Copyright 2012 Robert Clark
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
SPACEFLIGHT NOW
Posted: July 9, 2012
http://www.spaceflightnow.com/news/n1207/10grasshopper/
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.
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.
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
SPACEFLIGHT NOW
Posted: May 18, 2012
http://www.spaceflightnow.com/falcon9/003/120518musk/
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.
http://www.silverbirdastronautics.com/LVperform.html
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.
http://www.spacex.com/falcon9.php
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
Cape's latitude.
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).
Bob Clark
Nice work Bob.
ReplyDeleteA good double check is:
* add the payload to the dry mass to get the burnout mass - 20564 kg.
* add the propellant load to the burnout mass to get the gross mass - 395564 kg.
* apply the rocket equation with the vacuum isp, 311, to get the total delta-v - 9017.76 m/s.
That seems low to me. With the lower payload of 3766 kg, it's 9611 m/s which is much more believable.
If your payload is a LEO satellite, or something else with its own propulsion, you could fly the SSTO on a once-around trajectory and let the payload do its own circularization burn. I imagine you could get the maximum payload that way.
Thanks for the comment. Remember the required delta-v to orbit is dependent on the additional losses it will incur such as gravity drag loss and air drag loss. The biggest of these is gravity drag loss. This will be reduced if you have a high initial thrust/weight ratio. Common estimates of delta-v to orbit in the range of 9,100 to 9,200 m/s are based on common initial T/W ratios of 1.1 to 1.2 for liquid fueled rockets.
DeleteWith 9 Merlin 1D's this is a sea level thrust of 1,323,000 lbs. But the 375,000 kg propellant mass, 13,000 kg dry mass and 7,500 payload mass gives a 395,500 kg gross mass, 870,100 lbs. This results in a 1.52 lift-off T/W ratio, accounting for the reduced delta-V needed for orbit.
You can try removing engines and see what payload you can get in the Schilling calculator. You can take off 1,2, or 3 and still have sufficient thrust by the sea level thrust values for lift-off.
You subtract off 450 kg from the dry mass value and 718 kN from the thrust value(vacuum) for each engine removed. You will see that eventhough the dry mass is reduced, the payload will be reduced because having a lower T/W value increases the gravity loss.
I like your idea of doing only a once-around trajectory. Any idea how you might input that into the Schilling calculator?
Bob Clark
Bob:
ReplyDeleteA question - would not an SSTO version of Falcon-9 launch a smaller payload at an only slightly-reduced launch cost? How do we make up the loss of payload mass/launch cost? Reusability?
I have no numbers, but wouldn't a one stage launch cost almost as much as a two-stage launch?
Just asking, I dunno the answers, myself.
GW
Good question. It would depend on how much is the cost of the second stage, and how much to integrate it onto the first stage.
DeleteReusability might actually do more to increase the advantage of SSTO over TSTO. In an interview with Popular Mechanics Elon suggested the hard part is actually returning the first stage to the launch site.
The problem is optimal staging speed will take the first stage quite a long distance away from the launch site. So to be able to get the first stage back to the launch site you either have to reduce the staging speed or retain a some amount of propellant for the return trip, or both. SpaceX will do both, though the reduced staging speed means not as much propellant needs to be retained.
This reduces the payload to only 60% of the value for the expendable version:
Elon Musk on SpaceX’s Reusable Rocket Plans.
By Rand Simberg
February 7, 2012 6:00 PM
The key, at least for the first stage, is the difference in speed. "It really comes down to what the staging Mach number would be," Musk says, referencing the speed the rocket would be traveling at separation. "For an expendable Falcon 9 rocket, that is around Mach 10. For a reusable Falcon 9, it is around Mach 6, depending on the mission." For the reusable version, the rocket must be traveling at a slower speed at separation because the burn must end early, preserving enough propellant to let the rocket fly back and land vertically. This also makes recovery easier because entry velocities are slower.
However, the slower speed also means that the upper stage of the Falcon rocket must supply more of the velocity needed to get to orbit, and that significantly reduces how much payload the rocket can lift into orbit. "The payload penalty for full and fast reusability versus an expendable version is roughly 40 percent," Musk says. "[But] propellant cost is less than 0.4 percent of the total flight cost. Even taking into account the payload reduction for reusability, the improvement is therefore theoretically over a hundred times."
http://www.popularmechanics.com/science/space/rockets/elon-musk-on-spacexs-reusable-rocket-plans-6653023
On the other hand for a SSTO you just let it complete its orbit to return to the launch site, so the weight penalty is not as great.
