I was skeptical of the cooling being cheaper in space. It is true that you can radiate to a much colder temperature in space, about ā60Ā°C equivalent. It does look like space cooling would be cheaper with your future launch costs for your constellation model. However, for your modular station model, you would need around 1 m diameter pipes to start, which would weigh a lot and pose a large single source of failure. Also, you would have to pump long distances, increasing the pump mass and energy use.
I think inference would be challenging because the satellite is in view for only a few minutes. I guess most queries take less time than this, but would you keep handing off the session memory?
Baseline A (100% renewable off-grid, $20,307/ākW-continuous): Solar at 28% CF, $1.10/āW installed, 4,643 W nameplate per kW-continuous ($5,107). Battery storage 80 kWh at $175/ākWh ($14,000 or 69% of total). Other $1,200. 5-year LCOE: $463/āMWh. Battery storage dominates because 99.9%+ uptime without fossil backup requires multi-day autonomy.
This is much more reasonable than people claiming that going off grid is cheaper than grid electricity with the same reliability. Still, you note that this capacity factor is reasonable for the desert, but typically there is around a two times seasonal variation. Since 80 hours of storage canāt handle that, you would need to oversize your PV more. But it wouldnāt change the results that much (~10%). And the gas turbine in your Baseline B solves this seasonal problem.
We include Baseline A however, since backlogs for turbines versus the abundance of solar and battery available suggest that it may be the fastest way to quickly scale energy production on Earth.
If you want 80 hours of storage for 100 GW, that is 8 TWh, which is years worth of current production, so I think youād have to pay a premium.
P_net = 2ĪµĻTā“ ā Ī±S ā Ī±F(Al Ć S + ĻT_earthā“) where Īµ = 0.92 (AZ-93 selective white paint emissivity), Ī± = 0.09 (solar absorptivity), S = 1,366 W/āmĀ², F ā 0.25 (Earth view factor), Al = 0.3 (albedo), T_earth ā 253 K.
For the longwave radiation coming from the earth, you would get Īµ absorption, not Ī± absorption. So the equation should be: P_net = 2ĪµĻTā“ ā Ī±S ā Ī±F(Al Ć S) ā ĪµF(ĻT_earthā“)
Also, the view factor to the Earth is 0.25 for one side of the radiator, but you are counting both sides for the emission, so I think the view factor should be 0.5.
So then at 20Ā°C: emitted 770 W/āmĀ², absorbed 248 W/āmĀ², net rejected 522 W/āmĀ² (not 633 W/āmĀ²).
Also note that if your fluid temp is 20Ā°C, the radiator will be lower average temp because of conductive thermal gradient. But with 1 mm of high-modulus pitch-based carbon fibre reinforced polymer, it doesnāt look like too much of a loss.
Footnote 17 seems to end abruptly: āThe scenarios in a bit more detail are as follows:ā
Re: cooling skepticism, actually this has been helpful. On review I think the net rejection will be greater than 633 W/ām2. Youāre right, we get absorption = Īµ for longwave radiation from Earth (Kirchhoff would not be pleased).
On view factor, hmm I think this will just vary over the orbital band. Computing the analytic per-face as F = (1/āĻ)[ĪøE ā Ā½sin(2ĪøE)] with sin(ĪøE) = Rā/ā(Rā+h) I get:
Altitude
F per face
F total
550 km
0.258
0.515
1000 km
0.194
0.388
2000 km
0.118
0.236
Maybe we should go worst case and also initial ODCs would prefer to be on the low end of altitude for as long as slots are available (lower cost to orbit, less radiation) You do I think want to go high enough to avoid occasional shading in dawn-dusk-SSO so perhaps ~675km and up. If we correct the absorptivity for Earth IR and take the low end view factor, I get your 522 W/ām2. That looks like a ~1% increase in total cost for ODCs if youāre right.
While checking this though it occurs to me you should be able to be have the radiators edge on to the sun while still radiating from both sides, something like this:
Basically a Starlink v3 with panels at 90 degree pivots. Then with shading from direct sunlight I think I get 650 W/ām2 for 675 km altitude, F = 0.473, so an improvement on radiator performance overall. Iāll have to think about this a bit more and potentially update the appendix. Certainly we can fix the erroneous use of Ī± in the 3rd term.
Agree loss from averaging over radiator temp looks modest.
Also agree that scaling the plumbing to a massive modular station architecture looks rough. Also there are issues with stresses/āstrains due to maneuvers for larger orbital platforms and some structural scaling that has to happen to avoid e.g. floppiness. My guess is that the architecture isnāt viable at least near-term.
