Orbital �v formulae questions

[kookoo_gr]

With the coming of the campaign mode and since i am doing the ksp wiki campaign a few questions rose while building my rockets and i would like my rockets to be mathematecally backed up and not building random overpowered rockets. I 've searched the forum and the wiki page but i didn't find any answer.

Given a ÃŽâ€v and a burn time for a stage i would like to know if there is a formula to calculate the maximum height/apoapsis for a rocket.

E.g. (the numbers are random and rounded for the example, if they are wrong please free to right them). I have a rocket with stage 1 (S1) with ÃŽâ€v 2000 and burn time 1m30s, S2 has 1500 ÃŽâ€v and 1m10s, S3 has 600 ÃŽâ€v and 2min and finally i have my transfer stage and lander. My design questions are: S1 how high will it go for Kerbin (or any other planet when there is a lander at another planet), then when S1 is dropped and S2 fires how high will it go and will S3 be able to make and orbit at 75km (or higher)? The transfer stage and lander MUST NOT use any fuel during the launch and when establishing an orbit, only for a Munar transfer/landing/return.

Also given the ÃŽâ€v of a ship/stage at orbit how can i calculate the maximum orbit i can reach (circulirize) without leaving a body's SOI. Also this applies for interplanetary orbits.

I have Mechjeb2/engineer redux for info purposes and i have a copy of the Kerbin system ÃŽâ€v requirements

[tavert]

Within the atmosphere, these things are a bit harder to calculate so there are rules of thumb (say ~4500 m/s for getting to low Kerbin orbit) but not super specific always-perfect numbers (yet - I and others may come up with tools to do so eventually). Once you're out in a vacuum though, yes there are calculations you can do for orbital transfers, assuming impulsive maneuvers (which means decent thrust-to-weight ratio).

Here's a good description of this type of formula, and the gravitational parameters, SOI radii, etc for Kerbal planets and moons can be found here.

We can work through a specific example if you have one in mind.

[Colonel_Panic]

With the coming of the campaign mode and since i am doing the ksp wiki campaign a few questions rose while building my rockets and i would like my rockets to be mathematecally backed up and not building random overpowered rockets. I 've searched the forum and the wiki page but i didn't find any answer.

Given a ÃŽâ€v and a burn time for a stage i would like to know if there is a formula to calculate the maximum height/apoapsis for a rocket.

E.g. (the numbers are random and rounded for the example, if they are wrong please free to right them). I have a rocket with stage 1 (S1) with ÃŽâ€v 2000 and burn time 1m30s, S2 has 1500 ÃŽâ€v and 1m10s, S3 has 600 ÃŽâ€v and 2min and finally i have my transfer stage and lander. My design questions are: S1 how high will it go for Kerbin (or any other planet when there is a lander at another planet), then when S1 is dropped and S2 fires how high will it go and will S3 be able to make and orbit at 75km (or higher)? The transfer stage and lander MUST NOT use any fuel during the launch and when establishing an orbit, only for a Munar transfer/landing/return.

Also given the ÃŽâ€v of a ship/stage at orbit how can i calculate the maximum orbit i can reach (circulirize) without leaving a body's SOI. Also this applies for interplanetary orbits.

I have Mechjeb2/engineer redux for info purposes and i have a copy of the Kerbin system ÃŽâ€v requirements

The engineer redux and kerbin system delta v map should give you effectively all the info you need to know. As far as launch heights and trajectories, burn time is a lot less important than TWR. Your thrust to weight radio will dictate what you can do with a given stage, and remember: your TWR will steadily rise as you burn fuel. Higher TWRs will always allow you to perform more efficient maneuvers, since you can time your burns more precisely, and do more burning at the optimal times for efficient transfers. However, higher TWR also implies you're carrying more engine weight, and unnecessarily high TWRs will come at the cost of lower delta-v.

For a launch on kerbin, You need 4500-4700 delta v to achieve low orbit. The rest of the orbits around kerbin will cost up to a maximum of around 2000 delta v assuming an orbit near minmus WITHOUT using any gravity assists. Realistically though you shouldn't have to spend more than 1000, since if you're going higher than the mun (800 dv to apoapsis at munar intercept) you can use the mun as a gravity assist to push up your orbit and partially circularize.

You also want a TWR to stay at around 2 during atmospheric ascent on kerbin, since above that will cause you to exceed terminal velocity, resulting in high losses to air drag, and below that you will spend too much time at low altitudes in thick air before accelerating to orbit, resulting in high losses to gravity. An ideal ascent will use radial staging and discard fuel tanks as soon as they become empty, while using fuel lines to keep the next stages full so all of your engines can burn constantly during ascent and not waste weight or thrust potential. You should aim for a beginning TWR of around 1.7 per stage, keeping in mind that it will increase as the stage burns, and that your first stage should have a higher TWR to accelerate your rocket up to terminal velocity as quickly as possible (solid boosters are good for this).

For more info, see my complete rocket design and launching tutorial, in my signature. It goes over a lot of that stuff in depth.