Kerbal Space Program - Efficient Launch into Orbit

[collinsmark]

Efficient launch into orbit.

Designing a small, simple, efficient and stable launch vehicle to get into Kerbin's orbit can be done pretty easily. But in order to avoid building oversized, overcomplicated, drag prone behemoths (like the one I was using in the first post of this thread), one first needs to know how to perform an efficient launch, in order to build a rocket that does so (rocket design post coming soon!).

Unfortunately, this is where much information found on the Internet is misleading, or just plain wrong.

Debunking section

This is from the Kerbal Space Program Wiki site, iki.kerbalspaceprogram.com/wiki/. I suppose since it's a wiki, I could correct it myself, but I'm rather lazy like that.

Claim: Upon reaching 10,000 meters: "Throttle your second engine down to 2/3rds power since the atmosphere is weaker here and won't slow you down as much, and you will save precious fuel."​

​

Truth: That's backwards. If anything, you should be increasing your throttle somewhat after reaching 10,000 meters. That actual amount depends on the specific rocket though, and how fast it's already traveling, so the "2/3" figure is pretty meaningless without more details about the rocket. My point is, holding back on the throttle is much more important in the lower, thicker atmosphere below 10,000 m than it is above it. Only continue to back-off on the throttle if you find yourself traveling at speeds greater than 300 m/s at the time when you hit 10,000 m altitude (the actual velocity depends slightly on the drag of your rocket, and you'd need pretty overpowered rocket for that to happen anyway, so 300 m/s is a good number for most any vessel). Terminal velocity increases quickly at altitudes above 10,000, which is why it's usually a good time to increase the throttle at this point. More on this below.​

Here is another one I heard from a YouTube video,

Claim: When getting into orbit, all your original "upwards velocity" is lost/wasted. In achieving orbit, it's only the "sideways velocity" that matters.​

​

Truth: That's a little misleading. (btw, the terms "upwards velocity" and "sideways velocity" are not my terms; they were from the video.) It's true that it's wasteful to go straight up for too long when achieving orbit. But not for the same reasons. Orbital energy has two components, kinetic energy and potential energy. The "upwards velocity" (as it was called) eventually gets converted to potential energy, which gets stored in the orbit (albeit initially, an extremely eliptical orbit). The true losses come from a) performing a maneuver such that a component of the thrust vector is parallel to the gravitational acceleration vector (gravity losses), in other words, increasing the apoapsis at a location other than the periapsis. There is a loss associated with the component of thrust being parallel to the gravity vector, which is why prograde and retrograde maneuvers are most efficient at apoapsis and periapsis. Also, orbital energy is only increased by the component of the thrust vector (your heading when you apply thrust) that is parallel with the velocity vector, i.e., parallel to your orbital prograde vector. And similarly, since the initial orbit is so terribly elliptical, it will invariably involve the following: b) later when the orbit needs to be circularized, it must involve course corrections (perpendicular to the velocity vector) that are done at higher orbital kinetic energies. It is most efficient to perform course corrections at the point of lowest, orbital kinetic energy. By that, the gravity turn should be done earlier rather than later. The optimal transition tradeoff between course correction losses and drag losses happens almost invariably at around 10,000 m altitude (specifically with Kerbin). So in conclusion, there are losses associated with this "upwards velocity" but it's not a total loss. I do agree however with the author of the video that going too far straight "up" is wasteful.​

"Optimal" (or at least quite efficient) method for achieving orbit (on Kerbin specifically)

1. Go straight up for the first 10,000 meters. During this time, adjust your throttle to limit your speed. If you go too fast you'll be wasting much or most of your thrust (and thus fuel) to drag forces. The velocity limit changes with height (altitude). At the initial lauch, start off at full throttle, but be prepared to quickly lower the throttle. I can't tell you how much "% throttle" you should adjust to, because it depends on the rocket. Rockets with very high thrust to weight ratio (TWR) will need to throttle back more. Rockets with very low TWR might not need to throttle back much if at all. Here are some general guidlines that should apply to most (nearly all) rockets:
   
   Below 1000 m, don't travel faster than around 100 m/s
   Below 3000 m, don't travel faster than around 130 m/s
   Below 7000 m, don't travel faster than around 200 m/s
   Below 10,000 m, don't travel faster than around 300 m/s
   Below 12,000 m, don't travel faster than around 400 m/s
   
   Note that the craft's speed will naturally increase as its mass decreases from less fuel. Increasing speed isn't necessarily a matter of increasing throttle, but often a matter of decreasing the throttle less frequently. After about 12,000 meters allow your rocket to increase speed fairly quickly. You would have to go out of your way to design a silly rocket with ultra high TWR and horrible drag such that you couldn't be at full throttle by 20,000. For any reasonable rocket, you should go to full throttle by about 15,000 m or so, if not before.
   
