The maths, the transfers, the rockets... ?

[Panichio]

So I've been reading all around the forum, and trying to absorb as much information as I can to help me design a suitable mission for another planet or moon. There has been so much talk and how-to threads, I feel a little confused and overloaded with different strategies, and why munar slingshots are not that good but are for this... Or why Hohmann transfers aren't always the most fuel efficient... Or the Oberth effect... Everything...

I would really love for someone to explain all of this, so that I can choose the most suitable method, and design the best rocket for the mission, as well as doing some of the maths myself. So basically, I'd like some help understanding all of the different things to know about deep space travel, just to clear things up, and eliminate my confusion. Does anyone have any links to a thread existing already, that has all this information? I hope I wasn't too vague...

Thanks in advance.

Edited September 13, 2012 by Panichio

[pebble_garden]

Let me be the first to say the title of this thread -- "The maths, the transfers, the rockets... ?" -- sounds like the opening line of some Beat poet treatise on rocket science, or perhaps an essay by Jorge Luis Borges.

And I'll likely be the only person to make such an observation, because I'm weird that way.

The maths, the transfers, the rockets...

Young men sailing bravely on the sea of space

to the siren song of slide rules

as they arc across the cosmos, daring fate

borne on Newton's wings

beyond the infinite, and back

into the arms of tearful wives

quickening those private heavens in their turn

Edited September 13, 2012 by pebble_garden

[UmbralRaptor]

There's enough misinformation/poorly thought out advice, and correct but highly limited tutorials that I'm not sure any such thread exists. The most comprehensive approach would be grabbing a textbook on orbital mechanics, or poking through wikipedia so you can learn the math/physics and judge each case for yourself. Hohmann vs Bi-elliptic transfers, the value of either vs gravitational slingshots, direct ascent vs rendezvous, etc all involve tradeoffs, so which is best is situationally dependent.

[Hillstache]

I would say one thing you could do is try some of the different strategies talked about in the various threads and see what happens. It's one thing to read about a Munar slingshot, but if you actually try an orbital manouvre with and without a slingshot you should be able to see the resulting differences.

From my own experience I just played around in KSP and discovered some of these things on my own, before I tried to apply any math to my activities. I found that once I had an intuitive grasp on some of the orbital mechanics, actually understanding what's going on was easier.

[Panichio]

Alright, thanks! I didn't think I was going to get a great poem along with some very helpful answers!

[Kosmo-not]

Oberth Effect is easy to understand. Work energy is defines as force (thrust in kN) multiplied by distance (in m). Power is defined as energy created over a period of time. Thrust (in kN) multiplied by velocity (in m/s) results in power (kJ/s or kilowatts). The Oberth Effect just says that a rocket can generate more power when it is going faster (same thrust but different velocity). This can add to your orbital energy at a greater rate.

[Panichio]

Oberth Effect is easy to understand. Work energy is defines as force (thrust in kN) multiplied by distance (in m). Power is defined as energy created over a period of time. Thrust (in kN) multiplied by velocity (in m/s) results in power (kJ/s or kilowatts). The Oberth Effect just says that a rocket can generate more power when it is going faster (same thrust but different velocity). This can add to your orbital energy at a greater rate.

Ah, right, I remember that one. I have been reading on Wikipedia about the Bi-elliptic transfer, which took me to semi-major axis, then to about five other articles Now I'm confused. I'll leave it 'till tomorrow...

[Nadrek]

I'm working through much the same things - the trig I haven't used in a long, long time, physics likewise, and orbital mechanics I've never studied in detail.

I've found searching the Web to be extremely limited; orbits can be circles, ellipses, parabolas, or hyperbolas. Unfortunately, most orbital equations I can find are simplified to either circles or ellipses (but not both). Arrowstar recommends the Vallado (http://www.amazon.com/Fundamentals-Astrodynamics-Applications-David-Vallado/dp/1881883140) third edition, with erratta (http://celestrak.com/software/vallado-sw.asp) - I won't have a copy for another couple weeks.

I'm documenting as much as I learn and code in the Autom8 thread (post #53 and after) for others - SimpleOrbitalMechanics is lua code (equations are very readable) for basic orbital equations; it doesn't depend on KSP or Mechjeb Autom8 at all (you could run it with lua on Linux, or Lua for windows (http://code.google.com/p/luaforwindows/) or just read the equations and notes. Learning the geometry seems a pre-req for the Keplerian orbital elements.

