Starship to Mars: faster than Hohmann transfer trajectories

[Robotbeat]

The only valid (positive) solution I get is about 1547K, or a change in temperature across the 4mm steel of just 50 degrees C.
 Corresponds to radiating 325kW per square meter.

You can't run 304L stainless steel at 1600K, it starts losing its strength properties at 1000-1100K.

You earlier said “melt.” But sure, whatever. 1100K works. Not much difference in the Delta-T.

[InterestedEngineer]

The only valid (positive) solution I get is about 1547K, or a change in temperature across the 4mm steel of just 50 degrees C.
 Corresponds to radiating 325kW per square meter.

You can't run 304L stainless steel at 1600K, it starts losing its strength properties at 1000-1100K.

You earlier said “melt.” But sure, whatever. 1100K works. Not much difference in the Delta-T.

There's a huge difference in the deltaT between the tiles (about 1600K) and the surface of the steel (1100K).

7.5x in emissions.

[Robotbeat]

The only valid (positive) solution I get is about 1547K, or a change in temperature across the 4mm steel of just 50 degrees C.
 Corresponds to radiating 325kW per square meter.

You can't run 304L stainless steel at 1600K, it starts losing its strength properties at 1000-1100K.

You earlier said “melt.” But sure, whatever. 1100K works. Not much difference in the Delta-T.

There's a huge difference in the deltaT between the tiles (about 1600K) and the surface of the steel (1100K).

7.5x in emissions.

No, I'm speaking of the delta-t between the front and back of the steel. This all started when you implied heat soak duration matters for the steel thickness. Keep up.

[InterestedEngineer]

No, I'm speaking of the delta-t between the front and back of the steel. This all started when you implied heat soak duration matters for the steel thickness. Keep up.

speaking of keeping up:

Radiation, convection, conduction... did I miss one?

The damagin gradiant is between the tiles and the surface of the steel.

[TheRadicalModerate]

No, I'm speaking of the delta-t between the front and back of the steel. This all started when you implied heat soak duration matters for the steel thickness. Keep up.

speaking of keeping up:

Radiation, convection, conduction... did I miss one?

The damaging gradient is between the tiles and the surface of the steel.

I'd think, at least in terms of conductivity through the skin/stringers, you should assume that the conductivity of steel is near infinite, and there's little to no gradient across the skin.  That should take care of hot spots.

It's obviously a different story if you're planning on using the skin as thermal mass.  Then you need to figure out how quickly the heat can be absorbed conducted along the skin, which'll tell you whether you have 30t of steel to work with, or closer to 60t.¹

I doubt that the skin can operate at much more than 800K, especially in the presence of LOX and GOX.  Even that temperature is gonna be interesting to have next to structures that lead to an inhabited cabin.

__________
¹Specific heat capacity is about 490J/kg-K, so 800K from 200K ambient will hold 8.8GJ @ 30t, 17.6GJ @ 60t.  That's not terrible in terms of peak heating duration for LEO reentry (~350kW/m²).  For 450m² of surface area, that would yield 56s with no re-radiation at all.  Too lazy to figure out the emittance.

[sdsds]

In the paper mentioned in the first post of this thread, somewhat buried in the end matter, is the location of the source code repository.

All data generated or analyzed during this study are included in this published article, or in the Github at https://github.com/jackSN8/mars-3-months

[Twark_Main]

For cargo missions you're using the one-pass aerocapture to maximize payload mass, not minimize ToF.

If you have a low arrival v∞, there's nothing to be gained by two-pass.  Just go straight in and have done with it.

Again, if it's "low" arrival v∞ then what that really means is that you left payload mass on the table. You should be re-entering at that same speed but with additional payload mass such that the ship is again right at the edge of the two-pass aerocapture speed limit.

Hopefully I explained it better this time.

 

"Clean them up before entry" is a single burn at apoapsis, if necessary.  A handful of meters per second, I'd expect. The required burn can be computed in milliseconds on a smartwatch.

It's only an apoapse burn if the intersection of your current plane and the target plane is at apoapse.  That only happens for an inclination change if apoapse is also on one of the (Mars-relative) nodes

You get lots of plane change during the capture and reentry pass, because of the nature of the aerodynamic guidance. Watch the Larry Lemke talk, and then watch the SpaceX Mars entry simulation.

Contingency prop is additive.  You budget for worst-case.  That's a worst-case "oops we need to raise periapse and figure this out" in addition to "oops, we're starting the flip-and-burn higher, and/or spending more time hovering looking for a good spot".

