And many planes were being shot down by German fire, and the casualties were huge. In some years of World War II, the chances of a member of a bomber crew making it through a tour of duty were about the same as calling heads in a coin toss and winning. As a member of a World War II bomber crew, you flew for hours above an entire nation that was hoping to murder you while you were suspended in the air, huge, visible from far away, and vulnerable from every direction above and below as bullets and flak streamed out to puncture you. “Ghosts already,” that’s how historian Kevin Wilson described World War II airmen.
Where to Armour?
So here was the question. You don’t want your planes to get shot down by enemy fighters, so you armour them. But armour makes the plane heavier, and heavier planes are less manoeuvrable and use more fuel. Armouring the planes too much is a problem; armouring the planes too little is a problem. Somewhere in between there’s an optimum.
The Statistical Research Group (SRG) was a classified program that yoked “the assembled might of American statisticians to the war effort—something like the Manhattan Project, except the weapons being developed were equations, not explosives. The military came to the SRG with some data they thought might be useful. When American planes came back from engagements over Europe, they were covered in bullet holes. But the damage wasn’t uniformly distributed across the aircraft. There were more bullet holes in the fuselage, not so many in the engines.
The officers saw an opportunity for efficiency; you can get “the same protection with less armour if you concentrate the armour on the places with the greatest need, where the planes are getting hit the most. But exactly how much more armour belonged on those parts of the plane?
Enter Abraham Wald, who was working at SRG at that time. Born in Hungary in 1902, the son of a Jewish baker, Wald spent his childhood studying equations, eventually working his way up through academia to become a graduate student at the University of Vienna where the great mathematician Karl Menger mentored him. As he advanced the science of probability and statistics, Wald’s name became familiar to mathematicians in the United States where he eventually fled in 1938, reluctantly, as the Nazi threat grew. His family, all but a single brother, would later die in the extermination camp known as Auschwitz.
And Wald came up with an interesting idea to the question of how much armour, and where.
The armour, said Wald, doesn’t go where the bullet holes are. It goes where the bullet holes aren’t: on the engines.
Wald’s insight was simply to ask: where are the missing holes? The ones that would have been all over the engine casing, if the damage had been spread equally all over the plane? Wald was pretty sure he knew.
The Missing Planes
The missing bullet holes were on the missing planes. The reason planes were coming back with fewer hits to the engine is that planes that got hit in the engine weren’t coming back. Whereas the large number of planes returning to base with a thoroughly Swiss-cheesed fuselage is pretty strong evidence that hits to the fuselage can (and therefore should) be tolerated. If you go the recovery room at the hospital, you’ll see a lot more people with bullet holes in their legs than “than people with bullet holes in their chests. But that’s not because people don’t get shot in the chest; it’s because the people who get shot in the chest don’t recover.
Wald put together a crude before-and-after diagram. The “after” image — the plane on the right — showed where the majority of the damage was, as indicated by the shaded regions. Wald determined that most of the plane — the wings, nose, and fuselage — had taken the worst beating, while the cockpit and tail were generally unharmed.
Wald theorized that the fact that the planes lacked damage in the cockpit and tail was more telling. Certainly, the Axis’ targeting of Allies’ planes was both indiscriminate and imprecise; there was little reason to believe that the Axis forces were aiming for, say, the nose, and intentionally avoiding striking the tail. Some planes had to have taken significant damage to the tail and cockpit, and all of those planes had something in common: they, unlike the ones in Wald’s data set, did not return back to base.
On Wald’s advice, the U.S. military leadership reinforced the cockpits and tails on its planes. The number of planes (and lives) saved during the World War and Korean and viet Nam wars are difficult to estimate, but the impact of this idea was huge.