cryogen

Might to be useful to know, Kerbal EVA suits violently explode at 800 Kelvin. Sorry Jeb!

It goes both ways. At a higher Tcold, conversion is less efficient, hence there's more waste heat. But, radiators radiate far more heat per unit area (scaling as T4), so their size might shrink, for some parameters. There's a tradeoff between efficiency and radiator size; saving radiator mass might push towards higher temperatures and hence lower efficiencies.

This is absolutely correct. Should clarify that this is for a rocket with a constant Isp: it's possible to get higher energy efficiencies by varying Isp over time (for example, different fuels in each stage, or variable ion voltage in electric thrusters). In the limiting case, you can approach 100% efficiency, if ve(t) = vr(t) -- if the exhaust speed is always equal to the rocket's speed, at a given time. Then, the exhaust has zero velocity in the initial reference frame -- its velocity backwards exactly cancels the rocket's forward speed when it was expelled, so it ends up stationary. All of the kinetic energy ends up in the rocket; none in the propellant. (This is only a limiting case though: the propellant mass diverges to infinity, as ve(t=0) approaches zero). Here's some maths. Imagine a rocket with a continuously varying exhaust velocity ve(ÃŽâ€v) (instead of parameterizing as a function of time, we're parameterizing in the cumulative delta-v of the rocket). And let U(ÃŽâ€v) be the cumulative energy of the propellant, that is δU = (1/2) δm ve2. (Ignoring thermodynamic losses here). The kinetic energy of the rocket (payload + structure) is KR(ÃŽâ€v) = (1/2) mR ÃŽâ€v2. We're interested in the energy conversion efficiency, η = KR / U. Of course η ≤ 1. A differential increase in ÃŽâ€v, by δÎâ€v, increases the propellant energy by: U(ÃŽâ€v + δÎâ€v) = (1/2) δm ve(ÃŽâ€v)2 + U(ÃŽâ€v) (1 + δm/mR) The left term is the kinetic energy of a differential mass of propellant δm, expelled with velocity ve2. Since we've increased the mass of propellant, we need more propellant to lift that propellant (rocket equation logic). The mass accelerated to ÃŽâ€v increases from mR to mR + δm, so we have everything before that multiplicatively. That's the term on the right, multiplying U(ÃŽâ€v). We can relate δm to δÎâ€v, according to conservation of momentum: δÎâ€v = δm * ve. U(ÃŽâ€v + δÎâ€v) = (1/2) δÎâ€v ve(ÃŽâ€v) + U(ÃŽâ€v) (1 + δÎâ€v/(mR ve(ÃŽâ€v))) d/dÃŽâ€v{ U(ÃŽâ€v) } = (1/2) ve(ÃŽâ€v) + U(ÃŽâ€v) / (mR ve(ÃŽâ€v)) [eq. 1] This gives us some intuition. Increasing Isp gives us two competing effects: it increases the marginal energy of the propellant (left term), but it also decreases the mass of that propellant, and thus the energy that goes into to accelerating it (right term). As ÃŽâ€v increases, the right term becomes more important (rocket equation!!), so the optimal Isp goes up. (You can solve in several ways, that the functionally optimal Isp function is just ve(ÃŽâ€v) = ÃŽâ€v. Easiest way is just to observe that that solution is 100% efficient, η=1, and you can't do better than that according to conservation of energy). For constant-Isp solutions, the maximum is at about ve(ÃŽâ€v) = 0.63*ÃŽâ€v. (This is what K^2's post focused on). By the rocket equation, if ve(ÃŽâ€v) = α ÃŽâ€v, the mass ratio is e^(ÃŽâ€v / ve) = e^(1/α), and the propellant fraction is ζ = (e^(1/α) - 1) / e^(1/α) . So 1/η = U/KR = (e^(1/α) - 1) ve2 / ÃŽâ€v2 = (e^(1/α) - 1) α2 (Alternatively you could get this by solving eq. 1 directly, with ve a constant). The maximum occurs where dη/dα = 0 (or d/dα [1/η] = 0): 0 = d/dα { (e^(1/α) - 1) α2 } 0 = 2 α (e^(1/α) - 1) - e^(1/α) (2 α - 1) e^(1/α) = 2 α e^(1/α) = (2 α) / (2 α - 1) e^(s + 2) = -2 / s | α -> 1/(s + 2) s e^s = -2 / e2 s = W(-2 / e2) α = 1/(W(-2 / e2) + 2) ~= 0.6275 η = 1/ { (e^(1/α) - 1) α2 } ~= 64.76 %