The risk is also incremental. If you save fuel by not doing the periapsis raise and lower unnecessarily, you have all the more margin left (and therefore lower risk, or higher payload for the same risk) in the "spend time hovering larger than expected G-FOLD divert to look for a good spot retarget to a pre-mapped safe landing site" contingency.

B) because you're unnecessarily adding orbits, increasing schedule costs and operational complexity.

Then go straight in.

Not the SpaceX way. They never leave "free" performance on the table (because it boosts performance-per-cost), and they won't do it in this case either.

You're not saving prop if you have to budget it for contingencies.  It just means that you're landing heavier.

Contingencies aren't black-and-white. If we're taking about the 17th load of solar cells, and there's a 5% chance you have to spend 60 m/s entering and leaving orbit, and in that case it means your maximum landing divert on a big flat plain drops from 5 km to 4 km, then by all means replace that extra fuel with extra solar panels. You just do the engineering balance of whatever gives you the lowest risk-adjusted expected shipping cost.

The heart of our disagreement is:

1) How much the intended post-aerocapture orbital parameters get torqued around by the vagaries of the aero environment.

2) How hard it is to do the observations to compute trajectory corrections with adequate precision in half a post-capture orbit.

With star trackers, sun trackers, horizon trackers, Phobos/Diemos tracking, excellent dead reckoning from multiple fused ring-laser gyroscopes, constant corrections in-flight to narrow the error margin (see Lars Blackmore's paper on F9 landing), and possible cooperation from multiple existing Mars orbiters, this is not a big worry for me.

The orbital mechanics for calculating the burn itself are undergrad level and computationally cheap. The only question is whether you get a high-accuracy fix in seconds vs minutes, not whether ENIAC can crunch the numbers in time.

3) Whether you can do all of those corrections with a single apoapse burn.

If the orbital mechanics demands that the burn happen exactly at apoapsis or just near-apoapsis it doesn't make a big difference to the actual delta-v budget. Not gonna be tricked into dying on this (semantic) hill.

Convince me that the answer to these are "not very much", "easy", and "an apoapse burn is good enough", and I'll cry "uncle".

I don't think we're that far apart really. Ultimately this disagreement (enter and leave orbit always vs only for contingencies) boils down to whether you assume ~50 m/s or ~100 m/s at the 95th percentile.

The big thing is that we should assume two-pass entry (vs direct entry), because it's the SpaceX Way and because Musk told us so. And this feeds into our assumption about the maximum speed at atmospheric entry, which is an important parameter for delta-v planning.

Ultimately all this is just so we can draw the correct darned delta-v pork chop plot (w options for split plane, hyperbolic, or braking burns).

[TheRadicalModerate]

If the orbital mechanics demands that the burn happen exactly at apoapsis or just near-apoapsis it doesn't make a big difference to the actual delta-v budget. Not gonna be tricked into dying on this (semantic) hill.

The semantic hill is somewhere else.

If you have any kind of plane orientation error (some combination of inclination and RAAN), the burn is at the intersection of the two planes.  That gives you two spots that can be rotated to anywhere in the orbit.  The odds of it being near apoapse are small.  The odds of your first chance to do the plane change being uncomfortably close to reentry on the downward leg are also relatively small, but what kind of risk are you willing to insert?  You mitigate that risk by raising the periapse enough that a burn abort or some other weirdness leaves you with some recovery options.

If you can do all the orbital adjustments you need near apoapse, or even somewhere else on the upward leg, cool.  But you need a contingency.

You can obviously take more risks with cargo flights.  I continue to think that crewed flights will be as lightly loaded as possible.  Landing prop is pretty sensitive to inert mass, especially on Mars, where you don't get near the delta-v benefit from the bellyflop as you do on Earth.

[Twark_Main]

If the orbital mechanics demands that the burn happen exactly at apoapsis or just near-apoapsis it doesn't make a big difference to the actual delta-v budget. Not gonna be tricked into dying on this (semantic) hill.

The semantic hill is somewhere else.

If you have any kind of plane orientation error (some combination of inclination and RAAN), the burn is at the intersection of the two planes.  That gives you two spots that can be rotated to anywhere in the orbit.  The odds of it being near apoapse are small.

...if you're just throwing trajectories at a dartboard, maybe. But the whole point is that SpaceX will be planning the trajectories to achieve high efficiency, and will be actively correcting the trajectory during atmospheric flight precisely to target that window.

