Starship On-orbit refueling - Options and Discussion

[OTV Booster]

I'm assuming that an 'ideal' mature transfer scenario allows 6 hours (21,600 s) for transfer. The depots orbit can be matched up every 12 hours, assuming a single launch site. Figure three hours for approach and docking and the same to undock and clear.

I think the single site has two launch opportunities a day, but they are not 12 hours apart.   There are also two landing opportunities a day.  This assumes the Depot orbit crosses the latitude of the launch site. Am I missing something?  If those two launch opportunities are far enough apart, then you still get an average of 12 hours for the full transfer operation. Each tanker will need some time (maybe 24 hours?) to sync with Depot's location in its orbit, and will need maybe the same amount of time after completion of fueling to move to the correct spot along the orbit to start its deorbit.  With all of this, I guess each tanker mission is about three days, so you need six tankers to maintain a 12-hour cadence.  I'm pretty sure you also need separate launch and catch towers.

I'm pretty sure it's close enough to 12 hours to make no difference. One ascending node and one descending node.


In theory, when the target orbit is the same inclination as the launch sites latitude, they can match orbits near dead on with no chase time. In theory. IIRC they have hooked up with the ISS with a six hour chase.


Fast turnaround for the tankers is not on the immediate horizon. Until they get some experience under their belt I'd expect to see a fleet of tankers, each doing only one transfer per campaign. They promise to be the simplest and least expensive variant.


Artemus will need two depots or one depot and one super tanker that will need some refilling. Each would be a separate campaign using the same tanker fleet. If the depot is near zero boiloff they can launch it well in advance, then launch the second depot or supertanker, refill as necessary and move it to where it needs to be. Once all the pieces are in place, crew launches.


Back to refueling: If the chase is six hours they can still launch every 12 hours and have a six hour deep pipeline bringing another tanker to the depot every 12 hours. Assuming the slowest transfer can be done in 12 hours.


With a full fleet of tankers that can collectively service one campaign, the timely return of the tankers is less of a concern. The biggest limitation on return is boiling dry.
Dropping only a couple of km after the transfer, the tankers would continually be opening the distance to the depot, but not so low that decay would be immanent. Bring 'em back as convenient. That said, yes, multiple pads would be a good thing (he said, wondering how OLM and tower will look after that first launch).

[TheRadicalModerate]

Surely you mean sun shielding, not insulation, since the transfer is occurring in a vacuum?

I was thinking more of the actual transfer plumbing, which will heat up radiatively but transfer heat to the prop flowing through it conductively.  If it's always shaded or insulated well enough that conductive transfer negligible, then it's not an issue.

[mikelepage]

I'm assuming that an 'ideal' mature transfer scenario allows 6 hours (21,600 s) for transfer. The depots orbit can be matched up every 12 hours, assuming a single launch site. Figure three hours for approach and docking and the same to undock and clear.

I'm also assuming that only the depot will have active cooling and that PV and maybe radiators will have to tuck away during transfer ops. These assumptions point to wanting a loading campaign done either as fast as possible (a tanker every 12 hours) or very relaxed with a chance to literally chill between loads. There is no aspect of Elon that is relaxed so a fast cadence looks like a good bet. Fast also means less wear and tear on the panel deployment mechanism.

There's a lot of assumptions here but you might think about tucking some of them into your noodling.

Thanks, and agreed that it's a huge trade space. I've also been assuming that only the depot will have active cooling, and will in fact have a number of optimisations for keeping prop cool that it doesn't make sense to install on every Starship (OT: whether that would lead to sending a single depot with each fleet of Starships that makes the Earth-Mars transit is an interesting question to me: the ability to keep one ship uncrewed and cold the whole trip seems like a good energy saving measure, then also, you have the capability to top up the rest of the fleet's header tanks with fresh cryo prop in the days before landing).

Just attaching a screenshot of what happens if you plug 21,600s into TheRadicalModerate's spreadsheet. It now requires 15 tanker trips to fill a depot, and thats with 300s hot gas thrusters going the whole time to create 5mm/s². I somehow doubt that losing nearly 40% of the propellant launched is really acceptable. With 70s ullage thrust, the transfers lose so much prop that the process never completes. If you go to 1mm/s² and 300s thrust you get to 5.7% losses over 12 tanker loads which is (maybe) acceptable.

