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KSP2 Release Notes
Everything posted by Ultimate Steve
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Hello everyone! One of my self imposed rules for my first KSP 2 save was to not make it into a mission report because I inevitably make up a story, and my willingness to make the story, post the story, and play the game get desynchronized and all three die. However, enough shenanigans have taken place, and I will only get to react to KSP 2's story for the first time once, so I thought I'd at least give this a short writeup. After all, what could go wrong? As of time of starting to write, I have just landed on Duna. All sections will contain spoiler warnings. Part 1 (Spoilers: Mun Quest):
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Hello, checking in to make sure I'm not missing something obvious. Workspaces can be useful for assembling multiple ships in a series or multiple ships intended to be used together (although the vessel naming system needs a serious overhaul to allow it to work at its full potential), but for standalone ships, which is, at least for early game, most of the ships you will be using, you will want one workspace per ship. In KSP 1, I build my ship, title it, and save it. If I change something after it, I'll press save at least once, maybe a few times because I'm paranoid like that. In KSP 2 I open up a new workspace. I build my ship, give it a name in the top right hand corner. Then I press save. I get a menu. I have to then give the workspace a name, and press save a second time. If I make a change to the craft, I have to press the save icon, then press the save button, and then press "Yes I want to overwrite the design I'm currently editing" button. All these extra clicks are adding small amounts of frustration each time I have to click several times to do what took one click in KSP 1, am I missing something about how to use workspaces or is this a case of poor design?
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Parts & Vessels Parts inside fairing heating up
Ultimate Steve replied to GradientOGames's question in Parts & Vessels
Reported Version: v0.2.0 (latest) | Mods: none | Can replicate without mods? Yes OS: Windows 10 | CPU: AMD Ryzen 5 1400 | GPU: 1650 | RAM: 16gb When I place some parts, such as the RA-15 and RA-2 relay antennas inside a fairing, launching too fast through the atmosphere will still heat them even if the parts are inside a protective fairing. Here is the ship, the Solar Challenger 2, although I have experienced this bug with other ships. I attempted to fix it by mounting a heat shield in front of the antenna, but that did not work either. Once it gets going fast enough, the relay antenna starts to heat up despite being visibly inside the fairing. Heating up some more. And, gone. Visibly gone once the fairing has disappeared. This is a separate bug but if I go slow enough to prevent overheating, antennas and docking ports (and maybe other parts?) do not appear to radiate heat away and will stay nearly overheated for the rest of the flight. To reproduce, enclose an antenna in a fairing and go fast through the atmosphere. Included Attachments: .ipsImage { width: 900px !important; } -
Okay, that three week cadence lasted about as long as summer did, it is winter break now, so maybe I'll get another one or two out before it ends, but then, what a scary thought, I'll have no more breaks until I retire unless I can't get a job post graduation... That doesn't make me sad or anxious or scared at all! Anyway, finally: Chapter Three: The Gilded Planet
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totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
Good catch, I somehow saw the stage 2 analysis and misread it as stage 1 in my head, my bad. A mistake that bad is inexcusable, and I do indeed have no excuse, and it calls into question the rest of my analysis. I am aware of that, which is why I said that my first analysis was not valid past the first 30 seconds or so. In the second part of the analysis, the x and y accelerations are broken out and trigged together separately according to that graph and the current pitch angle. But yes, I did not really question the validity of that set of data, as the method I think they used to separate horizontal and vertical (finding vertical velocity by numerically deriving the altitude telemetry, using that and the total velocity to find horizontal velocity, and numerically deriving both to find both accelerations) is only as good as the available telemetry and timestep. Since we can see the accelerations change more or less in line with the mass flow and mixture ratio changes, I'm inclined to believe that the current numerical way is good enough on these timescales, but if the telemetry we have can't be trusted, then any conclusions based on it are little better than speculation. I also thought about the pitch angle method, I would have done that analysis above for the whole flight with a spreadsheet if that data was available, but I don't think pitch angle data is available unfortunately. -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