This is exactly how they land F9 on a postage stamp in the ocean.  The odds of that (by random chance) are very small too...

The odds of your first chance to do the plane change being uncomfortably close to reentry on the downward leg are also relatively small, but what kind of risk are you willing to insert? You mitigate that risk by raising the periapse enough that a burn abort or some other weirdness leaves you with some recovery options.

If you can do all the orbital adjustments you need near apoapse, or even somewhere else on the upward leg, cool.  But you need a contingency.

You can obviously take more risks with cargo flights.  I continue to think that crewed flights will be as lightly loaded as possible.  Landing prop is pretty sensitive to inert mass, especially on Mars, where you don't get near the delta-v benefit from the bellyflop as you do on Earth.

You might mitigate it that way (and in that rare case, I say it's okay to slightly eat into your landing fuel margin), but doing it 100% of the time and having that fuel be 100% additive with all other propellant margin as a hard-and-fast rule is unnecessary.

I think we're agreeing more than we're disagreeing here.


Anyway, with two-pass aerocapture what does the maximum no-braking reentry speed get boosted by? I seem to recall it's roughly a 20% increase in entry velocity, due to the non-linear relationship with peak heating.

[meekGee]

If the orbital mechanics demands that the burn happen exactly at apoapsis or just near-apoapsis it doesn't make a big difference to the actual delta-v budget. Not gonna be tricked into dying on this (semantic) hill.

The semantic hill is somewhere else.

If you have any kind of plane orientation error (some combination of inclination and RAAN), the burn is at the intersection of the two planes.  That gives you two spots that can be rotated to anywhere in the orbit.  The odds of it being near apoapse are small.

...if you're just throwing trajectories at a dartboard, maybe. But the whole point is that SpaceX will be planning the trajectories to achieve high efficiency, and will be actively correcting the trajectory during atmospheric flight precisely to target that window.

This is exactly how they land F9 on a postage stamp in the ocean.  The odds of that (by random chance) are very small too...

The odds of your first chance to do the plane change being uncomfortably close to reentry on the downward leg are also relatively small, but what kind of risk are you willing to insert? You mitigate that risk by raising the periapse enough that a burn abort or some other weirdness leaves you with some recovery options.

If you can do all the orbital adjustments you need near apoapse, or even somewhere else on the upward leg, cool.  But you need a contingency.

You can obviously take more risks with cargo flights.  I continue to think that crewed flights will be as lightly loaded as possible.  Landing prop is pretty sensitive to inert mass, especially on Mars, where you don't get near the delta-v benefit from the bellyflop as you do on Earth.

You might mitigate it that way (and in that rare case, I say it's okay to slightly eat into your landing fuel margin), but doing it 100% of the time and having that fuel be 100% additive with all other propellant margin as a hard-and-fast rule is unnecessary.

I think we're agreeing more than we're disagreeing here.


Anyway, with two-pass aerocapture what does the maximum no-braking reentry speed get boosted by? I seem to recall it's roughly a 20% increase in entry velocity, due to the non-linear relationship with peak heating.

I kinda agree, but it's only semantics since the F9 example is a poor analogy - F9 starts out well after all the reentry dynamics discussed above are over and done.  When you're in F9 territory, you're no longer potentially going back to orbit.

But yeah, I agree they need to learn how to "fly it in" all the way from reentry interface, including any potential capture-only maneuvers.

[Twark_Main]

Indeed the flight regime and trajectory goals and abort modes are very different, I'm not drawing any analogies there. But as you reference the "fly it in" approach when designing the guidance algorithm is much the same as F9, namely that you're correcting error at multiple opportunities (burns and controlled aerodynamic phases), but as expected the net error still grows somewhat during atmospheric maneuvers even with active aero corrections.

I'm heavily referencing the attached figure from Lars Blackmore who does GNC at SpaceX in a paper describing how they achieved the precision F9 landing. Again the shape of the trajectory is completely different, but the approach toward controlling dispersions is the same.

[meekGee]

Indeed the flight regime and trajectory goals and abort modes are very different, I'm not drawing any analogies there. But as you reference the "fly it in" approach when designing the guidance algorithm is much the same as F9, namely that you're correcting error at multiple opportunities (burns and controlled aerodynamic phases), but as expected the net error still grows somewhat during atmospheric maneuvers even with active aero corrections.

I'm heavily referencing the attached figure from Lars Blackmore who does GNC at SpaceX in a paper describing how they achieved the precision F9 landing. Again the shape of the trajectory is completely different, but the approach toward controlling dispersions is the same.

