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I've been constructing a custom solar system lately, and being the math geek I am, I decided to try and create a Dv map for my system. The only problem being that I have no clue what I'm doing. I can't even seem to recreate the numbers I see on Dv maps for the stock game. I know that I should consider the Vis-Viva equation and assume everything's co-planar and perfectly circular but is there something I'm missing? I would also like to discuss about any other formulas, such as which would yield the most effective results. I would really appreciate it if somebody could enlighten me on this subject. It would also help other system-builders with their work.

So, for reasons, I'm trying to get a probe to Eve as quickly as I reasonably can, for certain definitions of "reasonable" -- and decided the way to figure this out was to start with the basic kinematics equation of .5at2+vt+d and do a lot of algebra starting with the conceit that we want the acceleration portion to equal d. This resulted in just deriving the brachistochrone equation like a doof: (total trip t = 2*sqrt(d/a), total dv = 2*sqrt(da)) Throw in the min distance from Kerbin to Eve being 3,668,900km, pick a comfortable acceleration, and there's the dv and burn time. However, that's assuming crazy things like instant re-orientation, and for a = 1m/s, leads to a 22 tonne ion craft I already have around but also a pair of 16.8hr burns. I could just make everything bigger to burn harder for less time, but that could make the lower stages get a bit out of hand. So, we come to realm of having a coasting phase, which highlights the fact that the brachistochrone equation is a special case of a more general equation, and we've just set coast time to zero. As such, instead of d being just a*t2/2, which was convenient, now it's a*ta2/2 + vmaxtcoast where ttotal = ta+tcoast and vmax= roughly(a*ta). I think I can maybe constrain it with a chosen ta -- say, 10hrs (I can handle a pair of 5 hour burns over a weekend), and a vaguely acceptable acceleration rate, say, 1m/s again, for ease. So to solve for the times, we substitute a*ta for vmax and ttotal-ta for tcoast a*ta2/2 + a*ta * (ttotal-ta) = d => (d-a*ta2/2)/a*ta = ttotal-ta => d/a*ta-ta/2 = ttotal - ta => ttotal = d/a*ta + ta/2 This gives us 1m/s2*(36ks)2/2 + 36km/s*(ttotal-36ks) = 648Mm + 36km/s*(ttotal-36ks) = 3668.9Mm => 3020.9Mm/36km/s = ttotal-36ks = 83913.89ks => ttotal = not much more...that kinda gets overwhelmed by coast time...of over 23 thousand hours. I might not've done that right. I blame it being after 2:30. Any thoughts/corrections?

If a spacecraft is travelling in a circular orbit around a planet with a gravitational parameter of G at radius R1, and wishes to make a 90 degree planes change to a circular orbit of R2, what is the optimal burn strategy? For example, a simple inclination burn followed by a circularization burn might be correct. If the gravity is very high, it might be correct to push the orbit far away from the planet do the plane change, and then come back. Since there are two burns, there are opportunities to spread the inclination change across both burns. How can an optimal split be made?

When selecting (non-wheeled) landing gear, how are you solving this problem: Given a landing mass, gravity, and anticipated impact speed: What is the correct gear count, type, spring strength, and dampening strength? I am using experience/guesswork to make my choices now, so answers in that ballpark won't help much. Looking for the mathematics behind the parts, or experimental results someone has collected.

So working on the XenonStorm Mk3's fuel pod design has once again lead me to an old question: "Given a bunch of drop tanks of equal mass and a certain overhead per stage in the form of decouplers (whose presence in upper stages negatively affect all stages below), how many stages before decoupler mass starts really getting in the way, and how many tanks should be in each stage?" Absent decoupler mass, the clear answer is purge dry mass at every opportunity, staging early and often, however, decouplers do have mass, and in the case of my fuel pod, over 1/10 the mass of an empty tank. Also, if later stages are too large, the dry mass can damage the mass ratio more than it would on an earlier stage. To explore the problem further, I built a silly spreadsheet, here dealing with 100 tanks across 10 stages: I put a few important quantities here and there, notably the full and empty numbers for my fuel tanks, decoupler mass (stack decoupler), thrust, Isp, g, and the mass of the ship itself as the ultimate payload. "excess ratio" comes about because when the same engines are used all the way, it's the ln(wet/dry) part of things that makes the delta-v happen, so I took the mass ratio of each stage and subtracted 1 to make them more easy to compare, and allow them to be summed in a way that wouldn't be affected by the number of stages. The fuel pod's actually 7 stacks of tanks stuck on the back of a 1.25-2.5m adapter plate, but for simplicity I've chosen to study the case of 1 long string of xenon tanks with decouplers in experimental locations. A bit of experimentation bore some odd results -- running with the 100 tank concept, I first tried to keep all stages about equal in mass ratio and thus delta-v, winding up with 3/4/5/6/9/11/14/17/23 yielding a sum exccess ratio of 1.1623 and a delta-v of 45.3km/s, as seen above. Reversing this pattern (on the stage early and often concept) gave 1.1612 and 42km/s, supporting the too much dry mass in a late stage argument. Trying something odd, I tested 10/10/10/10/10/10/10/10/10/10, getting 1.1726 and 44.78km/s. I was expecting that to be worse, but very confusingly, the mass ratio sum is better than the even dv split distribution while the delta-v is worse. I'm no longer sure that the sum of the mass ratios really means that much...that or I messed up a formula. I then tried messing around with less stages, trying 12/15/19/23/31 for 1.1784 and 43km/s and 7/11/17/26/39 for 1.1788 and 43.6km/s All of this is of course just half-blind experimentation, though. I get the sense that there's something I picked up in algebra 2 or possibly differential equations that'd lead to a far better solution, as well as answer related questions like whether the fundamental results change noticably with different fuel tanks for decoupler masses. @GoSlash27's stuff on the reverse rocket equation is excellent, but doesn't answer weirder questions like "how much delta-v can I get out of a set number of identical fuel tanks by varying the staging?" What blade made of math might provide a more general solution? Edit: wow, that table looked like a toilet happened. Have a screenshot instead, or a copy of the spreadsheet itself: https://dl.dropboxusercontent.com/u/59091477/Monstrosities/Staging Theory.xlsx