Bob Clark
Have you ever considered nuclear thermal SSTO? What are your thoughts on that?
ReplyDeleteMy feeling is that it will be awhile before large amounts of nuclear material being launched into space regularly will be acceptable to the public.
DeleteAnyway it's not needed. Chemical propulsion SSTO can be done like tomorrow. Or at least by the end of the year when the Falcon 9 v1.1 is supposed to come online.
Bob Clark
If SSTO is so easy, then why haven't we done it before now? Why is NASA and the private companies using staged rockets?
DeleteA fair question. During the 50's and 60's looking at the rocket engines and materials available then rocket engineers concluded it was infeasible to create a SSTO. So multi-stage vehicles were used. Unfortunately, since it was the case you couldn't get a SSTO then during this defining period of the development of spaceflight, it came to be regarded as received wisdom that SSTO's were impossible with current technology.
DeleteHowever, in point of fact with the high efficiency engines developed in the 70's such as the SSME's for hydrogen and the NK-33's and RD-180's for kerosene then SSTO's became feasible to carry significant payload. And in fact with the development of lightweight composites for aircraft in the 80's and 90's such SSTO's can even have have payload fractions that match or exceed those of the multi-stage rockets currently used.
However, it still will be the case you can carry more payload using multi-stages. So for those in the industry who acknowledge SSTO's are now doable their response is why bother? But a key fact is that if you now use those SSTO-capable stages as first stages, then you can carry even more payload than with usual multi-stage rockets. So developing SSTO-capable stages is important even actually for multi-stage rockets.
Still beyond that the usefulness of SSTO's is that they make possible small launchers that can be privately owned that would allow gas-and-go operation, a la small business jets.
For a good discussion of the history of SSTO's and their importance see here:
Halfway to Anywhere: Achieving America's Destiny In Space.
Harry G. Stine (Author)
http://www.amazon.com/Halfway-Anywhere-Achieving-Americas-Destiny/dp/0871318059
Bob Clark
So Venturestar would've succeeded if it had been privately funded?
DeleteThe problem with the X-33/VentureStar is that if you intend to make a SSTO, especially a reusable one, then the margins are so slim that you should be sure you use both weight optimized stages and Isp optimized engines.
DeleteHowever, the non-cylindrical tanks they used meant that even if you used composites to reduce their weight they still would have weighed twice that of comparable capacity, aluminum, cylindrical tanks. And since the fuel tanks make up a major part of the dry mass of a rocket, this severely reduced the payload capacity.
It was attempts to keep the weight of those tanks as low as possible that led to their failing. If instead the other proposals for a reusable SSTO were selected, the DC-X based version or the shuttle orbiter based version, then we would have had SSTO's flying already.
It is also important to keep in mind that SpaceX has shown that rocket development as privately funded can cut development costs by a factor of 5 to 10 times. Then instead of those proposed reusable SSTO's costing billions of dollars to develop, as privately funded they could have been done for a few hundred million dollars, well within the capability of the larger aerospace companies to develop on their own.
Bob Clark
I'm afraid , it's not correct to use Shilling programm. Delta V to reach leo probably is 8.6 km/s for such boosters, because gravitation loses are smaller in comparison with a tree stage rocket. In this case 8.6 / 3 = 2.87. ln (17.58) = 2.87. 1/30 -1/17.58 = 0.023459 . 1/ 0.023459 = 42.63 . 397500 /42.63 = 9 400. 9 400 kg is really value, if dry mass is 13000 and propelant mass is 375 000 kg.
ReplyDeleteThanks for the calculation. I would really be happy if you could indeed get a 8.6 km/s delta-V, and that high a payload with the Falcon v1.1 first stage.
DeleteHowever, the gravity-loss is highly dependent on the thrust/weight ratio. Because for the Falcon 9 v1.1 without the upper stage your weight would be reduced, the T/W would be increased so the gravity loss would be reduced.
But I don't know if it would be reduced to the extent to cut the required delta-V to orbit to only 8,600 m/s.
Bob Clark