From the diagram, aerodynamic flight increases dispersion, vacuum burns reduce it.

For Mars aerocapture, the first aerodynamic phase will have to contain the dispersion to a degree that there's enough fuel to subsequently recover.

There's quite a wide window for that recovery.

At the edges of the window are the extreme cases of "stuck in orbit with not enough propellant to land" and "land immediately even if in the wrong location".  In the context of a Mars-bound fleet, if a single ship does that, it might be survivable.

[TheRadicalModerate]

Indeed the flight regime and trajectory goals and abort modes are very different, I'm not drawing any analogies there. But as you reference the "fly it in" approach when designing the guidance algorithm is much the same as F9, namely that you're correcting error at multiple opportunities (burns and controlled aerodynamic phases), but as expected the net error still grows somewhat during atmospheric maneuvers even with active aero corrections.

I'm heavily referencing the attached figure from Lars Blackmore who does GNC at SpaceX in a paper describing how they achieved the precision F9 landing. Again the shape of the trajectory is completely different, but the approach toward controlling dispersions is the same.

From the diagram, aerodynamic flight increases dispersion, vacuum burns reduce it.

For Mars aerocapture, the first aerodynamic phase will have to contain the dispersion to a degree that there's enough fuel to subsequently recover.

There's quite a wide window for that recovery.

This.

Furthermore, an F9 flies back into one of the greatest concentrations of PNT equipment in human history, and it's aiming for a specific, stationary spot on the ground.  An aerocapturing Starship has neither the PNT resources, nor does it have a fixed reference point.

At least in a direct EDL, you know where you're going, and you can get some advantage from TRN.  With aerocapture, there's some set of position/velocity vectors that will yield a satisfactory solution, but both vectors have much greater dispersion.

At the edges of the window are the extreme cases of "stuck in orbit with not enough propellant to land" and "land immediately even if in the wrong location".  In the context of a Mars-bound fleet, if a single ship does that, it might be survivable.

A Mars-bound fleet only helps you if one ship can land safely, refuel, and mount a rescue.  If you have a robust base up and running, off-target landings can lead to fairly routine rescues.

I have a prejudice against thinking too much about what's possible with Elonville up and running, because I think that's at least 50 years away.  So I tend to limit my thinking about entry speeds and accuracy to the first handful of synods that can support human missions.  In that environment, you'd better have plenty of margin built in, because you're going to be your own rescue party.

[meekGee]

Indeed the flight regime and trajectory goals and abort modes are very different, I'm not drawing any analogies there. But as you reference the "fly it in" approach when designing the guidance algorithm is much the same as F9, namely that you're correcting error at multiple opportunities (burns and controlled aerodynamic phases), but as expected the net error still grows somewhat during atmospheric maneuvers even with active aero corrections.

I'm heavily referencing the attached figure from Lars Blackmore who does GNC at SpaceX in a paper describing how they achieved the precision F9 landing. Again the shape of the trajectory is completely different, but the approach toward controlling dispersions is the same.

From the diagram, aerodynamic flight increases dispersion, vacuum burns reduce it.

For Mars aerocapture, the first aerodynamic phase will have to contain the dispersion to a degree that there's enough fuel to subsequently recover.

There's quite a wide window for that recovery.

This.

Furthermore, an F9 flies back into one of the greatest concentrations of PNT equipment in human history, and it's aiming for a specific, stationary spot on the ground.  An aerocapturing Starship has neither the PNT resources, nor does it have a fixed reference point.

At least in a direct EDL, you know where you're going, and you can get some advantage from TRN.  With aerocapture, there's some set of position/velocity vectors that will yield a satisfactory solution, but both vectors have much greater dispersion.

At the edges of the window are the extreme cases of "stuck in orbit with not enough propellant to land" and "land immediately even if in the wrong location".  In the context of a Mars-bound fleet, if a single ship does that, it might be survivable.

A Mars-bound fleet only helps you if one ship can land safely, refuel, and mount a rescue.  If you have a robust base up and running, off-target landings can lead to fairly routine rescues.

I have a prejudice against thinking too much about what's possible with Elonville up and running, because I think that's at least 50 years away.  So I tend to limit my thinking about entry speeds and accuracy to the first handful of synods that can support human missions.  In that environment, you'd better have plenty of margin built in, because you're going to be your own rescue party.

