PakledHostage

Or not... It was probably too obvious to say that the remaining optimisation can be realised by tweaking the ascent profile. But I\'m afraid that the mathematics of 'gnarly optimal control theory' are beyond me so my only remaining approach to optimising the ascent profile is through experimentation. Looking at jqhullekes\' video again, I see that he is more precise with his orbit insertion burn than I am. Even so, I am getting close to his results. I will give my pilot some training and give him another go. In the mean time, I hope one of the experts out there will take on solving this problem analytically.

Done. I usually do it by method ( and it looks to me like jphullekes does too in his video. His initial apoapsis at MECO1 is above 73 km but his periapsis has decayed into the 72 km range when he\'s finished his orbit insertion burn. I\'ve tried (a) and © without seeing any improvement. I have a sense that the 'curvature' of the ascent trajectory between pitchover and orbit insertion burn is critical to realising the final few kg of improvements that are possible for this rocket.

Nice work! How did you pick the initial conditions for the orbits? Does Minmus\' orbit change noticeably if you use slightly different initial conditions?

Check out the Optimal Ascent Profile for this spacecraft challenge. That rocket can easily get you into a 75 km circular orbit. From there, it only takes about 70-80 m/s Delta-V to get up into a 120 km circular orbit. The guys on the challenge\'s leaderboard are reaching the 75 km circular orbit with about 400 m/s Delta-V to spare. Plenty for your purposes. And while the pitchover altitude and angle will probably vary from rocket design to rocket design (the jury\'s still out on this point), the optimal pitchover altitude for the rocket in the challenge seems to be somewhere between 7500 m and 10000 m. There\'s a good video that was put together by jqhullekes that shows the challenge rocket reaching orbit with near record remaining fuel levels.

Here\'s a plot that might help: It was created by launching a rocket sonde to 80km, recording temperature, pressure and density along the way using a sensor plugin. Specifically: dAtmosphericPressure = FlightGlobals.getStaticPressure(); dAtmophericDensity = FlightGlobals.getAtmDensity(dAtmosphericPressure); dExternalTemperature = vessel.flightIntegrator.getExternalTemperature(); Density is 1.2 x e ^(alt/-5000) Pressure is 1.0 x e ^(alt/-5000) The complicating factor is that the aerodynamic drag model in the game doesn\'t use \'q\' in the normal way. The game\'s drag equation has an extraneous mass term and there also seems to be an extra density scaling factor of 0.0008 that gets applied to the density equation I\'ve quoted above. Check out the Mini Challenge: Max Altitude with this supplied spacecraft challenge and the Kerbal Science: The atmosphere of Kerbin thread for details. People like Closette, Kosmo-not and The_Duck seem to be the authorities on this.

Nice flying! I tried a bunch of launches last night and got to the point where I can reliably get into orbit with about 87 kg fuel remaining, but I wasn\'t able to beat your or Tarmenius\' efforts. My results are probably still useful when compared to yours, though. I have been starting my pitchover into a gravity turn about 2500 m higher than you do; I\'m probably on the other side of optimal. I\'ll try again this evening with your method.

Thank you for posting the link to the NASA PowerPoint slides. Plasma physics, high temperature gas dynamics and even heat transfer are well outside my expertise. But as so often happens, KSP has lead me down the rabbit hole and I\'m enjoying learning something new. The 15 km/s figure comes from a textbook chapter titled Returning from Space:Re-entry, but I don\'t know the title of the book and I can\'t find links to the rest of the chapters on the FAA website where I found this reference. Even so, there is some very good information there about re-entry heat and the physics of re-entry. Some of it would probably even be useful for refining a re-entry model so that it works well for both capsules and space planes. The textbook says on page 4.1.7-322: 'Convection is the primary means of heat transfer to a vehicle entering Earth’s atmosphere at speeds under about 15,000 m/s. (For a re-entry to Mars or some other planet with a different type of atmosphere, this speed will vary.)' I don\'t know why the 15000 m/s value is significant and why it would be different on Mars, but that will be my next mystery to investigate.