NERVA launch is very unlikely to work. Here's Kirk Sorensen's analysis: http://selenianboondocks.com/2010/06/ssto-ntr-bad/ Simplified: if you have a nuclear thermal SSTO, with an excellent (optimistic) Isp of 900 s, it needs a mass ratio of at least e^{ (9,200 m/s) / (g * 900 s) } = 2.83 ...according to the rocket equation, with 9.2 km/s delta-v to LEO. (If instead you were to stage an NTR, then the nuclear 1st stage would crash back to earth, which is probably unacceptable. Moreover: there's less economic rationale for having high Isp in a low delta-v first stage -- it'd likely be cheaper to pay the mass penalty and use simpler chemical boosters like RP-1. Exotic, high-Isp propulsion is more useful, the higher up the rocket it's used). So the propellant fraction ζ would need to be 1 - 1/2.83 = 65%, leaving <35% for engines, structure, and payload combined. So the engine TWR would need be at least 3 just to lift off the ground (rocket TWR > 1), and likely higher than 10 to get any payload to orbit. That's the fatal flaw of NTRs: their TWR is too low. The NERVA rocket had an empty TWR of just under 1. The more performant NTR engine Kirk cites has a TWR of 3, which doesn't lift off the ground either. This combination of Isp and TWR doesn't add up. So NTR SSTO even might be technically impossible, at this time. We'd need much higher TWR's: we'd need more compact, lightweight, higher power-density nuclear reactors than can currently be built.

Actually, they won't! The first stage (core, excluding boosters) will have 7,440 kN of sea-level thrust (4x RS-25), and a gross mass of 979 tonnes, for a TWR of about 0.78. The main engines wouldn't be able to the lift the first stage above the ground. https://en.wikipedia.org/wiki/Space_Launch_System (sidebar) The same was true of the Shuttle. The main engines didn't have enough thrust to lift the external tank, which was their fuel source. I believe it's the same RL-10B2 as the DCSS -- here's a source: https://www.nasa.gov/sls/interim_cryogenic_propulsion_stage_141030.html

I wonder if they could use the tiny 2nd stage from Falcon 1e (Kestrel engine), and install it under the Falcon Heavy fairing (as a 3rd stage)? The rocket equation also closes for that.. http://www.spacelaunchreport.com/falcon.html Don't know. It's in ATK's catalog though.

Small update, made a new C3 chart:

