Exoscientist

I’d like to get some feedback on the calculations here: Starhopper+Starship as a heavy-lift launcher. Triple-cored Starship for super-heavy lift. 2nd UPDATE, 9/2/2019: Starhopper as a lunar lander. https://exoscientist.blogspot.com/2019/07/starhopperstarship-as-heavy-lift.html Note: for the rest of this post, as well as in the blog post, I used the term “Starship” for its familiarity but I’m referring to the tanker version, not the version with the passenger quarters. The blog post argues that SpaceX should return to the originally planned high mass ratio version of the Starship, at ca. 25 to 1 rather than the current 10 to 1. The current mass ratio is quite poor for a dense-propellant rocket. SpaceX has been aiming to advance the state of rocketry, not go backwards. Then the Starship (the tanker version without passenger quarters) now used as a first stage plus a likewise weight-optimized Starhopper-sized upper stage could be a 100 ton class launcher in expendable mode. Note this would mean you would have a fully orbital-class launcher without the expense and extra time required developing the SuperHeavy booster. Then you would use triple cores a la the Falcon Heavy to get a 300 ton launcher. This approach would have multiple advantages. The biggest advantage is not needing the huge SuperHeavy at all. Because the Superheavy is three times the size of the Starship we can estimate its development cost as three times that of the Starship. In contrast, based on the Falcon Heavy experience, developing the triple-cored version would only cost 50% more than developing the Starship itself. The individual production cost would also be less, needing 1/3rd fewer engines. There is also the time element. Because of the Starhoppers small size and the fact it was already largely developed, aside from the required weight-optimizing, it could be produced along side the Starship at proportionally low cost. This is important because a 100 ton class launcher is commonly taken as the size-needed for a manned lunar mission. Then we could have a manned lunar mission mounted by next year in 2021 when Starship is expected to start flying. Another advantage is more controversial: the Starship, i.e., tanker version, at a 25 to 1 mass ratio and high Isp methane engines could be SSTO at significant payload. This would also be true for the weight-optimized Starhopper. This would go a long way to making manned-spaceflight routine since these smaller, simpler SSTO versions would be much more affordable and simple to operate and you could have independent companies and even private owners flying their own versions, both for point-to-point transport and for flights to LEO. The rocket equation shows the SSTO capability for the expendable mode. Here’s an argument that the extra weight needed for reusability, using weight optimized systems, would still allow significant payload as a SSTO: Short, stubby wings have been proven viable for return from space, so the large, heavy wings like the Space Shuttle are not required: The weight of the wings for the X-37 have not been revealed, however we can get an estimate from another vehicle the Skylon: For the Skylon the wing weight was only 2% of the landed weight. This is 2% of the full gross weight because it used a horizontal liftoff. But since the Starship will be using a vertical liftoff and non-lifting trajectory, the wings only have to support the weight of the vehicle on return, so that 2% will be calculated on just the dry weight. The landing gear weight can be taken as only 3%, or perhaps only 1.5%, of the dry weight: https://yarchive.net/space/launchers/landing_gear_weight.html Finally, the thermal protection as SpaceX’s PICA-X might only add on additional 8% of the dry weight. So these extra systems required for reusability will only add a proportionally small amount to the dry mass, so subtract only a proportionally small amount from the payload. Bob Clark

Isn’t it presumptuous to say they won when several companies have been granted contracts to develop a lander with the final decision to come later? Bob Clark

We can always be optimistic. There is no law that Boeing has to build the EUS, especially since it already has the contract for the SLS core stage. Perhaps we can start a letter writing campaign to Bridenstine to open up a competition for the EUS, like they did for the lander, with preference for the cryogenic upper stages already being planned. Bob Clark

An EUS can also mean a smaller lander that you want to send to the Moon with a single launch of the SLS. The Boeing EUS is unaffordable. But there will be several cryogenic upper stages that will be available as early as 2021 that could be used for a much cheaper EUS: Bob Clark