Re: inference, not my area of expertise and I donāt think the computer architecture totally decided but from looking into it I think it looks like youād only be handing off the query and response. The routing should be the same as for traditional satellites so this problem is already ~solved (though you may need to scale the satellite mesh as demand/ātraffic increase). The orbital compute is in a polar orbit so typically not overhead. The trip in a kind of worst case scenario might look something like this:
User ā ground station (letās say 100 Gbps uplink from ground station)
Ground station ā uplink satellite(s) (whichever is in view at the moment, can stream seamlessly as multiple pass overhead)
Intersatellite link hop, routing toward wherever the GPUs are, letās say there is as yet only one cluster in orbit and it takes 15 hops to reach it, each at ~100 Gbps (Starlink v2)
Arrive at cluster ā run inference ā return output (this is where the KV cache, session memory etc. stays, in the compute cluster)
ISL hops routing back to ground station (say 15 hops at 100 Gbps again, each is maybe 5.5 ms)
Downlink to ground station ā serve output to user
For example I think for a 100 GB workload through a 100 Gbps optical ground station, total time is ~8 seconds serialization/ātransfer, essentially the same ~8 seconds as terrestrial on 100 Gbps direct connect, plus something like 175 ms of constellation overhead.
Re: terrestrial solar and battery. Good points: these make terrestrial microgrids look a good bit worse. For solar on Earth in addition to the seasonality weāre also assuming some of the best solar sites in the world so this should be fairly bullish for terrestrial data centers. We didnāt spot any fundamental blockers to scaling microgrids through some combo of solar overbuy + battery and gas but prices may be at a premium either for turbines or for batteries as you say. In some sense it seems like the data center buildout may have hyperscalers acting like water flowing down hill, pivoting into whichever buildout channel offers least resistance at the moment. Similarly if ODCs start going up en masse there could be lower lying supply chain issues that emerge. The most biting constraint of all is probably chips and memory.
I dug in a little more, and I think your Earth cooling estimate is high at $2.5ā3.0B/āGW with water chillers. An NREL study was more like $0.7B/āGW with water chillers. Also, we may be able to dispense with the water chiller (as you have assumed in space), and then it could be even cheaper. So I doubt itās actually going to be cheaper to cool in space. However, your point that cooling in space doesnāt wreck the economics still stands.
If we correct the absorptivity for Earth IR and take the low end view factor, I get your 522 W/ām2. That looks like a ~1% increase in total cost for ODCs if youāre right.
I was using 550 km, so I agree that higher up, you would have more net radiation leaving the radiator.
As for your bent configuration, that is creative to avoid the sun incidence. However, then you would have radiation from the solar panels to the radiator, and since the solar panels will be warmer than the Earth, I think it will work out worse overall.
Agree loss from averaging over radiator temp looks.
Iām glad to see this rigorous analysis!
I was skeptical of the cooling being cheaper in space. It is true that you can radiate to a much colder temperature in space, about ā60Ā°C equivalent. It does look like space cooling would be cheaper with your future launch costs for your constellation model. However, for your modular station model, you would need around 1 m diameter pipes to start, which would weigh a lot and pose a large single source of failure. Also, you would have to pump long distances, increasing the pump mass and energy use.
I think inference would be challenging because the satellite is in view for only a few minutes. I guess most queries take less time than this, but would you keep handing off the session memory?
This is much more reasonable than people claiming that going off grid is cheaper than grid electricity with the same reliability. Still, you note that this capacity factor is reasonable for the desert, but typically there is around a two times seasonal variation. Since 80 hours of storage canāt handle that, you would need to oversize your PV more. But it wouldnāt change the results that much (~10%). And the gas turbine in your Baseline B solves this seasonal problem.
If you want 80 hours of storage for 100 GW, that is 8 TWh, which is years worth of current production, so I think youād have to pay a premium.
For the longwave radiation coming from the earth, you would get Īµ absorption, not Ī± absorption. So the equation should be:
P_net = 2ĪµĻTā“ ā Ī±S ā Ī±F(Al Ć S) ā ĪµF(ĻT_earthā“)
Also, the view factor to the Earth is 0.25 for one side of the radiator, but you are counting both sides for the emission, so I think the view factor should be 0.5.
So then at 20Ā°C: emitted 770 W/āmĀ², absorbed 248 W/āmĀ², net rejected 522 W/āmĀ² (not 633 W/āmĀ²).
Also note that if your fluid temp is 20Ā°C, the radiator will be lower average temp because of conductive thermal gradient. But with 1 mm of high-modulus pitch-based carbon fibre reinforced polymer, it doesnāt look like too much of a loss.
