RGClark
Mathematician
- Joined
- Jan 27, 2010
- Messages
- 1,635
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- Points
- 36
- Location
- Philadelphia
- Website
- exoscientist.blogspot.com
In post #136 I argued that small, low cost SSTO's are doable
now using lightweight design and high efficiency engines. However,
I was surprised to find after doing the calculation you don't even need
the high efficiency engines to get the SSTO. The low efficiency SpaceX
Merlin engines would be sufficient for example, IF you have altitude compensation.
The impetus for trying the calculation was from a report by SpaceX
that you could get the same performance from a planned heavy lift
first stage using a lower performance Merlin 2 engine compared to the
high performance RS-84 engine. The reason was the lower Isp of the
Merlin was made up for by its lower weight:
SpaceX Propulsion.
http://images.spaceref.com/news/2010/SpaceX_Propulsion.pdf
Now note that the biggest single contributor to the vacuum Isp of an
engine is not the chamber pressure, but the nozzle length. For
example, the Merlin Vacuum raises its vacuum Isp to 342 s from the 304
s Isp of the Merlin 1C by having a longer nozzle, even though the
chamber pressure remains the same, ca. 100 bar.
So I'll redo the calculation for the SSTO using the SpaceX Falcon 1
first stage but using Merlin engines this time. We'll assume that
using altitude compensation we are able to get an engine with the same
vacuum Isp as the Merlin Vacuum but able to launch from ground.
We'll use the soon to be introduced Merlin 1D:
SpaceX Plans To Be Top World Rocket Maker.
Aug 11, 2011
By Guy Norris
San Diego
http://www.aviationweek.com/aw/generic/story.jsp?id=news/awst/2011/08/08/AW_08_08_2011_p27-354586.xml&headline=SpaceX%20Plans%20To%20Be%20Top%20World%20Rocket%20Maker&channel=defense
Using the 160 to 1 thrust/weight ratio and 155,000 lbs. vacuum thrust
given, it has a mass of 970 lbs., 440 kg. However, this would make it
overpowered for the Falcon 1 first stage only. So we'll use two copies
of this stage powered by a single Merlin 1D.
The original Falcon 1 first stage with the Merlin 1C engine has a dry mass
of 1,360 kg. I estimated the mass of the Merlin 1C in the prior post to
be 650 kg. So without the engine, the stage weighs 710 kg. So two of
them will be 1,420 kg without engines, and adding on the Merlin 1D
engine gives this a mass of 1,860 kg.
The propellant mass of the two copies of the first stage is 43,080
kg. Then to calculate the payload that can be carried I'll again just
use the vacuum Isp and take the required delta-V as 9,150 m/s. We
conclude a payload of 1,140 kg can be lofted:
342*9.8ln(1 + 43,080/(1,860 + 1,140)) = 9,160.
Now we'll estimate how much the payload can be if we use a higher
energy density fuel such as methylacetylene and use lightweight
composites for the stage. I'll get a rough idea how high the Isp can
be for this case by assuming it is increased proportionally to the
same degree as for the high efficiency engine case. That is, using
methylacetylene in the high efficiency case resulted in increasing the
vacuum Isp to 384 s from the 360 s vacuum Isp for the kerosene.
Assuming the vacuum Isp will be increased to the same proportion here
gives us a vacuum Isp of 365 s for methylacetylene and the Merlin 1D
engine.
For the reduced stage weight using composites, assume again it will
be reduced by 40% aside from the engines. Then the stage weight with
the Merlin 1D engine will be .6*1,420 + 440 kg = 1,290 kg. Then will
be able to loft a payload of 2,320 kg:
365*9.8ln(1 + 43,080/(1,290 + 2,320)) = 9,160 m/s.
Also, quite likely SpaceX could make a half-size version of the
Merlin 1D engine. So you could use a single copy of the Falcon 1 first
stage. Then the payload would be approximately cut in half, 570 kg for
the kerosene/standard stage version and 1,160 kg for the
methylacetylene/composite stage version.
Note that low chamber pressure, low performance engines can also be
used to power the SSTO's is extremely important. Such engines have
less complicated combustion cycles and have to withstand much less
strenuous operating regimes. This makes them cheaper, simpler, easier
to maintain, and easier to make reusable. So the most costly component
of any rocket, the engines, become markedly cheaper for the proposed
SSTO.
