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I have a hypothesis about the rocket equation, hoping someone can help me either disprove with counter example, or give an informal proof that it is always correct: For every two stage rocket with total mass M, and a payload weight of P, if the bottom stage engine (called E1) with ISP of I1 and the top stage (called E2) has an ISP of I2, and also I1 < I2, then: There is never a two-stage rocket design of payload P and total mass M where E1 is placed on the top and E2 is placed on the bottom that has more dV than the best two-stage design which has E1 on the bottom, and E2 on the top. in other words, if I have a 12 ton rocket with a 1 ton payload, a swivel on the bottom stage and a terrier on the top stage, and the fuel is split optimally. There's no design for a 12 ton rocket with the terrier on the bottom and the swivel on top that will be better in terms of dV.

Hey there, I wanted to work on my own designer for optimal stages. Anybody know of the algorithm to calculate optimum fuel sizes for a given payload, engine weight, and Isp? I'm aware of Optimal Rocket Calculator, which doesn't handle NERV or DAWN engines. It also doesn't handle drop tanks. I think Optimal Rocket Calculator also uses brute force.

Hello! I’ve been playing KSP for a while now and have become quite confident in my abilities. Although, I’m still having trouble with gravity assists. Is there an equation of some sort that I can use to calculate my speed after the slingshot/brake? Ex. Before assist craft is going x m/s, after the assist the craft is going y m/s I also would like to know if there is an equation I can use that will tell me the orbital velocity at a certain altitude above a body. Ex. At h meters with d degrees of inclination, the craft must be going x m/s to maintain a circular orbit If you have any other useful equations that would be nice, thanks!

Greetings, Messing around making a space sim game, but in the orbital calculations, atm im a bit stuck with if eccentricity is actually a vector depicted in a 1x3 matrix with I J K But ive often seen it refereed to as a scalar/magnitude. Im using the formula here

I have problems learning the multiplication table as an adult. I'm an adult, but I’ve always had problems with math, despite having Asperger’s, but i'm quite good in technical stuff i would have loot of problems if not use calculator i just wonder does is possible to improve my math go to engineering studies?

As I was lying in bed trying to fall back asleep this morning, I was amusing myself with some mental math, namely the Fibonacci sequence. Starting with 1, add the previous number to get the next number in the sequence. 1,1,2,3,5,8,13,21,34... I was messing around a bit with the relationships between the numbers, and hit on something kind of cool. If you take any two consecutive numbers in the sequence, square them, and add them together, you'll get the number in the sequence found by adding the places of the consecutive numbers together. For example, sequence places 3 and 4: 2^2+3^2=13, which is 7th number in the sequence. For sequence places 4 and 5: 3^2+25^2=34, which is 9th in the sequence. This holds true for any pair of consecutive Fibonacci numbers, as far as I can tell. If you want the fancy formal notation of this, it would look something like: For Fn=Fn-1+Fn-2 F1=1, F2=1, Fn+(n+1)=(Fn)2+(Fn+1)2 (If I've done that wrong, please tell me. My math education has only touched on sequences and their notation very briefly.) I have no idea why this happens, or if it's good for anything. I'm chalking it up to the golden ratio being spooky. I couldn't find anything on the wikipedia page for the Fibonacci sequence about this particular feature of it, but I'd be really shocked if it wasn't mentioned somewhere already. Anyway, I thought this was neat and wanted to share. Hope somebody finds it interesting.

My plane was doing 0.13 fuel units per second, so i figured i'd time how long it takes to expend a unit of fuel, it took 23.56 seconds. But my calculations predicted far different from that result. My calculations are bellow. 0.13 units/s 1/.13 = 7.6923076923076923076923076923077 (seconds delay between each unit use) As you can see i predicted ~7.69 seconds, but i expirienced 23.56 seconds. A ~206.37% increase. I've added a screen-shot i took around the time of calculations in-case it helps. Can anyone tell me where i went wrong in calculations or if something like my frame rate is causing odd updates or something? (I had on average 11 FPS, and i timed the fuel expenditure with a stopwatch with 1/100 second accuracy. Also note that in the screen shot it has .09 but at the time of calculation it had .13)

Just wondering if any maths / rocket surgery people out there that might be able to point me in the right direction for formula to work out the following for an airless body in KSP. The question I'm trying to work out is for the bodies in the game that allow a Synchronous orbit, and given the limiting factor of SOI of the body, how close could I get to the surface with a vessel using an Eccentric Geosynchronous orbit? ie something like a Molniya orbit that had the same sidereal duration as the body it was orbiting.