Footnote 17 seems to end abruptly: āThe scenarios in a bit more detail are as follows:ā
Hey David, thanks for this excellent comment.
Re: cooling skepticism, actually this has been helpful. On review I think the net rejection will be greater than 633 W/ām2. Youāre right, we get absorption = Īµ for longwave radiation from Earth (Kirchhoff would not be pleased).
On view factor, hmm I think this will just vary over the orbital band. Computing the analytic per-face as F = (1/āĻ)[ĪøE ā Ā½sin(2ĪøE)] with sin(ĪøE) = Rā/ā(Rā+h) I get:
Altitude
F per face
F total
550 km
0.258
0.515
1000 km
0.194
0.388
2000 km
0.118
0.236
Maybe we should go worst case and also initial ODCs would prefer to be on the low end of altitude for as long as slots are available (lower cost to orbit, less radiation) You do I think want to go high enough to avoid occasional shading in dawn-dusk-SSO so perhaps ~675km and up. If we correct the absorptivity for Earth IR and take the low end view factor, I get your 522 W/ām2. That looks like a ~1% increase in total cost for ODCs if youāre right.
While checking this though it occurs to me you should be able to be have the radiators edge on to the sun while still radiating from both sides, something like this:
Basically a Starlink v3 with panels at 90 degree pivots. Then with shading from direct sunlight I think I get 650 W/ām2 for 675 km altitude, F = 0.473, so an improvement on radiator performance overall. Iāll have to think about this a bit more and potentially update the appendix. Certainly we can fix the erroneous use of Ī± in the 3rd term.
Agree loss from averaging over radiator temp looks modest.
Also agree that scaling the plumbing to a massive modular station architecture looks rough. Also there are issues with stresses/āstrains due to maneuvers for larger orbital platforms and some structural scaling that has to happen to avoid e.g. floppiness. My guess is that the architecture isnāt viable at least near-term.
Re: inference, not my area of expertise and I donāt think the computer architecture totally decided but from looking into it I think it looks like youād only be handing off the query and response. The routing should be the same as for traditional satellites so this problem is already ~solved (though you may need to scale the satellite mesh as demand/ātraffic increase). The orbital compute is in a polar orbit so typically not overhead. The trip in a kind of worst case scenario might look something like this:
User ā ground station (letās say 100 Gbps uplink from ground station)
Ground station ā uplink satellite(s) (whichever is in view at the moment, can stream seamlessly as multiple pass overhead)
Intersatellite link hop, routing toward wherever the GPUs are, letās say there is as yet only one cluster in orbit and it takes 15 hops to reach it, each at ~100 Gbps (Starlink v2)
Arrive at cluster ā run inference ā return output (this is where the KV cache, session memory etc. stays, in the compute cluster)
ISL hops routing back to ground station (say 15 hops at 100 Gbps again, each is maybe 5.5 ms)
Downlink to ground station ā serve output to user
For example I think for a 100 GB workload through a 100 Gbps optical ground station, total time is ~8 seconds serialization/ātransfer, essentially the same ~8 seconds as terrestrial on 100 Gbps direct connect, plus something like 175 ms of constellation overhead.
Re: terrestrial solar and battery. Good points: these make terrestrial microgrids look a good bit worse. For solar on Earth in addition to the seasonality weāre also assuming some of the best solar sites in the world so this should be fairly bullish for terrestrial data centers. We didnāt spot any fundamental blockers to scaling microgrids through some combo of solar overbuy + battery and gas but prices may be at a premium either for turbines or for batteries as you say. In some sense it seems like the data center buildout may have hyperscalers acting like water flowing down hill, pivoting into whichever buildout channel offers least resistance at the moment. Similarly if ODCs start going up en masse there could be lower lying supply chain issues that emerge. The most biting constraint of all is probably chips and memory.
I dug in a little more, and I think your Earth cooling estimate is high at $2.5ā3.0B/āGW with water chillers. An NREL study was more like $0.7B/āGW with water chillers. Also, we may be able to dispense with the water chiller (as you have assumed in space), and then it could be even cheaper. So I doubt itās actually going to be cheaper to cool in space. However, your point that cooling in space doesnāt wreck the economics still stands.
Iām glad it was helpful!
I was using 550 km, so I agree that higher up, you would have more net radiation leaving the radiator.
As for your bent configuration, that is creative to avoid the sun incidence. However, then you would have radiation from the solar panels to the radiator, and since the solar panels will be warmer than the Earth, I think it will work out worse overall.
Incomplete?
Your other points make sense.
Seems to be a formatting error and itās supposed to be in the main text, referencing the table.