Starship to Mars: faster than Hohmann transfer trajectories

[Holger Isenberg]

Missions to Mars with the Starship could only take three months

It's less a technical issue for missions with humans on board. At least for the first few missions you want to be able to freely return in case the braking burn fails. And for that the trajectory usually requires around 6 months from Earth to Mars with the unpowered return then adding a year or so.

But maybe a lucky crazy extremely fast Earth to Mars powered trajectory exists with free return around another planet if the planets are aligned correctly? But in that direction only Jupiter exists as candidate and the radiation there isn't human-friendly.

[Oersted]

I wonder if there's any advantage to aerobrake the  maximum amount, then on the way out do a retro-burn,  to a velocity just enough to stay in orbit, and second pass EDL.

You should get more Oberth advantage applying the braking before the aerocapture, when the speed is higher.

Braking using rockets will however be more precise, so maybe a longer burn before athmospheric entry and a shorter one when exiting would be advisable.

[Robotbeat]

You can always use RCS to fine tune trajectory.

[TheRadicalModerate]

I went back to the drawing board on the Mars EDL problem.  I'm not sure what I came up with is that useful, but here goes:

1) We don't know much about Starship aerodynamics.  I'm relying heavily on the old estimate that Starship is likely to operate mostly in the L/D = 0.5 neighborhood, and I'm assuming that lift is just enough to compensate for the difference between gravity and centrifugal acceleration.  Beyond that, most things are normalized to the assumption that IFT-5 and -6 seemed to do OK in the peak heating environment produced when Starship was going about 7000m/s at a stable altitude of 69km.  Both the Earth and Mars models shown below rely on that being an environment well within the envelope of tolerability.

2) I'm still assuming that Starship magically appears at a particular altitude at the specified speed, and spends all of EDL there, until it magically drops into the bellyflop.  This is obviously untrue, but it made for a nice, simple model.  Whether it's useful, I leave to you.

3) I'm measuring three things:

a) Peak heat rate, compared to the reference speed and altitude (temp1.png below).  1.0 is the same flux.  >1 is a higher flux.  I'm deriving this using the assumption that heat rate is proportional to v³*sqrt(density).

b) Acceleration on the vehicle/crew, in G (temp2.png below).  This is based on the assumption that, to keep the ship stable at the target altitude:

lift = μ/(altitude+planetRadius)² - v²/(altitude+planetRadius)
drag = 2*lift  (i.e. L/D = 0.5)
acceleration = sqrt(lift² + drag²)/earthG

c) The least likely of the three to bear any resemblance to reality:  The ratio of time to kill all the entry speed, compared to what that time would be if the Starship at the reference altitude (69km) and speed (7000m/s) would take to do its deceleration (temp3.png below).

I'm assuming that acceleration is constant (not true), and that everything happens at the altitude under study (really, really not true).  However, I think this should give a relatively good idea of how many times longer the vehicle's heat soak period will be at various combinations of altitude and speed.  (Spoiler alert:  of the three quantities, this seems most likely to be a problem.)

I was too stupid to figure out analytically if the ratios of the distance covered was good enough, so I solved for time, and then took the ratio with respect to the reference value.  I derived the reference by fiddling with the time until it killed all the speed at 69km, 7000m/s entry speed.  It's really just two kinematic equations, solved for the interesting quantities:

distance = -v²/(2*drag), with drag computed as in quantity #b.
time = [-entrySpeed + sqrt(entrySpeed² - 4*drag*distance)]/drag

Then the ratio is just referenceTime/time.

4) All three of the quantities are just computed for every pair of <altitude,speed>, for both Earth and Mars.  I couldn't think of a way of plotting them that was more enlightening than looking at the numbers, so you'll just have to deal with the numbers.

5) The color codes are arbitrary, based on only two semi-solid data points:
a) 69km, 7000m/s works OK
b) We should expect lunar entry speed, ~12km/s, to be OK at some altitude, so that's the outer boundary of "green", straying a bit into yellow.  Yellow is stuff that's kinda marginal (based on green being kinda OK), and red is stuff that's clearly not gonna work.