I had a big long thing typed out but then realized I had multiplied by the wrong number somewhere and had to restart. In short, I have a large number of problems with the assumptions you made, but Raptor is indeed not operating at 100 percent of its advertised thrust. I have more problems with your conclusions, but let's just walk through the re analysis for now. This analysis only covers stage 1. I initially went to the raw video but then downloaded the data used to make the graphs you used after I had to restart after I was confident they matched well enough. I added columns for acceleration, smoothed acceleration, and expected mass at that point given the linear decrease you would expect at full throttle (this is not a valid assumption beyond the first 30 seconds or so of flight as any off nominal throttle would cause the mass to diverge). This analysis also assumes vertical flight by adding 9.81 to the acceleration, this is also not a good assumption outside of the initial 30 seconds. I then made a column for the current thrust, and another column for the fraction of the expected thrust (throttle). From my own double checking, Raptor is producing at or above 90 percent of its advertised thrust for at least the first 30 seconds of flight . Spikiness is probably down to inconsistencies in the source video but I am not sure. Due to the assumptions mentioned earlier, ignore everything after 30 seconds or so, it is not valid. The ramp up at the beginning may either be due to my implementation of the smoothing filter, or possibly the original source data has had a smoothing filter applied to it. Telemetry might also have a lag of a few seconds. EDIT: This section has some good points, but argues against a strawman. I somehow misread his stage 2 analysis as a stage 1 analysis, this a monumentally stupid error and I have no idea how I didn't catch it. Keeping it in for the good bits, but Exoscientist did NOT calculate stage 1 as having burned from 80% to 5% of its fuel. You used this graph to estimate fuel flow rate: Which has the starting fuel capacities at 80 percent, which does not seem right at all. Per official SpaceX telemetry, this is the stage 1 fuel load at liftoff: That's not quite full, but that looks like a lot more than 80 percent to me. Plus measuring fuel levels can be tricky, I'm not 100% convinced that sensor is fully accurate, as we have no idea what type of sensor they are using, and measuring exact fullness of a fluid container that big probably doesn't have an easy solution. The person who made the plot you used also had this pointed out to them, realized their mistake and uploaded a new version on the reddit thread you linked (update upon further inspection, this is in your blog post, but you used the numbers from the false one): Your math in the expected fuel consumption of 23.1 tons appears correct given the assumptions you made. However, just simply by inspection, it cannot be running at this throttle level for the entire 150 second burn, as it would consume more than the 3400 tons of estimated propellant. Using your numbers of 80% and 5%, that is 75% of 3400 tons burned in 150 seconds, or 17 tons of propellant per second, as you found. Using the corrected graph, with what appears to be 95 percent to 10 percent drop, we get instead ~19.25 tons per second, implying 83% throttle average if we assume a linear relationship between thrust and mass flow rate. I will return to my discussion about the accuracy of this data and whatever sensors are providing it. If it is some sort of distance sensor, which measures the height of the fuel in the tanks, it is possible they printed the raw value instead of accounting for the tank geometry, and this value could also be affected by slosh and possibly pitch if drag is significant enough to cause an offset in the fuel level from horizontal. If the sensor is of that type and the raw value is used, the first and last 5 percent or so would hold much less fuel than the rest. There also might be zeroing differences. A "full" tank with 3400 tons of propellant needs some volume free for pressurant, and will not actually be 100% propellant, so on this type of sensor, a full tank might show up as 95% full or so. I also don't know the methodology of how this data was extracted from the X livestream, the small rounded bars at low resolution don't seem conducive to precise analysis. Is the true value at the tip of the )? Or at the base? Middle? This could give us an offset as well. If the bottom 5 percent holds half of what a normal 5 percent would, and the top 5 percent is pressurant by design, it then comes out to 21 tons per second or 91% throttle, but I wouldn't put any stock in this number either, there are simply too many things we don't know. But either way from this graph, if I am reading your blog post right, you saw a constant slope and assumed a constant throttle, and also assumed a linear relationship between mass flow rate and thrust, where when