $D_1$ be the distance of bullet piercing if it has to get through.

Let $T_2$ be the thickness of Russian tank. $D_2$ be the distance of bullet if it has to pierce Russian tank. $D_1 = D_2$. With that ${D_2}^2 > {T_2}^2$. Assuming positive roots, we have $D_2 > T_2$. Now since $T_1 = D_1$. Plugging this, $T_1$  > $T_2$. So even for a lesser thickness, Russians managed provide better armour and agility. More the slant, lesser the thickness of metal and distance traveled by the bullet will be more.

Weight of the German tank was 62.72 tonnes against Russian tank’s 29.2 tonnes. But still Russian’s design had the design advantage and thus Russians were able to win World War II.

Now, do you agree that a good design can win you a world war?