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tahanson43206,
LOX/LH2 may be able to perform an expendable SSTO mission, but the real issue is the LH2 propellant volume and the low thrust-to-weight ratio (TWR) of LH2 fueled engines.
LH2 Engine TWR: 75:1
LCH4 and RP1 Engine TWR: 150:1 to 200:1
At the thrust levels demanded for a 100t class payload, about 1.5X whatever GLOW happens to be, using LH2 adds considerable engine mass.
LOX is 1,141kg/m^3. LH2 is 71kg/m^3. LOX has 16X the density of LH2 per unit volume, yet tank mass per unit volume of propellant stored will be the same between LOX and LH2, up to 3g of vehicle acceleration. LH2 internal pressurization loads drives propellant tank mass. This useful tidbit of information comes from NASA.
LOX/LH2 Isp (Vac): 450s
LOX/RP1 Isp (Vac): 360s
LH2 provides a 25% Isp increase over RP1.
1m^3 of LH2, at 71kg/m^3 and 142MJ/kg, stores 10,082MJ/m^3
1m^3 of RP1, at 810kg/m^3 and 43MJ/kg, stores 34,830MJ/m^3
RP1 provides a 345% volumetric energy density increase over LH2.
Can LH2's 25% fuel economy advantage over RP1, somehow overcome RP1's 345% energy density increase over LH2?
Delta IV (all LOX/LH2 stages): 249.5t GLOW; 8.51t payload to LEO (3.411% of GLOW)
Falcon 9 (all LOX/RP1 stages): 549t GLOW; 22.8t payload to LEO (4.153% of GLOW)
Delta IV Heavy (all LOX/LH2 stages): 733t GLOW; 28.79t payload to LEO (3.927% of GLOW)
Falcon 9 Heavy (all LOX/RP1 stages): 1,420t GLOW; 63.8t payload to LEO (4.493% of GLOW)
There's your answer. RP1 fueled vehicles are heavier because they take more payload to orbit than the LH2 fueled vehicles. Even as a percentage of GLOW, payload-to-GLOW is higher for RP1 than LH2. Both rockets are fabricated from Aluminum alloys and both use gas generator cycle engines.
At some point, stage volume, thus stage dry mass fraction, combined with low engine TWR, really starts to become a problem for LH2 because it eats into your payload mass fraction.
Do we imagine that these problems will become more or less severe as we both scale-up the rocket to deliver a 100t payload and push the entire vehicle mass from the ground, all the way to orbit?
Why is the payload mass fraction of Delta IV Heavy lower than a Merlin powered vehicle that never achieves the sea level Isp of the RS-68A and RL-10 engines that power the Delta IV and Delta IV Heavy?
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Delta IV Common Booster Core
Dry Mass: 28,850kg
Dry Mass Less Engine(s): 22,110kg
Gross Mass: 226,400kg
Total Propellant Mass: 199,550kg (150m^3 of LOX, at 1,141kg/m^3, 171,150kg and 400m^3 of LH2, at 71kg/m^3, 28,400kg)
Fuel Stored Energy: 4,032,800MJ of stored energy, at 142MJ/kg
Dry Mass Fraction (Dry Mass / Gross Mass): 12.74293%
MJ of Stored Energy per kg Dry Mass (4,032,800MJ / 28,850kg): 139.78510MJ/kg
RS-68A Engine Mass: 6,740kg
RS-68A Mass Flow Rate: 1,400kg/s
RS-68A Sea Level Thrust: 3,137,115.1N (sl); 3,560,000N (vac)
Delta IV Common Booster Core Sea Level Total Impulse Calculation
199,550kg / 1,400kg = 142.53571 seconds of total firing time
142.53571 seconds * 3,137,115.1N = 447,150,942N-s of total impulse
447,150,942N-s / 28,850kg = 15,499N-s total impulse per kg of dry stage mass
447,150,942N-s / 226,400kg = 1,975N-s total impulse per kg of gross stage mass