throttling engines in real life, you can only do that to a point, you can also vary the mixture ratio to increase or decrease exhaust velocity and throttle that way. But why are we even using that graph anyway when you posted this far better one on Reddit a while back? From this graph it is very clear that there are at least four, possibly five separate throttle regimes, and that the mixture ratio varies throughout the flight. The slopes are, well, not visibly different, but they are with a ruler up to the screen. I was unable to find how you got this graph, but I am going to assume it is from the same raw data as the other graph, just properly plotted. In that case, the same sensor biases could apply if they exist. In either case, we can see by the variations in slopes and differential slopes, we can see that Raptor is altering its throttle by altering both mass flow rate and mixture ratio, which makes this a very complicated problem to figure out its thrust at any point in flight from this information alone. The simple F = mdot(u9-u0) formula cannot be used here as we do not know the isp of Raptor at all of its different mixture ratios and mass flow rates. Fortunately, we also have the acceleration data which you also used: The first 30 seconds or so seems to more or less match what I found, so it can probably be trusted, although I'd love to double check how the pitch data was extracted given that we only had the low resolution indicator on the livestream. Especially for the tail end of stage 2, it could skew the results if that indicator is inertial to the vehicle or fixed to local up/down. I do see pretty obvious throttle changes on that graph, though, which correlate to the earlier fuel graph. So, what I see in general is a gradual throttle down to maintain a constant acceleration near max Q, and then either a gradual throttle up or holding at that throttle level (or some combination thereof). After this the throttle tapers off towards the end of the burn. Redoing your analysis at the marked yellow bars, horizontal acceleration is 11m/s^2 (at the marked point it does not look like 10 to me) and vertical acceleration is about 6m/s^2. Plus the 9.8, vertical becomes 15.8. This is at about 95 seconds, and the pitch of the vehicle at this point in the flight was about 57 degrees above the horizon. (although as I said earlier the accuracy of this pitch data is questionable) Doing some simple trig, we can estimate vertical from horizontal as 16.94m/s^2 or horizontal from vertical as 11.26m/s^2, so there's a bit of inaccuracy somewhere, as expected when rounding to whole numbers. Net Starship acceleration is either: Via pythagoras: 19.25 Trig given horizontal: 20.2 Trig given vertical: 18.84 Which are similar to, but generally higher than what you found. Now, as for the expected acceleration at this point in flight (T+95), there's about 42% propellant remaining. Taken naively as a fraction of the booster's 3400 tons of propellant, the stack has a mass of about 2928 tons at this point in the flight, and the expected acceleration is 25.43m/s^2 using the sea level thrust. As for a vacuum, you have fed the vacuum isp back through the F=mdot(u9-u0) equation assuming constant mdot, which may not be the case, as Raptor may prioritize to maximize isp in some situations and thrust in others, by varying mixture ratio and mass flow rate (as we saw above, it does do this), so this assumption is a bit flawed. The source for the 363s number is also a NSF article from 2014, so I would not take stock in that either. That was the 4.5MN version of Raptor, which had 321s at sea level. I've looked and I cannot find an up to date vacuum isp or vacuum thrust value for non vacuum raptor. If you do find one, please let me know. Assuming your number of ~30m/s^2 as the worst case, Raptor is producing somewhere between 63 and 80 percent thrust at this point in the mission. This is not really a good faith analysis though without good numbers for Raptor's vacuum stats, so a wide range is the best I can do. At its worst, though, this would indeed mean that Raptor is throttling down to possibly below 2/3 at this point in the mission. So, from the data, your analysis appears to say that Raptor operates at below 75% throttle for most or all of the flight, the wording is unclear. My analysis shows that Raptor does operate at at least 90 percent of advertised thrust for a significant amount of time, and throttles down a lot throughout the rest of the flight, including to values in the rough range of what you were saying. From that, you conclude: Which is quite the leap. In two mini paragraphs you take that, assume that throttle has a linear relationship between pressure ratio (I just passed a class over these exact equations, a clean obvious linear relationship is anything but the case), and conclude that: Raptor has a leaking problem big enough to warrant throttling down Throttling down would solve the leaking problems The observed throttling down is to solve the leaking problems This throttling down would drop the payload by 1/3 This