How do I calculate the D/v required to reach a specific orbit from the surface of a body?

[StellarumSectatio]

How do I calculate the D/v required to reach a specific orbit? Not a Hohmann Transfer, an ascent directly from the surface of a body (Specifically Europa in my case) To a 60 kilometer orbit. I have absolutely no idea how to go about this.

[K^2]

You come up with an ascent profile and integrate thrust over it. There is no simple shortcut here.

There are some ways to get rough estimates, but no such thing as a formula for it.

[Xannari Ferrows]

Actually, there is a formula you can use, but I'm not sure you would want to see the size of it. I do have it, though.

[Yru0]

You come up with an ascent profile and integrate thrust over it. There is no simple shortcut here.

There are some ways to get rough estimates, but no such thing as a formula for it.

I've heard this brought up here and there, but calculus has never been my strongest suit so it's passed right over my head.

What do you mean by 'integrate thrust' over the ascent profile? Do you plot the ascent path as a function and then integrate it? If so, what do you mean by 'integrate thrust over it'? :3

[K^2]

Yeah, essentially. Given some thrust profile T(t) and specific impulse I(t), the mass flow rate is given by m'(t) = -T(t)/I(t), while dV is accumulated at the rate V'(t) = T(t)/m(t). So if you know thrust and I_SP as a function of time, you can simply take an integral from liftoff to orbit and obtain the dV budget. Of course, by this point, you've solved the problem for which you're trying to get dV in the first place. You essentially need to know the entire trajectory and how much fuel you're burning at every moment of time. In other words, what you really need to do is solve for ascent profile. And that's an even more complicated task, which typically involves considerable numerical skills.

For a planet without the atmosphere, good ascent profiles are pretty well known. They involve constant-altitude burn until you attain orbital speed, proceeding to prograde burn until you attain transfer speed to desired orbit. From there, it's identical to Hohmann. The actual dV budget still depends a LOT on TWR, but at least, it's a simple enough thing to compute for a given TWR. Once you throw in atmosphere, this becomes an almost impossibly complex problem to get a perfect answer for. You can get a good ascent profile, though, which is typically all you care about.

Actually, there is a formula you can use

Only for rough approximations. This isn't something you can put into a formula.

[Ralathon]

Actually, there is a formula you can use, but I'm not sure you would want to see the size of it. I do have it, though.

Yea, sure you do... If I recall correctly you couldn't even tell the difference between a proof and a gut feeling during that "derive the area of a circle via triangle" thread you made a while back.

There is no single formula for this since the optimal ascent path depends on the staging and TWR of the ascent vehicle.

I've heard this brought up here and there, but calculus has never been my strongest suit so it's passed right over my head.

What do you mean by 'integrate thrust' over the ascent profile? Do you plot the ascent path as a function and then integrate it? If so, what do you mean by 'integrate thrust over it'? :3

He means that you find the thrust of the vehicle as a function of time and then integrate it. Then you plug in the time of engine cutoff and you have the dV of the ascent.

[Xannari Ferrows]

Yea, sure you do... If I recall correctly you couldn't even tell the difference between a proof and a gut feeling during that "derive the area of a circle via triangle" thread you made a while back.

There is no single formula for this since the optimal ascent path depends on the staging and TWR of the ascent vehicle.

I'd prefer to not talk to you anymore. I'd hate to use your client as a test subject. Be thankful I at least assumed that you knew what you were doing. Would you show a tutorial for how to play a game at a tournament?

Edited May 22, 2015 by Xannari Ferrows