447,150,942N-s / 199,550kg = 2,241N-s total impulse per kg of propellant
Delta IV Common Booster Core Vacuum Total Impulse Calculation
142.53571 seconds * 3,560,000N = 507,427,128N-s of total impulse
507,427,128N-s / 28,850kg = 17,588N-s total impulse per kg of dry stage mass
507,427,128N-s / 226,400kg = 2,241N-s total impulse per kg of gross stage mass
507,427,128N-s / 199,550kg = 2,543N-s total impulse per kg of propellant
Notional Delta IV Common Booster Core equipped with 2X RS-25D Engines
Dry Mass: 28,850kg - 6,740kg + (3,177kg * 2) = 28,464kg
Dry Mass Less Engine(s): 22,110kg
Gross Mass: 228,014kg
Total Propellant Mass: 199,550kg
RS-25D Engine Mass: 3,177kg
RS-25D Mass Flow Rate: 514.49kg/s
RS-25D Thrust: 1,860,000N (sl); 2,279,000N (vac)
RS-25D Powered Delta IV Common Booster Core Sea Level Total Impulse Calculation
199,550kg / (514.49kg/s * 2) = 193.92991 seconds total firing time
193.92991 seconds * (1,860,000N * 2) = 721,419,265N-s total impulse
721,419,265N-s / 28,464kg = 25,345N-s total impulse per kg of stage dry mass
721,419,265N-s / 228,014kg = 3,164N-s total impulse per kg of stage gross mass
721,419,265N-s / 199,550kg = 3,615N-s total impulse per kg of propellant mass
RS-25D Powered Delta IV Common Booster Core Vacuum Total Impulse Calculation
193.92991 seconds * (2,279,000N * 2) = 883,932,530N-s total impulse
883,932,530N-s / 28,464kg = 31,054N-s total impulse per kg of stage dry mass
883,932,530N-s / 228,014kg = 3,877N-s total impulse per kg of stage gross mass
883,932,530N-s / 199,550kg = 4,430N-s total impulse per kg of propellant mass
Falcon 9 Booster Core
Dry Mass: 25,600kg (includes ~2,000kg of reusability hardware)
Dry Mass Less Engine(s): 21,370kg
Gross Mass: 436,500kg
Total Propellant Mass: 410,900kg (287,400kg densified LOX and 123,500kg densified RP1)
Fuel Stored Energy: 5,310,500MJ of stored energy, at 43MJ/kg
Dry Mass Fraction (Dry Mass / Gross Mass): 6.07102%
MJ of Stored Energy per kg of Dry Mass Fraction (5,310,500MJ / 25,600kg): 207.44141MJ/kg
Merlin 1D Engine Mass: 470kg (4,230kg for all 9 engines)
Merlin 1D Mass Flow Rate: 229kg/s
Merlin 1D Thrust: 657,000N (sl)
Falcon 9 Booster Core Sea Level Total Impulse Calculation
410,900kg / (229kg/s * 9) = 199.36924 seconds of total firing time
199.36924 seconds * (657,000N * 9) = 1,178,870,316N-s
1,178,870,316N-s / 25,600kg = 46,050N-s per kg of dry stage mass
1,178,870,316N-s / 436,500kg = 2,701N-s per kg of gross stage mass
1,178,870,316N-s / 410,900kg = 2,869N-s per kg of propellant
When we compare a staged combustion LH2 fueled engine with a gas generator RP1 engine, we finally arrive at a total impulse per unit of stage gross mass value favorable to LH2, but notice how that total impulse per unit of stage dry mass value is still well below RP1. For a SSTO, the stage dry mass is going all the way to orbit with the payload, so the less stage dry mass that you need for a given total impulse, the more payload you get to deliver to orbit. If we remove the reusability hardware mass from the Falcon 9 booster core's dry mass, LH2 will fall even shorter.
If the reusability hardware (grid fins, landing legs, cold gas thrusters, etc) weighs ~2,000kg, then the Falcon 9 Stage Dry Mass Fraction is only 5.40664%, so all of the other performance numbers measurably improve as well.
