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Dr Clark,
I decided to evaluate what an extendible / vacuum nozzle might net in terms of improved payload performance:
The Russian RD-0124 engine, a non-developmental LOX/RP1 engine in active service, has a vacuum Isp of 359s.
https://en.wikipedia.org/wiki/RD-0124
323.1s is 90% of that 359s Vacuum Isp
Mass Flow Rate (mdot) = Thrust / (Isp * g0)
3,452,113.5kg-f = 33,853,669N
mdot = 33,853,669N / (323.1 * 9.80665)
mdot = 33,853,669N / 3,168.528615
mdot = 10,684.35kg/s
6,508,946,390N-s / 33,853,669N = 192.267s
192.267s * 10,684.35kg/s = 2,054,248kg
Propellant Mass savings is 131,041kg, which nets an additional 7,407kg of payload to orbit. That amount of payload performance improvement would more than cover the mass allocation for the extendible nozzles. We need all the payload performance we can get for SSTOs, so I'll take it.
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For kbd512 and RGClark ...
There must be a trade-off between the benefits of a variable geometry nozzle and just using two engines with the appropriate nozzles. All existing space access systems just use multiple engines instead of a variable geometry design.
It seems likely to me that the weight penalty of a second engine is pretty close to the weight any viable variable geometry scheme would have. GW Johnson has provided plenty (an abundance) of documentation on the challenges facing anyone who wants to try to create a variable geometry nozzle with known materials and techniques.
The second engine will need the plumbing to route fuel and oxidizer it's way, so that will definitely add mass.
Because it is possible readers of this post may not be familiar with GW's offerings, the bottom line is that the junction between the extension and the atmosphere bell is where a bit of tricky engineering is required.
GW tells me that if a vacuum engine is used for atmosphere propulsion, the tip will burn off right where the end of the atmosphere engine bell would be if the system were designed for atmosphere. If an extension is shifted forward to mate with the atmosphere bell, the junction is where the challenges will arise. GW seems to think it would be difficult to keep hot gases from burning through whatever seal your engineer team might come up with.
The hardware to shift the vacuum extension forward would have mass.
Why not simply design an SSTO with both engine types and eliminate the complexity of variable geometry?
The market opportunity I see is for a one person-to-LEO transport that is reusable, and a one way delivery of material comprising the vehicle itself to LEO for use in construction of a larger vessel such as the 500 passenger transport proposed by kbd512, or the 1000 person transport proposed by RobertDyck.
(th)
Last edited by tahanson43206 (Today 06:32:50)
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The trouble with mixing two engine types in an SSTO is the very same problem SpaceX's "Starship" would have if one tried to make it an SSTO: you are too short on thrust to begin with, limited by what will fit behind the stage. Adding a second engine type just makes that even worse! You have to have enough thrust to launch "smartly", which is takeoff thrust/weight near 1.5 or more (never less), or your gravity is loss increases dramatically. Why? You end up burning the vast majority of your propellant in only the first ~5 km off the pad, leaving you still moving very subsonic!
Before the recent design updates, "Starship" was in the neighborhood of 120 tons inert and 1200 tons propellant if fully filled. At ZERO payload, that's a launch weight of 1320 tons. It is normally configured with 6 Raptor engines, 3 sea level in the neighborhood of 250-300 tons sea level thrust (call it 275), and 3 vacuum engines which would be nearer 150-200 tons thrust (call it 175), if unseparated at sea level, which strongly limits exit bell expansion ratio.
By the way, raising vacuum expansion ratio with constant chamber and flow rate makes the exit area bigger, so that fewer engines like that, will actually fit behind the stage! The takeoff thrust problem really gets unsolvable very quickly, if you attempt what might otherwise seem obvious!
Thrust is mdot*Vexit + (Pe - Pa)Ae, where the pressure term is quite strongly negative at sea level for an unseparated vacuum engine. (Thrust would be almost zero with a separated bell, which would further destroy itself in a single handful of seconds.)
Separation-limited vacuum engines (like the current vacuum Raptor) inherently have utterly-lousy sea level thrust! There is simply no way around that! 3x275 + 3x175 = about 1350 tons with all 6 burning at sea level on "Starship". That's thrust/weight only 1.02 at liftoff, which is long known to correspond to gravity losses WAY TO HELL-AND-GONE ABOVE 20% (or more) of LEO speed, not the 5% of an efficient system. Add only 30 tons of payload to this example, and this thing CANNOT budge a single inch off the launch pad, no matter how much propellant it has!
And there is NO ROOM behind it for more engines! Making the tankage hold 1300 or even 1400 tons really does not change that picture very much at all.
All SSTO designs face exactly the same thrust problem as trying to make an SSTO out of "Starship"! You cannot have any more engines, because those added would lie outside the stage diameter! That doubles-or-more your drag, and way-more-than-doubles your drag loss, which with a really clean shape of the right L/D ratio is about 5% of LEO speed.
There is simply way-far-more to this entire question than just Isp and mass ratio in the rocket equation! I have long tried to communicate that, but unsuccessfully!
And by the way, if sea level thrust gets reduced by the backpressure term, so does the corresponding sea level Isp, for the same combustion chamber design and total propellant flow rate. Which is EXACTLY why you need to look at engine/nozzle ballistics, and not just pull Isp's out of some table in some reference.
