Kinematic Equations

[Pandarist]

I'm trying to calculate the acceleration needed to to get right right velocity at the right time to get a couple missions done, but I'm having trouble. I'm using MechJeb to show and control my acceleration, though it seems like it's a Kerbal problem rather than MechJeb. As I never took physics in high school this is kinda new to me, but I found Kinematic Equations online, and the one in particular that was relevant is as follows:

Velocity(final)^2=Velocity(initial)^2+2*a*d

I plug in the values I'm looking for,

260m/s^2 = 0m/s^2 + 2 * a * 4200m

Apply the exponents,

67600m^2/s^2 = 0m^2/s^2 + 2 * a * 4200m

Eliminate the 0 because it's 0,

67600m^2/s^2 = 2 * a * 4200m

Simplify the right side,

67600m^2/s^2 = a * 8400m

Divide both sides by 8400m to end up with,

8.047619048m/s^2 = a

Now looking at MechJeb's acceleration (that I assume it's reading from Kerbal itself) and forcing it not to exceed that, my rocket doesn't even leave the ground.

I'm not quite sure how Kerbal calculates acceleration, but at some point I figured I'd try adding in 1G of gravity to see if that was what was confusing me, leaving me with 17.85426905m/s^2, but even if I bump it up to 20m/s^2 it never reaches the velocity I want at the altitude I want. Am I using this math wrong? Is there some other math I should be using? Or is Kerbal just a little weird with its math?

Edited October 10, 2014 by Pandarist

[mhoram]

The formula you have applied is based on the assumption that a is constant during the whole time, but this is not the case in the example you try to calculate.

The acceleration is actually based on the sum of the three forces Drag, Gravity and Thrust.

Drag does not stay constant, because it increases with velocity and decreases with pressure.

Gravity does not stay constant, because it decreases with altitude.

And thrust increases with spent fuel.

So this formula is not the one you need.

Another thing you could check is if the acceleration MJ displays, is based on all 3 forces or only on thrust - but according to what you have written, it seems like the later is the case.

If you want to delve into the details of how acceleration is calculated, have a look at chapters 5&6 of http://forum.kerbalspaceprogram.com/threads/93426-Physics-of-KSP.

[RizzoTheRat]

It gets complicated really quickly.

Force = Mass x Acceleration; but your mass changes as you use fuel

Drag (real world) = 0.5 x air density x Velocity^2 x Drag coefficient x Area; but density changes with altitude, and KSP's standard model uses a bodge for drag coefficient x area. I the real world (and I guess in FAR) that changes again when you hit transonic speeds.

I have a degree in Aeronautical Engineering and that document Mhoram produced makes my head swim, I need to work through it properly at some point

I do all my atmospheric testing with planes rather than rockets, much easier to get the required height and speed, and with the new parts in 0.25 I'm managing to make some better aircraft too.

[Lukaszenko]

I'm guessing, based on the values you are using, that you are sitting on the launch pad, and want to get to a velocity of 260 m/s in 4200 m....and you're trying to solve for what acceleration is needed to achieve this?

If that's the case, then indeed 8 m/s^2 is what you need. However, you must keep in mind that gravity is trying to pull you down at 9.81 m/s^2 (but can't because the ground is stopping you). If you want to actually lift off the ground, your acceleration has to be AT LEAST 9.81 m/s^2. If you want to go straight up at 8 m/s^2, then your rocket needs to provide thrust for 9.81 + 8 m/s^2.

As mentioned, once you get moving then drag starts working against you. Gravity also decreases with the square of the distance (from the CENTER of the planet), but this is probably not a huge effect at 4200 m.

[Pandarist]

So it sounds like the reason those equations don't work is the same reason a stationary car spinning its tires on ice would incorrectly indicate a high speed?

I'll look into the other equations for gravity and drag then, thanks a lot