I'm not going to bother with Merlin-1D's vacuum thrust or a staged combustion RP1 fueled engine because the point is already made. Total Impulse delivered per unit of stage dry and gross / wet mass, is higher for a Falcon 9 booster core with its 9 Merlin engines, at sea level, than it is for the Delta IV booster core with its RS-68A engine in a vacuum.
This simple math comparison uses real engine and stage performance numbers applicable to real rocket booster core stages, with the exception of the notional RS-25D powered Delta IV Common Booster Core, thrown in just to show that not even a staged combustion LH2 fueled engine beats a gas generator RP1 fueled engine in terms of total impulse delivered per unit of dry stage mass.
In this example, RP1 provides substantially greater stored energy per unit of dry stage mass AND gross stage mass, despite LH2's clear Isp advantage over RP1. LH2 gross / wet mass is clearly much lower, yet stage dry mass is NOT. We can substitute-in whatever stage fabrication materials we wish to use for both vehicles, but if we use the same materials for both RP1 and LH2 powered vehicles, that result is NOT GOING TO CHANGE! In the same way that gravimetric energy density has major impact on the performance of battery operated aircraft vs those powered by hydrocarbon fueled engines, volumetric energy density greatly affects the total impulse delivered by rockets fueled by RP1 vs LH2.
The "proof" is in the delivered payload tonnage to LEO per unit of vehicle dry mass fraction. It's higher for RP1 than it is for LH2, despite the fact that the gross / wet mass of the RP1 fueled stage is much higher than it is for the LH2 fueled stage. For a SSTO, this matters even more than for a TSTO. Orbital rocketry is about converting mega-joules of stored energy into thrust, for a given dry vehicle mass fraction, which in turn determines how much payload mass fraction you get.
For a SSTO, you do not get to "delete" 2/3rds of the vehicle's total dry mass on the way to orbit. For these two real rockets powered by real engines, RP1 clearly provides more stored energy to convert into thrust than LH2 does, per unit of vehicle dry and gross / wet mass fractions.
In this example, our stage dry mass per Newton-seconds of total impulse delivered, for RP1, is 297% that of LH2. Our gross / wet mass per Newton-seconds of total impulse delivered for RP1 is still 137% greater than it is for LH2. Despite that fact, our dry stage mass is still lower for RP1, even though we're carrying 240% more propellant mass in the RP1 fueled stage, as compared to the LH2 fueled stage.
LH2's Isp advantage over RP1, when burned by the RS-68A, cannot overcome RP1's density impulse and Merlin-1D's thrust-to-weight advantage. I didn't have to guess at anything, extrapolate anything, or use advanced rocketry knowledge.
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For kbd512 re Gemini evaluation of carbon vs LH2
I was surprised to see that your proposal appears to hold up fairly well. I am not surprised the LH2 solution held up. What ** is ** interesting is that Gemini ended up leaning slightly in your direction.
(th)
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Let's consider the energy efficiency of RP1 vs LH2, purely from an energy consumption per kilogram of useful payload perspective.
D4M = Delta IV Medium (all stages fueled with LH2)
F9B5 = Falcon 9 Block V (all stages fueled with RP1)
Note: D4M is a single Common Booster Core powered by a single RS-68A, with no strap-on solid rockets, and an upper stage powered by a single RL-10. D4M's vehicle dry mass is significantly greater than a F9B5, despite delivering less than half the payload to LEO of a F9B5. Fuel mass for both stages of D4M is 4.9X less than both stages of F9B5, and total propellant mass for the D4M's Common Booster Core is almost exactly 50% that of a F9B5 booster core. One would think that the superior Isp of Hydrogen burning engines and half the propellant mass would translate to a lighter dry stage mass for the D4M Common Booster Core, yet the opposite is true. Both stages of D4M are significantly heavier than both stages of F9B5. Both the propellant tanks and engines of D4M are heavier than the propellant tanks and engines of F9B5.
