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# Thread: A handy chart for Aerocapture at Jool

1. ## A handy chart for Aerocapture at Jool

Hi all,

Here's a little something I made for fun this afternoon: it's a Jool aerocapture chart.

Big Version

This chart gives the periapsis distance for aerocapture into a variety of different orbits after entering Jool's SOI.

To use it, exit time acceleration once in Jool's SOI. Find the curve corresponding to the orbit you want after aerocapture. Find where that curve intersects your orbital velocity (measured on the navball). The y-axis reading then gives the periapsis distance that should aerocapture you into that orbit.

This chart should be enough to get you reasonably close (delta-v wise) to any target orbit. For calculating other aerobraking maneuvers, I'd suggest using my aerobraking calculator: http://alterbaron.github.io/ksp_aerocalc (The plot was obtained using the same approach used there.)

(NB: This chart assumes that your ship does not have lift surfaces. These might mess up your results if you have any. Use right at SOI entry for best results.)

Let me know what you think!

2. Oh my god man this is one of the most amazing things I have ever seen!

THIS IS SOME ACTUAL SCIENCE TO DO WITH KERBAL SPACE PROGRAM!

Because remember kids... the difference between science and screwing around is writing it down.

3. Not just science; color coded science! With a graph!

This looks very useful, and I'll have to save that calculator to my favorites!

4. Ooh, nicely done. I'll have to knick this for the Drawing Board

Incidentally, I've been trying to crack the math for aerobraking myself, but I've had a bit of trouble lately. Unfortunately, calculus is one of the subjects I've never studied, but I'm pretty good with college-level algebra, and I can do some stuff with geometry (including conic sections). Think you could help me demystify some of it?

5. Originally Posted by Specialist290
Incidentally, I've been trying to crack the math for aerobraking myself, but I've had a bit of trouble lately. Unfortunately, calculus is one of the subjects I've never studied, but I'm pretty good with college-level algebra, and I can do some stuff with geometry (including conic sections).
You don't need to know much calculus to do these sort of calculations numerically (which is what I did here.) But you do need some comfort with forces in physics.

Basically, draw the free body diagram for the craft. You'll have a force due to gravity, and a force due to air drag. You take the net force from the free body diagram and set F=ma, or a = F/m.

Once you have the acceleration as a function of position and velocity, you can "plug the formula into a computer program to have it numerically solve for the path that the object will take."
I say this loosely, because the book-keeping can get rather tedious. But it's simple at heart.
This number crunching is based on calculus and can be summarized as "step forward in time, re-calculate forces, update position and velocity, and repeat."

Everything else is just a bit of tricky geometry.

6. I cheat... I use the predictor in MechJeb's landing system.

7. Originally Posted by NeoMorph
I cheat... I use the predictor in MechJeb's landing system.
That's true, but wouldn't you feel more like a rocket scientist using a chart?

8. This looks incredibly useful. I love that the SOI-transition velocity scale goes up to 5000m/s!

9. Originally Posted by Pyotor Gagarin
This looks incredibly useful. I love that the SOI-transition velocity scale goes up to 5000m/s!
Well, you never know what people will do . . .

10. Here's some mathematical details, for those who are curious:

Let r = (rx,ry) be the vector from the center of the planet to our ship, and v = (vx,vy) be the velocity vector of the ship.
Then the force of drag is given by the following equation:

Kp = 1.2230948554874*0.008
FD = -0.5 Kp P0 exp((R0-norm(r))/H0)norm(v) d m A v

Where Kp is the conversion factor between pressure and density given on the wiki, P0 is the pressure at sea level (1atm for Kerbin), H0 is the atmosphere scale factor (5000m for Kerbin), R0 is the radius of the planet (needed since the vector r extends from the center of the planet), d is the coefficient of drag, m is the ship's mass, and A is the "cross-sectional area" of the ship, which is a constant in-game. The velocity v is a vector, don't forget!

Note that in the real world, there is no factor of "m" in the above equation.

The force of gravity on the ship is simply:

FG = - m(mu/norm(r)^3)r

Where mu is the gravitational parameter of the planet (3.53 x 10^12 for Kerbin).
Note that r is a vector!

Then the total force on the ship is just F = FD + FG. (A vector sum).

Note that norm(r) means the vector (cartesian) length of r.

These equations are used to simulate the trajectory of a ship as it passes through a planet's atmosphere. Here's a quick method that works o.k.:

Say the ship has a current position r=(rx,ry) and a velocity (vx,vy). We calculate a net force of F=(Fx,Fy) using the above equations at the current position and velocity.

Our acceleration is, by newton's law, a=F/m

Call our current time t. Consider a small time step dt. The velocity at time t+dt is approx. v+a*dt.
Likewise, the position is approx. r+v*dt.

Using this new approximate position and velocity, we can calculate F anew. Do this, rinse, repeat, and you're pretty much done. If you hold on to all your old values of "r" as you go, you have the path that the ship followed through the atmosphere. You also have its velocity at every point in time.

Neat, huh?

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