I speculated on a HLV using the Russian RD-171 engines here: https://exoscientist.blogspot.com/2012/05/low-cost-hlv.html Bob Clark

Thanks. I think the equations we discussed will be able to give the ideally optimized engine nozzle Isp’s. What needs to be worked on now are the trajectory equations including the gravity turn and the air drag equations. Any suggestions? Bob Clark

Thanks for doing the calculation. I assume you take into account that with fixed nozzles there is also a backpressure term given at the end of the equation here: F = q × Ve + (Pe - Pa) × Ae Also, as you know sea level engines are somewhat overexpanded at sea level because they also want to get good performance at vacuum. So the exit pressure for the fixed nozzle engine isn't really 1 atm at sea level. For the SSME's I think it's at around 1/3rd atm. For the Vulcain engines versions 1 and 2 the overexpansion is even worse. I think around at 1/4th atm for the Vulcain 1 and 1/5th atm for the Vulcain 2. You can get an idea about the degree of overexpansion for the Vulcain 1 at sea level from this graphic: At sea level the ideal Isp is significantly better than what the Vulcain 1 gives. I did a rough estimate and found for the currently-used Vulcain 2 because of its even higher level of overexpansion, its sea level thrust could be increased ca. 30%(!) by given it ideal expansion at sea level. This is important because higher lightoff thrust can reduce gravity drag. The increase for most engines wouldn't be this great though because most aren't this greatly overexpanded. For some other engines I tried I estimated the increase was less than 10% better sea level thrust by giving it ideal sea level expansion. For the parameters that go into the equation for the exhaust velocity, combustion temperature, molecular weight of combustion products, specific heat, etc., I've used the shareware program Rocket Propulsion Analysis, http://propulsion-analysis.com/index.htm. Bob Clark

Assuming we can use the equation for the exhaust velocity ve dependent on ambient pressure, we still need to calculate the flight path to orbit. For simplicity sake we can use the “gravity-turn” trajectory: Gravity turn A gravity turn or zero-lift turn is a maneuver used in launching a spacecraft into, or descending from, an orbit around a celestial body such as a planet or a moon. It is a trajectory optimization that uses gravity to steer the vehicle onto its desired trajectory. It offers two main advantages over a trajectory controlled solely through the vehicle's own thrust. First, the thrust is not used to change the spacecraft's direction, so more of it is used to accelerate the vehicle into orbit. Second, and more importantly, during the initial ascent phase the vehicle can maintain low or even zero angle of attack. This minimizes transverse aerodynamic stress on the launch vehicle, allowing for a lighter launch vehicle.[1][2] https://en.m.wikipedia.org/wiki/Gravity_turn#Launch Doing a google search turned up several references on calculating gravity turn trajectories. For this first level analysis I’m looking for some easily implemented ones if anyone knows of any. Also, some kerbal RealSolarSystem mod simulations have been done using aerospike nozzles for SSTO’s. Aerospike nozzles are the closest we have to ideal adaptive nozzles. Anyone want to give it a try with aerospike engines replacing the engines on the F9, Delta IV, Atlas V or other first stage boosters? Bob Clark

Dragon01 mentioned the equation for Isp was linear. It’s not really, but this reminded me of something I’m puzzled about. Fixed nozzles on a sea level engine are a compromise. They are overexpanded for sea level operation so they can get good Isp in vacuum.This should mean they get optimal Isp at some intermediate altitude, not at sea level and not in vacuum. But actually in graphics of engines they show the Isp either constant or increasing towards vacuum conditions. The graphic would be expected instead to look like this: Taken from this page: http://www.braeunig.us/space/sup1.htm But using the first image above we might be able to model approximately the Isp according to altitude by two straight lines, both for the fixed nozzle case and for the adaptive nozzle case. For the fixed nozzle case it would be an inclined straight-line to the altitude of 15,000m, then switching to a constant, i.e., flat-line thereafter at the vacuum Isp value. For the adaptive nozzle case, it would be two inclined straight lines. The first would be steeper than the second with the transition at around 15,000m to 20,000m. Bob Clark

