Monday, April 27, 2015

W is for . . .

This month I'm posting Mad-Cool-Math Nuggets.


 Image courtesy: rsteup

W is for Wald, as in Abraham Wald and a memo he wrote during WWII about damage to planes that had flown over Germany and returned. The idea for this blog comes from the article Five Statistical Problems That Will Change The Way You See The World from the site Business Insider.

As a member of a statistical research group, Wald's job was to collect data on which parts of a plane were hit the most by German fire. This information was supposed to help determine where the planes might be reinforced. So far, so good?

Now Wald found more bullet or flak damage to the fuselage and fuel systems than to the engines, so guess which parts he recommended to reinforce?

The fuselage and fuel system, right? No! Here's the twist: He was collecting data from planes that had returned, not the ones that were shot down. So Wald reasoned that the fuselage and fuel system could handle serious damage from bullets and return, while the engines could not. In other words, the returned planes showed little damage to the engines because the engines that did sustain serious damage never made it back.

Smart fellow.

This kind of statistical research in WWII was the beginning of Operations Research, which uses techniques from other mathematical sciences, such as mathematical modelingstatistical analysis, and mathematical optimization, to get optimal or near-optimal solutions to complex decision-making problems. (Wikipedia) That was a mouthful, wasn't it?

Here is some information about the plane in the image above from the photographer:

A beautiful C-47 at the 2009 Geneseo, NY air show. This aircraft originally served with the 12th Air Force in the Mediterranean Theater in 1943 and the 9th Air Force in England 1944-1945 as part of the 316th Troop Carrier Group. It was one of the lead aircraft of the first strike of the D-Day invasion on June 6th, 1944. More info at 1941hag.org.

Impressive! Coincidentally, Geneseo is practically next door to where I live, Rochester, NY.


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33 comments:

  1. He was a smart fellow. The ones that made it back showed where the plane could take damage.

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  2. That was an interesting bit of history!

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  3. Never mind "hello", you had me at the picture of the C-47 :)

    For some reason, that ugly bird is one of the most beautiful planes I've ever seen and I LOVE finding them at airplane museums - or even at some random airports (like Long Beach, CA)

    That guy Wald really was smart - I bet he and his team saved countless lives... thanks for sharing.. .I'd never heard of him before :)

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  4. Very interesting. I love learning more about WWII. My grandfather was in Normandy. Thanks for sharing!

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  5. I never heard of Abraham Wald, but he does sound like a smart fellow. You surprised me with this post by talking about a person. :)

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  6. Smart guy, and very interesting post. I need to look into operations research to see if it's anything in it for me. Will do >:)

    Cold As Heaven

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  7. Brilliant! Simply brilliant. Loved this post. This is the kind of info I love to learn! Lisa, co-host AtoZ 2015, @ http://www.lisabuiecollard.com

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    1. Glad you liked it. I hadn't heard of Wald until recently myself.

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    2. Glad you liked it. I hadn't heard of Wald until recently myself.

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  8. How interesting. There's so much I don't know about the world's history,

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  9. Funny how a process that came out of necessity had such far ranging applications. Wald was a smart cookie.

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  10. Definitely a smart fellow! It makes sense to look at what planes could come back with damage and where they took too much damage and crashed.

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  11. wow - Wald is certainly not a name we hear about, but he certainly contributed a great deal. Very cool nugget of info

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  12. He sounds like a smart cookie. Of course the planes getting shot down are probably the ones that need more reinforcement.

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  13. That makes perfect sense. Also, that seems pretty logical that the planes that received heavy damage to the engines didn't make it back because, duh, getting back requires the engine part. Excellent thinking process though.

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  14. Yes, that's brilliant. Of course you'd want to reinforce the engines. Obvious when you think about it.

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  15. Now that is a brilliant mind. Thanks for doing this highly original and informative blog! His story is worth telling for sure.

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  16. Very informative about strengthening planes. I'll check out your Amazon link.

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