It is a fair point and I appreciate the discussion about radiative heat transfer, but I wonder if we’re not barking up the wrong tree? I did some more reading this evening and it seems that the black tiles on the bottom of the Space Shuttle were designed to maximise radiative heat transfer rather than minimise it. They have an emissivity of 0.8 because they are designed to dissipate heat by radiation during re-entry. Maybe someone with some expertise on the shuttle TPS would like to comment? Also, I read this evening that radiative heating isn’t a significant factor for objects entering Earth’s atmosphere until speeds exceed about 15 000 m/sec. That would seem to validate your concerns about extremely high speed atmospheric entries, N2maniac, but I wonder if it is really a significant enough effect at typical KSP entry speeds that we need to ask that Squad add it to the game?

Thanks! I\'m using the unmolested values out of the game engine. I retrieve them using: dAtmosphericPressure = FlightGlobals.getStaticPressure(); dAtmophericDensity = FlightGlobals.getAtmDensity(dAtmosphericPressure); Good point. The temperature of the shock layer reached a peak of about 2500 K for this re-entry. I will look at the influence of radiation for temperatures in that range. That being said, I did some more reading this evening and it seems that radiative heat transfer only becomes important for Earth atmospheric entries when speeds exceed 15 km/s. I read that a useful rule of thumb for estimating peak shock layer temperatures (in degrees Kelvin) during Earth re-entry is to use the magnitude of the re-entry speed in m/s. In this case, the re-entry speed is about 2200 m/s (relative to the surface), and the peak shock layer temperature is 2500 K. We\'re at least in the right ballpark... One option may be to apply the re-entry heat to the forward most components in the stack during re-entry. If the forward most components (i.e. the ones oriented within some tolerance of the prograde direction) can handle the heat, then nothing happens. If they can\'t, then the spacecraft blows up. If it were done that way, then a heat-shield component could be added at the base of the pod, much like in Vostok\'s excellent suggestion over in the KSP development section. It should be fairly easy to determine whether the heat shield component is facing within some tolerance of prograde during re-entry.