   
   
   
   [Figure 1. First 10,000 meters]
2. We need to step back a little to the 10,000 m altitude point. At 10,000 meters, take a relatively sharp turn to the East (right). (You might still be throttling your engines at this point, so there's more than one thing going on here.) This adjustment is called "the gravity turn, or "gravity roll." Turn until your rocket is pointed about 40-45 degrees above the horizon. Now, you may ask, "is it possible to optimize this, instead of a blanket statement 'turn 45 deg right at 10,000 m'?" Yes, in truth it is possible to optimize it. But it's hardly worth it. The optimal solution in almost every case is something very similar to "make a relatively sharp right to 45 deg at 10,000 m," regardless of your rocket. You could put in the math and fluid dynamics to optimize it, but it's hardly worth the trouble, and you won't gain much by doing so. Suffice it to say this: if your rocket is extremely underpowered, with a very low thrust to weight ratio (TWR), you may need to start your gravity turn a little below 10,000 meters, and a little more gently. For everything else, it's a fairly sharp turn at 10,000 meters.
   
   
   
   
   [Figure 2. Start gravity turn]
   
   
   
   
   [Figure 3. Continue gravity turn]
3. If and when your prograde vector passes your heading vector (you can see this on the navball), change your heading to stay on top of your prograde vector. Continue this until your altitude is about 20,000 meters or so. Remember, you are increasing your orbital energy by aligning your heading (thrust vector) and your prograde vector.
4. Above 20,000-40,000 feet, adjust your heading such that it lies in between the prograde vector and the artificial horizon on the navball. At this altitude, drag forces are pretty negligible for the velocities we're presently at. But there is another trade-off. Like I keep mentioning, it's only the component of the thrust that's parallel to the prograde vector that adds energy into the orbit. But since you're not at apoapsis, there is also some gravity loss since you're not traveling parellel to the horizon. So we reach a compromise by angling the ship to point in-between the two. Continue this until your desired apoapsis is reached (at least 70,000 meters).* Once a desired apoapsis is achieved, you can cut the engines.
5. If you've been to orbit before, and you are familiar with the "maneuver node" tool, now is a good time to use it. Set up a prograde maneuver at your apoapsis, and bring up your periapsis. Using the maneuver node tool is nice because it estimates the burn time for you. If you are not familiar with the maneuver node tool yet, this might not be the best time to experiment with it. So alternatively (without the maneuver node tool), prepare to burn prograde sometime before you reach your apoapsis and continue burning until your periapsis rises to its desired level. The amount of time that you start the burn before reaching your apoapsis depends on your rocket. But as a rough guess, somewhere around 30 seconds or so is typical.

*(If you're trying to win an efficiency contest, you might gain a tiny bit by only bringing your apoapsis in step 4 to only about 63,000 meters or so, then follow through with step 5, and finish up with circularizing the orbit with a Hohmann maneuver on the other side. But that's efficiency overkill if you ask me.)

Here's a summary of the above looking at the map view.

[Figure 3. Gravity turn, map view]

[Figure 4. Prepare to sync up with velocity vector]

[Figure 5. Drag forces becoming negligible. Increase thrust in the prograde direction to add energy to the orbit.]

[Figure 6. Remain at maximum thrust in the direction between prograde and the horizon.]

[Figure 7. Continue the same until desired apoapsis is achieved.]

[Figure 8. Once desired apoapsis is achieved, set up a maneuver node to finish it off, or alternatively, burn prograde near apoapsis]

[Figure 9. Thrust, and how it relates to position relative to apoapsis]

Things can get tricky in step 5 if your rocket is very underpowered. If you don't have the thrust to bring your periapsis up, you might find yourself in trouble. If you find yourself far past apoapsis, and still don't see a periapsis, keep your heading slightly on the blue side of the artificial horizon (on the navball). It's a little wasteful that way, but it might just buy you some time.

[Figure 10. Thrust with an underpowered (low TWR) vessel]

At the risk of being redundant, orbital prograde and retrograde maneuvers are the only way to increase and decrease the energy of an orbit (assuming no other forces are involved like drag). I repeat it because it is kind of important. If you ever do a purely radial or normal maneuver, you only change the shape of the orbit. That might be difficult to tell with the maneuver node tool, because it assumes that the thrust vector remains constant, even though the planned velocity vector changes accordingly (thus the velocity vector will eventually contain prograde or retrograde components parallel to the thrust). But if you were to adjust the ship's heading (and thus thrust direction) to always remain perpendicular with the velocity, you would never change orbital energy by only radial or normal maneuvers (and assuming that the orbit does not pass through a solid surface such as Kerbin, with the ship in that part of the orbit).