Some web references I've used are:

http://what-when-how.com/remote-sensing-from-air-and-space/a-few-standard-orbits-orbital-mechanics-interlude-remote-sensing/

http://www.braeunig.us/space/orbmech.htm

http://www.faqs.org/faqs/space/math/

https://en.wikipedia.org/wiki/Orbital_period

https://en.wikipedia.org/wiki/Rocket_equation

https://www.earthobservatory.nasa.gov/Features/OrbitsCatalog/

https://en.wikipedia.org/wiki/Semi-major_axis

https://en.wikipedia.org/wiki/List_of_mountains_on_the_Moon

https://en.wikipedia.org/wiki/Standard_gravitational_parameter

https://en.wikipedia.org/wiki/Sphere_of_influence_%28astrodynamics%29

https://en.wikipedia.org/wiki/Standard_gravity

https://en.wikipedia.org/wiki/Gravitational_constant

https://en.wikipedia.org/wiki/Kepler_orbit

Edited September 16, 2012 by Nadrek

[maltesh]

Circles are just ellipses with eccentricity 0, and a semimajor axis (and semiminor axis) equal to their radius. Almost anything that deals with ellipses will work with circles.

Hyperbolas can get a bit tricky. It really depends on what you're doing with them.

This would be the reference that was of most equational help when I was writing my orbital calculator.

http://www.nature1st.net/bogan/orbits/kepler/orbteqtn.html

This link was also pretty useful.

http://www.braeunig.us/space/orbmech.htm

And there's a Google Doc in my signature that does some discussion of the Keplerian Orbital Elements as present in the persistent.sfs file.

[Panichio]

Wow, thanks guys, and thanks KSP. Never did I think I would be reading up on all of this. It's amazing how much people can try and learn and teach themselves willingly, all to be able to succeed in a video game, it's great.

[Monkster]

The trick for success is to use the method that works best for you. We can all sit and talk until the cows come home about every pro and con of each sort of orbit/transfer/rendezvous technique there is. But if you manage to get your Kerbals to the Mun, by getting a slingshot off Minmus via the sun, (apart from being worshipped as some form of sorceror) it will make you feel warm inside and people will probably try your method of doing things.

Tutorials help with KSP, and there are many fantastic ones out there. They only help to a certain extent though, sure if you wanted to you could copy everything you have seen in guides and either fail or succeed each time. Take what you think works best for you out of each thing you watch, read or listen to. Apply it to your own designs, if it works for you, keep it, if not then bin it. That's the beauty of this game. "X" person designed this rocket. I like "this, this and this but, definitely not that".

Pretty much all the tutorials and guides out there give you an excellent example of what to aim for. They will give you the basic design for a craft, orbital techniques and all the trimmings. Who's to say that you can't combine twenty of the things you have seen and then launch yourself on a figure eight orbit between Kearth and the Mun? The only reason it's not been mentioned before is because nobody (I did a quick search of the forums so please feel free to correct me) has done it

TL;DR

All of the tutorials and guides you see are correct, it's all down to personal preference, technique for doing things or what colour hat you are wearing on the day.

[Arrowstar]

Arrowstar recommends the Vallado (http://www.amazon.com/Fundamentals-Astrodynamics-Applications-David-Vallado/dp/1881883140) third edition, with erratta (http://celestrak.com/software/vallado-sw.asp) - I won't have a copy for another couple weeks.

I do indeed! As a professional astrodynamicist, I believe it to be a wonderful reference text with lots of applications, both basic and advanced.

[Tommygun]

A game that makes you do homework.

I haven't decided if that's a good thing or not.

[Nadrek]

Circles are just ellipses with eccentricity 0, and a semimajor axis (and semiminor axis) equal to their radius. Almost anything that deals with ellipses will work with circles.

Until you ask KSP where the Apoapsis or Periapsis of a circular orbit is, or the time to them. Or want some of the orbital elements of a circular, equatorial orbit using an equation that assumes an elliptical orbit... or a non-equatorial circular orbit. I'm finding all kinds of fun special cases.

Edited September 17, 2012 by Nadrek
Where the Ap or Pe is, not what it is :)

[Panichio]

The trick for success is to use the method that works best for you. We can all sit and talk until the cows come home about every pro and con of each sort of orbit/transfer/rendezvous technique there is. But if you manage to get your Kerbals to the Mun, by getting a slingshot off Minmus via the sun, (apart from being worshipped as some form of sorceror) it will make you feel warm inside and people will probably try your method of doing things.

Tutorials help with KSP, and there are many fantastic ones out there. They only help to a certain extent though, sure if you wanted to you could copy everything you have seen in guides and either fail or succeed each time. Take what you think works best for you out of each thing you watch, read or listen to. Apply it to your own designs, if it works for you, keep it, if not then bin it. That's the beauty of this game. "X" person designed this rocket. I like "this, this and this but, definitely not that".