My key takeaway/question is whether propellant loss due to milli-G acceleration is the only reason to do prop transfers as fast as the system allows. Everything else (I think) pushes you towards taking your time - you probably wouldn't launch a tanker more than once a day (at least at first) so a 6+ hour prop transfer isn't going to be the limiting factor, and lower transfer speed means less sloshing/swirling in the tank.

[DanClemmensen]

If we need nearly continuous low acceleration and we think this will waste too much propellant, perhaps we need to look a high efficiency thrusters. Specifically, ion thrusters of some sort. Something like the Gateway PPE. This would be part of the Depot, not the tankers, so the cost of lifting it to orbit is only incurred once. Ideally, we would use some magical thruster that uses CH₄ or O₂ instead of Xenon.

Question: how much thrust is needed to maintain 0.5 mm/s² for a max-loaded Depot/tanker combo?

[TheRadicalModerate]

My key takeaway/question is whether propellant loss due to milli-G acceleration is the only reason to do prop transfers as fast as the system allows. Everything else (I think) pushes you towards taking your time - you probably wouldn't launch a tanker more than once a day (at least at first) so a 6+ hour prop transfer isn't going to be the limiting factor, and lower transfer speed means less sloshing/swirling in the tank.

For the parameters you have set here, the transfer mass flow is only 6.9kg/s.  Also, the longer you take at a particular acceleration, the more delta-v you wind up spending.  If you take 21,600s at 5mm/s², you're expending more than 1600m/s of delta-v.  Your depot/tanker will wind up in a much higher orbit, and both vehicles will have to spend a bunch of delta-v to get back to the depot's parking orbit.

[DanClemmensen]

My key takeaway/question is whether propellant loss due to milli-G acceleration is the only reason to do prop transfers as fast as the system allows. Everything else (I think) pushes you towards taking your time - you probably wouldn't launch a tanker more than once a day (at least at first) so a 6+ hour prop transfer isn't going to be the limiting factor, and lower transfer speed means less sloshing/swirling in the tank.

For the parameters you have set here, the transfer mass flow is only 6.9kg/s.  Also, the longer you take at a particular acceleration, the more delta-v you wind up spending.  If you take 21,600s at 5mm/s², you're expending more than 1600m/s of delta-v.  Your depot/tanker will wind up in a much higher orbit, and both vehicles will have to spend a bunch of delta-v to get back to the depot's parking orbit.

I think the maneuver during propellant transfer is a big circle, so the net change in position is zero. This introduces a very small lateral acceleration which should not affect the transfer.

[TheRadicalModerate]

If we need nearly continuous low acceleration and we think this will waste too much propellant, perhaps we need to look a high efficiency thrusters. Specifically, ion thrusters of some sort. Something like the Gateway PPE. This would be part of the Depot, not the tankers, so the cost of lifting it to orbit is only incurred once. Ideally, we would use some magical thruster that uses CH₄ or O₂ instead of Xenon.

Question: how much thrust is needed to maintain 0.5 mm/s² for a max-loaded Depot/tanker combo?

F = ma, baby.  m = 95t + 1450t + 120t + 150t = 1,815,000kg.  a = 0.005m/s² 0.0005m/s².  Thrust = 9075N 908N.

Electric propulsion usually generates 60mN/kW.  So you'd need 151MW 15.1MW of power to drive the coupled system.  Nope.

Update:  Thanks to tbellman for catching that I'd dropped a decimal--with no change in the conclusion.

I think the maneuver during propellant transfer is a big circle, so the net change in position is zero. This introduces a very small lateral acceleration which should not affect the transfer.

OK, fair point.  But... 1600m/s spent on ullage acceleration?

[edzieba]

On geysering and slosh reduction: The early Jupiter missiles used a system of floating bodies inside the tank covering the propellant/ullage gas interface to reduce propellant slosh (after observation that transporting water tanks with lumber floating in them significantly reduced slosh) prior to the introduction of anti-slosh and anti-vortex baffles to the tank walls. I've previously suggested this floating body system may be repurposed as an insulator layer for reduction of ullage gas heating, but it could also serve to reduce the effects of geysering from propellant pumping, by absorbing stream and droplet energy in trying to move the more massive (in discrete terms) floats rather than allowing droplets to continue unimpeded.

