Landing at the KSC from any orbit [Math]

[hikoriyami]

The last few months I’ve started to get into reusable crafts. The main hiccup in my reusable vehicles has always been getting them to land back at the runway. I thought for sure that there was a mod that would tell you when you need to burn to get yourself back to the KSC. There are a couple of mods that tell you where you will land, once you’re already landing, but none can tell you when to start your burn to land where you want to.

I decided to take up reading Katherine Johnson’s work with NASA. She is the original genius who figured out where John Glenn’s capsule would land. Her work is very complicated, involving trigonometry and calculus. But I could par it down to basic algebra by ignoring things we do not need to worry about in KSP.

Below is the video I have made describing these calculations and how to use them. 

To start off: the KSC is almost exactly on the equator at 74.34 W. This is where we want to land.

We need two things: the rotation rate (or day) of the planet (kerbin) and the time until periapsis.
With this information we can convert the rotation of the planet into usable coordinates to tell us when we should begin slowing down.

We then need to flip the coordinates to give us the coordinates of apoapsis and factor in the atmosphere. The equations are listed below.

Edited February 19, 2017 by hikoriyami

[FawkesTheFirebird]

IS this how scott manley lands at the space center every time?? Or is this something else?

[Vanamonde]

This tutorial has been moved to the Tutorials subforum. 

[Long Finger]

On 2/19/2017 at 10:46 PM, hikoriyami said:

 

 

This is very interesting. Do you have an internet link to Johnson's original work?

[hikoriyami]

2 hours ago, Long Finger said:

 

This is very interesting. Do you have an internet link to Johnson's original work?

It is linked from her biography page at NASA

It's a long, but incredibly interesting read.    

The application of the math outlined in the above paper gets even more interesting.

Edited March 9, 2017 by hikoriyami

[Nightside]

Thank you for this, going to try it now!

[xendelaar]

 very interesting and way better than precise landing by infinite trail and error. thanks!

[Pecan]

On 2/19/2017 at 10:46 PM, hikoriyami said:

...I decided to take up reading Katherine Johnson’s work with NASA. She is the original genius who figured out where John Glenn’s capsule would land...

I can recommend the film 'Hidden Figures' for anyone interested.  It's mostly about the sexism and, especially, racism 3 pioneering black women faced in early-60s America while working at NASA but there's a fair bit of 'how the hell do we space?' in there too.  Plus, it's just a really inspiring feel-good film :-)

[Yoochem]

Thanks for posting this! I'd love to learn a bit more about the actual math needed to calculate reentries, and this is a great start. How did you get your value of 1.2 though? Is there a way to calculate this without trial & error? The point of using this kind of math would be to avoid that (very Kerbal!) style of playing of course.

By the way, coincidentally just saw that movie Hidden Figures a few days ago. It covers a lot of different topics, from spaceflight to human rights; I'd recommend watching it!

[Spricigo]

3 hours ago, Yoochem said:

The point of using this kind of math would be to avoid that (very Kerbal!) {trial & error}  style of playing of course.

Even if is not enough to completely avoid trial & error,  sufficient to reduce it by a fair amount. Often,  theory only comes so far as to a prediction with small but noticeable error

[hikoriyami]

On 6/27/2017 at 6:51 AM, Yoochem said:

Thanks for posting this! I'd love to learn a bit more about the actual math needed to calculate reentries, and this is a great start. How did you get your value of 1.2 though? Is there a way to calculate this without trial & error? The point of using this kind of math would be to avoid that (very Kerbal!) style of playing of course.

The value of 1.2 is the average deceleration in Gs you experience on reentry until landed. This helps calculate how far before the landing you should burn. For example, a slow decent may have a value of 0.5 while a very quick high G burn will have a value of 2.1.

On 6/27/2017 at 10:43 AM, Spricigo said:

Even if is not enough to completely avoid trial & error,  sufficient to reduce it by a fair amount. Often,  theory only comes so far as to a prediction with small but noticeable error

I never found a way to solve for the average deceleration, but it can be fairly accurately guestimated by using the thrust of the engines, or the steepness of the decent combined with the atmospheres thickness.

On 6/27/2017 at 6:51 AM, Yoochem said:

I can recommend the film 'Hidden Figures' for anyone interested.  It's mostly about the sexism and, especially, racism 3 pioneering black women faced in early-60s America while working at NASA but there's a fair bit of 'how the hell do we space?' in there too.  Plus, it's just a really inspiring feel-good film :-)

By the way, coincidentally just saw that movie Hidden Figures a few days ago. It covers a lot of different topics, from spaceflight to human rights; I'd recommend watching it!

Yep, love this movie. Only problem I have with it is the beginning where they "fix" the car by bridging the battery terminals (don't do that!). The writer probably meant for that scene was to jump the starter motor, but that got changed by someone on set during filming. 

There is definitely some room to expand on these formulas and I am working on ways of doing so. The expansions can include: orbits that are not circular, other bodies, and orbits longer than a day.

[EdwardB3020]

Is the black line separating the time to periapsis and rotation period a division line because it was a bit unclear in the video. 

Edited December 12, 2022 by CaptWhitmire
Clarity