The guys at Squad may already have an idea for how they’re going to implement re-entry heating in the game, but the Kerbal Science: The atmosphere of Kerbin thread got me thinking about re-entry and how it could be implemented. I thought I’d take a stab at it myself. And while I realise that I may have gone off the deep end a bit with this little project, it turned out to be kind of fun. I’d be interested to hear other forum member’s feedback about it. Accurate modelling of re-entry dynamics is extremely complex and would require (at a minimum) the use of computational fluid dynamics. That obviously isn’t going to be done in a game. Instead, I would think that a method would have to be found that would have low computational overhead, yet still maintain some physical significance. Having looked through some papers on the subject and dusted off an old textbook or two, I came up with what I think would be a good model. It is based on the assumption that a re-entry vehicle forms a detached supersonic shock, and that the shock stays detached all the way down to trans-sonic speeds. Example I recorded telemetry data for a capsule re-entering Kerbin’s atmosphere and then used the equations in the 'Background' section below to estimate the air temperatures that the capsule would have experienced during re-entry. In my test, the 1.45 tonne chute/pod/sensor assembly was placed into a 1 km x 85 km orbit for re-entry. The 1 km periapsis resulted in a fairly shallow re-entry trajectory and a maximum g-loading of 4 g’s. Even so, the pod would have experienced an extreme environment during that re-entry. Initial mach numbers during my spacecraft’s re-entry approached Mach 8. This high Mach number results in very high temperatures inside the spacecraft’s supersonic shock, but little heating would have occurred during this part of the re-entry because the air is still too thin to transfer much heat. Although shock layer temperatures outside the spacecraft approach 2500 K during the early part of the re-entry, the spacecraft’s temperature wouldn’t have started to rise significantly until 50 km altitude. Maximum heating occurs between 40 km and 30 km altitude, and the maximum spacecraft temperature of 1800 K occurs at 26 km altitude. Our intrepid Kerbals were still moving at about Mach 5.4 at that time. The spacecraft then rapidly cools to equal the static air temperature by the time it reaches about 8000 m. In calculating the data plotted in this example, I picked values of K1 and Cp that made the spacecraft temperature data “look rightâ€. These would have to be experimented with in the game to get the desired behaviour. As stated in the 'Background' section below, K1 would be hard coded in the game, while Cp could be a parameter in each part’s part.cfg file that could be adjusted to account for whether or not a part is, for example, a heat shielded part. I’ve included some additional plots below. Background The spacecraft begins re-entry with both kinetic and potential energy which is dissipated during the descent. The orbital energy is dissipated in chemical energy, light energy, atmospheric kinetic energy, sound energy, heat energy, etc. Some of the energy also heats the spacecraft itself. Calculating the amount that it heats the spacecraft is what I’m focused on. That heating is dependent on the external air temperatures (shock layer temperatures) surrounding the spacecraft during re-entry. Fortunately, there’s a relatively simple equation that could be used to simulate the temperatures that the spacecraft is exposed to during re-entry. It takes advantage of the fact that a detached supersonic shock (normal shock) forms ahead of the spacecraft as it re-enters. The temperature rise through a normal shock in an ideal gas is approximately given by: (1) Where M is the Mach number, T1 is the temperature from the in-game atmospheric temperature profile and gamma is the heat capacity ratio of the ideal gas that the shock forms within. If we assume that Kerbin’s atmosphere is an ideal gas1 with heat capacity ratio gamma = 1.4, then the above equation reduces to: (2) Similarly, if Kerbin’s atmosphere is an ideal gas, then the speed of sound is just (3) And while Equation (2) is increasingly inaccurate at high Mach numbers because the heat capacity ratio gamma cannot be assumed to be constant, we’ve got to remember that this is just a game! If we take these liberties, then calculating Mach number and shock layer temperatures that the spacecraft is exposed to during re-entry is trivial. All that remains, then, is to approximate how much heating occurs as a result of the temperature that the re-entry vehicle is exposed to. The spacecraft is heated during re-entry by forced convection. Heat transfer due to forced convection can be modelled according to equation (4) below. (4) Where h is the heat transfer coefficient, A is a representative area, T2(t) is the current air temperature from equation (2) above, and Tcraft is the current spacecraft surface temperature. The heat transfer coefficient “h†is a function of atmospheric viscosity, density, heat capacity, thermal conductivity, as well as the spacecraft’s geometry and the airspeed. Of these variables, the one that experiences the greatest variation throughout the re-entry is density. In fact, density experiences several orders of magnitude more variation than all of the other parameters, even when considering conditions inside the detached supersonic shock. As a result, for the purposes of an in-game re-entry heating model, equation (5) could be used to estimate the convective heat transfer coefficient. (5) Equation (5) is derived from the definition of h for laminar forced convection. Well designed re-entry vehicles maintain laminar flow over large areas because this results in lower heat transfer rates. In the laminar flow case, h is a function of the square root of the Reynolds number. Reynolds number is, in turn, a function of the fluid density, viscosity, velocity and a characteristic length. Early in the re-entry, where densities are very low, Reynolds numbers are low enough that laminar flow is relatively easy to maintain. K1 in Equation (5) is a constant chosen to give desirable qualities to the game’s re-entry heating model. Equation (4) can be combined with Equation (5) to give Equation (6) (6) And the result from Equation (6) can be used in Equation (7) below to iteratively calculate the spacecraft’s temperature at any time during the re-entry (if we assume a uniform temperature distribution within the spacecraft part). (7) Where Cp is the spacecraft part’s specific heat and m is the spacecraft part’s mass. Both of these values would come from the part’s part.cfg file. Summary This method is based on the assumption that the re-entry vehicle forms a detached supersonic shock, and that the shock stays detached all the way down to trans-sonic speeds. This may not be a valid assumption for some configurations (i.e. space planes), but it may still be “good enoughâ€. And while some of the equations above may 'look ugly', they really aren\'t that bad. I calculated the values plotted in this post using just an Excel spreadsheet. The method can also be 'tuned' to give desirable heating response by adjusting one or two parameters. As a result, it is also easily adjusted to yield different atmospheric heating characteristics for different planets. Anyway, as I said above, the guys at Squad may already have an idea for how they’re going to implement re-entry heating in the game but I found putting this post together to be a fun exercise. I’d be interested to hear other forum member’s comments about it. I hope some of it is useful. 1 Kerbin’s atmosphere cannot be an ideal gas given its current pressure, density and temperature distribution. This is very easy to fix however. The pressure distribution needs only to be re-defined as Defining pressure in terms of this equation results in the “Kerbin Standard Atmosphere†shown in the plot below. The difference in pressure distribution is slight. Would this affect anything other than the altitude at which the chute opens?