So there are equations everywhere to show how to get the amount of delta-v your rocket has but what if you want to find out how much you need. Known variables: Isp (use the one in game), Delta-v , and Payload (this includes everything that not the fuel tank even the engine) e^(v/[Isp*9.81]) = A (8[p{a}-p])/(9-A)=Wet mass (how much fuel not including the tank)

Hi guys, This was bugging me after the last metric vs imperial thread. What if we use a non 10 based number system? Ok let's just take the one that all imperial system based know, the 12 based but instead of going from 1 to 12 it goes from 1 to 10 (e.g. 1-2-3-4-5-6-7-8-9-a-b-10) a and be replace 11 and 12. it result in 10/3 to be equal to 4 instead of 1,3333 (or 1/3) in the 10 based system, 3*5 = 13 instead of 15, 5*2 is a instead of 10 and so on (i guess you see what i meant). How much will that affect all the calculus made in history and can someone with the 10 based system understand the result of those calculus if you explain them how your system work? How long will it take for him to understand? 12 base is pretty easy but imagine it's a little more complicated, let say 14 based one or 22 based one. This is a part of what if we meet an intelligent life form, can we understand each other can, can we understand their math?

(Aerodynamics aside) do adapters, like the two Rockomax Brand Adapters affect the structural integrity of a craft, or are they merely aesthetic? In other words, if an adapter is placed between a 2.5m tank and a 1.25m tank, is that design stronger in some way than a 1.25m tank connected directly to a 2.5m tank? Is there a (hopefully launch pad) experiment that can be devised to prove either case? What is the KSP stress model? How does it determine when two parts have undergone enough shear, torsional, or tensile stress for their connection to fail?

Can anyone recommend some good resources on the mathematics of orbital mechanics? I'm comfortable calculating Hohmann transfers (including alignment angle, dV budget, etc.), I can calculate dV for stages and total craft, but I'm having a hard time figuring it out past there. I'd love to be able to calculate the dV required for plane changes the new trajectory from a gravity assist the launch window for non-Hohmann transfers porkchop plots map out a spiral transfer for low thrust engines and plan re-entry trajectories. I expect some of these problems have known simple solutions, and some will require numerical integration. I'm comfortable setting up and solving either method. My background: I'm a chemical engineer. I'm comfortable solving ODEs (ordinary differential equations) and PDE (partial differential equations). I don't usually work in multi-dimensional calculus, but I do understand the basics of dot and cross products. There was a point in time in college where I was better with those. My trig is pretty good, but my calculus in cylindrical or polar coordinates isn't great. I usually use MathCAD for complex problem solving but don't have access to it right now. So I usually set up Eularian integrators in excel when I can't work out exact solutions. With a little work I could make it run Runge-Kutta instead. I've read the wikibooks articles on orbital mechanics, as well as these links http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html http://www.braeunig.us/space/orbmech.htm http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec14.pdf http://www.bogan.ca/orbits/kepler/orbteqtn.html

Hi everyone, I’m trying to predict the maximum height of my rocket flying straight up in the kerbin atmosphere and am stuck. My ship is one flea booster with a Mk1 pod and a Mk16 chute flown by a kerbal. It weighs 2.44t full and 1.39t empty. The flea has an ISP of 140 asl - 165vac. Using the asl ISP I got 772.0166 delta v. From here I used some kinematics equations and figured that the speed at the end of the burn should be 685.16m/s and the maximum height of the flight would be 23926.72m When I tested it out in the sandbox with drag turned off I ended up going 29606m high and the speed at the end of the burn was 704m/s So I think the numbers were off because as the rocket flys up the ISP improves meaning I actually had more delta v than calculated. Another thing I thought might have affected it was the force of gravity changing the further away from kerbin I got (I used a constant 9.81). How do I improve my calculations to account for changing ISP and gravity? Or was I missing something else? If anyone is feeling ambitious I would also really appreciate an explanation of how to add drag in as well because the formulas on the atmosphere wiki are not making any sense to me.