Credit: Ed Kyle's Falcon 9 page.
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 Falcon 9 first stage:
Reusable rocket prototype almost ready for first liftoff.
BY STEPHEN CLARK
Posted: July 9, 2012
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 311 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. For the calculation we'll need the F9 dry mass and propellant
mass. 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.
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.
I'll actually calculate the payload for the first stage of the new version of
the Falcon 9, version 1.1. The Falcon Heavy will use this version's first stage
for its core stage and side boosters. SpaceX expects the Falcon 9 v1.1
to be ready by the end of the year.
Elon Musk has said version 1.1 will be about 50% longer:
Q&A with SpaceX founder and chief designer Elon Musk.
BY STEPHEN CLARK
Posted: May 18, 2012
I'll assume this is coming from 50% larger tanks. This puts the
propellant load now at 375,000 kg. Interestingly SpaceX says the side
boosters on the Falcon Heavy will have a 30 to 1 mass ratio. This
improvement is probably coming from the fact it is using the lighter
Merlin 1D engines, and because scaling up a rocket actually improves
your mass ratio, and also not having to support the weight of an upper
stage and heavy payload means it can be made lighter.
So I'll assume for this SSTO version of the Falcon 9 v1.1 the mass
ratio is 30 to 1, which makes the dry mass 13 mT.
To estimate the payload I'll use the payload estimation program of
Dr. John Schilling:
Launch Vehicle Performance Calculator.
It actually gives a range of likely values of the payload. But I've found
the midpoint of the range it specifies is a reasonably accurate estimate
to the actual payload for known rockets.
Input the vacuum values for the thrust in kilonewtons and Isp in
seconds. The program takes into account the sea level loss. SpaceX
gives the Merlin 1D vacuum thrust as 161,000 lbs and vacuum Isp
as 311 s:
FALCON 9 OVERVIEW.
For the 9 Merlins this is a thrust of 9*161,000lb*4.46N/lb = 6,460
kN. Use the default altitude of 185 km and select the Cape Canaveral
launch site, with a 28.5 degree orbital inclination to match the
Input the dry mass of 13,000 kg and propellant mass of 375,000 kg.
The other options I selected are indicated here:
Then it gives an estimated 7,564 kg payload mass:
Launch Vehicle: User-Defined Launch Vehicle
Launch Site: Cape Canaveral / KSC
Destination Orbit: 185 x 185 km, 28 deg
Estimated Payload: 7564 kg
95% Confidence Interval: 3766 - 12191 kg
This may be enough to launch the Dragon capsule, depending on the mass
of the Launch Abort System(LAS).
UPDATE, Sept. 26, 2013:
See more accurate calculations using Dr. John Schillings Launch Performance Calculator here:
The Coming SSTO's: Page 2.
UPDATE, August 26, 2014:
This blog post actually used the estimated specifications for the Falcon Heavy side boosters, as this was supposed to have an even better mass efficiency than the core stage. However, Elon Musk gave a speech where he gave some values for the Falcon 9 v1.1 first stage that allow us to estimate the propellant and dry masses for the stage. Then we can calculate the payload capability of a F9 v1.1 core stage SSTO itself. I estimate it as ca. 5,000 kg:
The Coming SSTO's: Falcon 9 v1.1 first stage as SSTO, Page 2.