6) Earth atmosphere model is an implementation (hopefully correct) of the International Standard Atmosphere, slightly jiggered to provide values for the thermosphere.  (Not an issue here, since I'm not computing anything above the mesopause.)  The Mars model comes from a cheesy chart I found on a NASA GRC set of courseware.


Some observations:

1) Heating rate for translunar entries on Earth is about 3x what the IFT tests have challenged the TPS with.  I can't say much more than that, but I infer that there's a certain amount of headroom on peak heating, all else being the same (which it isn't).

Mars heating rates aren't too bad.  (Mars heat-soak times are another story.)

2) Mars entry accelerations aren't as high as I thought, but a lot depends on how much acceleration a de-conditioned crew can handle and be able to function right after landing.  You could get to 8km/s of periapse speed with only 5G.

Earth is likely worse, given that returning crews will be extremely de-conditioned.  12km/s is a bit less than 9G.

Remember:  this is an extremely stupid model.  Note that Apollo returns maxed out at ~7G, so the 9G is quite a bit wrong by that standard.  This indicates that there's something wrong with my constant-altitude assumption.  However, in this entry regime, you need significant negative acceleration to keep from exiting the atmosphere, so I'm not quite sure what I'm doing wrong.¹

3) The real killer is the heat-soak time (the third pair of tables).  Translunar entries require almost 4x the time to kill the speed as the reference entry.  Given how melty IFT-5 and -6 were in places, it doesn't seem like Starship has a huge amount of margin in this respect.

Things are even worse on Mars, where a 7500m/s entry needs almost 7x the time to kill the speed.  I'm betting that this is going to be a big problem.


Again, I'm not sure how useful all this is.  The model is here, if anybody wants to play with it.  It's entirely possible that I've screwed something up--let me know.

I'm also open to suggestions about how to improve things, short of fully simulating a jillion different trajectories.  Full simulations would also require guessing at real lift and drag coefficients, real emissivity, and real thermal conduction coefficients, none of which we have.  I'm relying heavily on L/D=0.5 being about right, and counting on that to allow us to make semi-valid relative comparisons.  Things change quite a bit if we move away from that.


_________
¹Is it possible that you could dive pretty low in the atmosphere, then reduce lift to slowly float up, counting on the loss of speed to keep you from skipping out entirely?  Seems kinda weird...

[TheRadicalModerate]

I wonder if there's any advantage to aerobrake the  maximum amount, then on the way out do a retro-burn,  to a velocity just enough to stay in orbit, and second pass EDL.

You should get more Oberth advantage applying the braking before the aerocapture, when the speed is higher.

Braking using rockets will however be more precise, so maybe a longer burn before athmospheric entry and a shorter one when exiting would be advisable.

You have a coarse maneuver and a fine maneuver.  Kill as much speed as possible just before entry interface.  Then, after exit, clean up your orbit.  There's no reason to hold back pre-entry.

(In my model, I have an option for "suicide aero", where the braking delta-v is taken off the periapse speed, and "safe aero", where it's taken off of arrival v∞.  The problem with suicide aero is that the braking maneuver and attitude preparation have to go perfectly, or you're dead.  Hence the name.  But suicide aero gives you maximal Oberth advantage.)

[Vultur]

2) Mars entry accelerations aren't as high as I thought, but a lot depends on how much acceleration a de-conditioned crew can handle and be able to function right after landing.  You could get to 8km/s of periapse speed with only 5G.

Earth is likely worse, given that returning crews will be extremely de-conditioned.  12km/s is a bit less than 9G.

How certain are we that deconditioning matters here? I don't think "bone and muscle loss from long term microgravity" and "pass out from lack of blood to brain due to g forces" are necessarily related at all.

And what does functioning right after landing have to do with anything? Aren't g force blackouts really short duration?


quote author=meekGee link=topic=63006.msg2693726#msg2693726 date=1749779823]

Planetary Protection requirements that 2023-era NASA and COSPAR uses are totally incompatible with Mars surface missions anyway, so it’s not worth entertaining them for this discussion.

Not talking about a Mars surface mission. It’s about a return to Earth after being on Mars.