change would increase refueling launches from 16 to 24 With no calculations. Especially the 1/3 payload drop, I want to know how you got that number. I do not understand how you can conclude this so confidently. I don't think we have enough information to conclude the reason behind the throttling, but off the top of my head, it could be any of these, likely some combination of many of them: Increasing isp at the expense of thrust For a reusable vehicle thrust is very important in the early stages of first phase flight. Raptor's design has been changed a lot for maximum thrust at the cost of isp in the past. The optimal engine changes with a lot of factors. It may be mathematically optimal to throttle in a certain way throughout the flight to alter isp and thrust to whatever is optimal at that time. Raptor has been observed making many changes to mixture ratio and mass flow rate throughout the flight Basically, the idea here is that Raptor operates in an inefficient but very powerful way early on, and then powers down somewhat to increase efficiency later on Maybe the numbers we have are wrong (in which case our baseline for 100% thrust is also wrong) Most mass numbers we have are conveniently rounded to the nearest 100 tons, this is not a lot of precision. Fuel and dry masses could be off by a lot. Has subcooling changed since the propellant numbers were first given? Raptor isp is always changing, there's no guarantee that 327s is the correct value, or that the raptors on the most recent booster were the version that had 327s Likewise, Raptor thrust is always changing. No guarantee that 230 tons is the correct value, or that the Raptors used were the 230 version. 230 could have been a dev value from when they were pushing it and not necessarily what they would set it to on any given launch. 230 could also be an "Emergency thrust" value or something like that. These numbers could also vary from engine to engine. Differences between non gimbaling and gimbaling raptors I have not seen this talked about, maybe they have different thrusts. Are they the same, just one without gimballing hardware? Or has the non gimballing version been pushed further due to less complexity? The non gimbaling one is I think called Raptor Boost, maybe those have the 230 thrust and the gimbaling ones have less. Maybe they have different isp. Maybe they have different other characteristics. Maybe they are throttled separately to optimize for any given time of flight. Could telemetry have been inaccurate? Later in flight, does telemetry analysis take into account reduced gravity both from altitude and centripetal acceleration from increased orbital velocity? Does drag play much of a role in reducing apparent acceleration? Throttling down for vibrational reasons Combination of engine vibrations and atmosphere based vibrations could cause problems in some areas Throttling down for structural reasons Does not explain why throttle is so low so much earlier Does explain further throttling towards the end of the flight Throttling down for aerodynamic reasons Starship is pretty aerodynamically weird with the grid fins, chines, and body flaps, it may have different requirements than normal vehicles Max Q throttling as per usual Is this normal? Is this even a throttle down? Well, obviously the throttle is decreasing for some reason This could be the correct throttle profile for whatever reason, the one they think they can get 150 tons from This throttle down is not necessarily associated with a payload cut and likewise an increase in refueling launch count If this is not normal, is this permanent? There are many prototypes until Artemis, the throttle cut cannot be assumed to be a permanent feature (or a temporary one) The design is constantly evolving, SpaceX is not the type of company that sees a problem and just lets it sit there, they will keep tweaking and changing Raptor until they are happy with it. NASA still seems to be happy with progress from what I've gleaned in recent statements, although this is the public facing side of things and should be taken with a grain of salt Engine problems Engines could leak Engines could have been de rated mid flight by the flight computer due to off nominal signals Systemic engine problems could merit a reduction in target thrust by 10% for early flights And I suppose that it is possible that despite working fine for 30 seconds at 90% throttle, 60-70% was deemed the safe maximum for the rest of the flight, and that 100% all the time was the baseline for 150 tons to orbit. I don't think it is a good idea to blame any one thing (let alone the worst thing) and then extrapolate that to the program as a whole. Most of those bullet points are easily more effort to analyze than I put in to this semester entirely, and many we don't have data for. -
I think the postcards are cool regardless of who does them. I think it's an excellent outreach program. Like a couple levels above the send your name to space thing. Granted I am somewhat biased, as I do have a space postcard of my own hanging up in my bedroom.