I did a bit of googling; I think you're right. Here're the current figures for the Europa Clipper (although they're very likely to change). The total (wet) mass at launch is 3,582 kg (first link). The launch C3's, for the slow, gravity-assist Atlas V option, and the fast, direct SLS option, are 15 km2/s2 and 82 km2/s2 resp. (second link). https://solarsystem.nasa.gov/europa/docs/Europa%20Clipper%20Info%20Sheet%2020130903.pdf http://www.lpi.usra.edu/opag/jul2013/presentations/Clipper_Summary.pdf Here's the C3 curve for the Falcon 9 (I think this is v1.0? Not sure). Either way it's probably a non-starter; even the payload to C3=0 (i.e. earth escape) is much less than the Clipper's mass. http://www.spaceflightnow.com/falcon9/001/f9guide.pdf What about Falcon Heavy? Well, it seems the specs haven't been published yet, so I did some extrapolating from some information that's already public. I used the marketing specs for the Falcon Heavy -- 21.2 tons to GTO, 13.2 tons to Mars Transfer. And I used specs from the Falcon 9 v1.1 upper stage, which I understand will be used unmodified (?) on the Falcon Heavy. (If there's a secret new stage under development, then this analysis is bunk). I used the vacuum Isp and wet/dry masses for this upper stage. http://www.spacex.com/falcon-heavy http://www.spaceflight101.com/falcon-9-v11.html Here's my extrapolation. Since the booster stages cut off well before GTO velocity, I'm assuming a fit of the rocket equation, to the GTO and Mars payloads, will roughly extrapolate the payload to higher C3's. There's tons of implicit assumptions here, too many to even discuss. This is a messy guesstimate at best. I did a nonlinear fit in Mathematica, using these values: [TABLE=width: 500] [TR] [TD]Isp[/TD] [TD]340 s[/TD] [/TR] [TR] [TD]F9-H stage mass, dry[/TD] [TD]3,900 kg[/TD] [/TR] [TR] [TD]F9-H propellant mass[/TD] [TD]92,670 kg[/TD] [/TR] [TR] [TD]delta-v from LEO to GTO[/TD] [TD]2.5 km/s[/TD] [/TR] [TR] [TD]C3 to Mars transfer[/TD] [TD]10 km2/s2[/TD] [/TR] [TR] [TD]F9-H payload to GTO[/TD] [TD]21,200 kg[/TD] [/TR] [TR] [TD]F9-H payload to Mars transfer[/TD] [TD]13,200 kg[/TD] [/TR] [TR] [TD]Effective perigee altitude for Oberth (guess)[/TD] [TD]100 km?[/TD] [/TR] [/TABLE] My estimate for F9-H's payload, for the SLS-direct trajectory, is 2,664 kg. This isn't very accurate at all, but it's much less than the Clipper mass (3,582 kg), so I think the conclusion is robust: F9-H can't do the direct Jupiter trajectory, with its current upper stage. The VEEGA trajectory is easily an option. F9-H's payload would be slightly less than the Mars transfer -- 11,549 kg for C3=15 km2/s2. update: On the other hand, a single Star-63F upper stage -- one of the larger solid rockets of the Payload Assist Module -- placed on top of the F9-H, could comfortably launch the Clipper on a Jupiter-direct trajectory. Take the Clipper mass (3,582 kg), add 10% margin (3,940 kg). Add on a 4,590 kg Star-63 F (total 8,530 kg). From my extrapolation, the F9-H could lift this much mass to C3 = 30.2 km2/s2. (This is a more comfortable estimate: it's very close to the Mars transfer that we have a datapoint for). Then the Star-63F can give us another 2,019 km/s boost, to a final C3 of 84 km2/s2. I think that would be credible! Star-63F specs: [TABLE=width: 500] [TR] [TD]Isp[/TD] [TD]297 s[/TD] [/TR] [TR] [TD]empty mass[/TD] [TD]326 kg[/TD] [/TR] [TR] [TD]gross mass[/TD] [TD]4,590 kg[/TD] [/TR] [/TABLE] http://www.astronautix.com/engines/star63f.htm https://en.wikipedia.org/wiki/Payload_Assist_Module

I have learned something

You're right! Huh, interesting. I got my figures from the in-game screen; I think it loses precision through rounding. The Array is described as having 0.02/sec for both fuel and oxidizer. Here's the relevant parameters from the .cfg's -- you're totally right:

That's the third poll option, "DC-I"! Sorry for the confusion!

