# ULA's plan for LH2/LOX 2nd stage that can maintain propellant for an extended period of time?

Business Insider's (long) article SpaceX's biggest rival has a 'genius' plan to cut its rocket launch costs more than 70% contains the statements sourced from ULA's CEO Tory Bruno:

Vulcan should lift 40 tons (nearly three school buses) into low-Earth orbit. That's less than SpaceX's Falcon Heavy, which can lift more than 70 tons — nearly five school buses — for one-fourth the price. But Bruno said there are big differences between the two systems that will make Vulcan competitive.

The key difference is the rocket's upper stage. Falcon Heavy currently uses a rocket-grade RP-1 kerosene as fuel, but it can freeze in space after a few hours. Vulcan's upper stage will use cryogenic oxygen and hydrogen, which are more resilient to the punishing temperatures of space.

LH2 and LOX have about the same molar density, but the stoichiometry requires twice as many moles of LH2. If the tanks are end-to-end, it would mean the LH2 tank intercepts close to twice as much geometrical exposure to the environment as the LOX tank. However, the Enthalpy of vaporization of LH2 on a molar basis is only one quarter that of LOX (see LH2 and LOX).

Further, at 1 atmosphere for example, LH2 boils at around 20K while LOX boils at around 90K. That means without active refrigeration, the heat loading would have to be of the order of $(4.5)^4$ times lower if LH2 was used (assuming passive radiation for cooling), which would be a real challenge in sunlight.

There are two three parts to this question. If I have to split them I will but it's possible an answer can address both at the same time.

1. Is ULA likely to consider putting the 2nd stage LH2 tank inside the LOX tank (or at least be surrounded by it coaxially)?
2. Unless the second stage is going to Jupiter or beyond, isn't the heating from Sunlight boiling the LH2 a more challenging problem than "freezing" of the RP-1? (See Does the NK-33 engine require subcooled kerosene so cold that it turns to wax? for some density vs temperature plots.)
3. In order to keep the LH2 cold for months, would the 2nd stage end up looking a little bit like the the JWST with those large metallized polymer layers deployed to block the Sun?

## Temperature of a Spherical Cow in Space:

Spherical cow as illustrated by a 1996 meeting of the American Astronomical Association, in reference to astronomy modeling. From here: "The image was created by Ingrid Kallick for the program cover of the 1996 annual meeting of the American Astronomical Association. An earlier version was created for the National Center for Supercomputing Applications. The artist gave permission for use to the University of Wisconsin Department of Astronomy. The STScI subsequently used the image. http://www.ikallick.com"

Equilibrium temperature happens when average power in equals average power out, or $\bar{P}_{in} - \bar{P}_{out}$. Averaging should be done over short term variations in attitude relative to the Sun and take into account eclipses for most orbits near the Earth, Moon, or another planet.

$$\bar{P}_{in} = I_{Sun} (1-a) \ \pi R^2$$

$$\bar{P}_{out} = \sigma \epsilon T^4 \ 4 \pi R^2$$

where $a_{vis}$ is the visible light albedo, $e_{ir}$ is the infrared emissivity (both should really be weighted averages over the appropriate wavelength ranges; @Tristan's and @Puffin's comments explain this better than their associated answers do), $\sigma$ is the Stefan–Boltzmann constant (about 5.67E-08 W m^-2 K^-4), and I is the intensity of sunlight, and for 1AU is the solar constant and about 1360 W/m^2. Solving for the average equilibrium temperature of said cow gives:

$$T \sim \left( \frac{(1-a_{vis})}{e_{ir}} \frac{I_{Sun}}{4 \sigma} \right)^{1/4}$$

For an average visible-light albedo of 0.95, and an average infrared emissivity of 0.95. this turns out to be about 130 Kelvin at 1 AU, and about 110 Kelvin near Mars, and because of the fourth-root, this varies only slowly with any of the parameters. It seems that space is much more LOX-friendly than LH2-friendly, and only moderate Sun-shielding measures would be necessary to get the LOX down below boiling at 1 atmosphere pressure, like simply having the 2nd stage face the Sun end-on, because cows are not actually spherical.