Pretty much all the tutorials and guides out there give you an excellent example of what to aim for. They will give you the basic design for a craft, orbital techniques and all the trimmings. Who's to say that you can't combine twenty of the things you have seen and then launch yourself on a figure eight orbit between Kearth and the Mun? The only reason it's not been mentioned before is because nobody (I did a quick search of the forums so please feel free to correct me) has done it

TL;DR

All of the tutorials and guides you see are correct, it's all down to personal preference, technique for doing things or what colour hat you are wearing on the day.

Thank you, I'll keep that in mind.

[khearn]

A couple of vary basic things to get you started for seat of the pants orbital mechanics:

- To change either your periapsis (point of closest approach) or apoapsis (point of farthest distance), do a burn at the opposite one.

- To raise the opposite one, burn prograde (in the direction you are moving in orbit). To lower it, burn retrograde (the other way). Going faster move you out, going slower moves you in.

- To match the inclination of another orbit (useful for getting to or from Minimus), wait until you're at the point where the orbits are crossing as seen from the side in map view, then burn straight up (or straight down) in relation to the orbital plane (not in relation to the planet your orbiting) to change your inclination to match. This isn't the cheapest way to do it, but it's the easiest.

When trying to match orbits for a rendezvous, first make sure your inclinations are matched so both orbits are on the same plane, then get the orbits fairly similar. Then follow these rules to move your ship in relation to the target:

- In takes you forward.

- Forward takes you out.

- Out takes you backwards.

- Backwards takes you in.

(paraphrased from Larry Niven's The Smoke Ring - an excellent sci fi book that will teach you some bits of orbital mechanics)

Just pointing at your target and burning won't work unless you're very close to each other. if you're the same distance out, but your target is in front of you in orbit, point inward and do a short burn. This will move you to a lower orbit, which has a shorter period, so you'll move forward closer to your target. If your target is even with you but farther outward, burn pointing forwards (prograde). This increases your orbital velocity, which makes your orbit get larger, which moves you outward towards your target. Et cetera.

The next thing to learn would probably be phase angles. If you're seen video tutorials for how to get to the Mun, you've probably seen the technique of getting in a low Kerbin orbit (LKO) and then waiting until you see the Mun rise and burning prograde at that time to get a transfer orbit that will be at the Mun's orbit when the Mun gets to that point in its orbit. Burn much earlier or much later and you get to the Mun's orbit when the Mun is in the wrong spot. That's because the Mun happens to be orbiting at just the right distance so that the angle it's at when it rises is just right to make that work. This is either a happy coincidence, or evidence of intelligent design (on the dev's part, to make things easier for seat of the pants flying).

The angle between your ship and the Mun, centered in the middle of Kerbin, is called the phase angle. and in this case (LKO to the Mun) its a little less than 90 degrees. If you're in a higher orbit, or going to something in a different orbit (like Minimus), it will be different. It's a measure of how far your target will move around it's orbit while you're moving around your transfer orbit. It takes a bit of math to figure it out, but it's not too bad. I'll leave the math as an exercise to the reader, since this is getting too long. Do a web search and I'm sure you'll find the formula.

[AmpsterMan]

I had some problems with orbital mechanics when i first started as well. The first person that replied to your post has very high quality videos explaining orbital mechanics in her signature. I suggest you check them out. They sure helped me out!

If you want to see a nice let's play together with some whacky, yet informational stuff then Scott Manley (aka Illectro) has great videos on youtube as well. Between these two people I have been able to play this game XD

As far as ship design, I think the two most important things to know are TWR and Dellta-V. TWR stands for thrust-to-weight ratio and is most important when you are in a gravity well (ie. taking off from Kerbin, landing on Mun, Minmus... etc) The higher your TWR, the faster you will escape Kerbin's lower, denser atmosphere. The second one, Delta-V is easy to understand but a little harder and more labor intensive to calculate. Basically, delta-v is how much energy your rocket can expend to move itself about. It stands to reason that to get into orbit requires less energy than to reach the moon. There is an equation that can help you to calculate exactly how much energy your ship can give you , but it is not REALLY necessary. Honestly, until now I haven't even bothered with delta-v and have been able to get to every celestial body in the Kerbol system as of yet.

TL;DR Pebble_Garden and Illectro have very good instructional videos, and learn about Thrust-to-Weight ratios and at least understand the concept of Delta-V

[nivvydaskrl]

At risk of sounding terribly self-promoting, my blog here on the KSP site (http://kerbalspaceprogram.com/forum/blog.php/6794-nivvydaskrl) has a lot of the math for various fun things, and I'm always looking for more things to write about. I do most of my posts based on questions from other people, so if you have any questions, shoot them my way and I'll answer them in (mind-numbing!) detail!