[tbellman]

Question: how much thrust is needed to maintain 0.5 mm/s² for a max-loaded Depot/tanker combo?

F = ma, baby.  m = 95t + 1450t + 120t + 150t = 1,815,000kg.  a = 0.005m/s².  Thrust = 9075N.

Electric propulsion usually generates 60mN/kW.  So you'd need 151MW of power to drive the coupled system.  Nope.

Dan asked about half a millimeter per second squared, while you calculated for five.  So you would only need 15 megawatt.

"Only"...

So your conclusion is correct anyway; that is still a "Nope", probably even a "No way in h***".

Heck, even an empty Starship at 120 tonne would need 60 N thrust for that acceleration, which would require 1 MW electric power, which is probably about an order of magnitude more than you can expect from solar panels carried on a Starship...

[Greg Hullender]

Electric propulsion usually generates 60mN/kW.  So you'd need 151MW of power to drive the coupled system.  Nope.

Is that really out of the question, though? I just skimmed "Temperature and Power Specific Mass Scaling for LEU Closed-Cycle Brayton Systems for Space Surface Power and Nuclear Electric Propulsion (Christopher G. Morrison, 2019), and it suggests that a 150 MW reactor would have a mass of about 150 tons (looking at figure 8 on page 5). Admittedly, that'd be a very advanced, high-temperature reactor, but it's not totally nuts.

Of course, if you can put that in orbit, you might as well use it to transport all payload except maybe human beings.

[DanClemmensen]

Question: how much thrust is needed to maintain 0.5 mm/s² for a max-loaded Depot/tanker combo?

F = ma, baby.  m = 95t + 1450t + 120t + 150t = 1,815,000kg.  a = 0.005m/s².  Thrust = 9075N.

Electric propulsion usually generates 60mN/kW.  So you'd need 151MW of power to drive the coupled system.  Nope.

Dan asked about half a millimeter per second squared, while you calculated for five.  So you would only need 15 megawatt.

"Only"...

So your conclusion is correct anyway; that is still a "Nope", probably even a "No way in h***".

Heck, even an empty Starship at 120 tonne would need 60 N thrust for that acceleration, which would require 1 MW electric power, which is probably about an order of magnitude more than you can expect from solar panels carried on a Starship...

Yep, TheRadicalModerate answered the question I should have asked instead of the question I asked. 

Apparently, ISS has 2500 m³ of panels to generate an average system power of 125 kW. That's 2m³/kw at the system level, so we would need 3.02 km² of solar panels to generate 151 MW. You would construct this nightmare using a whole lot of Starship flights and then use it for thirty years. You don't want to accelerate the panels or batteries, so by the time you have done all the engineering you probably should be looking at a different solution.

[OTV Booster]

I'm assuming that an 'ideal' mature transfer scenario allows 6 hours (21,600 s) for transfer. The depots orbit can be matched up every 12 hours, assuming a single launch site. Figure three hours for approach and docking and the same to undock and clear.

I'm also assuming that only the depot will have active cooling and that PV and maybe radiators will have to tuck away during transfer ops. These assumptions point to wanting a loading campaign done either as fast as possible (a tanker every 12 hours) or very relaxed with a chance to literally chill between loads. There is no aspect of Elon that is relaxed so a fast cadence looks like a good bet. Fast also means less wear and tear on the panel deployment mechanism.

There's a lot of assumptions here but you might think about tucking some of them into your noodling.

Thanks, and agreed that it's a huge trade space. I've also been assuming that only the depot will have active cooling, and will in fact have a number of optimisations for keeping prop cool that it doesn't make sense to install on every Starship (OT: whether that would lead to sending a single depot with each fleet of Starships that makes the Earth-Mars transit is an interesting question to me: the ability to keep one ship uncrewed and cold the whole trip seems like a good energy saving measure, then also, you have the capability to top up the rest of the fleet's header tanks with fresh cryo prop in the days before landing).

Just attaching a screenshot of what happens if you plug 21,600s into TheRadicalModerate's spreadsheet. It now requires 15 tanker trips to fill a depot, and thats with 300s hot gas thrusters going the whole time to create 5mm/s². I somehow doubt that losing nearly 40% of the propellant launched is really acceptable. With 70s ullage thrust, the transfers lose so much prop that the process never completes. If you go to 1mm/s² and 300s thrust you get to 5.7% losses over 12 tanker loads which is (maybe) acceptable.

