I was running some numbers, and just got a surprising result. I’m wondering if someone can check my work.
The AIAA paper by Boeing, presented in Pasadena last fall, has a reference mission of 8.3 MT thrown at Jupiter for the fast trip with no gravity assists with the Block 2 cargo version. They specify a C3 of about 85 km^2/s^2. Here’s the table I’m looking at.
When I back that out, I end up with a departure velocity from LEO of about 6.5 km/s. With a stage fraction of 0.1 (that is, the ratio of the stage dry weight to loaded weight) and an Isp of 465 (referencing RL-10), and sixty tonnes in LEO (that’s the latest I’m hearing for FH with the upgraded cores), I can do that mission with a single flight. If we do two flights, I can throw 24 MT. Here’s my spreadsheet. Am I getting something wrong? Because that implies that they could do an even bigger mission with a 130 MT SLS. Here’s my spreadsheet.
[Update a few minutes later]
OK, I do see one slight problem, but I don’t think it affects my results much. I sized the “rubber” stage to the 2nd-stage requirement, so it’s probably a little undersized for the first stage. That is, when I change the payload mass, I get a slightly different propellant load in the first stage, though in actuality it should be independent of that.
[Update a few minutes later]
I’m wondering if the problem they have is that the EUS is oversized for the mission, so it wastes a lot of propellant shoving the parasitic stage mass? If so, that would be kind of hilarious.
But it is also possible that I’ve done the calculation wrong, which is why I’d like more eyes on my work.
[Update a couple minutes later]
D’oh!!
I do see an error. I double the potential energy as well as the kinetic when solving for departure velocity in line 13. BRB.
[Update a few minutes later]
OK, I guess I was wrong when I said I was wrong. Still not seeing the problem, if there is one.
[Update a while later]
I should note that the numbers don’t look obviously wrong, or bother me intuitively. I’m just trying to understand the disparity with the SLS mission, which supposedly has twice the throw weight.
[Late-afternoon update]
Looking at the Wikipedia page for EUS (I know, but it’s usually not a bad source for things like this), mass properties are pretty scarce. All it says is that it can carry 129,000 MT of propellant, which makes no sense, since that’s the throw weight of the SLS, and leaves no margin for structure. So huh. It’s almost like the whole program is a Bravo Sierra jobs program.
[March 28th update]
I just had an email exchange with one of the paper’s authors. They are using the Block 1B configuration, which only has 105 tonne capability. So my numbers seem to be right.
[Bumped]
Rand wrote: “With a stage fraction of 0.1 (that is, the ratio of the stage dry weight to loaded weight) and an Isp of 465 (referencing RL-10), and sixty tonnes in LEO (that’s the latest I’m hearing for FH with the upgraded cores), I can do that mission with a single flight. ”
Are you saying instead of utilizing the SLS block I you would instead use the Falcon Heavy with the same upper stage that would be used by NASA on the SLS?
I’m saying that it seems to be as good as the SLS Block 2 with some generic cryo upper stage, including the EUS, if it ever happens. Though the EUS might be too big and inefficient.
Sorry if this has been mentioned already (there’s a comment above mine that I cannot get to display) but I don’t see any mention (above or in the spreadsheet) of the ISP you’re using for FH in order to calc its delta/v?
I suspect I’m missing something obvious here.
Nevermind, I can see Rand’s reply now, and I was misunderstanding what he was proposing.
>It’s almost like the whole program is a Bravo Sierra jobs program.
Quelle horreur!
” All it says is that it can carry 129,000 MT of propellant, which makes no sense, since that’s the throw weight of the SLS, and leaves no margin for structure.”
Rand, you are thinking it will be 129,000 MT to orbit. The EUS will perform it’s own orbital insertion and burn a good chunk of that prop doing that. I bet it uses at least a third of that amount to do just that.
That’s a good point. I sure wish I had more data on SLS performance, though.
Too bad we don’t have something totally unique and useless like a *cough*prop depot*cough* to top it off so it really would have 129,000MT of fuel on orbit.
Then we could do stupid things like double TLI/TMI throw weight and possibly even return and re-use the upper stage as an extra big-ass tug.
Refuelable upper stages means potentially a lot of cheap vehicles hanging around in orbit.
Can we all check our units here? I see a lot of references to “129,000 MT” floating around. I assume “MT” stands for “metric tons” (aka “tonnes”). If it doesn’t, please enlighten me further. If it does, you all need to knock those three zeros off. 129,000 kilograms (aka “kg.”) is roughly the projected LEO throw weight of the SLS Block 2. That’s 129 metric tons, not 129,000. I’m reasonably sure even the entire Vertical Assembly Building doesn’t mass 129,000 metric tons.
Yes, it’s tonnes. I just calculated that a FH plus ACES can do the same mission in a single launch.
That’s good news, though Rep. Culberson may not agree. Sen. Shelby certainly won’t. But by the time both SLS and ACES are slated to be in service and the Europa mission hardware is ready to go, FH should already have both a lengthy flight history, a lower base price and a Raptor-powered upper stage. Perhaps Rep. Culberson, if he’s still in office and still a man of influence over space matters, could be brought around to the FH camp if Elon agrees to launch the mission from Brownsville instead of Kennedy.