Quick and dirty How to calculate the launch azimuth

[-DDD-]

Hello word! Have you ever ask yourself how to spend the minimal amount of   ΔV for matching planes? If so this is the guide for you. I know that in the 99% you launch rocket toward east but if you are using mod like RSS or you need to rendezvous with a target in an inclined orbit you want to know what is the azimuth that save you to do the most inefficent burn in the spaceflight, the matching planes burns or inclination change burns.

 First of all a precisation launch azimuth=launch heading :-) 

So you need timewarp until the target orbit cross your launch site so you are directly under the ascending or descending node of your target so when you will launch is like you are doing a plane change manouvre but you are starting from a velocity equals to zero, so for the oberth effect is free! PS: For a precise alignment you can set the camera to the planet and move it until you see the target orbit as a line.

Now you know when launch, for know at what heading launch there is a bit of trigonometry.

For the spherical trigonometry we can calculte the azimuth for any inclinaton that is smaller than our latitude with this formula:

Cos(Inc) = Cos(Lat)*Cos() Where  is our launch azimuth, inc the target inclination and Lat is the our latitude.

Now we have only to single out :

= arcos[cos(inc)/cos(Lat)]

But this formula is not 100% precise because it consider a non rotating planet, for example for the ISS from cape canaveral give us 44.98° or 135.02°

If you want a more precise azimuth you need to take account of the rotating velocity of the planet and the math involed start to being a bit more complicated

If you are a true masochist here can find the dimostration: http://www.orbiterwiki.org/wiki/Launch_Azimuth#Rotation_of_the_Earth

If not this is the final formula: sqrt(V_Target*sin() - V_Chaser*Cos(Lat))²+(V_Orbit*Cos())²) 

Where V_Target is the orbital velocity of your target and V_Chaser is your orbital velocity at launchpad

Using this formula instead of the previous one you save 284 m/s for a launch to the ISS from Cape Canaveral.

Spoiler

Alternatively you can use MJ

 

Edited July 12, 2016 by -DDD-

[swjr-swis]

"Quick and dirty" in random triple A title: <explain how to aim somewhat ahead/above the target for instant headshot>

"Quick and dirty" in KSP: <adds specific explanation of how to calculate, including trigonometric functions, RL examples and researched article references>

 

I love what KSP does to its players.

Edited July 12, 2016 by swjr-swis

[-DDD-]

Lol, with the title i mean to ask foginess for my terrible english, but i can't see people that launch towards east for rendezvous with a vessel in polar orbit

[swjr-swis]

13 minutes ago, -DDD- said:

terrible

Improvement is always possible, but I understood all of it, trigonometry and all. You did good, way better than I would in some other languages (and sometimes, my own).

My response was a joking compliment, really.