You're worried about an Andromeda strain type organism that is not affecting the settlers but would affect earth?
[/quote]

It's a possible regulatory constraint. Definitely not a real world possibility, IMO with current biological knowledge we can totally rule out any such possibility, but those aren't necessarily the same thing.

[TheRadicalModerate]

How certain are we that deconditioning matters here? I don't think "bone and muscle loss from long term microgravity" and "pass out from lack of blood to brain due to g forces" are necessarily related at all.

I'm not certain they're correlated.  However, I'd be a lot more worried about strains to ligaments and other connective tissue than passing out.

And what does functioning right after landing have to do with anything? Aren't g force blackouts really short duration?

The period immediately after landing is a really good time to have the crew mobile and alert.  There's likely a pretty deep stay/no-stay checklist to go through.  Even if the only place to escape to is Mars orbit to wait to prepare for an abort, that can be a lot better than tipping over or waiting for a prop leak to strand you.

You're worried about an Andromeda strain type organism that is not affecting the settlers but would affect earth?

It's a possible regulatory constraint. Definitely not a real world possibility, IMO with current biological knowledge we can totally rule out any such possibility, but those aren't necessarily the same thing.

Let's forgo the food fight.  I only brought restricted Cat V up in the context of propulsive vs. aerocapture or direct EDL returns.  Given that you'll likely have the propellant to do propulsive returns and massively reduce the risk of exposure of anything to Earth's biosphere, why would you not do that?

[Robotbeat]

There’s no massive risk reduction from doing it propulsively.

What you’re doing is condemning astronauts to greater health risks due to longer duration transit in space. Sacrificing the astronauts’ health to the religion of COSPAR

[TheRadicalModerate]

There’s no massive risk reduction from doing it propulsively.

What you’re doing is condemning astronauts to greater health risks due to longer duration transit in space. Sacrificing the astronauts’ health to the religion of COSPAR

I get about 2.6 extra months on the return:  6.7 for propulsive vs. 4.1 months for direct EDL. 

Both of the above numbers assume that the Starship is fully fueled on the martian surface and doesn't refuel in LMO.  If LMO refueling is available, the difference is 1.3 months (4.9 propulsive vs. 3.6 direct EDL).

[Vultur]

How certain are we that deconditioning matters here? I don't think "bone and muscle loss from long term microgravity" and "pass out from lack of blood to brain due to g forces" are necessarily related at all.

I'm not certain they're correlated.  However, I'd be a lot more worried about strains to ligaments and other connective tissue than passing out.

If people are well strapped in etc, do you get that at only 5 or 6 g?

I'm pretty sure New Shepard pulls something like 5 g and people up to 90 have flown on it.

And what does functioning right after landing have to do with anything? Aren't g force blackouts really short duration?

The period immediately after landing is a really good time to have the crew mobile and alert.  There's likely a pretty deep stay/no-stay checklist to go through.  Even if the only place to escape to is Mars orbit to wait to prepare for an abort, that can be a lot better than tipping over or waiting for a prop leak to strand you.

Yeah, I wasn't questioning whether functioning right after landing was important; I was saying this level of g forces shouldn't impair it.

Let's forgo the food fight.  I only brought restricted Cat V up in the context of propulsive vs. aerocapture or direct EDL returns. 

Maybe this should be on another thread, but OTOH I am not sure the issues are really separable. Whether aerocapture/aerobraking at Earth is viable does affect trajectory.

Given that you'll likely have the propellant to do propulsive returns and massively reduce the risk of exposure of anything to Earth's biosphere, why would you not do that?

Well, if you are convinced (as I am) that the risk of exposure to Earth biosphere is zero (and can be known to be zero), then reducing an already zero risk is irrelevant/meaningless.

[OneSpeed]

I went back to the drawing board on the Mars EDL problem.
...
I'm also open to suggestions about how to improve things, short of fully simulating a jillion different trajectories.  Full simulations would also require guessing at real lift and drag coefficients, real emissivity, and real thermal conduction coefficients, none of which we have.  I'm relying heavily on L/D=0.5 being about right, and counting on that to allow us to make semi-valid relative comparisons.  Things change quite a bit if we move away from that.