One of the few papers that calculated the flight averaged Isp for the standard bell nozzle version of an engine and one fitted with alt.comp was this paper by Dana Andrews et.al.: Rocket-powered single-stage-to-orbit vehicles for safe economical access to low Earth orbit. July 1992Acta Astronautica 26(8-10):633-642 DOI: 10.1016/0094-5765(92)90153-A Dana G. Andrews E.E. Davis E.L. Bangsund https://www.researchgate.net/publication/245138678_Rocket-powered_single-stage-to-orbit_vehicles_for_safe_economical_access_to_low_Earth_orbit (This is behind a paywall but you can get a free copy through interlibrary loan from any university or public library.) I was surprised it showed the flight averaged Isp was 447s for the standard engine. The alt.comp version was a little higher at 460s. The flight averaged Isp is important since it allows you to make a rocket equation estimate of the payload using a single number for the Isp. Then you can get quite significant payload as an SSTO either for the standard version or the alt.comp version. However, it is known an SSTO is better realized using dense propellants. This is because their lower Isp is more than made up for by their higher density. Bob Clark

Quite correct. But these were quite expensive engines. The point of this exercise is to match the best vacuum Isp for vacuum optimized upper stage engines, using the less expensive lower chamber pressure engines, while still being able to launch from sea level. The F9 first stage engine’s vacuum Isp would be extended from 312s to ca. 365s and the Delta IV’s from 412s to ca. 465s. Because of the exponential nature of the rocket equation this would result in significant increase in payload. Robert Clark Not necessarily. Just as a TSTO doesn’t necessarily have to have return capability. IF it is found with alt.comp it can offer significant payload then it can be determined if there is sufficient payload to add reusability systems. Bob Clark

You are quite right; there are a lot of variables. For simplicity sake, you can imagine the nozzle attachment is one that can be extended so the the exhaust gas pressure matches the ambient pressure. This was the idea behind an extensible nozzle investigated for the Apollo Saturn V rocket though not implemented: https://www.alternatewars.com/BBOW/Space_Engines/Rocketdyne_Engines.htm For the Falcon 9 and Delta IV first stages this would result in a quite high increase in the vacuum Isp’s. From 312s to ca. 365s for the F9 first stage and from 412s to ca. 480s for the Delta IV first stage. Bob Clark

I think I know which equation you mean. It’s the first one on this page: http://www.braeunig.us/space/sup1.htm Here it is on that page:: F = q × Ve + (Pe - Pa) × Ae where F = Thrust q = Propellant mass flow rate Ve = Velocity of exhaust gases Pe = Pressure at nozzle exit Pa = Ambient pressure Ae = Area of nozzle exit The problem is the Ve is quite complicated depending on ambient pressure. Bob Clark

Perhaps you can point me to the equation you mean. The equation that gives the exhaust velocity, which equals g*Isp, is quite complicated in its dependence on ambient pressure therefore altitude: from, https://en.m.wikipedia.org/wiki/Rocket_engine_nozzle#One-dimensional_analysis_of_gas_flow_in_rocket_engine_nozzles Bob Clark

I’m actively seeking collaborators to calculate the payload possible by adding altitude compensating attachments to existing rockets: https://www.researchgate.net/project/Single-stage-to-orbit-SSTO Elon Musk said the Falcon 9 booster could be SSTO, but with small payload. Altitude compensation can increase the payload, but by how much? Bob Clark

I like your calculation. I noticed you gave a dry mass for the BFR Starship, which is the version of the BFR upper stage with the passenger quarters for 100 colonists on a Mars flight.. But you did not give a dry mass for the tanker, which instead has just a big empty fairing in that space What do you estimate the dry mass of the tanker version of the upper stage to be? What do you estimate the delta-v of the empty tanker upper stage to be? Bob Clark

Expendable SSTO would also be useful to test. Remember all rockets including the F9 were tested in an expendable mode. Bob Clark

