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Who Else Does Rocket Science MATH?


LexiSilva
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I just started designing my rockets using pen and paper and calculator, and I was wondering who else does?

What I mean is I do NOT use KER or Mechjeb; instead, I learned the equations for delta-V and TWR and I use them to design my rockets, from suborbital to orbital, and hopefully to the Mun someday! :D

- LexiSilva, Casual Rocket Scientist

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I always wanted to take the time and do such, and maybe fly to the mun using calculations only or something of the like. Then I asked myself whats the difference between this and actually studying for my calculus homework Haha.

Edited by MKI
my phone makes typos happen
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You can use calculator buttons and stats in the game:

For example: delta V is isp(exact same number as in game) * mass(full, take in-game numbers add up and times by 1000), and mass (empty, same procedure) * 9.81

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Yeah, I sometimes do the math on my rockets, although I use kerbal engineer to figure out TWR and dV. I know how to calculate them myself, but I simply don't want to spend time on recalculating it every time i make a change to my rockets. However I do the math for orbit transfers myself because I don't want to fiddle with maneuver nodes forever and I want to do them as efficiently as possible.

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You can use calculator buttons and stats in the game:

For example: delta V is isp(exact same number as in game) * mass(full, take in-game numbers add up and times by 1000), and mass (empty, same procedure) * 9.81

I think it is great that you do it. For I look at my computer as a big calculator when I use KER. But I do designed what my rocket needs on paper all the time. I just let KER do the final delta-V for me.

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I make a lot of graphs in Excel... It's the only KSP-related thing I do at work, but when people walk by and see Excel on the screen they automatically assume you are doing your job... (Well unless you have one of those awful jobs where they don't let you use Excel...)

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I just started designing my rockets using pen and paper and calculator, and I was wondering who else does?

Do it long enough and you can start eyeballing delta-v. Remember a few log values and can interpolate the rest.

If x is close to 1 then ln(x) ~ x-1

ln(1.5) ~ 0.4

ln (2) ~ 0.7

ln (2.71) ~ ln(e) ~ 1

ln (7) ≈ 2

Simples!

I usually scribble ideas on paper, but most of my design is done using brute force iteration with a Python program; I give it certain constraints and it runs through every possible combination of parts* within those constraints to find the one that best suits what I want; then I work out how to put those bits together. The familiarity with the various parts and equations it's given me is more valuable than any specific result.

*loosely speaking. Things would be implausibly slow if you really considered every part, so I selectively manually disable consideration of Mainsails for lifting off Gilly and so on. That could be automated, but it'd take lots of thinking.

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I do the math to figure out the underlying concept behind something - like in my KSP videos where I explore Delta-V. After that, everything is done in KSP experimentally, without MechJeb or Engineer or anything.

Now that I know the concepts, I know how to quickly figure out (with just my phone calculator) when to leave Kerbin for {Insert Target Planet Here}. Dam, I still need to make the videos on Kepler's Laws - I have the scripts done.

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Here's the real challenge: Use math instead of the map view to get to the mun, minmus, or even another planet by using your altitude, heading, and speed to figure out your orbit

"Maybe someday..." - Magic Conch Shell

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I've more-or-less been doing all of the math for my rockets following the first couple of weeks I played.

I like math.

I started with some simple spreadsheets.

Refueling_sheet.png

Vessel_sheet.png

But then I determined that manual data entry was for the birds, so I started writing support scripts to parse the game files.

KSP_Components_py.png

Then I started doing some advanced orbital changes, and wanted to know more specifically what kind of burns I'd need to support them.

Orbit_py.png

I'm trying to find the envelope covered in integral calculus where I derived this piece of goodness, but I've not found it yet so it's probably gone.


tBurn = m0 / mDot * (e^(dV * mDot / F) - 1)

BurnTime_sheet.png

Eventually, I realized it was way more effective to just write the math into a mod, so I took over VOID and integrated Kerbal Engineer into it. ;) I still use a few of my old sheets for sorting out maneuvers when planning a mission.

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I've done quite a few missions using the old pen and paper technology. For figuring out TWR, delta-v, interplanetary transfer windows, orbital rendez-vous, the works. I find it so much more satisfying to complete a mission using my own mathematical intellect rather than mechjeb, transfer calculators or anything like that. Makes me think 3 years doing maths at university wasn't entirely in vain.

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I've done quite a few missions using the old pen and paper technology. For figuring out TWR, delta-v, interplanetary transfer windows, orbital rendez-vous, the works. I find it so much more satisfying to complete a mission using my own mathematical intellect rather than mechjeb, transfer calculators or anything like that. Makes me think 3 years doing maths at university wasn't entirely in vain.

Can you tell me how to do the latter two?

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Can you tell me how to do the latter two?

You start with the equation that orbital period is proportional to the semi-major axis to the power 1.5. For a circular orbit, that's radius to the power 1.5. So T = k*(a^1.5) where T is time to complete one orbit, a is semi-major axis (or radius, which is usually close enough), and k is some proportionality constant that doesn't matter because it cancels out. In the case of Earth, we can set all the constants to be equal to 1. The Earth's semi-major axis is 1 AU, the orbital period is 1 year, etc. So if we say Earth is 1 Astronomical Unit from the sun and know that Mars averages about 1.52 AU from the sun, then we know that Mars completes one orbit in time T where T = 1.52^1.5 = 1.87 years which is about 684 days. Actually it's 687, but close enough since we're using approximations, and mid-course corrections don't tend to cost a lot of fuel.