Hi, everyone! I have a nasty problem to solve. Half by physics, half by math. And hope UE4 can help me with that too. I have an object in the space. We know the center of its mass (C). There also a lot of engines/thrusters. We know where are they placed (P1...Pn) and in which direction they turned (D1...Dn). Each engine has maximum thrust (0...Ti). All those values we know. Tasks are: 1) We should be able to move (strafe) the object in the space by custom normalized vector (V) with custom thrust power (0 <= T <= 1). 2) We should be able to turn the object on the place centered on (C) with custom thrust power (0 <= T <= 1). 3) Of course, there are situations, where it's impossible. If so -> T = 0. Any thoughts or formulas?

Hi guys So, I was wondering what you guys do before you build rockets. This is what i do:

Hello Everyone, I've been wondering for a little over an hour about this now, how can you calculate the delta-v from needed to get into orbit of a body once you enter its Sphere of Influence? On many delta-v maps like this one there is a delta-v needed to get into orbit (mun: 310m/s). I understand the Hohmann transfer which gives the other values but I don't know how to get the delta-v needed to get into orbit once you're intercepted by a body. So can anyone help please?

Hey everyone, I recently have been sucked into this game, and I'm loving the math. My question is this simple, determine the altitude a rocket will achieve on full fuel burn of a single stage. I've done a lot of research and have come up with the following example problem to test my algorithm/process of calculation. Let me know what you guys think of below and what I'm missing or potentially a force I haven't considered into the calculation such as lift, as you'll see my answer is off by nearly 3,300m. (For the sake of simplicity the rocket travels straight up in a vertical dimension only.) Known Values of my Rocket: Full Mass [MFull] (Entire Rocket) : 7.5t (7,500kg) Empty Mass [MEmpty] (First Stage Depleted) : 4.5t (4,500kg) Fuel Mass [MFuel] (Both LQ and OX) : 3.0t (3,000kg) Isp [Isp] (Reliant Engine) : 265 sec Thrust [FT] (Thrust Force Atm.) : 205.2kN (205,200N) LQ Rate [BLQ] (Burn Rate of LQ) : 7.105 u/sec OX Rate [BOX] (Burn Rate of OX) : 8.684 u/sec LQ Volume [VLQ] (LQ Fuel 45% Mix) : 270 u OX Volume [VOX] (OX Fuel 55% Mix) : 330 u Known Values of Kerbin: Accel. Kerbin [g] (Accel. of Gravity) : 9.81 m/sec^2 First I will calculate the time required to burn through the fuel mixture. This time will be needed in the final calculation. Tburn =VLQ /BLQ =VOX / BOX << >> 270u / (7.105u/sec) = 38.0 sec Next I convert burn rate units from volume/sec to units of kg/sec. (I assume 1u = 5kg of both LQ and OX) BLQ_M = BLQ * (5kg/u) << >> (7.105u/sec) * (5kg/u) = 35.525 kg/sec BOX_M = BOX * (5kg/u) << >> (8.684u/sec) * (5kg/u) = 43.42 kg/sec BTOTAL= BLQ + BOX << >> 35.525kg/sec + 43.42kg/sec = 78.945 kg/sec (M *Dot = Mass Flow Rate) Determine effective exhaust velocity of rocket motor related to Specific Impulse and Gravity. (NASA Formula) Ve= Isp * g << >> 265sec * 9.81m/sec^2 = 2,599.65 m/s Determine acceleration of rocket (Found this formula on a physics forum, not sure if valid) a = Ve ( BTOTAL / MFULL ) - g << >> 2,599.65 m/s * (78.945kg/sec / 7,500kg) - 9.81m/s^2 = 17.554 m/s^2 Apply classical kinematic physics equation for displacement with acceleration. (Vertical Axis only...) deltaX = 0.5 * a * (Tburn^2) << >> 0.5 * 17.554m/s^2 * (38sec ^ 2) = 12,673.988m So in the end this calculation results in an effective altitude of 12,673.98 meters. If anything, I expect drag (if simulated) among other forces to take away from this value. Instead the opposite occurred, my actual test flight while holding steady to the center of the NavBall resulted in roughly 16,000 meters altitude at 38 seconds into flight (after stage finished burning). Any ideas?