I have provided the spreadsheet tools and the instructional lessons, for free, to be able to do this work correctly. That's the stuff accessed by links posted right here on these forums.
GW
Last edited by GW Johnson (Today 13:29:10)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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tahanson43206,
The RL-10B-2 engine uses a RCC extendible nozzle. This nozzle extension is about the same size and weight as what a Vacuum-optimized Merlin requires. It appears as though the real payload benefit to a hypothetical Space Shuttle mass SSTO vehicle so-equipped, is no more than about 2,300kg, based upon the nozzle hardware mass required to equip 40 Merlin engines. That's more than what I thought it would be, and most of the mass appears to be the nozzle extension itself, rather than the deployment mechanism, which has almost negligible mass per engine. The extension hardware is only 10 to 20lbs per engine.
Apart from the cost of the nozzle extension, the nozzle mass increase pretty much kills this idea. You would get more useful payload by cutting the weight of each engine by using the same RCC material for all the major engine components, combined with a staged combustion cycle. The Merlin is a marvel of gas generator engine tech, but staged combustion always provides higher Isp.
That 116,120kg mass to orbit value is inflexible because 6,508,946,390N-s delivers 116,120kg to orbit. We know this because that was the Total Impulse provided by 3X RS-25 engines affixed to the Space Shuttle and 2X SRBs.
When I use Silverbird Astronautics Launch Vehicle Performance Calculator, this is what I get:
Inputs
Launch Vehicle: User Defined
Number of Stages: 1
Strap-on Boosters?: No
Dry Mass: 26,372kg
Propellant Mass: 2,185,289kg
Thrust: 33,854kN
Isp: 304.2s (90% of Vacuum Isp for the RD-180)
Default Propellant Residuals?: Yes
Restartable Upper Stage?: No
Payload Fairing Mass: 0kg
Launch Site: Cape Canaveral (USA)
Destination: Earth Orbit, Apogee 185km, Perigee 185km, Inclination: 45 degrees
Outputs
Launch Vehicle: User-Defined Launch Vehicle
Launch Site: Cape Canaveral / KSC
Destination Orbit: 185 x 185 km, 45 deg
Estimated Payload: 78,854kg
95% Confidence Interval: 58,892kg - 103,231kg
When the dry mass is adjusted downward to only 13,426kg (4,315kg RCC engines + same 9,111kg propellant tank mass)
Estimated Payload: 91,813kg
95% Confidence Interval: 71,844kg - 116,164kg
ISS orbit, same RCC engines:
Destination Orbit: 400 x 400km, 45deg
Estimated Payload: 86,900kg
95% Confidence Interval: 67,807kg - 110,215kg
ISS orbit, same RCC engines, 323.1s Isp (90% of RD-0124 Isp):
Estimated Payload: 108,038kg
95% Confidence Interval: 86,343kg - 134,287kg
This appears to be little better or worse than the real Space Shuttle if we added the hardware for resuability. The only measurable performance improvement achieved during the STS program came from making the External Tank lighter. These payload performance estimates confirm that a modestly better Isp from the same engines and propellant mass confers a meaningful payload performance advantage, but only when greater dry mass doesn't immediately replaces that useful payload mass.
Historical Space Shuttle GLOW and Propellant Mass: 2,032,096kg; 735,602kg LOX/LH2 plus 997,904kg APCP, 1,733,506kg total
SSTO Space Shuttle GLOW and Propellant Mass: 2,301,409kg; 2,185,289kg LOX/RP1
The historical Space Shuttle has a propellant mass reduction of 451,783kg, but both LH2 and APCP are much more expensive than RP1.
The SSTO Space Shuttle carries 587,443kg of RP1. The real Space Shuttle carried 106,261kg of LH2 and 159,665kg of solid fuel within the APCP oxidizer / fuel combo mixed into the propellant grain of the solid rocket boosters, or 265,926kg in total. The remainder of the solid propellant mass was AP oxidizer.
LOX: $0.27/kg
RP1: $2.30/kg
APCP: $5.00/kg
LH2: $6.10/kg
LCH4: $8.80/kg
Hydrazine: $75.80/kg
SSTO Space Shuttle Fuel Cost
LOX: 1,597,846kg * $0.27/kg = $431,418
RP1: 587,443kg * $2.30/kg = $1,351,119
Total Propellant Cost: $1,782,537
Historical Space Shuttle Fuel Cost
LOX: 629,341kg * $0.27/kg = $169,922
LH2: 106,261kg * $6.10/kg = $648,192
APCP: 1,733,506kg * $5.00/kg = $8,667,530
Total Propellant Cost: $9,485,644
That makes the propellant costs 5.3X cheaper for the SSTO Space Shuttle vs the real Space Shuttle, despite the fact that the SSTO Space Shuttle is burning 452t of additional propellant. Most of what the SSTO variant is burning is LOX. RP1 exhaust doesn't produce HCl, either, unlike APCP. We lacked the materials and engine tech necessary for any kind of SSTO when the real Space Shuttle was designed, so that's a moot point.
If whatever changes you're making to the vehicle lead to a greater dry mass, then you need more engine power and more propellant, period.
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GW,
Is there any reason why you cannot have multiple turbopumps feeding propellants into the same combustion chamber (so that you can use a much larger nozzle without singular gigantic turbopumps)?
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