Math formulas

[Drag146]

Hi everybody,

I am planing to do a interplanetary missions and I would like to do them very efficient.

So I would like You to give me some math formulas that would help me do such missions, for example: formula to calculate deltaV that you have and you need or TWR formula. Those are just examples, I would be thankful if You gave me more than these examples.

-Drag146

Edited June 19, 2013 by Drag146

[stupid_chris]

You can find most of the equations you will need here.

However, this is an extremely tedious work and a single error could set your whole craft off. I therefore recommend you give Kerbal Engineer a try, it will calculate delta V and TWR for you without affecting your gameplay, it's really just an automatic calculator

[capi3101]

If you're wanting to update your data as the mission progresses (i.e. if you want to see how much delta-V your mission has left)

1) In 0.20, go the map screen, pop open your craft information window and your resources window.

2) Make note of your craft's current mass.

3) Sum up the amount of liquid fuel and oxidizer and divide it by 200. The result is the mass of your remaining liquid fuel.

3A) If you have monoprop, divide the amount by 250. The result is the mass of your remaining RCS.

4) Subtract the mass of your liquid fuel (and monoprop if you have it) from your current mass. The result is your dry mass.

5) Use your current mass and the dry mass result in the Tsiolkovsky Rocket Equation to calculate your remaining delta-V. You'll also need to know your current stage Isp.

That's if you want to do things by hand.

[Drag146]

However, this is an extremely tedious work and a single error could set your whole craft off.

After a week of messing around (exploding rockets and stuff) I want to start taking this simulator/game more seriously. That's why I would like to do some of that work myself

because I really like maths and physics and it would be great opportunity to learn something new.

Anyway, thanks for that calculator, I will use it when I will get bored of doing calculations myself

-Drag146

[stupid_chris]

After a week of messing around (exploding rockets and stuff) I want to start taking this simulator/game more seriously. That's why I would like to do some of that work myself

because I really like maths and physics and it would be great opportunity to learn something new.

Anyway, thanks for that calculator, I will use it when I will get bored of doing calculations myself

-Drag146

I know the feel KSP is free to play however you want it, so if you find your fun in doing things yourself than go forth!

[Guest]

Kerbal Engineer Redux, because alt-tabbing to spreadsheets is tedious and boring. The flight engineer is pretty nice for mission planning as well; lots of math rolled into one program.

[Mr Shifty]

This page has some really great math explanations for orbital mechanics and interplanetary transfers:

http://www.braeunig.us/space/

alexmon's interplanetary transfer calculator uses that math to calculate fuel usage for various transfer ellipses.

http://alexmoon.github.io/ksp/

[tomf]

I wrote a rather rapid run through of calculating the delta v requirements here http://forum.kerbalspaceprogram.com/showthread.php/27171-Calculating-interplanetary-delta-v

[TheQuietShadow]

The best formula I found is: E=MC2

[Mr Shifty]

I wrote a rather rapid run through of calculating the delta v requirements here http://forum.kerbalspaceprogram.com/showthread.php/27171-Calculating-interplanetary-delta-v

Your explanation is the clearest I've seen. I used your numbers to put together a spreadsheet, and an interesting fact fell out:

Your most efficient Hohmann transfers happen when you start and end at an orbital radius that is twice the magnitude of the escape or injection hyperbola semi-major axis.

Example: for your Kerbin to Moho example in the link you provided, the SMA of the escape hyperbola from Kerbin is -650.039km. If you want the most efficient altitude from which to start your escape burn, you should start at a radius of about 1300km (altitude of 700km because of Kerbin's radius.)

[tavert]

That's only counting the cost of leaving from that altitude, not the cost of getting up there in the first place. When you combine the two I'd be very surprised if it were ever a better idea to do an interplanetary ejection burn at high altitude.

[Mr Shifty]

That's only counting the cost of leaving from that altitude, not the cost of getting up there in the first place. When you combine the two I'd be very surprised if it were ever a better idea to do an interplanetary ejection burn at high altitude.

True, but I imagine you could use the most-efficient-altitude information to plan where to put your refueling stations. You can, for instance save yourself 500m/s by refueling at 13Mm for a Kerbin-to-Eve burn rather than from 100km.

For instance, a Hohmann burn from Kerbin to Eve is most efficient from a starting altitude around 13Mm. This is fairly close to the Mun's orbit, which means getting a gravity boost from the Mun is doubly efficient for Eve transfers and that a refueling station around the Mun might be a good idea.

Conversely, Hohmann transfers are least efficient for an intial/final orbit ratio of 15.8, which is again, very close to the ratio from 100km parking orbit to the Mun's altitude: (100km+600km)/(11400km+600km) = 17.1. It's worth noting that a bi-elliptic transfer is actually more efficient going from 100km to the Mun's altitude than a Hohmann transfer.

[tavert]

Fuel doesn't magically appear at high altitudes, you have to expend fuel to put it there. If you're Kethane mining from Mun or Minmus that's a slightly different story, but launching from Kerbin, don't lift the fuel any higher than you absolutely need to.

[Mr Shifty]

Fuel doesn't magically appear at high altitudes, you have to expend fuel to put it there. If you're Kethane mining from Mun or Minmus that's a slightly different story, but launching from Kerbin, don't lift the fuel any higher than you absolutely need to.

Use case:

I have a transfer vessel with 5000 m/s of delta-V fully fueled sitting in 100km Kerbin orbit.

Option A:

- Leave directly for Eve from 100km Kerbin orbit.

- Assume that getting captured by Eve takes zero fuel because of aerobraking.

- Delta-V required for transfer is 1101 m/s ejection burn, leaving 3899 m/s to play around with.

Option B:

- Expend fuel in Kerbin's SOI to put a ship with some fuel and a docking node up at 12,907km.

- Burn 1201 m/s to get the transfer vessel up to 12,907 km.

- Dock and refuel the transfer vessel.

- Delta-V required for Eve transfer is 511 m/s, leaving 4489 m/s available to play around with.

It's probably true that the 500 m/s isn't going to make a big difference to many missions, but I can envision situations where it might be important. And fuel from Kerbin is essentially free. It's easy to get it up to Munar altitude, and Munar altitude is worst case. (It actually takes less fuel to get to Minmas altitude than to the Mun's.)

Edited June 19, 2013 by Mr Shifty

[tavert]

I think you meant 3899 for option A. You have a point, in the sandbox technically everything is free, but that doesn't mean there isn't reason to try to minimize total fuel consumption for your mission architecture. If you need 4489 m/s available after reaching Eve, it's cheaper overall to add the extra 590 m/s capacity to the transfer vehicle itself. This will require less total fuel than bringing the 1201 m/s worth of refueling capacity up to the high altitude.