Here are two more Mun maps: (Ref: Kerbin Geographic Society)

MechJeb fears you the way us mortals fear Chuck Norris!

My gut tells me that it will depend on the thrust-to-mass ratio of the stack. Rockets with lower ratios will probably do better with a longer vertical ascent phase. There\'s also the added complexity that modulating the throttle will help on rockets that have high thrust-to-mass ratios. (Ref. Mini Challenge: Max Altitude with this supplied spacecraft) I\'ve been wrong plenty of times before, though... Let us know what you find out?

Awesome! Interesting that at least one of the human pilots is still doing better than MechJeb. I\'ll have to try again myself over the weekend. I\'ve updated the leaderboard.

What happens if you turn off the SAS/ASAS? I\'ve only ever encountered 'spinning wildly' once while in Kerbol orbit, and that was when I had a SAS on my spacecraft. I was able to stop the spinning by turning the SAS off and controlling manually. In my case, the controls were reversed in one hemisphere of the navball, but not in the other. The SAS couldn\'t handle that and caused the ship to spin wildly. It took a fair bit of luck to get it back under control, but I was able to control fine once I had it gathered back up. I mention it because I get the sense that it is more common to use SAS or ASAS, than not to. Maybe the common thread is what I experienced? I\'ve flown countless missions into Kerbol orbit, and I\'ve only ever encountered the Kraken the one time I had a SAS installed. And if SAS isn\'t the common thread, then maybe there\'s more than one bug... Kraken and Kraken Jr?

Nice job! I\'ll update the leader board. I guess that means you started your pitchover manoeuvre at about 1500-2000 m? I started mine at what works out to about 11000 m. I also tried pitching over to start a gravity turn at relatively low altitude (~5000 m) and pitching over very high (~30000 m). The 5000 m test got me close to your result while the 30000m test failed to even reach orbit. There\'s an optimal pitchover altitude/angle between those extremes; I suspect we can get close to it by experimenting.

No problem. Let\'s sacrifice some Kerbals for science! I\'ve updated the challenge above to use your design and I\'ve flown one attempt myself. That effort reached a 75.3 km x 75.7 km orbit with 84.2 kg of fuel remaining. It did not use MechJeb. I\'m interested to see what can be done with this configuration, both with and without MechJeb! Prior to launch, I switched to “orbital speed mode†on the navball by clicking on the speed readout. The prograde reticle then showed the orbital velocity vector rather than the “surface†velocity vector. After launching, I climbed vertically at 100% throttle until the prograde reticle was centred on the navball’s 60 degrees latitude line. I then pitched over and performed a gravity turn, still buring at 100% throttle. MECO1 occurred when my apoapsis reached 75 km in the map view. Orbit insertion burn was completed at close to 100% throttle, but a few trim manoeuvres were also required to circularise my orbit.

I obviously missed that one... But it seems to be a MechJeb only challenge. I\'ll leave this challenge up for a bit though in case someone wants to take it on. I think testing this configuration has value because it seeks insight into the Ascent paths discussion currently going on over in the general discussion area. Presumably it isolates the variable of pitchover altitude, but I could turn out to be wrong. If anyone wants to suggest an alternate test configuration, please feel free.

I have been meaning to post a challenge that would help us learn something about this topic for quite some time. I finally decided to take the plunge since there seems to be some interest in this thread. Please have a look at the Optimal Ascent Profile for this spacecraft challenge and give it a try.

Because I didn\'t know you could do that! Thanks for the heads up. I\'ll modify my post.

