How to calculate launch windows?

[Jovus]

As part of my slow-going project to make an RSS launch autopilot for an arbitrary orbit-capable rocket, I've run into a small issue.

How do you calculate launch windows?

I've already properly figured out how to calculate the launch azimuth from an arbitrary launch site into an arbitrary parking orbit (assuming the launch site inclination is <= orbit inclination; I'm not doing bi-elliptic transfer calculations yet). What I don't have is a way to find when the launch site is in the plane of the target orbit.

Anyone feel like walking me through it? My spherical geometry is rusty, and these days I just don't have a lot of time on my hands to brush it up again.

[Nibb31]

The porkchop analysis is pretty good: https://en.wikipedia.org/wiki/Porkchop_plot

Luckily, MechJeb has this included. Not sure if it works with RSS.

[Jovus]

I should have been more clear.

I'm not concerned with interplanetary windows yet. All I want is the (twice daily) window when a launch site is in the same plane as an inclined orbit around Earth. (Or some other arbitrary planet.)

[ElWanderer]

I have a kOS library that tries to calculate this. I've only just documented it (most of my code is uncommented, so I'm slowly adding separate readme files), but hopefully that'll explain the maths behind what I'm doing, even if the kOS code itself is of no use/interest. Check out the etaToOrbitPlane function.

Library: https://github.com/ElWanderer/kOS_scripts/blob/master/scripts/lib_launch_geo.ks

Documentation: https://github.com/ElWanderer/kOS_scripts/blob/master/documentation/lib_launch_geo_readme.md

[magnemoe]

15 hours ago, ElWanderer said:

I have a kOS library that tries to calculate this. I've only just documented it (most of my code is uncommented, so I'm slowly adding separate readme files), but hopefully that'll explain the maths behind what I'm doing, even if the kOS code itself is of no use/interest. Check out the etaToOrbitPlane function.

Library: https://github.com/ElWanderer/kOS_scripts/blob/master/scripts/lib_launch_geo.ks

Documentation: https://github.com/ElWanderer/kOS_scripts/blob/master/documentation/lib_launch_geo_readme.md

As i suspected you have to launch a bit before you pass below the orbital plane of target, you launch with the inclination of target.
KOS uses an fixed value for the lead time who is half the time you need to reach orbit. 

[Jovus]

@ElWanderer Thanks, that was exactly what I needed. I was missing the ARCSIN(TAN(current_latitude)/TAN(target_orbit_inclination)) bit, and trying something around converting to a ground track and comparing secants. (It was ugly. It didn't work. I'm not proud.)

Your method works like a charm.

[ElWanderer]

14 minutes ago, Jovus said:

@ElWanderer Thanks, that was exactly what I needed. I was missing the ARCSIN(TAN(current_latitude)/TAN(target_orbit_inclination)) bit, and trying something around converting to a ground track and comparing secants. (It was ugly. It didn't work. I'm not proud.)

Your method works like a charm.

Glad that helped. I just wish I could remember where I found that function; from memory it was a book which shows up in Google search, but where it shows you every other page rather than the whole thing. In this case the bit I needed was on a page I could see!