Some rough calculations

Happy New Year!

Well I decided to check out some data on info I gleaned online to refine my size calculation, namely infer how much fuel the 2 tanks would contain and by extension (say + 25%) how much we can have for the ship's dry mass.

From this:

2

and assuming a total length of 90 meters (i.e 300 ft or so) we can deduct a 10 meters radius for the liquid hydrogen tank (20% of the total length in diameter, roughly) i.e 30 ft.

That gives us (thanks to http://www.thomas-jahnke.de/technik/umrechnungen/sphetank.htm)   4,188.800 m^3 of capacity (i.e 31334 gallons). Assuming liquid H2 filling 90% of it considering some losses we have about 4,000,000 liters of H2 (roughly 30,000 gallons).

Probably we could organize a BBQ for every single inhabitant of America for that kind of capacity... sadly Nature is a harsh mistress and this is barely good enough to propel a few tens of tons of payload (including the spaceship itself) to space and back.

Not like Spaceship 1, which is pretty much a joke i.e a simple ballistic flight to 60 miles up and back. Here we need not only to get where the air is thin enough to not be a problem plowing at 5 mi/sec through it (or 7.9 km/s) but also accelerate to said speed of mach 30+

All in about 10 minutes or so.

From that deduction of how big the H2 tank is... we can now build the rest of the Firefly... first the O2 tank: Since we need a 2-1 ratio of H to O since we will nozzle out water vapor at speeds 4 X a bullet from a high powered rifle, that means we will need 8 units of mass of O2 to burn 1 unit of mass of H2 (H2= 1+1=2
O2= 16 + 16 = 32 and we have 2H2 + O2 = 2H2O).

One glorious liter of liquid H2 is about 70 grams (or 1/3 of a lb!!! i.e

a density of 70.8 kg/m³ (at 20 K)) and our calculation above show us we will have about 280 metric tons of the hellish liquid (paradoxically very very cold). So we will need 2000+ tons of O2.

 

OUCH!!!  That's way too much.

If we want to just have 200 tons of O2... we will just need 25 tons of liquid H2. That can fit in a smaller tank: 30 ft in diameter or 9 metric meters.

200 metric tons of liquid O2 will fit in a much smaller tank: The density of liquid oxygen is around 1141 kg/m^3 or around 9.50 lb/gal. So a 7 meters diameter tank (or 25 ft) will do.

That puts the total weight of the fuel at roughly 225 metric tons or 700,000 lb. If we now take on the calculations for the Skylon to allow for a 20% extra for everything else i.e the dry weight of the spaceship, we can have about 45-50 tons worth of that.

Disappointing huh? welcome to the holy grail of astronautics: the SSTO!!!

For a pure rocket to reach orbit we need a delta V of roughly 9500 meters per second (that's 27,000 ft per second or Mach 25+). Assuming about 10 of losses due to aerodynamic drag etc...

The Skylon design only allows for 6500, making up the rest with an air-breathing scheme to compensate the dismal dynamics of the first minute of space flight, where up to 1/3rd of the fuel is wasted away... to go where a modern passenger jet goes i.e slightly subsonic speed at 30,000 ft!!!!

How is the delta V calculated? It is called the Tsiolkovsky's final velocity equation: Muzzle velocity of the rocket engine X e^-( full weight/dry weight ) = delta V.

Assuming 4000 meters per second and e-(270/45 i.e 6) = 1.7 we get about that i.e 6.5-6.7 km/sec of delta V.

Not bad... but we just have less than 50 tons for the entire spaceship.

Do not expect a jaccuzzi and showers with hot water!