Launch �V-Formula?

[guest91111]

Hello,

I'm a video producer for my own youtube channel, and I want to make a series. But I need to know if there's a certain formula to calculate how much ÃŽâ€V I need to get from 0m into orbit. Does anyone know if such formula does exist. And if yes, can you please post it here. You'll be in the credits in the first video of the series (Only your forumname, and if you don't want to be in the credits, you can tell me that!)

[Pecan]

This current thread will probably help: http://forum.kerbalspaceprogram.com/threads/73205-How-can-i-calculate-geostationary-orbit

"0m" is a problem though, since you don't start at the centre of a body but on its surface - and presumably with some rotational deltaV too (unless it isn't rotating). In an atmosphere your ascent trajectory can put the calculations all over the place and wherever you are it depends on TWR too so there is no single solid formula. For Kerbin the 'standard' figure is 4,500m/s though.

[AmpsterMan]

Moved this thread to a more appropriate place.

[brdavis]

I need to know if there's a certain formula to calculate how much ÃŽâ€V I need to get from 0m into orbit.

Short answer… I don't think so. But I'm ready to be corrected

It's going to depend on a heck of a lot. You would need to take into account what the T/W ratio is, as well as what the ascent profile is (where do you start your gravity turn, etc.). As one example, picture two identical spacecraft… one with a T/W ratio of 2.0, and one with a T/W ratio of 0.9. The first will perhaps reach orbit, but the second would just sit on the ground… even infinite delta-v isn't going to do it.

You can make some rough estimates… For example, picture a really poor way of doing it: one big impulsive kick from the launching pad, and then at the peak of the "arc", one big impulsive kick sideways to acquire orbital velocity. If you want to use this to reach a circular orbit at, say, 100 km, it will take roughly a delta-v = sqrt( 2 g h ) = sqrt (2 g (100 km) ) to "toss up" the spacecraft to that height, and then a kick sideways of delta-v = sort ( G M / a ). That's a lousy way of doing it (not efficient), but it's one estimate.

A second way would be to launch with a single impulsive kick right from the ground into a Hohmann transfer orbit that just "kisses" the ground, and just "kisses" the desired orbit. That's just a standard transfer orbit calculation.

None of these are "right" - an actual gravity turn is different, and atmospheres play a significant role that's hard to calculate exactly (not only does atmospheric density matter, but so does scale height, which is different for each planet… but, hey, at least the designers used a constant scale height instead of a temperature-varying one ).

So now… what are you trying to communicate in your video? Because the complete problem is perhaps more than you want to deal with in a YT video (do some research on the Goddard problem if you desire).

PS- Why, yes I have spent the last couple days trying to work out exact delta-v's for a Duna-Ike mission. So i might be a bit buried in calculations… but for some of us lost souls, that's half the fun.

[Starstrider42]

There aren't any formulas (for the reasons the other posters have mentioned, that it really depends on your exact trajectory through the atmosphere), but I've found the map at http://forum.kerbalspaceprogram.com/threads/41652-A-more-accurate-delta-v-map very helpful. It includes typical launch delta-V's for all planets and moons.

[UmbralRaptor]

For an airless world, you can get useful numbers with relatively few approximations. eg: Tavert's charts. For back of the envelope calculations, you can just work out the relevant orbital speed and guess at gravity losses based on burn time.

In principle one can put together a formula for ÃŽâ€V requirements on a world with an atmosphere. In reality, it wouldn't be solvable analytically, and you would need some numeric approximation.

[rkman]

Apparently there is not simply a formula for this, for planets with an atmosphere it requires a whole lot of complicated mathematics that's hard to figure out even for people who know a whole lot of complicated mathematics.

See http://forum.kerbalspaceprogram.com/threads/46194-I-need-someone-help-me-do-some-math-for-launch-optimization

[mhoram]

K^2 gave a nice approximation in the "I need someone help me do some math for launch optimization" thread:

A rule of thumb for minimal delta-V is orbital velocity + drag/gravity losses on vertical assent (4gH/v_t), and the later works out to be just shy of 2km/s for Kerbin. So any optimal ascent method should show something in the neighborhood of 4.3km/s for orbit.

Edited March 22, 2014 by mhoram

[Elington]

Hi,

If that can help I worked on this app when facing the same question: Ascent Komputron - rocket simulator, ascent optimization, aerobraking

It can simulate and optimize the trajectory of a rocket model taking into account thrust, gravity and drag (stock, not "FAR"). If the vessel can make it to orbit you get a reading of the total spent DeltaV together with the drag, gravity and steering losses.

Cheers,

David

[freeskier93]

Of course there are formulas! You really thing actual engineers just guess and hope they have enough fuel? There are 5 main components for total change in velocity:

- Burnout velocity (basically what velocity is needed for a certain orbit)

- "Loss" due to gravity

- Launch velocity

- Drag losses

- Steering losses

When paired with MechJeb KSP is extremely consistent. Drag losses and steering losses are the hardest to predict in real life and virtually impossible to predict in KSP. However, in my testing, when using MechJeb drag losses can be closely estimated for a planet and steering losses are negligible. You also need to factor in launch azimuth angle, flight path angle, launch latitude, and desired orbit inclination. These are all relatively simple "plug and chug" equations.

Edited March 23, 2014 by freeskier93

[rkman]

These are all relatively simple "plug and chug" equations.

So what do these equations look like? Where are they?

It sure seems there is not just one formula.