F9B5 Energy Economics
Fuel Masses: 123,500kg (booster); 34,275kg (upper stage); 157,776kg (total)
157,776kg of RP1 * 43MJ/kg = 6,784,368MJ of total fuel energy
6,784,368MJ / 22,800kg to LEO (fully expended) = 297.56MJ/kg of payload to LEO
297.56MJ / 43MJ/kg = 6.92kg (2.24 gallons of RP1 per 1kg of payload to LEO, at 3.084kg/gal)
D4M Energy Economics
Fuel Masses: 28,400kg (booster); 3,763kg (upper stage); 32,163kg (total)
32,163kg of LH2 * 142MJ/kg = 4,567,146MJ
4,567,146MJ / 8,510kg to LEO (expendable-only) = 536.68MJ/kg of payload to LEO
536.68MJ / 142MJ/kg = 3.78kg (14.12 gallons of LH2 per 1kg of payload to LEO, at 3.733gal/kg)
LH2 vs RP1 Payload-to-Orbit Fuel Efficiency Comparison
536.68MJ/kg (D4M/LH2) / 297.56MJ/kg (F9B5/RP1) = 1.80360
D4M vs F9B5 Payload to Orbit
8,510kg (D4M payload to orbit) / 22,800kg (F9B5 payload to orbit) = 0.37325
D4M vs F9B5 Booster Total Impulse
447,150,942N-s (D4M) / 1,178,870,316N-s (F9B5) = 0.37930
D4M vs F9B5 Booster Dry Mass
28,850kg (D4M) / 25,600kg (F9B5) = 1.126953125
Conclusions
D4M consumes 80% more fuel energy than F9B5 while delivering only 38% as much payload to orbit, with a mass increase of 13% over F9B5. On top of that, D4M also costs more than F9B5, which is why it was retired. If you increase the booster dry mass of the LH2 solution by 338%, using a triple booster core Delta IV Heavy configuration, then you can get 5,990kg more payload to orbit than F9B5.
Key Takeaways
Whatever propellant mass efficiency advantage LH2 provides over RP1, it clearly doesn't translate into lower vehicle dry mass, lower total energy consumption, nor even improved payload performance. If anything, the opposite appears to be true. As the size of the vehicle scales-up to deliver more payload to orbit, that vehicle dry mass problem only gets worse, never better, because materials don't become any stronger as you increase the size of a structure. You will see a relative improvement in vehicle dry mass as you increase the propellant tank diameters, thanks to the cube-square law, yet any LH2 powered vehicle is still going to end up being significantly heavier than a RP1 powered vehicle for the same delivered payload mass.
Even when we compare the total impulse of a notional RS-25 powered D4M operated purely in a vacuum vs a Merlin powered F9B5 operated purely at sea level, the total impulse generated per unit of vehicle dry mass advantage is lopsidedly in favor of F9B5.
If you invoke a D4M with Carbon Fiber propellant tanks with only 60% of the mass of the actual historical D4M's Aluminum propellant tanks, powered by a pair of lighter and higher-Isp RS-25D engines, you will still fail to generate a total impulse per unit of dry vehicle mass figure that's higher than a Merlin powered F9B5, constructed primarily of Al-2195 alloy. That's how horrendously awful LH2 is as a fuel choice for a SSTO or TSTO.
Total impulse generated per unit of dry vehicle mass, not propellant mass, is the figure of merit that either makes or breaks SSTOs, and the primary reason why there are none. That figure of merit is either sky-high, as it would be for a RP1 fueled rocket with Carbon Fiber propellant tanks and staged combustion engines, or SSTO doesn't work.
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This suggests that overall propellant volumetric energy density is a more important consideration than mass energy density. Musk chose LNG propellant as a compromise between the mass energy density of H2 and the volumetric energy density of heavier hydrocarbons.
https://commons.m.wikimedia.org/wiki/Fi … to-license
Hydrogen is even weaker than these figures show it to be. A great deal of infrastructure and additional energy are needed to manufacture it. Storing and handling hydrogen on the ground is also very costly and dangerous.