I wouldn't focus on the first landing.  The first flights will be conservative, and by the time you do aerocapture, there will be sufficient infrastructure in place to provide everything but the actual aerocapture flight rules...

I don't know how adaptive current EDL flight algorithms are. They obviously actively stick to a trajectory, but do they adapt the trajectory to achieve final goals in response to how well the flight is going?  I think that's beyond the current state of the art.

For reliable aerocapture, I think that what needs to happen  as part of "fly it in".

I like the two-pass approach because it provides a built-in recovery opportunity on top of all that.  When you have hundreds of ships coming in, you'll have a few that for whatever reason won't get it exactly right, and they can use landing propellant to save the day.

Timeline wise, once they have the basic flight down (4-6 years) IMO you'll see hundred of ships right away. That GigaBay, it's more than just a customer for the Sushi restaurant. It's there for a reason.

[Robotbeat]

Note that you likely wouldn’t be doing aggressive fast transfers until you have lots of spacecraft and infrastructure. If there’s a missed aerocapture, you may well have the resources to send a rescue ship to rendezvous with supplies and fuel.

[sdsds]

Note that you likely wouldn’t be doing aggressive fast transfers until you have lots of spacecraft and infrastructure. If there’s a missed aerocapture, you may well have the resources to send a rescue ship to rendezvous with supplies and fuel.

I'm guessing this is in reference to crewed flights. Fast transfers could also be used to widen the departure windows for cargo flights, right?

[TheRadicalModerate]

Note that you likely wouldn’t be doing aggressive fast transfers until you have lots of spacecraft and infrastructure. If there’s a missed aerocapture, you may well have the resources to send a rescue ship to rendezvous with supplies and fuel.

I agree that you can do low-margin aerocaptures when you have adequate infrastructure to rescue ships that have off-nominal captures.  However, that still leaves the following questions:

1) What's the tradeoff between the aggressiveness of your time-of-flight and the risk to humans of longer trips?  Is a month shorter ToF worth trimming your contingency prop margin from 3σ to 2σ?  Is two weeks?

2) The same question we started with: What are the maximum arrival entry speeds for both the aerocapture and direct EDL cases?  If we know those numbers, it's fairly straightforward to work backward to get viable pairs of v∞ and braking delta-v, which then tell you what your departure v∞ can be, which gives you your ToF.

I'm guessing this is in reference to crewed flights. Fast transfers could also be used to widen the departure windows for cargo flights, right?

That's a good point.  It's an especially good point if you're looking to design an uncrewed test campaign for Starship entries at Mars.

[Twark_Main]

1) What's the tradeoff between the aggressiveness of your time-of-flight and the risk to humans of longer trips?  Is a month shorter ToF worth trimming your contingency prop margin from 3σ to 2σ?  Is two weeks?

In theory economics should "optimally" answer this question, via the statistical value of human life. This is supposed to be the amount we're willing to spend (in insurance premiums or safety systems) to prevent one statistical death.

Currently, for Americans, this is approximately $10 million per life.

So you just take the ticket price (which can be calculated based on the number of refilling flights and passengers per Starship) and subtract the probability of death (from cancer due to a long transit, and from death due to a missed capture), and the mission parameter that gives you the lowest total risk-adjusted ticket cost to Mars should be the "optimum."

Emotional reactions are one thing, but this is how adults actually handle risk in the real world. Cue the Fight Club quote.... 

[Robotbeat]

I should point out that if the rocket isn’t reliable enough for pretty high safety for humans (say, 99.999% safety or higher), then your reuse number for launch is also likely to be low, in which case your cost is high.

High reuse only works with high reliability, so far from being a tradeoff with safety, these things are actually well-aligned.

[TheRadicalModerate]

I should point out that if the rocket isn’t reliable enough for pretty high safety for humans (say, 99.999% safety or higher), then your reuse number for launch is also likely to be low, in which case your cost is high.

High reuse only works with high reliability, so far from being a tradeoff with safety, these things are actually well-aligned.

But your safety number is dependent on proper allocation for contingencies.  Your pLOC should be considerably less than the probability of an off-target aerocapture or a burn failure.  You build in time to work the problem, design a workaround, and execute it.

If you have a 3day capture orbit (70 x 76,560km), the cost to raise periapse from ~70km to 200km and lower it again is less than 10m/s.  So if you're in any doubt about your entry corridor, that's a pretty small price to pay.  That doesn't account for the cleanup costs to get the corridor right, but you have a day and a half to figure out whether you can do any corrections on the first orbit, or whether you need to raise and reappraise.