OK so i have been looking for a way to mathematically figure out how to rendezvous with anther spacecraft with out using the map as a challenge and i have been reading on Wikipedia on orbital rendezvous, and i think i have come to an partial understanding of it but i am not sure. so here is what i know that i have to do. first i have to go either higher or lower than the target, phasing orbits, and then at a certain moment i have to speed up to catch up with the target when in a matching intersection, and then after the burn i have to point retrograde on target mode on navball and fire at closest approach when i get to the separation distance. now here is the article that i have been reading and i partially understand it except for the ARC-TAN, SINE, TAN. https://en.wikipedia.org/wiki/Orbit_phasing so its just the arc tan, sine and tan that get me off cause i have no idea what they are

I've taken on the project of writing an interplanetary trajectory optimization tool and a comparison of algorithm efficiency for the problem at arbitrary starting points. Looking further into the problem, however, I have a question that I can't seem to answer. When you optimize an interplanetary trajectory in a patched-conics approximation like KSP, how do initial and target orbit influence the problem? Specifically, I understand how the 'interplanetary' part works. Given the position of two planets, you can calculate the orbit that will intersect one position at one time (the departure date) and the position of the other at another time (the arrival date) easily by cranking through Lambert's Problem for the solar orbit case. However, how do you account for leaving the orbit of the start planet and arriving in orbit of the destination planet? Put another way, how do you calculate ejection angle or the optimum burn to leave/enter the patched conic gravity well?

Hey folks, I could use some help/input from anyone who likes a healthy dose of math and physics! I'm building a base on the Mun with a lab and mining/ISRU capabilities. The idea is to use a shuttle to hop around and collect science, then bring it back to the lab and fill up the tanks on the shuttle. So a common problem I have is figuring an efficient path from base to destination (and back). Right now I basically just point in whatever feels like the right direction, give myself some altitude, and burn prograde until my trajectory I comes down in the right area. I got curious about the optimal ways to do this, so I posted on Reddit to see if anyone knew of an existing tool/calculator that would be of use. Not learning of one, I thought it might be a fun exercise to give the math a shot myself. We've begun with a simplified problem: (1) no drag/atmosphere, (2) perfectly spherical planet, (3) non-rotating planet. I'd like to try tackling 2 and 3 as well (1 is more than I want to bite off), but we'll see where it goes. Anyways, the optimal case seems to be an elliptical orbit with initial and final locations located on the latus rectum of the second focus. This geometry minimizes the semi-major axis and thus orbital energy. I've put everything so far in a spreadsheet: https://docs.google.com/spreadsheets/d/1JIUHIAujZuQdvPRIo-FTho82QcEqVLeuRe-lLiM_b-I/edit#gid=0. The next step I'm trying to solve is how to determine alpha, the pitch angle for the initial burn. We've got an equation that solves it for the optimal case, but I'm struggling to work out a general equation for any sma/eccentricity. With that problem solved you'll be able to input a minimum apoapsis in order to clear terrain/obstacles. If I can get that done, I'll look next differing elevations and then a rotating body. Just a note on terms... I've been using θ to represent the angle between initial/final location (measured from center of planet), and α to represent the pitch (flight path) angle for the burn. If anone wants to catch up on the discussion we've had so far, here it is: https://www.reddit.com/r/KerbalAcademy/61tm0f. I wanted to move the discussion here, partly because a forum format is more useful in this case and partly because I'm hoping to get some new voices involved. If you can contribute I'd love the help! Bonus points if you take the end results and turn them into a program or mod.

