staplic

Alright, probably a stupid question, but am I missing a version of MechJeb for the 0.22 release that works in career mode?

a note for anyone using the derivation I posted, i got ahead of myself a bit and forgot a factor of t in the integral deriving x. It's fixed now but the term (V-phi-I)t is actually (v-I)t-0.5phi t^2.

Since there wasn't an equation I decided to try and develop one, and I've almost got it, but unfortunately my mathematica software is maxing out my CPU trying to simplify this in closed form so I'll just post the fragments up here to see if someone else can simplify it (or point out an error in it, as is always a possibility): First I computed the total minimum delta-v needed for touchdown using conservation of energy: Start with Potential Energy in orbit (a height h above the surface) and subtract from it the potential energy at the surface: (-μMm)/〖(ÃÂ+h)〗^2 -(-μMm)/ÃÂ^2 = Net Potential Energy where μ = gravitational parameter (G in our universe) M = Mass of planet/moon (referred to as 'the body') m = mass of rocket à= radius of the body This simplifies to: (mÕ*(2ÃÂh+h^2))/〖(ÃÂ+h)〗^2 where: Õ = acceleration due to gravity at the surface of the body. this must be equal to the Kinetic Energy gained = 0.5m v^2. The m's cancel and since you started with 0 vertical speed the final v is your total vertical delta v, combine this with the horizontal speed you have to kill and delta-v = √((2Õ*(2ÃÂh+h^2))/〖(ÃÂ+h)〗^2 +vh^2 ) where: vh = horizontal speed Using this we can then calculate the burn time: t= (m*I/T)*(1-â…‡^((-v)â„I)) where t= time I = specific Impulse of your rocket T = Thrust of your rocket v= delta-v calculated above. In a similar method to how we derived the total delta-v we can find our vertical velocity as a function of vertical height x where we will start our burn this velocity Y is: Y=(ÃÂ*√(2Õ(h-x)*(h+x+2ÃÂ)))/((ÃÂ+h)*(ÃÂ+x)) where all variables are as previously defined. Lastly since we want our velocity to be zero at touchdown we know that: dx = Y+at dt with a = (T/(m-nt))-Õ where n is the mass flow rate m-dot. notice a is a function of time so integrating this function we get: x = (Y-I)*t-0.5Õ*t^2 + (m*I^2/T)*Ln[(m*I)/(m*I-T*t)] in theory solving this last equation for x (recall Y is a function of x as well) and plugging in the values calculated above you can solve for x in terms of h, rho, phi, I, T, and m, all of which are known to you at the time you start your descent. When attempting to solve for x you run into a fairly nasty looking fourth order polynomial to solve and then work your way through each of the four solutions to figure out which one yields a positive real result (and if there are two which one actually works). Like I said earlier my mathematica kernal timed out and shut down when I attempted to have it simplify[solve[]] this, but if we get it in a simplified closed form I wouldn't think it would be too difficult to have a computer crunch the numbers.

I've been looking for a formula or a guide on exactly when to initiate a deceleration burn while landing on a planet that will get you to a safe landing speed and minimize the delta-V involved in the burn. I've been experimenting with this in game a bit too, but I'm finding it difficult to find that window in the first place from which to fit a model. If I start burning before the window, my speed will drop to 0 then I have to shut down (or I start going up again) and then I have to burn again later to kill off the speed I gain from falling. Conversely if I burn to late my speed doesn't fall enough and a blow up on impact. Without a formula I've been erring on the side of going early, but as I move on to progressively more difficult objects to land on (Tylo for instance) I'm trying to conserve as much delta-v as possible.