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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Calliban,
As an engineer, do you understand all the calculations I presented to evaluate Total Impulse per unit of vehicle dry mass?
tahanson43206,
Let's compute the volumetric energy density efficiencies for the following fuels:
LCH4 (not the same thing as LNG), at 422.8kg/m^3 and 55.5MJ/kg
HTPB (solid propellant), at 920kg/m^3 and 20MJ/kg
N2H4 (Hydrazine), at 1,021kg/m^3 and 19.5MJ/kg
HFO (Heavy Fuel Oil / "Bunker Fuel"), at 1,010kg/m^3 at 41MJ/kg
LH2: 71kg/m^3 * 142MJ/kg = 10,082MJ/m^3
HTPB: 920kg/m^3 * 20MJ/kg = 18,400MJ/m^3
N2H4: 1,021kg/m^3 * 19.5MJ/kg = 19,909.5MJ/m^3
LCH4: 422.8kg/m^3 * 55.5MJ/kg = 23,465.4MJ/m^3
RP1: 810kg/m^3 * 43MJ/kg = 34,830MJ/m^3
HFO: 1,010kg/m^3 * 41MJ/kg = 41,410MJ/m^3
CBP (Carbon Black Powder): 1,700kg/m^3 * 32.8MJ/kg = 55,760MJ/m^3
Volumetric Energy Density of Alternative Fuels Compared with RP1
CBP: 160.092%
HFO: 118.892%
RP1: 100%
LCH4: 67.371%
N2H4: 57.162%
HTPB: 52.828%
LH2: 28.946%
When over 90% of the vehicle's volume is filled with propellant, as is the case for all orbital class rocket vehicles, vehicle dry mass becomes sensitive to propellant density. Since CBP and HFO would pose a severe coking problem for a rocket engine, and HFO is also loaded with Sulfur in most cases, RP1 is the most energy dense and readily available propellant for minimizing vehicle dry mass.
There are no clever "tricks" to skirt around major volumetric energy density differences when fractional improvements in propellant mass efficiency can't overcome volumetric inefficiencies which are multiples of propellants with much higher volumetric energy densities. You need as high an Isp as you can manage, but more importantly, you need sufficient density to minimize vehicle dry mass if you intend to accelerate 100% of the vehicle dry mass, plus the useful payload, to orbital velocities. The only known way to do that is to minimize the vehicle's volume, which is enabled by RP1 and hampered by far less dense propellants like LH2 and LCH4, or propellants with much lower thermal output per unit of mass, such as Hydrazine and solids like APCP and HTPB.
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For kbd512 re #306
RP1 is the most energy dense and readily available propellant for minimizing vehicle dry mass.
This is a statement that deserves a moment of focus.
I am hoping you (or someone) will focus intently on this statement, and provide a simple 100 word or so confirmation it is correct. I don't know if it is correct or not. That's a benefit of being an observer when situations like this come up.
What I'm imagining is a very simple comparison.
We could define some arbitrary amount of energy.
We should be able to accurately compute the volume and mass of that amount of energy for LH2 and for RP1.
What I am expecting is that the mass of RP1 would be far greater for two reasons.
However, the volume of LH2 would be far greater.
I wonder if you might be thinking about tankage to hold these two liquids?
(th)
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tahanson43206,
Using RP1 (kerosene) as the fuel of choice permits rocket vehicle designers to minimize the propellant volume and maximize the total units of thrust generated per unit of engine mass and total vehicle dry mass for an orbital launch vehicle. This feature of RP1 is particularly important for SSTOs, but also important for TSTOs.
Vehicle dry mass scales by engine thrust-to-weight ratio and propellant tank volume, because for any significant payload to orbit, the propellant tank mass represents the majority of the vehicle's total dry mass (engines + propellant tanks). The cube-square law does help limit propellant tank mass increase as the propellant tank volume increases, but the end result will still be heavier propellant tanks and therefore higher vehicle dry mass when substantially less dense propellants, such as LH2, are substituted for RP1, when the goal should be equal or better payload performance with RP1. The vehicle dry mass comparison between Delta IV Medium and Falcon 9 Block 5 outright proves this. This is merely another way of saying that you cannot increase propellant tank volume by 10% or more, on account of LH2's exceptionally low volumetric density, yet still somehow arrive at a lower vehicle dry mass, as compared to RP1.