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totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
How would it land then with just the vactors? -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
Granted this is from a long time ago and is pulled off of reddit, so accuracy is dubious, but should be in the right ballpark. Non subcooled Lox is 1141 kg/m3, which comes out to 16.6 tons. Non subcooled methane is 8.63kg/m3, so about 8.63 tons. -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
The 33 don't count for this analysis, this is just about restarting in flight, which is a significantly different environment than ground start. -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
All 33 don't need to restart, though, I think it is just the ring of 10. Current slightly educated speculation points to an issue with the dynamics of the fuel feed system and not with raptor itself. Some of the support for this is that one of the engines that stayed lit the whole time also failed. A review of the video shows that 9 of the 10 did reignite successfully, just something catastrophic happened over the next 20 seconds. -
totm dec 2023 Artemis Discussion Thread
Ultimate Steve replied to Nightside's topic in Science & Spaceflight
Gateway has grown on me. It's engineering benefits are questionable, but I've gradually learned the lesson that in this era, cost and engineering aren't what you need to optimize for. The best most cost effective program is going nowhere if you don't have political support, and even if it does its not going to go on for very long. For better or worse, support is the thing to optimize for these days. Artemis is very very good at this. It's gotten legacy contractors, new contractors, democrats, republicans, Canada, Japan, ESA, and many others all behind a Lunar program and Gateway is a wonderful part of that, both as sunk cost infrastructure to point to and a relatively easy place for contractor or international participation. A pit stop in NRHO is a small price to pay if it means that a semi sustainable Lunar program actually happens instead of being cancelled. -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
Given that we are talking about solar's flaws... This is definitely a tangential comment, but when discussing space based solar, something that isn't talked about often enough is that it gets rid of solar's biggest disadvantage, which is that it can't act as a baseload power source. There are no no clouds in space, there is no snow in space, there is (almost) no night in space (high orbit), you aren't tied to a peak at a certain time of day, and in the event of overproduction you can either rotate the satellite slightly or beam the excess into deep space. Granted, there's still a bajillion other problems with space based solar, of which the biggest is probably economic, but a guy can dream! -
Many months in the making, a new grand tour record jointly designed and flown by @camacju and myself! Music video: Technical details video: Almost 4 tons lighter than the previous record, and we thought of nearly a ton of optimizations during the time it took to fly, so 6.8 is definitely possible. I'm not sure how far this optimization can continue, but I have a hunch that enough stuff will be discovered to make 6 tons a reality some day. Edit: Silly me, forgot the exact mass. 7719kg with Bill, 7673 (or maybe 7674 depending on how it is rounded?) without Bill.
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totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
It is also possible that the published timeline accounted for some number of expected engine outs. I don't think this would be the case, but it is possible. -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
I can't wait until Starship deploys a Starlink, then this silly suborbital vs. Atmospheric unstable orbit vs. Orbit debate can end. -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
Not that surprising, iirc the FTS is mainly intended to unzip the tanks to disperse the propellants, stop the vehicle from producing thrust, and create a small boom in the air instead of a big one on the ground. The front would likely survive this and I don't think it necessarily has to be a problem. -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
SECO! -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
5 minutes. See yall on the other side of this! Although it may take longer, apparently they are still working a few boats. Might hold at T-40. -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
Confirmation that hot staging is all 6 engines, not what I expected. Spicy! -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
Another thought, subcooling the propellants (I forget if starship does this or not) could provide a buffer against boiloff. Propellant seems to have an average of about 2kJ/kg K of heat capacity. At 100 tons per mission, that's 200MJ of free ish cooling per Kelvin. If everything is subcooled by 5K, that's a gigajoule. At the 36300ish watts of heating I calculated above, that is about seven to eight hours of boiloff buffer. Not much given that we were talking about days between flights, but enough to be significant. -
totm nov 2023 SpaceX Discussion Thread
Ultimate Steve replied to Skylon's topic in Science & Spaceflight
