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Note it doesn't have to equal the two stage F9 in payload, but only be able to lift enough payload to be profitable. The partially reusable, two-stage F9 is able to lift in the range of 16 tons to LEO. Suppose a fully reusable SSTO F9 is able to lift, say, 8 tons to LEO. If a customer only needs 8 tons to LEO, why should he pay for the higher capacity? Keep in mind most payloads to LEO do not need the full 16 tons to LEO of F9. SpaceX wanted to give the F9 FT the higher capacity so it could cover those customers that needed it. But in reality it's a small proportion of the customers who do.

The heat shield mass probably can be less than your estimate. According to the Spaceflight101 page on the F9 FT, the diameter is 3.66 m and the height of the first stage is 42 m. The full area of the cylindrical first stage is Pi*(3.66)*(42) = 490 m^2. But we'll only need to cover the bottom half, so only 245 m^2. Then the mass of the PICA-X heat shield will be in the range of 5,000 kg.

Also, nobody knows how much the F9 with altitude compensation can get to LEO because nobody ever calculated it for dense propellants.

  Bob Clark

Thanks for that equation. I think I can find the answer to the question following that.

By the way, here’s an article I’m reading about various methods to improve rocket nozzle performance:

JOURNAL OF PROPULSION AND POWER Vol. 14, No. 5, September– October 1998
Advanced Rocket Nozzles.
Off-design operations with either overexpanded or under- expanded exhaust flow induce performance losses. Figure 3 shows calculated performance data for the Vulcain 1 nozzle as function of ambient pressure, together with performance data for an ideally adapted nozzle. Flow phenomena at different pressure ratios Pc/Pamb are included in Fig. 4. [The sketch with flow phenomena for the lower pressure ratio Pc/Pamb shows a normal shock (Mach disk). Depending on the pressure ratio, this normal shock might not appear, see, e.g., Fig. 2.] The Vulcain 1 nozzle is designed in such a manner that no uncon- trolled flow separation should occur during steady-state oper- ation at low altitude, resulting in a wall exit pressure of Pw,e ~ 0.4 bar, which is in accordance with the Summerfeld criterion. The nozzle flow is adapted at an ambient pressure of Pamb ~0.18 bar, which corresponds to a ? flight altitude of h ~ 15,000 m, and performance losses observed at this ambient pressure are caused by internal loss effects (friction, diver- gence, mixing), as shown in Fig. 1 and Table 1. Losses in performance during off-design operations with over- or un- derexpansion of the exhaust flow rise up to 15%. In principle, the nozzle could be designed for a much higher area ratio to achieve better vacuum performance, but the ?flow would then separate inside the nozzle during low-altitude operation with an undesired generation of side-loads.
https://www.researchgate.net/profile/Ge … ozzles.pdf

I’m trying to understand that passage I quoted. It seems to be saying the exit nozzle pressure is both 0.4 and 0.18.

  Bob Clark

For the hypothetical SSTO you discuss at 900,000 kg propellant and 50,000 kg dry mass, it’s about twice the gross mass of the Falcon 9 FT, so give it a vacuum thrust twice that of the F9 FT, so at 16,000kN. So plug this into the Launch calculator you linked.

There are a few quirks of this launch calculator you need to keep in mind also. First, the calculator always takes the vacuum values of the Isp and thrust even for the first stage. This is because it already takes into account the diminution at sea level. Secondly, the “Restartable Upper Stage” option should be clicked “No”. This always reduces the payload when clicked “Yes”, eventhough in this case there’s no upper stage.
Thirdly, taking the launch site as Cape Canaveral you should set the launch inclination as 28.5 degrees to match the launch site latitude. This is a fact of orbital mechanics that altitude, or payload, is maximized by launching in a direction to match the latitude of the launch site.

Doing this, I get a payload of 26 tons for the expendable mass. But as I said this calculation has limited accuracy. The reason is this calculator was designed for fixed nozzles. What really needs to be done is a true trajectory simulation that takes into account the actual variation of Isp with altitude.