here is a thread about some forum rules some weird stuff get inspired and drop yours feel free to use spoiler and disclaimer disclaimer: this is just weird and might not totally follow the forum rules while it might be slighty more complicated applied on a daily basis at various scale

UPDATE: New thread created for 3D model that does everything this model does and more. Original post below: I've been exploring optimization solutions lately for my interplanetary communications network, and was having a hard time wrapping my head around some of the math and picturing the system in my head. So I did some research and learned some equations and relationships and found a nice free graphing software to bring it all together. I worked out the polar coordinate equation for each planet's elliptical orbit and plotted it. What came of the exercise was a scale model of the Kerbol System, viewed from the top down, with all planets' orbits represented accurately in terms of: major and minor axes foci (Kerbol in the correct position) eccentricity longitude of ascending node (how a planet's orbit is tilted relative to a reference direction) argument of periapsis (where the Pe is located; given relative to the longitude of the ascending node) (As far as I can tell, imgur album embedding is broken at the moment--please correct me if I'm wrong--so forgive the screen-captures.) ^Model overview ^Inner planets ^Tidied up a little (disabled grid-lines, too) ^Just Kerbin, Jool, and Eeloo nicely visualized The only thing this tool doesn't properly portray is orbital inclination, as that would be in a third dimension. I may look into that soon. We'll see. To use: Download and install GeoGebra on damn-near any platform, or use the web app Download the .gbb file I've l inked here from Dropbox Open, explore, modify... enjoy! At the moment, it's a fairly bare-bones item, with only the most essential information included, but it may just end up growing into something more substantial, whether for my own use, or at the request of the community. I don't know if any licensing is necessary here, but if it is, let's say.... MIT (referring only to the .gbb I've shared. GeoGebra has its own licensing policy). A few notes for clarity: Scale is in megameters (1Mm = 1,000km = 1,000,000m Visibility of elements can be turned on/off in the left pane. This can help with crowding when zoomed out past the inner planets. Π is used to denote the location of the ascending node (normally I would use ☊ but GeoGebra does not support it) Ω denotes the longitude of the ascending node (an angle) ω denotes the argument of periapsis (an angle) γ is used to denote the reference direction, along the x-axis (normally I would use ♈ but GeoGebra does not support it)

So I had always known how to find how much delta-v a spacecraft had but what about efficiency. The efficiency is the ratio of mass wet to delta-v relative to mass dry you can graph the relationship with v=isp*ln(1+w/d) Final I took calculus and I've written an equation so you can find the best amount of fuel based on of payload(anything that is not fuel tanks) and the added weight of the fuel tank shells and isp also you can change the efficiency the payload isp, isp is p, and efficiency is e first, divide e by 10000 side note the value is just representative how close you are the curve the farther from 100 the less efficient however it is necessary to do so often second multiple I by 9.81 (from the game given amount) use the formula below and that is the amount of fuel you should use i/(3√((3/4)^2-p/2))

Simple as that. When i was a youngling during my high school days, i disliked math and she disliked me back, like every kid does here where i'm from. After i enrolled in a law college, math kind grew on me. Well, at least the abstract approach to it (ie wikipedia articles like this https://en.wikipedia.org/wiki/Tarski's_undefinability_theorem), in which i like reading it, but barely grasp 2,5% of what it actually means). So to say the least, this relationship issue remained somewhat unaltered, but with a plot twist. I now loved math, but she totally did not love me back, still. Then i met Jebediah, Bill, Bob and Valentina, and it changed my life. Now that i'm older, wiser and more patient. I think its time to put the multiplication table out of the cabinet and teach myself orbital mechanics. Therein lies the will to change How to do it? Any tips from the smart people around here on this issue? Any good books on how to get things done? Any online free courses that you know of? I want to be able to actually understand the problems, being able to solve it the hard and easy ways. But it doesn't hurts to ask, are there any life hacks or cheats available? To further enlight the spectrum of my math skills, they are that of a 12 years old (6 years old by japanese standards). The goal is to have somewhat a a grasp of college level calculus, at least into the introduction of it. By then i'll be realized as a human being already, and maybe i'll finally figure out how to to dock directly after ascent. Thanks!!! [snip]