Envelope math time. Let's go worst case scenario here. Starship radiates no heat, reflects no heat, and has 500 square meters of area exposed to the sun. 1380W/m2 hits Starship from the sun, for a total of 690000W. The latent heat of vaporization of oxygen is 214,000J/kg, and Methane is 510,000J/kg. Oxidizer to fuel ratio is roughly 3.5, so average latent heat of vaporization is ~280,000J/kg. In this scenario where zero mitigation is taken and all of the heat hitting Starship goes towards boiling off the propellants, Starship loses about 2.5 kilograms per second. It will spend ~60% of its time in sunlight (probably a bit high, but again, worst case scenario), so a whole 129.6 tons of propellant is lost from Starship per day. Starship would have to launch nearly one refueling flight per day just to keep up with the losses, in the optimistic 150 tons to orbit reusable config (about the higher end of what has been estimated for reusable mode). This is obviously not a realistic scenario, but it highlights how conservative assumptions can lead to large estimates. Stainless steel has something like an albedo of 0.6 (60 percent reflected, 40 percent absorbed), and with the nose facing the sun at all times, the exposed surface area is about 64 square meters. This decreases the incoming power to around 36000W. Starship will also naturally radiate some heat away. LOX is about 54K, CH4 is around 90K, some of the ship isn't up against cryogens at all, but I will assume the ship's skin is at an average of 60K, conservatively low. Stainless steel's emissivity, I'm finding a large range, let's go for something conservatively low at 0.55 (values up to 0.85 are reported). Starship's surface area is about 1500m^2, it should be higher probably, but again, conservatively low. Plugging those into the Stefan-Boltzmann equation gives a radiative flux of, uh, about 600W. Not great. Radiative flux scales with temperature to the fourth power, but we still won't get nearly enough flux even raising the entire skin temperature to 110K, the upper end of methane boiling temperatures. One thing that could be done is to have a double hull for the nose cone, which is pointing towards the sun here, which is moderately well insulated from the rest of the tanks. This could even be done by just having the nose cone empty as with a normal non depot starship. The interior would be coated to reduce interior radiation transfer. This would allow the, worst case scenario, 64 square meter circle to get much hotter than the rest of the ship and radiate more effectively. The nose is conical, but I'm not sure how to do the math on that, so I'm going to take the volume of an equivalent sphere (should be roughly equal to that of a half sphere stretched by a factor of 2, but not exact). This gives a surface area of about 250 square meters. To offset the rest of the flux from solar heating, the nose would have to rise to about 260-270K. Conduction to the rear of the ship over the surface area of the very thin tank walls (let's be extremely generous and assume 5 centimeters thick taking into account internal radiation bypassing the nose shield and stringers and such) (surface area ~1.4 square meters) (90K CH4 tank immediately behind 270K nose cone) will be calculated also. The section between the tank and the nose is, what, 10 meters long on an unmodified non depot starship? The depot one may be different but the extra length helps us here. Heat getting to the fuel is now 369W, and as we found earlier, Starship radiates about 600W by itself. Even assuming it doesn't, we have reduced the boiloff, in theory, to 114kg/day. Even if I'm off by a factor of 10, just by pointing Starship in the right direction, with not that much modification, that's like a ton of fuel per day, which is well manageable. Unfortunately, it isn't that simple because the Earth is reflecting and radiating heat as well. This ends up totaling roughly 345W/m2 averaged over night and day at the surface, as the Earth is (mostly) in equilibrium, and has four times as much surface area as it does cross sectional area. If Starship is 400km up, this decreases slightly to about 305W/m2, although the atmosphere is further out than the surface so it will be a bit higher than that. Now we get into the wonderful world of materials having different reflectivities and emissivities for different wavelengths, and I'm going to handwave this and say everything is the same as it is coming from the sun. Starship is pointing at the sun, so can't really control its Earthwise orientation. Averaged over the orbit, I'm going to assume an average Earth facing cross sectional area of 300 square meters (450 is the max, 64 is the minimum, approximately at least, this whole post is filled with approximations). With the same albedo of 0.6, Starship will receive an average of 36,600W from the Earth. Due to our solar mitigations, assuming they actually work, the Earth radiation now dominates and is much more difficult to protect against. It is possible the heat shield has better radiative characteristics and could be oriented towards Earth for maximum effect, but the depot probably won't have a heat shield... It could have some other thermal protection in its place, though. This is beyond the scope of my analysis. Total power reaching the fuel is roughly 36,600-600+370 = 36,370W. This is about 0.13kg/s, or 11.2 tons per day. Not great. If we conservatively estimate 100 tons of propellant per trip, and a full load of 1300 tons required, that is 13 trips for the principal, and then 1 more trip for every 9 days it takes. If we assume two ships per week, or one ship every two weeks from each of the four pads, that is a total of 22 refueling launches over the course of 77 days if I did the math right. Keep in mind that this is all an extremely rough approximation, but it shows how upper teens could be a realistic number. High ones could also be realistic if the assumptions on capacity, flight rate, load needed, and thermal protection were changed. We simply don't know enough. If my calculations are correct, and Earth heating is the driving force, deep space boiloff should be incredibly minor. Unfortunately this means pointing the crew compartment at the sun, which is explicitly what they talk about not doing for Mars.