About the rocket-that-dared-not-speak-its name.

[Robert Clark]

No, SSTO is not a four-letter word though it is sometimes treated that way by those in the industry.

I've been arguing that SSTO's are actually easy because how to achieve them is perfectly obvious: use the most weight optimized stages and most Isp efficient engines at the same time, i.e., optimize both components of the rocket equation. But I've recently found it's even easier than that! It turns out you don't even need the engines to be of particularly high efficiency.

SpaceX is moving rapidly towards testing its Grasshopper scaled-down version of a reusable VTVL Falcon 9 first stage:

Reusable rocket prototype almost ready for first liftoff.

BY STEPHEN CLARK

SPACEFLIGHT NOW

Posted: July 9, 2012

http://www.spaceflightnow.com/news/n1207/10grasshopper/

SpaceX will be duplicating in this what the DC-X accomplished in the early 90's. The DC-X was a scaled down, low altitude test vehicle for a full-scale SSTO VTVL vehicle. So could the full-sized Falcon 9 first stage act as a VTVL SSTO?

SpaceX deserves kudos for achieving a highly weight optimized Falcon 9 first stage at a 20 to 1 mass ratio. However, the Merlin 1C engine has an Isp no better than the engines we had in the early sixties at 304 s, and the Merlin 1D is only slightly better on the Isp scale at 310 s. This is well below the highest efficiency kerosene engines (Russian) we have now whose Isp's are in the 330's. So I thought that closed the door on the Falcon 9 first stage being SSTO.

However, I was surprised when I did the calculation that because of the Merlin 1D's lower weight the Falcon 9 first stage could indeed be SSTO. I'll use the Falcon 9 specifications estimated by GW Johnson, a former rocket engineer, now math professor:

WEDNESDAY, DECEMBER 14, 2011

Reusability in Launch Rockets.

http://exrocketman.blogspot.com/2011/12/reusability-in-launch-rockets.html

The first stage propellant load is given as 553,000 lbs, 250,000 kg, and the dry weight as 30,000 lbs, 13,600 kg. The Merlin 1C mass hasn't been released, but I'll estimate it as 650 kg, from its reported thrust and thrust/weight ratio. The Merlin 1D mass has been estimated to be 450 kg. Then on replacing the 1C with the 1D we save 9*200 = 1,800kg from the dry weight to bring it to 11,800 kg.

The required delta v to orbit is frequently estimated as 30,000 feet per second for kerosene-fueled vehicles, 9,144 m/s. When calculating the delta v your rocket can achieve, you can just use your engines vacuum Isp since the loss of Isp at sea level is taken into account in the 30,000 fps number. Then this version of the Falcon 9 first stage could lift 1,200 kg to orbit:

310*9.81ln(1 + 250/(11.8 + 1.2)) = 9,145 m/s.

Then the Falcon 9 first stage could serve as a proof of principle SSTO on the switch to the Merlin 1D engine.

Bob Clark

Edited July 21, 2012 by Robert Clark

[Enthalpy]

Hi Bob, my two cents worth of comments...

 

You know we agree about the ease of SSTO (and less so about their usefulness).

 

Falson 9's mass ratio can be improved with a small effort. Their tank design with plain metal sheet is meant to save money more than weight. Even with hydrogen, Ariane 5 achieves 100kg of dry mass (all included for that stage) per ton of propellants, and the Shuttle's external tank (without engines nor anything) 36kg/t. With kerosene+oxygen, a tank mass around 12kg/t is obtained just by the better propellant density. My extruded tank construction may improve further.

 

In the atmosphere, recent kerosene engines aren't better than 307s (RD-170). They improve in vacuum (338s).

 

The other difficulty of an SSTO design is the deep throttling needed to keep the acceleration bearable (or even at 1G for vertical landing) as the tanks go empty. Kerosene, which needs a higher mass ratio than hydrogen to achieve orbit, needs an even deeper throttling which no kerosene engine has yet demonstrated - as opposed, the RL-10 has proven it can.

 

But if an SSTO stage has 9 kerosene angines and can shut off all but one, the acceleration is reasonable. If the remaining engine can throttle to 1/3 it can land vertically. Or if this first stage doesn't reach orbit, throttling gets easy.