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I've always found the relative impact velocity of the foam piece with respect to the shuttle quite surprising. There is some clarification of this in the CAIB report, chapter 3, page 60 (http://www.nasa.gov/columbia/home/CAIB_Vol1.html):

THE ORBITER “RAN INTO” THE FOAM “How could a lightweight piece of foam travel so fast and hit the wing at 545 miles per hour?” Just prior to separating from the External Tank, the foam was traveling with the Shuttle stack at about 1,568 mph (2,300 feet per second). Visual evidence shows that the foam de- bris impacted the wing approximately 0.161 seconds after separating from the External Tank. In that time, the velocity of the foam debris slowed from 1,568 mph to about 1,022 mph (1,500 feet per second). Therefore, the Orbiter hit the foam with a relative velocity of about 545 mph (800 feet per second). In essence, the foam debris slowed down and the Orbiter did not, so the Orbiter ran into the foam. The foam slowed down rapidly because such low-density objects have low ballistic coefficients, which means their speed rapidly decreases when they lose their means of propulsion.

There is a quick back of the envelope calculation that we can do to understand this better.

The force due to drag on an object is described by the following equation (http://en.wikipedia.org/wiki/Drag_equation):

F = (1/2)p(v^2)(C_d)A

where p is the density of the fluid the object is moving in, v is the velocity of the object relative to the fluid, C_d is the coefficient of drag and A the cross-sectional area. C_d is around 1 for most geometries (http://en.wikipedia.org/wiki/Drag_coefficient).

In the CAID report, the dimensions of the foam is estimated to be 19x11.5x11.5 inches, which is roughly 0.5x0.3x0.15 meters. Assuming the foam fell with the smallest surface pointing down (a bad assumption), we can estimate A to be 0.045 m^2.

According to Wolfram Alpha, the density of air at 20km, the altitude at which the foam broke off, is 0.089 kg/m^3. The initial velocity of the foam was about 1568 mph which is around 700 m/s.

Plugging all of this in to the above equation gives:

F ~= 981 kg*m/s^2

The mass of the foam was estimated at 1.6 lbs, or around 0.7 kg, and using F=ma we can calculate the acceleration to be about 1400 m/s^2. The foam traveled for 0.16 seconds before striking the shuttle, and assuming that the above force was constant during that time (thus overestimating the change in velocity), that would result in a delta_v for the foam of 224 m/s, which is about 500 mph.

This is all assuming of course I didn't make some trivial mistake with the math, which I probably did.

It would be great if someone with more knowledge than me could chime in about drag near the speed of sound (or multiples of the speed of sound).

The CAIB set up a dramatic recreation of the incident in which it used a nitrogen gun to fire a piece of foam at ~500mph at a test panel. NASA was not happy with the idea of the experiment feeling it was a waste of time. There were audible gasps from the crowd of engineers when the foam punched a head-sized hole in the panel. Bingo.


Came here to make sure that this article was posted. It's an engaging and well written examination of the followup to the Columbia's loss. Thanks for linking to it!

It boggles the mind.

I'm also extremely curious to know how much the Shuttle stack accelerated during those 0.161 seconds the foam wasn't attached to it...

Not a whole lot. The Shuttle's max acceleration during launch was around 3 gees, and at this phase I believe it was more like 2.5 gees. 0.161 seconds at 3 gees is under 5 meters/second change in speed.

Thanks very much. I had always assumed the Shuttle's max acceleration was a lot higher than that, given how fast the thing seems to get moving in such a short amount of time.

It takes about eight minutes to get to orbit. Which is quick, but not super quick. Reasonable accelerations reach really high speeds when you just keep doing them for minutes at a time. For example, a fast race car might be able to pull off a similar acceleration, but only for a few seconds before it can't go any faster.

Acceleration at liftoff is lower than maximum acceleration during the rest of the launch.

Most of the mass in a rocket is fuel. As the fuel is burned off, the same amount of thrust gets divided over a progressively lower remaining mass.

The Shuttle stack has a mass of 2.03 million kg at launch, and delivers 30.45 MN of thrust. That's 15.0 m/s² of acceleration, or 1.53 g's. (Because it's thrusting vertically, though, it only accelerates upward at 0.53 g's.) This is much lower than the maximum acceleration attained later in flight.

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