I confirm Landarin's maths. Fuel Cells, and Fuel Cell Arrays (the bigger one), output 400 and 450 units of electricity respectively, per unit of combined (fuel + oxidizer). (E.g.: the Array produces 18 electricity units/sec, out of 0.02/sec fuel and 0.02/sec oxidizer, for a total of (18/sec) / (0.04/sec) = 450). Since both fuel and oxidizer weigh 5 kg/unit, their mass efficiencies are 80 electric units/kg and 90 electric units/kg resp. The IX-6315 "Dawn" produces 2.016 kN of vacuum thrust, while consuming 8.81 electricity units/sec, and 0.489 units/sec of xenon gas. Xenon weighs 0.1 kg/unit, so that's 0.0489 kg/sec of propellant flow. And the fuel cell (Array) consumption is 8.81 units/sec / (90 units/kg) = 0.0979 kg/sec. (So, the (fuel+oxidizer) / xenon ratio is exactly 2:1, neat). The overall Isp is 2,016 N / (0.0489 kg/s + 0.0979 kg/s) / g = 1400.0 seconds Repeating the math for the less efficient (smaller) Fuel Cell, it's 2,016 N / (0.0489 kg/s + 0.1101 kg/s) / g = 1267.7 seconds - - - Updated - - - By the way, this is totally unrealistic. In the real world, burning chemical fuel for electricity, and using that to power an ion thruster, would be way worse than the plain chemical engine. Like Isp < 80 s. The energy density of stoichiometric (H2+ 1/2 O2) is 15.9 megajoules/kg. (Derivation: ÃŽâ€fH° of H2O (l) is 285.8 kJ/mol; a mole of water weighs 18 grams; 285.8 kJ/(18 g) = 15.88 MJ/kg). And, a real ion thruster with a 4,200 s Isp would have a power demand of, at minimum, KE / p = [(1/2) (42 km/s)2 / kg] / [42 kN s / kg] = 21 kW / N. So with a 100% efficient H2/O2 fuel cell, the specific impulse (H2/O2 only) would be (15.9 MJ / kg) / (21 kW / N) / g = 77 seconds It really is that bad! Reminder, LH2/LOX combustion engines go up to 465 s (see ESA's Vinci engine). The root problem is, I think (?), the mismatch between the energy density of H2/O2, and the much higher energy density of 40 km/s exhaust. Higher ve means both less propellant mass, and higher specific energy, which means more fuel cell mass. We're way above the "knee" of the curve: we're increasing fuel cell mass much faster than we're saving xenon mass. I won't second-guess why Squad made fuel cells so powerful. They're much better at balancing gameplay than I am

I'm curious what people more informed than me think! Most of these concepts didn't go far, their projects cancelled over either technical or political problems. With 2015 technology, and a well-funded development budget, would any of these be promising today? Or were these all dead ends? [TABLE=width: 800] [TR] [TD]X-30 / National Aerospace Plane[/TD] [TD]X-33 / VentureStar[/TD] [/TR] [TR] [TD][/TD] [TD][/TD] [/TR] [TR] [TD] Suborbital or SSTO spaceplane Air-breathing scramjet engine Horizontal takeoff & landing [/TD] [TD] SSTO spaceplane Linear aerospike engine Composite LH2 tank (controversial) Vertical takeoff, spaceplane landing Metallic heat shield, radiatively cooled [/TD] [/TR] [TR] [TD] [/TD][TD] [/TD][/TR] [TR] [TD]DC-I / Delta Clipper (pictured is smaller DC-X test vehicle)[/TD] [TD]MAKS spaceplane (Soviet)[/TD] [/TR] [TR] [TD][/TD] [TD][/TD] [/TR] [TR] [TD] SSTO rocket Vertical takeoff & landing [/TD] [TD] Air-launched SSTO spaceplane Expendable external tank LH2/RP-1/LOX tripropellant [/TD] [/TR] [/TABLE] (All images from Wikipedia, under Creative-Commons license)

Well they have direct evidence now, http://onlinelibrary.wiley.com/doi/10.1002/1521-3773(20011105)40:21%3C4062::AID-ANIE4062%3E3.0.CO;2-X/abstract

There's a bit of confusion. Density and Isp are unrelated. Specific impulse only measures how much impulse a unit of mass will impart -- it doesn't care about volume. Density is important too (of course): denser fuel means smaller rockets, less drag and probably lower tank mass. The source article, in Nature, suggests O4 could be an interesting rocket oxidizer because it's denser than liquid O2 -- not necessarily more energetic: http://www.nature.com/news/2001/011116/full/news011122-3.html Is it more energetic than O2 (which would give it higher Isp)? Well, maybe I guess? It's a different molecular form, so it could have a higher enthalpy of formation. I can't find an answer by Googling: I'm not sure if this has been measured. (edit: but see below...) We do know ozone (O3) has +143 kJ/mol enthalpy relative to O2, which gives it a theoretical 20-30s of Isp advantage, so I think it's plausible O4 could have an advantage too. (In John D. Clark's Ignition, he says ozone is unlikely to ever be used in an actual rocket engine (pp. 112-114), because it's too unstable to spontaneous decomposition. (That's an amazingly fun book by the way -- you can find PDFs online, because it's out of print)). https://en.wikipedia.org/wiki/Standard_enthalpy_change_of_formation_(data_table) https://books.google.com/books?id=BfR0LexeuREC&pg=PA437 As for the molecular mass difference (O4 weighs twice as much), that shouldn't matter. It would be completely combusted, so it's the molecular mass of the products like H2O that are relevant for Isp, not the oxidizer mass. update: I found a theoretical paper that estimates O4's enthalpy of formation, using computational quantum chemistry. They think it's 93 - 95 kcal/mol (389 - 397 kJ/mol), which is almost three times that of ozone (!). So if it were stable (more so than ozone, which I'm very skeptical of), it could have a really huge Isp advantage. http://www.ncbi.nlm.nih.gov/pubmed/15268030