My key takeaway/question is whether propellant loss due to milli-G acceleration is the only reason to do prop transfers as fast as the system allows. Everything else (I think) pushes you towards taking your time - you probably wouldn't launch a tanker more than once a day (at least at first) so a 6+ hour prop transfer isn't going to be the limiting factor, and lower transfer speed means less sloshing/swirling in the tank.

Um, uh... We'll, maybe we should think of 21,600 seconds as a window. Running simple minded numbers that even I can handle, using the whole window would be a transfer of only ~7kg/sec. Divvied up, it's ~1.4kg methane and ~5.5kg O2. Someone else can figure out the volume.


With a lot of hand waving, I'd say that this would be somewhere near what's needed when starting with an empty receiving tank, and at the highest settling thrust. Maybe that 5mm/s^2, but lower if possible. As the propellant level rises thrust can drop and transfer rate increase. The first 150t load would most likely be the most expensive, propellant wise and wouldn't need the full window. Each following load would need less settling thrust and less transfer time. Something to keep in mind is that the thrust/transfer rates may be very different for methane and O2.


The .5mm/s^2 needed for Centaur might be higher than needed for SS. Different sizes, different thrusters, different fuel, different team. Whatever is needed, I think we'll be looking at a range, not one number.


Does anybody have an intelligible comparison of the viscosity of water at 20C vs methane and O2 at both boiling and slightly above freezing?

[DanClemmensen]

OK, let's start over. Assume we need 5 mm/s² accelleration, and we want to use centrepital force. We mount the tanker atop the depot and then sling them from a cable with tanker toward the center of rotation, and start spinning. We need another mass at the far end of the cable. let's say that otehr mass is 1/10 the mass of our tanker+depot+propellant. For a cable that is 1100 meters, the tanker+depot CoM will be 100 meters from the center of rotation. The formula is
    accel = (rotational rate squared) * radius
I get a rotational rate of 0.42 RPM.     Is this correct?

Tension in the cable in Newtons is mass the complex times 0.005 m/s², which is not a lot.

Practical considerations:
    How to connect the cable to the depot so as to still allow the tanker to dock atop it? I think this will require a wide set of spreaders. CoM must stay "below" the attachment point even for a full tanker on an empty depot unless the tanket is stabilized to the cable using the tanker's chopstick catchpoints.
    How to spin up after docking the tanker and spin down before undocking?  I think thrusters on the depot.
    How to keep the cable from tangling when not spinning? I think make it slightly rigid, possibly using a pressurized pipe.
    What is the right length and the right mass for the counterweight? I think 100 meters is too short for CoM to center of spin since the gradient is too high (tanker too light, depot too heavy). A longer cable means a lower rotation rate.
    How much energy is needed to spin up and spin down? ( too much math for me right  now).

[OTV Booster]

On geysering and slosh reduction: The early Jupiter missiles used a system of floating bodies inside the tank covering the propellant/ullage gas interface to reduce propellant slosh (after observation that transporting water tanks with lumber floating in them significantly reduced slosh) prior to the introduction of anti-slosh and anti-vortex baffles to the tank walls. I've previously suggested this floating body system may be repurposed as an insulator layer for reduction of ullage gas heating, but it could also serve to reduce the effects of geysering from propellant pumping, by absorbing stream and droplet energy in trying to move the more massive (in discrete terms) floats rather than allowing droplets to continue unimpeded.

Any idea what the floats were made of on the O2 side?

[OTV Booster]

OK, let's start over. Assume we need 5 mm/s² accelleration, and we want to use centrepital force. We mount the tanker atop the depot and then sling them from a cable with tanker toward the center of rotation, and start spinning. We need another mass at the far end of the cable. let's say that otehr mass is 1/10 the mass of our tanker+depot+propellant. For a cable that is 1100 meters, the tanker+depot CoM will be 100 meters from the center of rotation. The formula is
    accel = (rotational rate squared) * radius
I get a rotational rate of 0.42 RPM.     Is this correct?

Tension in the cable in Newtons is mass the complex times 0.005 m/s², which is not a lot.

