Titan II stage 1 is often mentionned (on the Internet) as a possible SSTO. But what is lacking is the maths. So I decided to fill that gap.
Secret projects is a highly visible forum in Google searches, by the way. That's the reason why I put this here.
Feel free to pick any hole in my maths, I'll correct it.
The Titan II stage 1 still hold an amazing record for rockets. With empty propellant tanks it weighed barely 10 000 pounds. Then when the tanks were filled it weighed 250 000 pounds.
Propellant mass fraction (PMF) is the ratio between the two weights, empty tanks and tanks filled.
In the case of the Titan II, it calculates the following way
1-(10000/250000) = 0.96
What is really interesting is that such PMF would allow the Titan II first stage to launch itself into Earth orbit. No booster, no second stage. A SSTO, although an expendable one.
9.81*296*ln(250000/10000) = 9347 m/s.
And indeed Earth orbit is somewhere between 9 km/s and 10 km/s depending on gravity losses, drag losses, and propellant density. The denser the propellants, the lower the drag and gravity losses. I've seen values as low as 8.9 km/s.
So our Titan II stage 1 SSTO can loft itself into orbit, although with slim margin.
What is really interesting is that one could swap the old LR-87 (gas generator cycle) for Proton RD-253 which uses the same storable propellants but staged combustion.
Thrust are quite similar, propellants are storable in both cases.
LR-87 vacuum specific impulse: 296 seconds.
RD-253 : 316 seconds.
9.81*316*ln(250000/10000) = 9978m/s.
And then, how much payload to orbit ? Between 2000 and 3000 pounds.
9.81*316*ln(252000/12000) = 9437 m/s with 2000 pounds of payload.
That was Titan II / Proton hybrid, both using storable propellants.
But Titan I used kerolox, just like many other advanced Soviet rocket engines - the N-1 Kuznetsov or Energiya RD-170 / 180 / 190 family.
Might be interesting to get Titan I stage 1 PMF and try to replace the LR-87 with, say, a RD-191. I'll give it a try later on.
A very interesting documents detailing the Titan varied stages and PMF
http://home.earthlink.net/~apendragn/atg/coef/Structural_Coef.pdf
Secret projects is a highly visible forum in Google searches, by the way. That's the reason why I put this here.
Feel free to pick any hole in my maths, I'll correct it.
The Titan II stage 1 still hold an amazing record for rockets. With empty propellant tanks it weighed barely 10 000 pounds. Then when the tanks were filled it weighed 250 000 pounds.
Propellant mass fraction (PMF) is the ratio between the two weights, empty tanks and tanks filled.
In the case of the Titan II, it calculates the following way
1-(10000/250000) = 0.96
What is really interesting is that such PMF would allow the Titan II first stage to launch itself into Earth orbit. No booster, no second stage. A SSTO, although an expendable one.
9.81*296*ln(250000/10000) = 9347 m/s.
And indeed Earth orbit is somewhere between 9 km/s and 10 km/s depending on gravity losses, drag losses, and propellant density. The denser the propellants, the lower the drag and gravity losses. I've seen values as low as 8.9 km/s.
So our Titan II stage 1 SSTO can loft itself into orbit, although with slim margin.
What is really interesting is that one could swap the old LR-87 (gas generator cycle) for Proton RD-253 which uses the same storable propellants but staged combustion.
Thrust are quite similar, propellants are storable in both cases.
LR-87 vacuum specific impulse: 296 seconds.
RD-253 : 316 seconds.
9.81*316*ln(250000/10000) = 9978m/s.
And then, how much payload to orbit ? Between 2000 and 3000 pounds.
9.81*316*ln(252000/12000) = 9437 m/s with 2000 pounds of payload.
That was Titan II / Proton hybrid, both using storable propellants.
But Titan I used kerolox, just like many other advanced Soviet rocket engines - the N-1 Kuznetsov or Energiya RD-170 / 180 / 190 family.
Might be interesting to get Titan I stage 1 PMF and try to replace the LR-87 with, say, a RD-191. I'll give it a try later on.
A very interesting documents detailing the Titan varied stages and PMF
http://home.earthlink.net/~apendragn/atg/coef/Structural_Coef.pdf