

Waiting for take-off ... - RiderOfGiraffes

I first did this decades ago, but still occasionally do it just for fun.<p>While waiting for a flight in the gate lounge (the waiting was in the gate lounge, not the flight) I was idly thinking about the acceleration during take-off.  Plane accelerates, you get pushed back into your seat, surely there was some way of measuring that.<p>Obviously you can have a pendulum and measure the angle during take-off, but then you need a protractor, and a calculator that can take the tan of the angle, and it all seems very difficult.<p>Then I realised that if the pendulum hung on a ten by ten square, the marks across the bottom were effectively units of m/s^2.  45 degrees is 1 gee which is about 10m/s^2, and it's linear in the tan of the angle, etc, etc, so the system is effectively calibrated.<p>So take a piece of card, mark about 1/12 of the distance from the bottom top right corner up, replicate ten times, cut a notch, hang the pendulum from there.  Mark the same distance ten times across the bottom and hey presto, a callibrated plumb-bob accelerometer.<p>Now use during take-off.  (Yes, you do get some funny looks).  In the first 5 to 10 seconds the acceleration ramps up roughly linearly to reach about 3 m/s^2.  That's held for about 25 to 30 seconds, so all up we get:<p><pre><code>    V = 1/2*(5*3)+25*3
      = 90m/s
      ~ 160 kts.
</code></pre>
Spot on.<p>The result was really lucky, because in truth the plane bounces around and the pendulum swings wildly.  It's tough to dampen the swinging and get accurate measurements, but it's amazing how accurate it turns out.<p>For extra credit - roughly how much runway was used?<p>EDIT: All this was to rotation - not to take-off.  Once the place tips up a plumb-bob accelerometer is somewhat compromised!
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RiderOfGiraffes
This was prompted by jgc's item "Damn the Torpedoes",

<http://news.ycombinator.com/item?id=878919>

which caused me to rootle a bit on his blog (fun - thanks John) and hence find
this:

[http://www.jgc.org/blog/2008/02/sum-of-first-n-odd-
numbers-i...](http://www.jgc.org/blog/2008/02/sum-of-first-n-odd-numbers-is-
always.html)

So this item is partly in answer to his question at the end.

For reference, pre 9/11 this exercise would often get me an invitation to the
flight deck.