I have been building out a surface grid of comm relays, and the southern hemisphere of Kerbin has a distinct lack of convenient mountains with LoS to the northern hemisphere. But look, I hear a little voice say; the south pole is such a nice place, with a constant view of the sun! How about a relay there that will be able to reflect signals off the mun and back to a station in the north which would then kindly forward the connection on to KSC! And hey; it would even be able to mount giant antennas for pointing at planets with constant contact all day and forever as well! From the mountain closest to the pole, I found it took a mere 5 relays flat on the ice cap to reach the pole (12.5km of radio distance with only 30m of terrain height!). A good sign surely! But no, it was not to be. When I finally sat down to determine how many struts and ladders I would need to assemble the radio tower with KAS, the harsh facts of geometry show their true nature. 1) The mun is 11400km away. The radius of kerbin is 600km. This means a 0.053 radian angle is needed to get LoS over the horizon. 2) Those 0.053 radians are 31.564km away from Kerbin's spin axis, as the tunnel bores. 3) Said tunnel ends up 869m beneath sea level of the pole, or 899m below the ice cap. 4) 0.053 radians on the LoS, across 31.564km to the axis, leaves a shocking 1.661km of height. 5) 1.661 km, minus the 899m to reach the ice cap, leaves... 800m of tower to build in order to see the equator of mun. Settling for sight of the matching pole of mun (200km higher up, giving 0.035 radians for the LoS angle), drops the tower requirement to 340m. To me this seems slightly plausible. It will take a KAS screwdriver, a huge pile of girders, many many ladders, and nerves of steel. Maybe a bucket of struts as well. However, the relay pairs on the way to the pole managed 12.5 km with only 30m of altitude each... 12.5km around Kerbin is almost 0.021 radians. If we build a ring of towers 12.5km from the pole, we'd only need 0.014 radians of sight line to see the pole of Mun. And that, my friends, works out to just 31m of radio tower above the polar cap. Hardly monumental, and in fact nearly trivial. It would require an infinite number of towers forming a circular wall at just 31m, but we can build them a little taller than that, and have 3 evenly spread instead. My dream of a single giant tower on the pole with LoS to everything always and forever will be quite Kerbal, and it shall be attempted, but it is still good to know that there is still a practical fallback option remaining. (And of course, if we neglect Mun, all other planets and moons are easily in LoS to Kerbin's poles thanks to the incredible distances; inclination means they'll only see one pole, but that's fine)

Calling all math nerds! So, I'm only a freshman in high school. That means that I have a pretty hard time with the equations used for orbital mechanics and things such as - in this scenario - Roche limits. I was thinking of using Hyperedit to put Laythe in orbit around Kerbin. I want to put it as low as I can to the Roche limit, so that I can reach it easily. Could anyone help me out?

I have been trying to find the formula that gives me the time ( or MeanAnomaly, same thing) to periapsis in a hyerbolic orbit. I spend some time searching google, wiki etc ( Totally didn't spend 6h searching...) and I found some info, but I can't figure out how to use it in code: https://en.wikipedia.org/wiki/Hyperbola http://conicsectionjpg.blogspot.si/2012/10/true-anomaly-of-hyperbola_2603.html This is my code right now: something to note is that I already have all other parameters calculated ( eccentricty, semiMajorAxis etc) If someone who knows the formulas could help me, I would Really apreciate it.