Not the recent version from the 90’s. But the 70’s version can be downloaded from the NASA technical reports server: Design of Liquid Propellant Rocket Engines Second Edition. https://ntrs.nasa.gov/search.jsp?print=yes&R=19710019929 Bob Clark

The delta-v to orbit is commonly taken to be 9.1 km/s for equatorial orbits because you get a 400 m/s boost by the Earth’s rotation for free. Also the dry mass for the BFS upper stage is given as 85 tons by wiki. But this is the version with the passenger quarters for 100 Mars colonists. The tanker version would weigh much less without the passenger quarters, perhaps only in the 50 ton range. Bob Clark

You get 400 m/s for free by launching near the equator, such as from Cape Canaveral. Taking this into account, the delta-v to LEO is often taken to be about 9,100 m/s or 30,000 ft/s: From Modern Engineering for Design of Liquid-Propellant Rocket Engines, p. 12.https://books.google.com/books?id=TKdIbLX51NQC&pg=PA12&source=gbs_toc_r&cad=4#v=onepage&q&f=false Because of the exponential nature of the rocket equation that 900 m/s difference between 10 km/s and 9.1 km/s accounts for a significant amount of payload. Bob Clark

The latest NASA budget suggests the Europa Clipper, an orbiter mission to the Jovian-system to study Europa, won’t fly on the SLS, but instead on commercial rockets: https://mobile.twitter.com/SpcPlcyOnline/status/1105131948903747584 However, instead of just an orbiter mission, by using commercial rockets, we can do it as an actual lander mission at a fraction of the cost of the SLS-based orbiter mission. In fact, it could be so low cost so as to be fully privately financed and at a profit. http://exoscientist.blogspot.com/2015/02/low-cost-europa-lander-missions.html This written in 2015. Since then the F9 has been increases in payload nearly 50% and the FH by nearly 25%. So the landers could be made larger or more capable in-space stages could be used to shorten the flight time. I had assumed that the Falcon Heavy couldn't carry the full Europa Clipper orbiter at 6 ton gross mass to Jupiter. And speculation had been the addition of a Star 48 solid-stage would allow the EC mission on a FH but it would require an Earth gravity-assist that would lengthen the flight time to 6 years. However, I was surprised when I ran the numbers that the upgraded version of the FH could do the mission with plenty of margin with the addition of one of the existing cryogenic upper stages. The extra margin would actually allow you to shorten the flight time from the 2.7 years expected with the SLS. Bob Clark

Didn't know the 7075 was known that long. The X-33 engineers did try replacing the carbon composite with aluminum-lithium, so perhaps the advantage of 7075 over aluminum-lithium was not sufficient to justify its expense. Note though there are now alloys significantly stronger than 7075 as well. Bob Clark

We now know that even reusability of a two-stage vehicle (TSTO) costs significantly in payload. For instance, the Falcon 9 loses 30% of it’s payload with first stage only reuse and 40% payload is lost with full reuse. Since the SSTO doesn’t have the expense of an upper stage, there really has to be an accurate reassessment which comes out ahead on a cost per kilo basis. I emphasize cost per kilo because even though the TSTO will carry more payload it will lose more payload on reusability and cost more because of the upper stage. Bob Clark

Correct about the complex shape being the problem. Actually, cylindrical carbon composite tanks were well understood even then. That’s what led Lockheed engineers to think they could solve the case of conformal, i.e., following the shape of the aircraft, tanks. Unfortunately, it turned out with carbon composites the weight turned out worse than metal tanks rather than saving weight. However, recent high strength metal alloys are even more weight saving than carbon composites. This means we can now build the X-33 with even better than the original expected performance and build the VentureStar with even better than the originally expected payload as an SSTO: DARPA’s Spaceplane:an X-33 version, Page 2. https://exoscientist.blogspot.com/2018/06/darpas-spaceplane-x-33-version-page-2.html Bob Clark

ESA may have no choice in the matter. SpaceX is progressingly rapidly to reusability and to reduced costs. The current version of the Ariane 6 does not allow reusability. By its scheduled time of full operation in 2023, it may already be obsolete. Bob Clark