Flying to Orbit

I want to fly into orbit. Here's why.

The Saturn V used to hold the record for the biggest rocket; I think it still does.

On the launch pad, fully loaded, fueled and ready to fly to the moon, the Saturn V weighs 6.6M lbs. Of this, 4.5M lbs is fuel for the first stage. The first stage has 5 engines that generate an aggregate 7.6M lbs of thrust. At lift off, this gives

7.6M - 6.6M = 1M lbs
thrust net of gravity to get things moving.

Recalling that a slug weighs 32 lbs, we find that the rocket has a mass of

6.6M lbs / (32 lbs/slug) = 210K slugs.  
Finally, we use a=F/m and find that the rocket comes off the launch pad with an initial acceleration of
1M lbs / 210K slugs = 4.8 feet/sec^2,
also known as
4.8 ft/s^2 * (g/32 ft/s^2) = 0.15 g
or
4.8 ft/s^2 * (mile/5280 ft) * (3600 s/hr) = 3.3 mph/sec
or
60 mph / 3.3 mph/sec = 18 sec
0.15 g? 3.3 mph/sec?? 0 to 60 in 18 seconds??? I can beat that in a VW Rabbit. Any way you look at it, this is a lose.

Eventually, things get better. At the point of first stage burnout, the rocket weighs only 2.1M lbs, and we have

7.6M - 2.1M = 5.5M lbs net thrust
2.1M lbs / (32 lbs/slug) = 66K slugs
5.5M lbs / 66K slugs = 83 ft/sec^2
or 2.6g, 57 mph/sec and 0 to 60 in 1.1 sec, which should pin your ears back nicely. Reality is probably even better, since by first stage burnout, the rocket is probably turning over on its side to accelerate into orbit, and gravity doesn't take as big a bite.

Still, it seems like there ought to be a better way. I mean, if I could put 7M lbs on a 747...well, the engines would tear the wings off the fuselage and go scuttling down the runway on their own. But aside from that, if I could really put 7M lbs on a 747, or even a good fraction of 7M lbs, I could...I could...I could fly it to orbit.

SpaceShipOne

On 2004 Jun 21, SpaceShipOne flew into space. Is this a better way?

Yes and no. SpaceShipOne is the second stage of a two-stage vehicle. The first stage is an airplane, called White Knight. White Knight carries SpaceShipOne to an altitude of 15,000 meters. SpaceShipOne then separates and climbs to 100,000 meters. This is arguably better than simply standing a rocket on its tail and blasting directly from sea level to orbit. On the other hand, SpaceShipOne didn't get to orbit: it only got to space.

Space

Space is the region outside the earth's atmosphere. The atmosphere doesn't have a definite upper boundary, but space is generally considered to start at an altitude of 60 miles, or 100,000 meters.

The potential energy of gravity is

E = mgh
so to lift something into space, you need
9.8 N/Kg * 100000 m = 1M N*m/Kg = 1M J/Kg

Orbit

To put something into orbit, you have to lift it into space, and you have to set it moving around the earth at 8 Km/second. Kinetic energy is
E = 0.5 mv^2
so to accelerate something into orbit, you need
0.5 * (8 Km/s)^2 = 32M m^2 / s^2 = 32M J/Kg
or more than 30 times the energy required to climb to space.

Heavy lifting

Space is exciting, and I hear that the view is fantastic, but if you want to stay long enough to get anything useful done, you really need to be in orbit. So let's take SpaceShipOne, and scale it up so that it carries 33 times as much fuel, and then scale it up some more so that it can actually lift all that fuel. We'll call this SpaceShip33.

Now we need a first stage, and you aren't going to carry something the size of SpaceShip33 to 15,000 meters under the belly of White Knight, or any other twin-hulled, gossamer-winged sailplane wanna-be. No, we need a heavy lift vehicle. Maybe a couple of big solid-rocket boosters strapped to its belly would get it there. Yeah, that's the ticket...it would look something like this.


Notes

record
Everything I know about the Saturn V I learned from the Guiness Book of World Records
slug
aren't English units wonderful?
could
people who know something about aeronautics tell me that it is actually very difficult to fly into orbit. Sigh...

Steven W. McDougall / resume / swmcd@world.std.com / 2004 June 29