I'm calculating the time from periapsis, but for some reason it always returns me a positive number. So in this case, the calculation results correct, it gives me 5 seconds since rocket passed periapsis. However here: And in this case it also gives me 5 s since we passed periapsis, it should be -5 s ( or orbital period - 5), but no it gives me the absolute value. Here is the code ( C#) GetStaticProperties(); // Calculates all the static parameters, like eccentricity semiMajoraAxis etc double e = _eccentricity; // works fine till here trueAnomalyAtStart = -Math.Acos( Double3.Dot(_eccV, posIn) / (e * Double3.Magnitude(posIn)) ); print ( (Double3.Dot(_eccV, posIn)) / (e * Double3.Magnitude(posIn) ) ); eccentricAnomalyAtStart = 2d * Math.Atan(Math.Tan(trueAnomalyAtStart / 2d) / Math.Sqrt( (1d + e) / (1d - e) )); anomalyToPeriapsis = (eccentricAnomalyAtStart - e * Math.Sin (eccentricAnomalyAtStart)); // ^ this is the anomaly to periapsis, this is what I actually use in the orbit math timeToPeriapsis = anomalyToPeriapsis / meanMotion; // this is used just to show player time to periapsis If anyone know what the problem is, I would really apreciate it.

Welcome to “Kerbin G 113”, a krash kourse in gravitaional mathematics. Disclaimer: This lesson is valid only in KSP version 1.1.3. It has come to our attention that even our most trusted slide rule jockeys occasionally are caught using those 'modern' electronic calculators. The so-called results obtained in this fashion are of course tedious, hence this mandatory back-to-basics krash kourse. First thing first, here is your approved course materials. First lesson When I say the g0 mark of your slide rule line up perfectly with the 9.81 mark, then the result is 9.81 and not a decimal more! Understood? Now go do the exercise; you are to divide the Kerbin GM by Kerbin R and then divide by Kerbin R again. Second lesson Repeat after me: “If I want to find a universal G, I will take GM and divide by M. I will choose one of the celestial bodies listed in the course material to look up GM and M. There are no other options than those listed”. That is good, now, just for the fun of it, calculate a universal G. Thank you. You did well today. Let us hope you all make it to “Kerbin G 12”, our advanced course where participants are entitled to extra decimals. Request I have a request for one of you badS talented artists. Could you please make an image of a Kerbal classroom with a black board. Maybe with a Kerbal professor and Kerbal students in it. On the blackboard it says at the top “KSP ver. 1.1.3” and it says “g0 = 35316 / 36 / 100 = 9.81 m/s2” with the 9.81 part rather over-sized. Preferably a reusable image, so that we may get a new one saying “KSP ver. 1.2” and “g0 = 9.80665 m/s2” once we get confirmation of that in version 1.2. The idea is that the two images can go side by side and help remind people of the version changes, if for instance they are building a Keo-stationary comms-network in the upcomming release. Edit: I hoped it would be obvious that the above post was meant to be entertaining.

So I'm putting together a spreadsheet - in part because KER is not up to date yet, in part for learning experience. Something I've meant to do for a while. Need someone who knows what they're doing to check my math logic here. What I've got going on: I've got a table of engine data and rather than make a user type in their vessel's Isp, I have them place a quantity next to each engine type. These quantities are 0 if none. Might put down they have 1 skipper and 2 thumpers, though. So from what I can tell, the way to measure combined Isp with combinations of engine types is a thrust-weighted average. I guess because thrust and isp are both in relationship to exhaust velocity? Check me here. The formula I've found is: thrust / (thrust 1* isp1 + thrust2*isp2 ...). Since I'm factoring in the quantity of these engines as well, I fist multiply thrust1 by quantity1, so if quantity is 0 the thrust and isp of that engine is removed from the picture. And if they have 2 or 3 of an engine, thrust is doubled, tripled, etc, affecting the weighting of the isp. So where T= total vessel thrust, Tx, Qx, and Ix are thrust, quantity used, and isp of engine number x, this is my formula... T/(T1*Q1/I1 + T2*Q2/I2 ...) (formula runs through every engine in the list this way so it changes as soon as engine count changes) If I tell it I have 1 terrier or 100 terriers, it correctly tells me my Isp is 345, can someone give me test cases and answers to run through my formula?