Liberty Ship

I forget where I first saw this... I was poking around on the Internet a couple of years ago, and found a lot of good stuff, this was probably in there. (Related to the Project Rho site, which I've mentioned before).

The Liberty Ship is truly impressive, something for our generation akin to the Saturn 5 rocket. A shame it will probably never be built...

I wanted to run some of the numbers, because I keep getting them jumbled (stupid units):
Mission mass: 2.722e6 kg (6e6 lbs)
Dry+empty mass: 7.258e5 kg (1.6e6 lbs)

The power is given as 80 GW, and the fuel mass flow is 178 kg/s. That translates (via ve = sqrt(2E/m)) to 29,981 m/s exhaust velocity (which matches well with the given 30k). That power sounds high, I will probably examine that in a separate post.

Thrust is ve * fuel mass flow, which yields 5.337e6 N (which roughly corresponds to the given 1.2e6 lbs, if 4.4N=1 lb force - which is what Google implies).

The biggest problem I ran into was finding the right delta v for LEO. Project Rho gives it as 11,180 m/s (before aero and grav drag). Wikipedia gives it as 7.8 km/s without drag (and 1.5-2 km/s drag).

The other problem is the total thrust is very low. With 7 engines, thrust is 37.357e6 N. Dividing that by the loaded weight (mission mass) gives an acceleration of 13.726 m/s^2 (1.4 g's). This will cause a very long lingering in the Earth's gravity well (rockets often use 10 g's for liftoff).

I'm not certain how to calculate the gravity drag. Project Rho gives vd = vo / a, which seems to allow for any velocity. It seems unlikely that any acceleration below 1 g can ever escape, but perhaps I am wrong...

Regardless, this gives us v_drag of 5,575 m/s - which cuts heavily into the given mission dv of 15 km/s (perhaps that is the intent). It is unclear what effect a lifting body has in these figures...

One alternative is to increase the fuel flow (to increase thrust, and decrease linger time). Unfortunately, this cuts into ve. The mass ratio (full mass divided by dry mass) is equal to exp(delta v / exhaust velocity) (that's the natural number, e, to the x power).

So any drop in exhaust velocity has an exponential effect on the mass ratio, which drives up propellant mass, which drives down cargo mass.

You can drive ve back up with engine power, but ve is the square root of power, so half ve must be made up with 4x power...