The Planetary Society is in favor of it: http://www.planetary.org/press-room/releases/2015/FY2016-Budget-Request.html Note they're talking about a Europa probe, not specifically a lander. It looks like the surface component has a political aspect: http://blog.chron.com/sciguy/2015/05/a-europa-lander-is-possible-jpl-scientists-say-and-congress-appears-likely-to-support-it/

Probably "Ganymede Gravity Assist".

It varies a lot. It depends how much patience you have to wait for gravity assists. Here's an actual study I found: a NASA concept for an Enceladus orbiter. They calculated a very low delta-v trajectory, with the tradeoff that it'd take 12 years from launch to Enceladus orbit. http://sites.nationalacademies.org/cs/groups/ssbsite/documents/webpage/ssb_059320.pdf (the chapter "Concepts of Operation and Mission Design") In their solution, the launch vehicle would lift to C3 = 11.7 km2/s​2, and the orbiter would use 2880.6 m/s of its own propulsion. That's roughly the same as 6.6 km/s from LEO to low Enceladus orbit. (If you're in LEO, it takes 3.72 km/s to reach C3 = 11.7 km2/s​2). The low-C3 launch is for a gravity-assist tour to Saturn (Venus-Earth-Venus-Earth-Saturn). This would take 8.5 years, plus one 350 m/s deep-space maneuver to set up a flyby. Saturn orbit insertion costs 960 m/s (eccentric orbit, low periapsis & high apoapsis). Transfer to Enceladus orbit is just 1041 m/s, but it uses 52 gravity assists from Saturn moons, taking 3.5 years. Remaining 484.3 m/s is "statistical".

I'm ignorant -- what are the ~optimal delta-v's to low Kerbin orbit, now that 1.0.2 rebalanced everything? Is there a thread or article calculating this?

We should rebalance the problem, and make this into a KSP challenge. Here's an idea, what about a spaceplane/rocket hybrid? Put wings and a heat shield around a single engine, so that it becomes an unmanned return-to-launchpad spaceplane. Stack a disposable propellant tank on top of that, and stack your payload on top of the propellant tank, under a standard rocket fairing. And that's your upper stage. Because the spaceplane doesn't have to contain either a cargo bay, passenger bay, or a propellant tank, it can be much smaller than the shuttle. The main tradeoff is that it can no longer return things from orbit. But for a launch-vehicle, this suffices. Put that on top of a flyback first-stage booster, and that's a 100% engine-reuse rocket, with excellent payload fractions. Has anyone designed something like this before?

Kryten, where do you find the data for launches?

Here's some Isp's in the context of Mars ISRU for NTR. Wrote this comment in another thread:

VAB price 4,726: Well that can't be good... What's a cheap way to control an SRB with unbalanced weights on it?

So, my first competitive test flight! (how do you link image galleries?) https://imgur.com/a/hgSHl 1.0.2, all stock, no mods, "normal" difficulty (100% reentry heating). Final altitude, 46,055 meters!

You could use balloons instead! They're much simpler and probably lighter. One JPL study proposes a teflon-coated Zylon balloon to lift a sample-return probe, and a three-stage solid rocket, from the surface to high altitude: "Venus Surface Sample Return: A Weighty High-Pressure Challenge" http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20010003946.pdf There's another concept somewhere that proposes a balloon-carried probe thats "hops" across the surface. Which gives you new options for thermal management, since you're at the surface for only minutes at a time, and can cool off at higher altitude.