D4M Booster vs F9B5 Booster Propellant Volume and Tank Mass Comparison
D4M: 450m^3; mass, less engine: 22,110kg
F9B5: 370m^3; mass, less engines: 21,370kg or ~19,370kg without reusability hardware installed
F9B5 tank mass is 87.61% that of D4M
F9B5 tank volume is 82.22% that of D4M
F9B5 payload to orbit is 2.68X greater than that of D4M, but only 2X the gross liftoff mass of D4M
D4M Upper Stage vs F9B5 Upper Stage Propellant Volume and Tank Mass Comparison
D4M: 76m^3; dry mass, less engine 3,189kg; 23,264kg LOX + 3,956kg (561,752MJ) LH2
1X 301kg RL10B-2 engine, 110.1kN, 465.5s Isp; 24.1kg/s mass flow rate
1,129.460580912863071s * 110,100N = 124,353,610N-s
226,770kg total LOX/LH2 (both stages) / 8,510kg = 26.64747kg propellant per 1kg of payload
28,850kg + 3490kg = 32,340kg total dry mass
(447,150,942N-s + 124,353,610N-s) = 571,504,552N-s Total Impulse (both stages)
571,504,552N-s / 8,510kg = 67,157N-s/kg of payload
F9B5: 98m^3; dry mass, less engine 3,450kg; 75,200kg LOX + 33,200kg (1,427,600MJ) RP1
1X 550kg Merlin-1D Vac engine, 801kN, 348s Isp; 236.6kg/s mass flow rate
454.353338968723584s * 801,000N = 363,937,025N-s
518,400kg total LOX/RP1 (both stages) / 22,800kg = 22.73684kg propellant per 1kg of payload
25,600kg + 4,000kg = 29,600kg total dry mass (with booster reusability hardware installed)
23,600kg + 4,000kg = 27,600kg total dry mass (expendable)
(1,178,870,316N-s + 363,937,025N-s) = 1,542,807,341N-s Total Impulse (both stages)
1,542,807,341N-s / 22,800kg = 67,667N-s/kg of payload
Total Propellant Volume Required per kg of Useful Payload
D4M: 526m^3 of total propellant volume; 16.17871kg of payload per 1m^3 of propellant volume
F9B5: 468m^3 of total propellant volume; 48.71795kg of payload per 1m^3 of propellant volume
Total Thrust Required per kg of Useful Payload
D4M: 67,157N-s/kg of payload
F9B5: 67,667N-s/kg of payload
D4M "beats" F9B5, a vehicle pushing 2X as much total mass into the sky, in this one category that doesn't help make the case for LH2 fueled SSTOs, nor TSTOs for that matter. It's fractionally better than RP1 here, meaning you could run the main engine(s) for about 1.5 seconds longer, or less, on a LH2 fueled vehicle before total thrust (an indirect measure of total energy expenditure) per kg of delivered payload equalizes between both vehicles.
Hopefully we now understand how greatly vehicle dry mass affects our vehicle's total energy expended per kg of useful payload. We're getting 3X more payload mass per cubic meter of propellant volume for the F9B5 when we include both stages of the D4M and F9B5 rockets. That's a reasonably good efficiency metric if you ask me. Rather than showing how great LH2 is, we're continuously illustrating how freakishly efficient a modern RP1 fueled vehicle truly is. Even for a TSTO, every little bit of vehicle dry mass increase has a serious effect on vehicle performance.
RP1 has an acceptable Isp (total units of thrust generated per unit of propellant mass expended) for SSTO and TSTO. It's not even close to being "the best", yet LH2's much higher Isp doesn't seem to help improve total vehicle dry mass. Delivery of payload to orbit is primarily a question of Total Impulse delivered per kilogram of vehicle dry mass, and this is where RP1 is a stand-out performer.
RP1 allows the vehicle's propellant tanks to occupy the least amount of physical volume, therefore reducing their mass, amongst all of the common liquid rocket propellants. Amongst the propellants I listed, RP1 (kerosene) is the most widely used energy dense fuel combusted in gas turbine engines. The turbopumps that feed liquid rocket engines are specialized gas turbines capable of force-feeding a tremendous mass of gaseous propellants into the main combustion chamber.
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