Now imagine you want to do a hohmann transfer orbit between Earth and Mars. That means your orbit will have a perihelion of 1 AU and an apohelion of 1.52. That makes your semi-major axis equal to 1.26 AU. That means your orbital period is 1.26^1.5 years = about 1.4 years. You want to rendezvous with Mars, so you're interested in the outbound leg of this journey, so total transfer time is half that; about 0.7 years. So you want to launch 0.7 years before Mars reaches the point where it'll be 180 degrees from your present location. That's 0.7 / 1.87 = 0.37 of a Martian orbit. Times that by 360 to get 136 degrees. So Mars should be 136 degrees behind the point that's directly opposite to the sun from where you are now. Subtract that from 180 degrees, and you get 44 degrees. So you want to launch when Mars is 44 degrees ahead of you in its orbit.

So, to apply that maths to the Kerbal universe, you need to measure Kerbin's orbital distance from the sun, and call that "one Kerbal astronomical unit", or 1 KAU. It's always worth setting known values to 1 because it makes the maths so much simpler. Then, all other planets' orbital distances can be measured in KAUs. Plug in those numbers, and you'll get your optimal launch timings. The same maths works for orbital rendezvous, you just have to remember that semi-major axis is measured from the centre of gravity, not from the surface. So if you're orbiting 100km above Kerbin (and Kerbin has a radius of 600km), then your semi-major axis is 700km.

I know, I'm a crap teacher. If I were there in person, I'd probably be able to explain it better.

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I decided I wanted to make a heavy lift vehicle that would put an orange tank into LKO. So… I worked out the math, on paper. I wanted to do a light-weight single-Kerbal mission to Duna… so, I worked out the math, every potential step of the way. Currently I'm aiming at going back to Duna with a two-Kerbal mission, including a Hitchhiker just so they have more room for the long trip, and they'll visit Ike as well… and working out all the math on paper. Including transfer windows, etc.

Why not use Engineer or MechJeb? Nothing more than personal preference. If I choose to run a marathon, it's not because I have a requirement to arrive at a place 26.2 miles away… the fun isn't in the destination, but the path you choose to take to the destination. :)

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-snip-

I know, I'm a crap teacher. If I were there in person, I'd probably be able to explain it better.

Made sense to me, man. It's like a ligtbulb turned on. So simple.

As for my own calculations, they were the sort of thing I did once, then couldn't be bothered to do it again. MJ is quite helpful at allowing me to design stuff faster.

But yeah, a certain element of work that makes the mission that much more rewarding was there when I did my own stuff.

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You start with the equation that orbital period is proportional to the semi-major axis to the power 1.5. For a circular orbit, that's radius to the power 1.5. So T = k*(a^1.5) where T is time to complete one orbit, a is semi-major axis (or radius, which is usually close enough), and k is some proportionality constant that doesn't matter because it cancels out. In the case of Earth, we can set all the constants to be equal to 1. The Earth's semi-major axis is 1 AU, the orbital period is 1 year, etc. So if we say Earth is 1 Astronomical Unit from the sun and know that Mars averages about 1.52 AU from the sun, then we know that Mars completes one orbit in time T where T = 1.52^1.5 = 1.87 years which is about 684 days. Actually it's 687, but close enough since we're using approximations, and mid-course corrections don't tend to cost a lot of fuel.

Now imagine you want to do a hohmann transfer orbit between Earth and Mars. That means your orbit will have a perihelion of 1 AU and an apohelion of 1.52. That makes your semi-major axis equal to 1.26 AU. That means your orbital period is 1.26^1.5 years = about 1.4 years. You want to rendezvous with Mars, so you're interested in the outbound leg of this journey, so total transfer time is half that; about 0.7 years. So you want to launch 0.7 years before Mars reaches the point where it'll be 180 degrees from your present location. That's 0.7 / 1.87 = 0.37 of a Martian orbit. Times that by 360 to get 136 degrees. So Mars should be 136 degrees behind the point that's directly opposite to the sun from where you are now. Subtract that from 180 degrees, and you get 44 degrees. So you want to launch when Mars is 44 degrees ahead of you in its orbit.

So, to apply that maths to the Kerbal universe, you need to measure Kerbin's orbital distance from the sun, and call that "one Kerbal astronomical unit", or 1 KAU. It's always worth setting known values to 1 because it makes the maths so much simpler. Then, all other planets' orbital distances can be measured in KAUs. Plug in those numbers, and you'll get your optimal launch timings. The same maths works for orbital rendezvous, you just have to remember that semi-major axis is measured from the centre of gravity, not from the surface. So if you're orbiting 100km above Kerbin (and Kerbin has a radius of 600km), then your semi-major axis is 700km.

I know, I'm a crap teacher. If I were there in person, I'd probably be able to explain it better.

Thank you so much! :D That is a wonderful equation and way to measure planetary distances!

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