  Bob Clark

I’ve been reading the literature for SSTO’s going back years and I’ve not seen a calculation yet giving an accurate simulation of a SSTO with alt. comp. for dense propellants. As I mentioned there are a few using hydrolox, since it had been thought that was the best approach because of the higher Isp.

Since the common feeling is SSTO’s have to use hydrogen, and SSTO’s are already considered sketchy, nobody is willing to do the calculation for alt. comp. using dense propellant.

I know you’ll find this hard to believe but the situation about alt.comp. with dense propellants literally is this:

Nobody has done the calculation because nobody thinks it’s worthwhile.
And nobody thinks it’s worthwhile because nobody has done the calculation.

  Bob Clark

I’d like to see the spreadsheet if you can send it.

I agree the vacuum Isp overestimates the delta-v achievable when using altitude compensation. I was using it for lack of any other options. Thus, in my researchgate.net page I set up a project for accurately simulating the delta-v and payload to LEO of an altitude compensating rocket.

It is notable though that commonly with fixed nozzle rockets the vacuum Isp is used to estimate the payload achievable to LEO. To do this, rocket scientists regard the loss of Isp at sea level as just another loss, like air drag loss, and gravity drag loss, and add on an additional amount to the delta-v required to LEO like they do for those other losses.

Then likely for the altitude compensating case you could use the vacuum Isp value if you add on the appropriate “loss” amount to the required delta-v to orbit.

Note too, the overestimation with using the vacuum Isp for the alt. comp. case might not be as bad as first thought because alt. comp. also improves sea level Isp and thrust. The reason is fixed nozzles are overexpanded for sea level operation as a compromise to get good vacuum operation. But with alt. comp. you can get optimal expansion at sea level also.

  Bob Clark

Elon on Twitter said hopefully the Starship will fly this week:

https://www.cnet.com/google-amp/news/el … -fly-soon/

Though weather in the Gulf may push it back to next week.

Presumably it will be a short hop test. But running the numbers the Starship could get a surprisingly high delta-v.

The latest version has 3 sea level and 3 vacuum engines. Presumably only the 3 sea level ones will be used at launch. So this will mean 3 x 200 tons = 600 tons of launch thrust. I’ll take the propellant load as 400 tons to allow for payload at later tests.

But launching the bare rocket could get 354*9.81Ln(1 + 400/120) = 5,100 m/s delta-v, past Mach 16.

This though is the delta-v as an expendable. Some of the propellant has to be used though for landing so the actual delta-v achieved will be less than this.

This scenario though illuminates the importance of achieving altitude compensation. Those 3 vacuum engines have to just stay idle during launch, like dead weight. Imagine instead having altitude compensation so all six engines could be used for liftoff. You would have 1,200 tons liftoff thrust. Nearly the full propellant load could be used. You would get in the range of 7,000 m/s delta-v. Actually it would be higher than this since the altitude compensation would also allow you to use the full vacuum Isp of the vacuum raptors of 380 s at high altitude.

This would mean quite a large portion of the Earth could be covered by point-to-point rocket travel. This represents a huge market for the Starship.

Bob Clark

Essentially what you’re asking for is a pressure-fed rocket to launch from the Moon’s surface. Because the orbital speed for Moon is so much smaller than for Earth, about 1.8 km/s for the Moon compared to about 7.8 km/s for Earth, this isn’t particularly hard.

Instead of balloons though use metallic or carbon fiber tanks commonly used for rocket propellant tanks with the propellant held under pressure.

You may have been conflating this question with another question: suppose you had a gas, could be even non-flammable such as air, or nitrogen, that is simply compressed under high pressure. Could this be used for a rocket that could reach lunar orbit?

My guess is probably yes. The Isp would be low though so it wouldn’t be very efficient. See table here: https://en.m.wikipedia.org/wiki/Cold_ga … ropellants

But the real problem is the low density of the gas, as indicated in the table on that wiki page, would result in a low propellant mass ratio.

