Built on Facts

The Shuttle on a Diet

Space Shuttle mission STS-132 is currently orbiting over our heads. It’s scheduled to land a week from now. After that, there’s two more launches and that will be that for the program. At that point the US will officially be out of the business of launching people into orbit, and there’s not a lot of prospect of getting back into that business in the near future. I don’t really regret the end of the shuttle program as such – it was never a really good human spaceflight strategy – but it’s a real shame we have nothing to replace it.

Oh well. To commemorate STS-132, how about a quick physics problem? First, take a look at STS-1, the first shuttle launch:

i-0cdd741843dd8ee3b325dc28828704a5-shuttle.png

Notice anything different in this photograph compared to most shuttle launches? The most obvious difference is the color of the external tank. Here it’s painted white. Now it’s not painted at all, and is left its normal dull orange. The reason for this is that the paint required to cover the whole external tank weighed about 600 pounds. That’s not much compared to the weight of the entire shuttle, which weighs more than four and a half million pounds. Still every bit makes a difference. Let’s estimate how much.

We’ll do this Fermi-problem style and use approximations. To a first estimate, the gravitational acceleration at the shuttle’s orbital altitude is about the same as it is on the ground. The apparent zero-g that the astronauts experience is a result of free fall, not a result of being very far away from the gravitational field of the earth. The potential energy gained by moving 600 pounds to orbit is:

i-d4bb9fe09d6b78eb832985821d8a307f-1.png

Where U is potential energy, m is the mass (in kilograms), g is the acceleration due to gravity, and h is the orbital altitude. Using the 206km insertion altitude, I get a figure of about 600 million joules. For the kinetic energy by virtue of orbital velocity, we can use the kinetic energy equation:

i-88516ca505d84f969b7ab15a965c3fb3-2.png

Shuttle orbital velocity is about 7.6 km/s, so that’s about 8 billion joules of energy. Adding, and we get about 8.6 billion joules or so of energy that would have to be used to get that paint into orbit. Compared to the total energy of the whole shuttle, that’s not much. But in absolute terms it’s quite a bit. 600 extra pounds of payload is nothing to sneeze at.

Comments

  1. #1 Art
    May 19, 2010

    All fine and good, very informative, but would the paint, possibly modified and reinforced, have kept the insulation from coming off in chunks? Modern urethane paints are tough, sometimes used to hold together blast walls.

  2. #2 Matt Springer
    May 19, 2010

    I’m not an expert, but it’s my understanding that the problem of detaching foam occurred on STS-1 and subsequent flights with and without paint before finally bringing down Columbia. As far as I know the paint didn’t make a difference one way or another.

  3. #3 Uncle Al
    May 21, 2010

    The Space Scuttle has a safety-downrated payload of 25 tonnes. In constant dollars it costs three times more than the use once and toss Saturn V to boost the same mass into low Earth orbit. Saturn V LEO payload was 119 tonnes.

    Space Scuttle orbiter gross liftoff weight is 110 tonnes. Lose the orbiter entirely, toss the solid fuel booter shells after use. The 2011 result equals a 1968 Saturn 5 for a modest incremental $500 billion in managerial expense chits.

    OTOH, no asstronaught will attract the really hot alien chicks if he is driving an Orion Apollo capsule.

  4. #4 Peter
    May 21, 2010

    As you have shown in previous posts, the physics of rocketry results in an initial fuel load several times the payload launched into orbit – so that 600 lbs is grossed up considerably if one looks at weight at launch.

  5. #5 Noumenon
    May 24, 2010

    Context would have been nice — I have no idea whether x billion joules is enough to go around the world or heat up a cup of coffee. Too lazy to work it out for myself though…