Practical considerations:
    How to connect the cable to the depot so as to still allow the tanker to dock atop it? I think this will require a wide set of spreaders. CoM must stay "below" the attachment point even for a full tanker on an empty depot unless the tanket is stabilized to the cable using the tanker's chopstick catchpoints.
    How to spin up after docking the tanker and spin down before undocking?  I think thrusters on the depot.
    How to keep the cable from tangling when not spinning? I think make it slightly rigid, possibly using a pressurized pipe.
    What is the right length and the right mass for the counterweight? I think 100 meters is too short for CoM to center of spin since the gradient is too high (tanker too light, depot too heavy). A longer cable means a lower rotation rate.
    How much energy is needed to spin up and spin down? ( too much math for me right  now).

While the concept looks promising in theory, tethers are hard. Your inflatable tube tether is ingenious and has the seeds of a deployment system embedded in it. Deployment is one of the really hard parts.


Tethers are something that deserve a lot more research than has been put into them. Another way of saying that is: they might be useful in another 5-15 years if somebody invests a lot of time, energy and money.
See: [size=78%]https://en.m.wikipedia.org/wiki/Space_tether[/size]


BTW, in LEO, a metallic tether normal to earth would be a wire cutting through magnetic field lines - potentially a generator to run some ullage thrusters but again, not ready for prime time.


In the time frame of Artemus, it looks like optimizing to minimize settling thrust is most practical. If it takes a few more tanker flights that's the cost of doing business.

[DanClemmensen]

While the concept looks promising in theory, tethers are hard. Your inflatable tube tether is ingenious and has the seeds of a deployment system embedded in it. Deployment is one of the really hard parts.

I don't think this is original with me. I think I saw it on the forum somewhere. I was certainly inspired by something here. There is no reason the inflatable stiffener must also be the tension member, so it's not necessarily an "inflatable tether". The stiffener might be the main part of the deployment mechanism, or not. After deployment it is only needed when the tether is not under tension.

The energy needed to spin the system up is apparently
  energy = mass * radius * acceleration.

I derived this from the flywheel equation.

Its really the energy stored in the counterweight plus the energy stored in the (depot+tanker), but I think the energy is evenly divided so I just doubled the energy stored in the (depot+tanker).
m=1,815,000kg.  a = 0.005m/s².  r = 100 (but probably more)

We therefore need
      e = 1,815,000kg *  100 m * 0.005m/s².
         = 907,500 Joules
for each spin-up and each spin-down. I have no idea how to convert this into expended propellant.

I suspect you are correct and this system cannot be developed in time for the first HLS mission: they will just throw extra tankers at the problem.

I also suspect the professionals will come up with an entirely different solution that is far superior.
             
   

[TheRadicalModerate]

It occurred to me that, if you engineer your pumping power so that it achieves the needed flow rate but causes the liquid to exit the outlet pipe at exactly ambient pressure, then there's no geysering possible.

You can figure out that pump power via the Poiseuille equation,¹ which tells you the pressure drop from the pump outlet to the ambient fill pipe outlet, and then you can derive the pump power² from the pressure drop.  So it requires a requires a variable-power pump to compensate for the ambient hydrostatic head at the outlet, but otherwise the prop will ooze out of the outlet at just the right rate with basically no kinetic energy.

______________
¹Poiseuille equation:

Δp = 8μLQ/(πR⁴)

Where:
Δp is the pressure drop through the pipe
μ is the dynamic viscosity (5.0E-5 Pa-s for LOX, 1.1E-5 Pa-s for LCH4)
L is the pipe length
Q is the volumetric flow rate (in m³/s, not kg/s)
R is the pipe radius

²The pump power is:

P = (Δp + p_outletHead)Q/η

where
P is the power (W)
η is the pump efficiency.

[mikelepage]

It occurred to me that, if you engineer your pumping power so that it achieves the needed flow rate but causes the liquid to exit the outlet pipe at exactly ambient pressure, then there's no geysering possible.

You can figure out that pump power via the Poiseuille equation,¹ which tells you the pressure drop from the pump outlet to the ambient fill pipe outlet, and then you can derive the pump power² from the pressure drop.  So it requires a requires a variable-power pump to compensate for the ambient hydrostatic head at the outlet, but otherwise the prop will ooze out of the outlet at just the right rate with basically no kinetic energy.