Certainly everyone who\'s played KSP for a while has, at some time, wondered how efficiently they\'re reaching orbit. You too must have wondered: 'Could I use less fuel if I pitched over sooner or later than I normally do?', or 'What if I modulated my throttle on the way to orbit?' And while the optimal ascent profile differs from rocket design to rocket design, I\'d like to propose an efficiency challenge where we compare apples to apples. Maybe we’ll all learn something? We certainly all learned a lot from Closette’s max Altitude with this supplied spacecraft challenge. This is what I came up with: Reach a 75.5 km (± 0.5 km) circular orbit with this spacecraft, using minimal fuel Method - Build a stock rocket using a MK-1 pod, ASAS, 3 liquid fuel tanks, 4 AV-R8 winglets and an LV-T30 liquid fuel engine. - Launch into a 75.5 km altitude (± 0.5 km) circular orbit - After reaching orbit, right-click on the lowest tank in the stack to bring up a window showing how much fuel you\'ve got left. - Post a screenshot showing your craft in orbit, with the fuel quantity window showing. Mods: None Restrictions: We’ll need to have two categories – MechJeb assisted and pure stock. Craft File: The .craft file is attached to this post. Please describe your method of reaching orbit along with your entry. LEADERBOARD (Unassisted) 1. jqhullekes - 89.5 kg remaining (Delta-V expended: ~4340 m/s) 2. tjoreilly - 89.4 kg remaining (Delta-V expended: ~4340 m/s) 3. Tarmenius - 88.7 kg remaining (Delta-V expended: ~4343 m/s) 4. PakledHostage - 84.2 kg remaining (Delta-V expended: ~4364 m/s) 5. Closette - 82.1 kg remaining (Delta-V expended: ~4374 m/s) 6. 7. 8. 9. 10. LEADERBOARD (MechJeb Assited)1 1. stucker - 87.3 kg remaining (Delta-V expended: ~4350 m/s) 2. Cryphonus - 85.5 kg remaining (Delta-V expended: ~4358 m/s) 3. Tarmenius - 85.1 kg remaining (Delta-V expended: ~4360 m/s) 4. Zephram Kerman - 84.7 kg remaining (Delta-V expended: ~4362 m/s) 5. Cruisix - 71.4 kg remaining (Delta-V expended: ~4424 m/s) 6. 7. 8. 9. 10. 1 There is already a similar challenge to this one for pilots who prefer to use MechJeb, but I\'m including a category here in case anyone wants to submit an entry.

The separate pressure data comes from a cheesy little data logger module that I wrote to fly aboard my spacecraft. It records parameters like pressure, density, speed, altitude, lat, lon (and now temperature, thanks to CaptainArbitrary) into a .csv file. I\'ve attached the data that I used to make the plots earlier in this thread, below. Using Excel to fit an exponential trend line to the pressure data, I get exactly the equation you quoted for density, while the equation for density is 1.2223 exp(-alt(m)/5000). While I don\'t know anything about MechJeb, I have used your density equation in my aerobraking/re-entry model with amazingly accurate results, so I know it is correct. The only way I can explain the discrepancy between the data that I recorded with my rocket sonde and the and the work you and Kosmo-not, et al, did in the max altitude with this supplied spacecraft thread, is that the drag equation is worse than we thought. It must be using pressure rather than density to calculate drag.

But that was kinda my point. The speed of sound in an ideal gas (which air nicely approximates) is a function of gamma, R and temperature. But Kerbin\'s atmosphere doesn\'t appear to be an ideal gas... Anyway, I agree about the game. It is fun to do and discuss sciencey stuff like this but let’s not get hung up on the details.

I think this will be difficult because it seems that Kerbin\'s atmosphere cannot be approximated as an ideal gas. I plotted pressure and density vs. altitude from sea-level through 15000 m below: Please just ignore the lack of units... This is raw data sampled directly from the game using a data recorder plugin. I then used CaptainArbitrary\'s temperature data to compute the ideal gas constant ® for Kerbin\'s atmosphere. If Kerbin\'s atmosphere were an ideal gas, then R should be constant. Unfortunately it isn\'t: The percentage of variation of R with temperature, pressure and density can be reduced by increasing the offset of the temperature scale from absolute zero, but I don\'t like this as an explanation. I\'d be interested to hear people\'s theories about why Kerbin\'s atmosphere doesn\'t behave as an ideal gas.

I guess Squad is trying to implement a thermosphere at the upper reaches of Kerbin\'s atmosphere. Once again, I’m impressed by their attention to detail! If you guys are interested, I found a short article about the Earth\'s thermosphere. There\'s a bit of an explanation there about what is going on here on Earth: I knew from my familiarity with the standard atmosphere that temperatures up there are extreme, but I didn\'t ever stop to investigate why. I\'ll have to read more about this when I get some time.