A possible answer to that is to store the “propellant” as a liquid, then allow the expansion of the propellant into a gas to provide the thrust, such as here:

Liquid Nitrogen Rocket with Steve Spangler on DIY Sci S01E06.
https://www.youtube.com/watch?v=yFNLq7qnmMQ

  Bob Clark

I did some preliminary calculations of the Ve from the equation I cited in post #17 and found it was in reasonable agreement to the graph of the Vulcain 1 under ideal expansion in that post. So we can use the equation with some efficiency factor of, say, .96 to .98, to calculate the Isp dependent on altitude for different engines.

As I mentioned I got the engine parameters such as combustion temperature, combustion products molecular weight, specific heat, etc., from the Rocket Propulsion Analysis program, http://propulsion-analysis.com/index.htm , to plug into the formula.

You can do a graph to see if you do get a similar shaped graph when you do the calculations for other engines under ideal expansion.

We also need to do the flight trajectory simulation for alt.comp. engines.  For this first level calculation we can do a “gravity turn” trajectory:

https://en.m.wikipedia.org/wiki/Gravity_turn

I’m looking for simple references to use for this calculation.

  Bob Clark

Here's the equation showing exhaust velocity dependent on nozzle exit pressure:

from,
https://en.m.wikipedia.org/wiki/Rocket_ … ne_nozzles

So we can calculate the Ve given the other parameters such as combustion temperature, molecular weight of the combustion products, etc. We can get those as calculated by the program Rocket Propulsion Analysis:  http://propulsion-analysis.com/index.htm

It's a derivative with user-friendly GUI of the program ProPEP. The program also calculates the vacuum and sea level Isp of the engine. I've found the vacuum Isp it calculates to be reasonably accurate for known engines. However, the sea level estimate it I found is not. I don't know why that is if anyone wants to experiment with the program. 

Still we can use it to calculate the parameters that go into the Ve equation above, then use that equation to calculate the Ve. Because of inefficiencies in nozzles, you won't get the exact value. But rocket engines are pretty efficient, commonly at the 96% range, so the Ve calculated should be pretty accurate.

Here's a graphic that shows what the Isp of the Vulcain 1 engine would be if it had ideal expansion at all levels:

Taken from:

Advanced Rocket Nozzles
August 1998 Journal of Propulsion and Power 14(1998):620-633
Source DLR
Gerald Hagemann Hans Immich T. van Nguyen G.E. Dumnov
https://www.researchgate.net/publicatio … et_Nozzles

You see the ideal expansion case is significantly better than the fixed nozzle case both at sea level and vacuum. We can use the graph to estimate the Isp for the alt. comp. case, at least for the Vulcain 1 engine. Also, by comparing the graph to our calculations we can determine how accurate our Ve calculations are.

But we still need to calculate the delta-v for other engines, such as the hydrolox RS-68 on the Delta IV, the kerolox Merlin on the F9, and the methanolox Raptor on the BFR.

Here's a graphic showing ideal expansion in general:

The parameter being displayed on the y-axis is nozzle thrust coefficient, not exhaust velocity. But they are proportional so the exhaust velocity graph would have a similar shape. If by comparing our Ve calculations for the Vulcain 1 to the graphic for the Vulcain 1 case, we can conclude out calculations are accurate then that will bolster our confidence in using the Ve equation for the other engines.

  Bob Clark

Thanks for that link. The vacuum Isp is highly dependent on nozzle size, or nozzle area ratio. For instance the hydrolox RL10-B2 engine with its long nozzle extension can get 465.5s Isp. And the methanolox vacuum Raptor is expected to have a 382s vacuum Isp.

Back in the late 90’s there was a lot of interest in SSTO’s with the research on the X-33 and the DC-X. Here’s a report that explored the options for fuels for an SSTO:

Alternate Propellants for SSTO Launchers.
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix Arizona
April 25 - 27, 1996
https://web.archive.org/web/20140215015 … llants.htm

It turned out the dense propellants offered better payload since their lower Isp was more than made up for by their higher mass ratios.

Bob Clark