(The 10,000 meter gravity turn figure, and the rough terminal velocity figures mentioned above were from experimenting with version v0.23.5 of the game. It's possible that these numbers might change in future game versions if the game's aerodynamic modeling is changed.)

Full Series
Part 1: Introduction and Basics
Part 2: Efficient Launch Into Orbit
Part 3: Rocket Design Basics
https://www.physicsforums.com/threads/kerbal-space-program-rocket-design-and-orbital-mechanics.970334/
https://www.physicsforums.com/threads/kerbal-space-program-getting-to-the-mun.970335/
https://www.physicsforums.com/threads/kerbal-space-program-getting-to-the-mun-part-2.970336/
https://www.physicsforums.com/threads/kerbal-space-program-preparing-to-land-on-the-mun.970337/
https://www.physicsforums.com/threads/kerbal-space-program-mun-touchdown.970338/
https://www.physicsforums.com/threads/kerbal-space-program-staying-on-the-moon.970339/
https://www.physicsforums.com/threads/kerbal-space-program-preparing-to-leave-lander.970340/
https://www.physicsforums.com/threads/kerbal-space-program-walking-on-the-mun.970341/
https://www.physicsforums.com/threads/kerbal-space-program-leaving-the-mun.970342/
https://www.physicsforums.com/threads/kerbal-space-program-rendezvous-and-docking.970343/
https://www.physicsforums.com/threads/kerbal-space-program-prograde-retrograde-and-approach.970344/
https://www.physicsforums.com/threads/kerbal-space-program-prepare-for-docking.970345/
https://www.physicsforums.com/threads/kerbal-space-program-docking-and-lander-reunion.970346/
https://www.physicsforums.com/threads/kerbal-space-program-heading-home.970347/
https://www.physicsforums.com/threads/kerbal-space-program-entering-Earth's-orbit.970348/
Part 19: Landing Back on Earth
Part 20: Launch for Duna
https://www.physicsforums.com/threads/kerbal-space-program-duna-probe-launch.970351/
Part 22: Duna Rocket Launch
https://www.physicsforums.com/threads/kerbal-space-program-duna-burn-and-periapsis.970354/
https://www.physicsforums.com/threads/kerbal-space-program-duna-oberth-effect.970355/
https://www.physicsforums.com/threads/kerbal-space-program-duna-mid-course-corrections.970356/
https://www.physicsforums.com/threads/kerbal-space-program-using-gravity-to-orbit-duna.970357/
https://www.physicsforums.com/threads/kerbal-space-program-landing-on-duna.970358/
https://www.physicsforums.com/threads/kerbal-space-program-exploring-duna.970359/
https://www.physicsforums.com/threads/kerbal-space-program-launching-off-duna.970360/
https://www.physicsforums.com/threads/kerbal-space-program-fast-return-path-from-duna.970361/
Part 31: Advanced Duna Flight Math
https://www.physicsforums.com/threads/kerbal-space-program-burn-2-to-escape-duna.970363/
Part 33: Returning to Earth From Duna

 

[cjl]

A minor nitpick - I've noticed that KSPers in general seem to really like to use the term "gravity turn" when what they actually mean is "pitchover". The pitchover is where the rocket's trajectory turns away from vertical, and begins to follow the desired ascent profile to orbit. Ideally, to minimize steering losses, you want to start it as early as possible (much earlier than 10km), but the initial pitchover in such a flight path is much less extreme than your example as well so the first 10-15km or so of flight ends up being pretty near vertical anyways.

A gravity turn is a careful optimization of the entire post-pitchover ascent profile, designed such that the rocket's thrust is always aligned with its direction of travel throughout the ascent. I don't think I've ever seen someone pull one off in KSP, in part because it is different for each rocket design. The basic idea however comes from the fact that for any rocket in a non-vertical orientation, the acceleration in the horizontal direction is simply F/M multiplied by the sine of the angle (I'll call it A) the rocket is pointing away from vertical, but the acceleration in the vertical is F/M*cos(A) - g. If we start from a stationary position, this will result in a trajectory with an angle away from vertical equal to arctan((F/M*sin(A))/(F/M*cos(A) - g)). If you're familiar with trig functions, you'll notice that because (F/M*sin(A))/(F/M*cos(A)-G) is bigger than sin(A)/cos(A), the resulting angle away from vertical will be larger than A, so the trajectory of an angled rocket will tend to be flatter than you would expect purely based on the angle of the rocket.