______________
¹Poiseuille equation:

Δp = 8μLQ/(πR⁴)

Interesting, I didn't realise this (/R⁴!!). Key takeaway being that fat pipes are your friend, since one assumes SpaceX were already going to pick the most efficient pumps possible.

Thought I should show you the current progress of my noodling (not the final product - the revisions of these animations will form part of my next youtube video). I should say that this began as a revision of my spin-G Starship work, but the configuration that I came up with seemed to be applicable to the propellant transfer problem.

This particular spin config - with the offset nose docking and dorsal-ventral rotation - was one that I hadn't considered until recently, but I'm liking it more and more (solar panels/radiators not yet shown, bi-directional ports assumed). It means you don't need to move the header tank at all. Even if you really did want to put the docking port on the nose, you'd have to figure out how to protect the port with the heat shield during EDL.

The offset port at the nose also avoids intermediate axis issues if you rotate in the dorsal-ventral plane. Obviously the pipes on the depot variant are pretty long, but they are all on the leeward side of the vehicle. This animation depicts 4 pipes on the arm (2x Methane and LOX, liquid and ullage) each with a diameter of 20cm. 

[OTV Booster]

It occurred to me that, if you engineer your pumping power so that it achieves the needed flow rate but causes the liquid to exit the outlet pipe at exactly ambient pressure, then there's no geysering possible.

You can figure out that pump power via the Poiseuille equation,¹ which tells you the pressure drop from the pump outlet to the ambient fill pipe outlet, and then you can derive the pump power² from the pressure drop.  So it requires a requires a variable-power pump to compensate for the ambient hydrostatic head at the outlet, but otherwise the prop will ooze out of the outlet at just the right rate with basically no kinetic energy.

______________
¹Poiseuille equation:

Δp = 8μLQ/(πR⁴)

Where:
Δp is the pressure drop through the pipe
μ is the dynamic viscosity (5.0E-5 Pa-s for LOX, 1.1E-5 Pa-s for LCH4)
L is the pipe length
Q is the volumetric flow rate (in m³/s, not kg/s)
R is the pipe radius

²The pump power is:

P = (Δp + p_outletHead)Q/η

where
P is the power (W)
η is the pump efficiency.

This looks like an upper limit on a dry receiving tank. Once the fluid depth reaches ~one inlet diameter it can pump a bit harder and let viscosity damp geysering. Given the consumption numbers we're seeing for settling, the transfer time looks critical.

[OTV Booster]

It occurred to me that, if you engineer your pumping power so that it achieves the needed flow rate but causes the liquid to exit the outlet pipe at exactly ambient pressure, then there's no geysering possible.

You can figure out that pump power via the Poiseuille equation,¹ which tells you the pressure drop from the pump outlet to the ambient fill pipe outlet, and then you can derive the pump power² from the pressure drop.  So it requires a requires a variable-power pump to compensate for the ambient hydrostatic head at the outlet, but otherwise the prop will ooze out of the outlet at just the right rate with basically no kinetic energy.

______________
¹Poiseuille equation:

Δp = 8μLQ/(πR⁴)

Interesting, I didn't realise this (/R⁴!!). Key takeaway being that fat pipes are your friend, since one assumes SpaceX were already going to pick the most efficient pumps possible.

Thought I should show you the current progress of my noodling (not the final product - the revisions of these animations will form part of my next youtube video). I should say that this began as a revision of my spin-G Starship work, but the configuration that I came up with seemed to be applicable to the propellant transfer problem.

This particular spin config - with the offset nose docking and dorsal-ventral rotation - was one that I hadn't considered until recently, but I'm liking it more and more (solar panels/radiators not yet shown, bi-directional ports assumed). It means you don't need to move the header tank at all. Even if you really did want to put the docking port on the nose, you'd have to figure out how to protect the port with the heat shield during EDL.

The offset port at the nose also avoids intermediate axis issues if you rotate in the dorsal-ventral plane. Obviously the pipes on the depot variant are pretty long, but they are all on the leeward side of the vehicle. This animation depicts 4 pipes on the arm (2x Methane and LOX, liquid and ullage) each with a diameter of 20cm. 

Very interesting and a nice render. If the depot never comes back that external plumbing is no problem at all.