Full simulations don't require guessing any of these properties, because we have actual flight data. Accurate lift and drag coefficients can be obtained for the range of speeds and angles of attack flown by FT-5 and 6.

E.g. FT-5 level flight at T+00:51:53 was producing 2.93m/s² of lift, and 4.16m/s² of drag, for a L/D of 0.704, somewhat better than 0.5. This was at +65° AoA, so the range of L/D available from +45° to +90° and then -90° to -45° is more like 1.2 to -1.2, and is certainly not a constant.

We don't need to know the emissivity or the thermal conduction coefficients because we know the velocity (V) and atmospheric density (ρ) of the flightpath, as well as the radius (R) of the Starship. From those, we can calculate the convective and radiative components of the heating.

Qconv = Kconv * V^3 * √ρ/R
Qrad = Krad * V^8 * ρ^1.2 * √R

Convective heating model: https://www.faa.gov/about/office_org/headquarters_offices/avs/offices/aam/cami/library/online_libraries/aerospace_medicine/tutorial/media/III.4.1.7_Returning_from_Space.pdf

Radiative heating model: Characterization of Stagnation-Point Heat Flux for Earth Entry, A. M. Brandis, Christopher O. Johnston

I've attached screenshots of the Earth and Mars peak heating for a range of radii. Peak heating for FT-6 at a 4.5m radius was 1.8MW/m², so as long as we don't exceed that heat flux, and the time the ship is exposed to it on Mars, the simulation should be within safe bounds.

Returning to the topic of the thread, "faster than Hohmann transfer trajectories", I've created a simulation that starts from a high elliptical Earth orbit (HEEO), giving an additional 3km/s of available ΔV compared to the trajectories in Jack Kingdon's paper. This enables a much larger pre-entry burn at Mars, with velocity at periapse reduced from an unbraked 13.3km/s to 8.8km/s. The simulation then shows a peak heating of 1.6MW/m², but importantly for a much shorter period than for the FT-6 re-entry. This is largely due to Mars lower gravity requiring less lift in the latter part of EDL, and hence being able to fly in a lower atmospheric density (with less heating) than that required for Earth. A short video and graphs are attached.

[Lampyridae]

There’s no massive risk reduction from doing it propulsively.

What you’re doing is condemning astronauts to greater health risks due to longer duration transit in space. Sacrificing the astronauts’ health to the religion of COSPAR

I get about 2.6 extra months on the return:  6.7 for propulsive vs. 4.1 months for direct EDL. 

Both of the above numbers assume that the Starship is fully fueled on the martian surface and doesn't refuel in LMO.  If LMO refueling is available, the difference is 1.3 months (4.9 propulsive vs. 3.6 direct EDL).

If you are coming back with enough propellant for a propulsive entry, then you have a bit more radiation protection, particularly right over the CH4 tank. The LOX could serve as a countermass for a tumbling pigeon type of artificial gravity.

Returning to the topic of the thread, "faster than Hohmann transfer trajectories", I've created a simulation that starts from a high elliptical Earth orbit (HEEO), giving an additional 3km/s of available ΔV compared to the trajectories in Jack Kingdon's paper. This enables a much larger pre-entry burn at Mars, with velocity at periapse reduced from an unbraked 13.3km/s to 8.8km/s. The simulation then shows a peak heating of 1.6MW/m², but importantly for a much shorter period than for the FT-6 re-entry. This is largely due to Mars lower gravity requiring less lift in the latter part of EDL, and hence being able to fly in a lower atmospheric density (with less heating) than that required for Earth. A short video and graphs are attached.

HEEO refuelling for this application sounds like an opportunity for lunar ISRU LOX.

[TheRadicalModerate]

We don't need to know the emissivity or the thermal conduction coefficients because we know the velocity (V) and atmospheric density (ρ) of the flightpath, as well as the radius (R) of the Starship. From those, we can calculate the convective and radiative components of the heating.

Qconv = Kconv * V^3 * √ρ/R
Qrad = Krad * V^8 * ρ^1.2 * √R

A few comments:

1) This is just the heating rate.  It doesn't tell you much about how long the vehicle can withstand that rate.  I've been trying to normalize that against the IFT-5/6 results, so that I can just make the Mars peak heating at some particular altitude proportional to v³ρ^½.  From there, you can normalize a heat soak time, which should give you a semi-decent figure of merit.