If you start with a rocket flying vertically, you can take advantage of this fact when making your turn towards orbit - after you pitchover (usually not by very much for real rockets - only a few degrees), the trajectory begins to angle over as well. When the trajectory passes the current pitch angle of the rocket, you begin angling the rocket to track the flattening of the trajectory, such that the rocket post-pitchover is always flying at zero angle of attack. This is a very good thing, since it minimizes non-axial loads on the rocket, and it eliminates steering losses after the pitchover (in your example, when you first pitch over at 10km, only 71% of the rocket's thrust is actually acting in the direction of travel, so you have pretty substantial steering losses for a period of time after that). The difficulty however is figuring out at what altitude to perform the initial pitchover, as well as how much to deviate from vertical. If done correctly, the trajectory will flatten due to gravity at a rate such that the rocket ends up horizontal at the desired altitude and at the correct time after launch to achieve orbit. This is also why it is called a "gravity turn" - you are never using the thrust of the rockets to alter the trajectory - you are always burning exactly along your trajectory, and using gravity to steer the trajectory into orbit.

 

[cjl]

Oh, and as for your figure 10, if you're flying that rocket the same way you were discussing before (45 degree pitchover at 10km), you probably can get it to space if you just adjust your ascent profile into more of a lofted trajectory. This involves intentionally staying a bit more vertical for a bit longer near the beginning of the flight, and making a more gradual turn towards orbit. This gives you a higher initial apogee, and (hopefully) a bit more time to burn at wide open throttle with your underpowered upper stage to build enough speed to make orbit. This is actually done with the Delta IV and Atlas V, if I remember right, since they have highly efficient but relatively underpowered second stages. You do burn slightly more fuel this way than with an optimal trajectory, but sometimes the smaller, lighter engine you can get away with more than makes up for the fuel difference.

 

[collinsmark]

The neat thing about Kerbal Space Program (KSP) is how easy it is to experiment. Just build a rocket and try things out!

A good measure of Kerbin launch efficiency is how much fuel the rocket has left once it completes circularizing a given, desired orbit around Kerbin. It's easy enough to jot down the remaining fuel from one trial to the next, then use the data for comparison.

Try different approaches, and see which works best! (Preferably by changing a single variable at a time, and using scientific method.)

 

[cjl]

The neat thing about Kerbal Space Program (KSP) is how easy it is to experiment. Just build a rocket and try things out!

Oh, believe me, I have. It isn't quite as brutally realistic as Orbiter, but it's realistic enough to teach a fair amount about orbital mechanics without the frustration inherent in a more accurate sim (like Orbiter). I also love the cartoonish aesthetic (especially the kerbals), and ease of building new rockets. I was mostly just complaining about inaccurate use of terminology, and giving you some suggestions on how to get a rocket with an underpowered second stage to a stable orbit. It's a great program though, and I definitely think it's a wonderful way for people to learn about spaceflight and orbital mechanics.

 

[collinsmark]

(in your example, when you first pitch over at 10km, only 71% of the rocket's thrust is actually acting in the direction of travel, so you have pretty substantial steering losses for a period of time after that).

I just took a look at the navball in the images I posted in the last post, and I think I can clear up some confusion by noting that the image in the first pitch-over showed the surface velocity vector. Perhaps I should have clicked on the navball to switch over to orbital velocity before taking the screenshot. (My bad for the confusion.)

When I made the comments about following the velocity vector after the pitch-over/gravity turn, I meant the orbital velocity vector, not the surface velocity vector. (I agree I should have made that more clear in both the text and the image.)

I hope this image might clear up some confusion.

I was talking about two things at once. There's a lot going on when you do the pitch-over (beginning of gravity turn), and I only used one image to convey multiple things.

At the time of take-off, the rocket has 0 surface velocity. But it already has significant tangential, orbital velocity due to the rotation of Kerbin.

When throttling down to keep at or below terminal velocity, one should monitor the surface velocity speed, since that's a more accurate number relative to the rocket's speed relative to the atmosphere. When I said, "go straight up," I meant that in terms of the surface.

But when I said "follow the prograde velocity vector" (and eventually place the ship's heading in between the prograde vector and the horizon) I meant the orbital prograde vector, not the surface prograde vector.

KSP will automatically switch from surface speed (and surface prograde vector) to orbital speed (and orbit prograde vector) at some given altitude. Or you can switch between them manually, by clicking on the box above the navball, circled in red in the above image.

Sorry, I wasn't very clear about that in my last post.

cjl, we're on the same page.