If the albedo of a hypothetical "LOX compartment" were 0.1 instead of 0.95 (if it were 18 times more absorbing of sunlight), the temperature would rise by the fourth root of 18, or about a factor of two (see my thoughtful (and unnecessarily down-voted) tutorial on the use of power laws in physics). That would put the RP-1 up near a balmy 273 K or 0C, "sub-cooled" and ready to go! This can be confirmed by the plot of equilibrium temperature of temperature for a spherical blackbody around each of the planets (ignoring eclipses and planetary albedo) found in this answer.

• If the LH2 tank is in the LOX tank, there should be only a small deposit of solid oxygen. Too much SOX means loosing oxygen for the burn as well as boiled off hydrogen by letting oxygen freeze – Uwe Feb 25 '18 at 12:45
• It's a good point, but I think if there are no mechanical problems with SOX, if it doesn't cause thinks to break or blow up (I mean cause them to erupt into a "fast fire anomaly" as Musk calls it), then an electric heater can always restore it to LOX, using power from solar panels, or if it's hibernating in deep space, perhaps even a liquid heat exchange from an RTG directly (which sounds messy and complicated). – uhoh Feb 25 '18 at 12:51
• 1 would cause too many problems prelaunch and be heavy 2 -yes 3 - maybe – Organic Marble Feb 25 '18 at 13:54
• @OrganicMarble it's the 80:20 rule; a question that takes more than 80 minutes to think about, write, and "debug" takes less than 20 words to answer ;-) – uhoh Feb 25 '18 at 14:05
• Well, you oughtn't expect Business Insider to be technically literate or coherent. That said, LH2 is hugely superior in specific impulse; it solves the problem that RP-1 has of needing a larger first stage to lift an equivalent payload/∆v worth of second stage. – Russell Borogove Feb 25 '18 at 15:32

The ACES stage is designed for a lifetime of weeks, not years.

1. The tanks will be simply stacked on top of each other. There's no plan to place the LH tank inside the LOX tank.

ACES design is optimized with long-duration cryogenic applications in mind. A number of passive-thermal management features are incorporated into the stage at the system level. The tank geometry design minimizes the exposed surface area. Warm equipment is isolated on a separate, thermally controlled shelf, and IVF systems provide a stable thermal environment regardless of vehicle orientation. This is critical for depot applications. Vapor- cooling paths, where vented hydrogen is used to intercept the remaining high-load heat paths, are integrated into the tank structure.

1. and 3: the plan is to use the boiloff to power an internal combustion engine. The Integrated Vehicle Fluids system replaces batteries, ullage thrusters, attitude thrusters and the tank pressurization system.

The long-term storage facility may be a separate ULA development called Long Duration CPS where they're looking at dewar storage.

Earth Departure Stage
– Mars or NEO return stage
– Lunar lander
– Propellant depot
- Return stage mission duration

Multi year mission with very low boil-off
– 1 year: 0.027%/day
– 2 year: 0.014%/day
– 3 year: 0.009%/day
– 4 year: 0.007%/day

On orbit fueling allows:
– Structure/insulation to not be driven by launch environment
– Reduced structural heat leak paths
– Very high mass fraction (>0.90)

• I like this answer, but the last link doesn't take me anywhere relevant, just to a ULA picture gallery. – Organic Marble Feb 25 '18 at 18:47
• and I fixed the last link. – Hobbes Feb 25 '18 at 19:10
• A mass is not measured in millitesla. The metric symbol for a metric tonne is t, see Wikipedia about tonne. Instead of t Mg may be used. But mT means millitesla. – Uwe Feb 26 '18 at 15:25
• Americans talking about metric units find it necessary to specify they're talking about metric tons, and not one of the two imperial variants of 'ton'. From the context it's obvious they're not talking about magnetic fields. – Hobbes Feb 26 '18 at 15:36
• Hey, but at SpaceX launch costs are measured in kiloTeslas. ;-) – SF. Sep 27 '18 at 6:11