2) I've never quite understood how you compute the nose radius of the vehicle.  I'm pretty sure it has more to do with shape, size, and distance of the (hopefully) detached shock than it does with the aspect of the vehicle.  For flying cylindrical bricks with high AoA, I have no clue how to quantify that.  That's another one of the reasons I'm trying to normalize everything for proportionality to the observed data.

3) The thing I'm having the most trouble with is the total heat soak, which should be proportional to the time the vehicle spends from peak heating to... some unquantified point where heating is negligible.

I'm pretty sure we could build a normalized model that integrates the constants of proportionality at every time step.  I'm hoping to find something quicker and dirtier than that.  However, that may not be possible.

Returning to the topic of the thread, "faster than Hohmann transfer trajectories", I've created a simulation that starts from a high elliptical Earth orbit (HEEO), giving an additional 3km/s of available ΔV compared to the trajectories in Jack Kingdon's paper. This enables a much larger pre-entry burn at Mars, with velocity at periapse reduced from an unbraked 13.3km/s to 8.8km/s. The simulation then shows a peak heating of 1.6MW/m², but importantly for a much shorter period than for the FT-6 re-entry. This is largely due to Mars lower gravity requiring less lift in the latter part of EDL, and hence being able to fly in a lower atmospheric density (with less heating) than that required for Earth. A short video and graphs are attached.

But the magnitude of the lift is larger in the early part of a lifting reentry, because the low gravity (and, more importantly, small radius) forces you to apply negative lift to keep the vehicle at the peak heating altitude.  Otherwise, the centrifugal acceleration will just send it off into space.

One thing I'd like to add to my model is the ability to compute how much delta-v is safely available to perform aerocaptures.  Any thoughts on a rule-of-thumb?  (I'm still trying not to have to simulate the whole entry trajectory, if possible.)

[sdsds]

Perhaps silly questions: can a vehicle use negative lift to stay in the upper atmosphere even though it is going faster than orbital speed at that altitude? Could it conceivably do that for multiple revolutions? Is the optimum approach going just deep enough into the atmosphere for that, which might be way above the peak heating altitude?

Effectively the negative lift is equivalent to increasing the mass of the planet. Does that make it easy to use orbital mechanics to calculate the needed lift to capture onto the parabolic vinf=0 arc?

[TheRadicalModerate]

Perhaps silly questions: can a vehicle use negative lift to stay in the upper atmosphere even though it is going faster than orbital speed at that altitude?

Depends.  There's only a certain amount of lift available at a particular density and speed.  L ~ ρv².  As long as there's enough lift and the vehicle is stable, yes.  But if the lift isn't there, you're going to skip out.

Could it conceivably do that for multiple revolutions?

Probably not.  That's too much heat soak time.  Eventually, the heat is conducted across the TPS, and the skin gets all melty.

Is the optimum approach going just deep enough into the atmosphere for that, which might be way above the peak heating altitude?

Heat soak time will get you here, too.  You want the highest tolerable pulse, at the highest tolerable inertial acceleration, for the shortest possible time.

Effectively the negative lift is equivalent to increasing the mass of the planet. Does that make it easy to use orbital mechanics to calculate the needed lift to capture onto the parabolic vinf=0 arc?

You can compute how much delta-v you need to scrub off, but the lift is accelerating the vehicle, so none of the vanilla-flavored orbit equations will help you.

[crandles57]

Perhaps silly questions: can a vehicle use negative lift to stay in the upper atmosphere even though it is going faster than orbital speed at that altitude?

Depends.  There's only a certain amount of lift available at a particular density and speed.  L ~ ρv².  As long as there's enough lift and the vehicle is stable, yes.  But if the lift isn't there, you're going to skip out.

Could it conceivably do that for multiple revolutions?

Probably not.  That's too much heat soak time.  Eventually, the heat is conducted across the TPS, and the skin gets all melty.

