brainwagon

Today,
Slashdot is reporting that the
BBC has announced that recent investigation of the Columbia disaster has shown that the foam that blew off and contacted Columbia’s wing could have resulted in damage consistent with the
catastrophic loss of the spacecraft.

In the test a 0.8kg piece of foam was fired by a nitrogen powered gun at a panel that was decommissioned from Atlantis. It contacted the wing at 850km/hour, and blew a 40cm square
hole.

Immediately the "cogniscenti" of slashdot set up a huge cry that such a large velocity
was unwarranted: that there was literally no way that the piece could have accelerated to such a
high velocity in such a short span of time. Most are just ignorant assertions, but some people try
to do the math, such as this one:

As far as I can see, I’d imagine that the foam falls from the fuel tank/booster onto the shuttle wing. The rate of fall should be only the relative acceleration that the shuttle experiences during the fall. (Since both foam and shuttle are presumably moving at the same speed when it detaches from the launcher)

So the total acceleration should be the acceleration of the shuttle (max 3G at liftoff according to a couple of web sources) plus normal gravity – call it 4 G. At most, the foam could fall the full 56 meters of the shuttle/booster/tank height (and most likely substantially less than that).

So, a quick (and probably hideously wrong) calculation based on v^2=2 * Accel * Distance shows that the end velocity of a body falling 56 meters at 4g should be about 33 meters/second, or 119 kph (74 mph)

Of course, the factor that they are missing is the enormous drag caused by the very unaerodynamic chunk of foam insulation as it detaches from the tank. The relatively low
mass and high drag of such a chunk causes it to decelerate very rapidly.
When the insulation disconnected, Columbia was 81 seconds into its flight, travelling at
Mach 2. Initial estimates indicated that the impact speed could not have been more than
500mph.

But do the math! At a relative speed of 500mph, a 1kg chunk of insulation has momentrum
equal to 0.5 * m * v^2, which is 25,000 joules or so. What does this mean? Well, let’s say
that I weigh 100kg (dreaming, I know, but it makes the math easier). If I am travelling 50mph,
then I have virtually the same kinetic energy as that chunk of foam.

I suspect that if you threw me at the Challenger wing at 50mph, something bad would happen.