max q

After my video post yesterday I got a few questions from a friend:

So, why do things entering Earth’s atmosphere tend to burn up (eg, meteors/asteroids) while spaceships [taking off] do not? Is it because the foreign bodies are entering an atmosphere, encountering more and more resistance the closer they get, while a spaceship is leaving the atmosphere, and therefore the resistance and accompanying friction?

In short, “yes”.

It turns out that the resistance isn’t actually due to friction though. It is due to air compression. When you move fast enough through the air (or anything) you need to push out of the way the stuff that was occupying the space you want to occupy. If you do this fast enough you compress the air in front of you. Remember the grade 10 chemistry classic: PV=nRT? If you crank up the pressure, the temperature increases correspondingly.

A couple of details are worth looking at to flesh this out a bit. The first is that acceleration due to gravity plays only a minor role when something enters the Earth’s atmosphere. Dropping something from above the Earth is much less catastrophic than you might think. XKCD explores this a bit with a look at dropping a steak from various altitudes. Most of the speed that needs to be bled off when landing a shuttle is actually the speed that was needed to be in orbit, not speed accumulated due to falling toward the Earth’s centre. Put the other way around, the energy needed to get into orbit is mostly needed to get moving fast enough to orbit, relatively little of it is needed to get high enough to orbit. When you come back down, you need to slow back down. Carrying up enough fuel to slow down gracefully would be challenging at best, so aerobraking is used.

Now to the pressure difference between takeoff and landing.

It is pretty much as you described, but here is a bit more detail. During liftoff the Space Shuttle would reach maximum dynamic pressure at about 42 km altitude. At this point it is travelling about 1 km/s and is generating a pressure wave of about 1,500 N/m² on the nose of the shuttle. But, as you pointed out the air is getting thinner, so that pressure starts dropping – so much so that the shuttle is throttled up at this point. The leading edge of the shuttle does not warm appreciably.

On reentry the shuttle hits the atmosphere going about 7.5 km/s. At first there is almost no air, but the shuttle is going super fast. At an altitude of 70 km there is less than 1/10,000th of the sea level atmospheric pressure so is generating a pressure wave of about 2,700 N/m². And this is increasing as the shuttle descends and air density increases (exponentially). Creative flight angles are used to try to slow down with some elegance but the shuttle still gets hot enough to glow.

Meteors are generally travelling even faster when they hit the atmosphere and exhibit very little aerodynamic elegance so they explode.

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2 Responses to max q

  1. Nanaimo Doug says:

    Not to be too pedantic, or to lower the tone, but…”to flush this out…”. So much meaning in one vowel. AND: what happened to the steak?
    Reminds me of a joke – buddy jumps out of a plane…parachute malfunctions…sees a guy rapidly rising, approaching from the ground. Buddy asks “do you know anything about parachutes?” Rising Man: “…no…do you know anything about gas barbecues?”

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