Is the optimum approach going just deep enough into the atmosphere for that, which might be way above the peak heating altitude?

Heat soak time will get you here, too.  You want the highest tolerable pulse, at the highest tolerable inertial acceleration, for the shortest possible time.

Interesting.

Probably also silly questions:

So it seems you are saying low deceleration for a longer time is worse for heat soak? While I doubt the range of lift will be available with a flying brick, is there any possibility you might want to vary the altitude so you build up heat then move to a higher altitude with much lower deceleration to try to allow the heat to dissipate somewhat then return to higher deceleration again? Presumably you need a much higher altitude for a heat dissipation phase and little lift would be available there so difficult to stop altitude gain and skipping out of atmosphere?

If that seems unlikely to work then does the optimum altitude steadily reduce as you lose speed?

[Robotbeat]

Heat soak isn’t necessarily a big problem for the bulk of the vehicle which can sort of cool itself with prop boiloff or backside radiative cooling. Maybe the fins? But even they can tolerate a lot, as we’ve seen.

I think stainless’ much higher softening temperature helps a lot in this case. Aluminum can’t dump a lot of heat through radiation at its softening temperature. If you compare aluminum alloys or thermoset matrix carbon fiber composite, which have a softening temperature of around 500K, versus Stainless which softens at around 1300-1350K, that’s a factor of 50 difference in radiative power according to the Stefan-Boltzmann law. So aluminum (Shuttle) and composite structure (like used for Dragon) are more reliant on heat soak delaying the heat pulse than a stainless steel structure is.


(1330K/(500K))^4 =~50.

[InterestedEngineer]

Heat soak isn’t necessarily a big problem for the bulk of the vehicle which can sort of cool itself with prop boiloff or backside radiative cooling. Maybe the fins? But even they can tolerate a lot, as we’ve seen.

I think stainless’ much higher softening temperature helps a lot in this case. Aluminum can’t dump a lot of heat through radiation at its softening temperature. If you compare aluminum alloys or thermoset matrix carbon fiber composite, which have a softening temperature of around 500K, versus Stainless which softens at around 1300-1350K, that’s a factor of 50 difference in radiative power according to the Stefan-Boltzmann law. So aluminum (Shuttle) and composite structure (like used for Dragon) are more reliant on heat soak delaying the heat pulse than a stainless steel structure is.


(1330K/(500K))^4 =~50.

heat transfer is terrible with stainless steel.   The steel below the tiles would melt before the back side got hot enough to dissipate the heat.

so you can only count heat radiated from the back side of the steel underneath the tiles (which radiates into the fuel and ullage).

what's the heat capacity of the ullage?  Not very much in terms of watts absorbed vs emitted.

[Robotbeat]

Heat soak isn’t necessarily a big problem for the bulk of the vehicle which can sort of cool itself with prop boiloff or backside radiative cooling. Maybe the fins? But even they can tolerate a lot, as we’ve seen.

I think stainless’ much higher softening temperature helps a lot in this case. Aluminum can’t dump a lot of heat through radiation at its softening temperature. If you compare aluminum alloys or thermoset matrix carbon fiber composite, which have a softening temperature of around 500K, versus Stainless which softens at around 1300-1350K, that’s a factor of 50 difference in radiative power according to the Stefan-Boltzmann law. So aluminum (Shuttle) and composite structure (like used for Dragon) are more reliant on heat soak delaying the heat pulse than a stainless steel structure is.


(1330K/(500K))^4 =~50.

heat transfer is terrible with stainless steel.   The steel below the tiles would melt before the back side got hot enough to dissipate the heat.

…

Untrue. Calculate it and show your work.

[TheRadicalModerate]

Heat soak isn’t necessarily a big problem for the bulk of the vehicle which can sort of cool itself with prop boiloff or backside radiative cooling. Maybe the fins? But even they can tolerate a lot, as we’ve seen.

Well, there's a heat soak limit somewhere.  The real question is how much margin is built into Starship beyond what's necessary to get it back from LEO reentry speeds.  If it's a factor of 10x, that's fine.  If it's a factor of 2x, that's less fine, especially if you're fighting lift, acceleration, and peak heating limits on Mars.