What is key though is to come up with ways to get the needed altitude
compensation without adding on too much to the engine weight. In a
following post I'll discuss some methods this might be accomplished.
Bob Clark
now using lightweight design and high efficiency engines. However,
I was surprised to find after doing the calculation you don't even need
the high efficiency engines to get the SSTO. The low efficiency SpaceX
Merlin engines would be sufficient for example, IF you have altitude compensation.
The impetus for trying the calculation was from a report by SpaceX
that you could get the same performance from a planned heavy lift
first stage using a lower performance Merlin 2 engine compared to the
high performance RS-84 engine. The reason was the lower Isp of the
Merlin was made up for by its lower weight:
SpaceX Propulsion.
http://images.spaceref.com/news/2010/SpaceX_Propulsion.pdf
Now note that the biggest single contributor to the vacuum Isp of an
engine is not the chamber pressure, but the nozzle length. For
example, the Merlin Vacuum raises its vacuum Isp to 342 s from the 304
s Isp of the Merlin 1C by having a longer nozzle, even though the
chamber pressure remains the same, ca. 100 bar.
So I'll redo the calculation for the SSTO using the SpaceX Falcon 1
first stage but using Merlin engines this time. We'll assume that
using altitude compensation we are able to get an engine with the same
vacuum Isp as the Merlin Vacuum but able to launch from ground.
We'll use the soon to be introduced Merlin 1D:
SpaceX Plans To Be Top World Rocket Maker.
Aug 11, 2011
By Guy Norris
San Diego
http://www.aviationweek.com/aw/generic/story.jsp?id=news/awst/2011/08/08/AW_08_08_2011_p27-354586.xml&headline=SpaceX%20Plans%20To%20Be%20Top%20World%20Rocket%20Maker&channel=defense
Using the 160 to 1 thrust/weight ratio and 155,000 lbs. vacuum thrust
given, it has a mass of 970 lbs., 440 kg. However, this would make it
overpowered for the Falcon 1 first stage only. So we'll use two copies
of this stage powered by a single Merlin 1D.
The original Falcon 1 first stage with the Merlin 1C engine has a dry mass
of 1,360 kg. I estimated the mass of the Merlin 1C in the prior post to
be 650 kg. So without the engine, the stage weighs 710 kg. So two of
them will be 1,420 kg without engines, and adding on the Merlin 1D
engine gives this a mass of 1,860 kg.
The propellant mass of the two copies of the first stage is 43,080
kg. Then to calculate the payload that can be carried I'll again just
use the vacuum Isp and take the required delta-V as 9,150 m/s. We
conclude a payload of 1,140 kg can be lofted:
342*9.8ln(1 + 43,080/(1,860 + 1,140)) = 9,160.
Now we'll estimate how much the payload can be if we use a higher
energy density fuel such as methylacetylene and use lightweight
composites for the stage. I'll get a rough idea how high the Isp can
be for this case by assuming it is increased proportionally to the
same degree as for the high efficiency engine case. That is, using
methylacetylene in the high efficiency case resulted in increasing the
vacuum Isp to 384 s from the 360 s vacuum Isp for the kerosene.
Assuming the vacuum Isp will be increased to the same proportion here
gives us a vacuum Isp of 365 s for methylacetylene and the Merlin 1D
engine.
For the reduced stage weight using composites, assume again it will
be reduced by 40% aside from the engines. Then the stage weight with
the Merlin 1D engine will be .6*1,420 + 440 kg = 1,290 kg. Then will
be able to loft a payload of 2,320 kg:
365*9.8ln(1 + 43,080/(1,290 + 2,320)) = 9,160 m/s.
Also, quite likely SpaceX could make a half-size version of the
Merlin 1D engine. So you could use a single copy of the Falcon 1 first
stage. Then the payload would be approximately cut in half, 570 kg for
the kerosene/standard stage version and 1,160 kg for the
methylacetylene/composite stage version.
Note that low chamber pressure, low performance engines can also be
used to power the SSTO's is extremely important. Such engines have
less complicated combustion cycles and have to withstand much less
strenuous operating regimes. This makes them cheaper, simpler, easier
to maintain, and easier to make reusable. So the most costly component
of any rocket, the engines, become markedly cheaper for the proposed
SSTO.
What is key though is to come up with ways to get the needed altitude
compensation without adding on too much to the engine weight. In a
following post I'll discuss some methods this might be accomplished.
Bob Clark
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