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# When to apply thrust and how much for LKO?

## Question

I've read about delta-V and how much is required for the lowest safe orbit around Kerbin, and I've built a rocket with sufficient thrust (ignoring drag for now). Now I'd like to know what an optimum trajectory would look like, and when/if it matters how thrust is applied throughout the trajectory.

For the trajectory, the goal is to go from facing straight up to 90 degrees from there in any direction (Parallel with Kerbin surface). If it takes some time to transition, then the trajectory forms a curve. The question is how round is that curve? Obviously you'd want to minimize the amount of distance travelled through atmosphere to reduce losses from drag, but the rest of the forces sort of escape me.

As for thrust, some needs to be used to reach altitude, and some needs to be used to transition to horizontal flight, but I'm not sure how much thrust (0-100%), how long to apply it, when in the trajectory to apply it, and how quickly to taper on/off.

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The optimum trajectory is: as flat as possible. There are only two reasons for it not to be perfectly horizontal on lift-off:

1. you cannot accelerate hard enough to go fast enough to reach orbit before you start falling down to the ground again
2. you cannot get streamlined enough to avoid huge drag losses in the lower atmosphere.

The answer to issue 1 is essentially the same as on any airless body: you start going upwards to clear the terrain, then burn as horizontally as possible while maintaining a minimal positive vertical component to your velocity. In other words, head for the horizon on the navball while making sure that the prograde marker stays very slightly above it.
The added complication of having an atmosphere is that your ship has drag, and that drag is probably (assuming normal ship design) going to be lowest when you're pointing nose directly forward and engines directly rearward. Therefore your only efficient solution is to be pointing prograde at all times. Drag also affects control over the ship, and you probably also have best control (assuming normal ship design...) when pointing exactly in the direction of travel.

And this brings us to neatly to issue 2: you want to get out of the lower atmosphere quickly, while always pointing in the direction of travel (especially while in the lower atmosphere...). Therefore you have to start vertically and make a gradual turn to horizontal as soon as possible but slowly enough to get out of the thick atmosphere.

That compromise: "as soon as possible but slowly enough to get out of the thick atmosphere", is your gravity turn.

So, the gravity turn has to be:

• perfectly smooth (therefore minimising drag and control problems), i.e. facing prograde exactly at all times,
• at full power at all times (otherwise you could use less engines, saving weight),
• ideally, at lower altitudes, executed at a speed not exceeding the terminal velocity of your ship at that point (since on reaching terminal velocity, drag = 1g, rising exponentially: you'd lose less by climbing for a bit longer rather than trying to climb a bit faster). This is really only an issue for the first few mostly-vertical kilometres.

Exactly what the gravity turn looks like will depend on your thrust-to-weight ratio.
A high TWR means you reach orbital velocity faster. Therefore the gravity turn has to be finished quicker - which means starting it more agressively off-prograde or launching at less than 90°. Therefore you end up going a lot faster in the lower atmosphere and losing more energy to drag (converted into a lot more heat on your ship's skin).
A low TWR means that the gravity turn has to be much more gentle. At the lowest feasible TWR, your gravity turn only comes to an end when you reach orbital altitude: you burn constantly from lift-off to orbit circularisation. You lose less to atmospheric drag and much more to gravity losses. What you lose on fuel, however, you more than make up for on cheaper and lighter engines.

And finally, to find that best trajectory, one of the easiest tools to use is available in vanilla via the map: time-to-Ap.
On lift-off, time-to-Ap is necessarily zero and rising. It therefore doesnt help much as you try to start your gravity turn right.
However, it becomes a very good indicator of efficiency when you're at around 8-12km altitude, 45° inclined to the horizon. At that stage, time-to-Ap should be around 30s or 40s or so, climbing slowly before stabilising, then remaining that way until you're nearly in orbit. The lower your TWR, the higher this number has to be. For a low TWR ship, you need to stabilise at around 50s. For a higher TWR ship, at 40s or less. Maintaining prograde lock and this time-to-Ap should get you very efficiently to orbit.
And conversely, if you have a low TWR and time-to-Ap starts falling below about 40s or 35s, you know that you've messed up and are losing vertical speed too fast. It's only recoverable (if at all) by aiming a lot more radially out, meaning a big loss of efficiency.

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The most efficient kind of ascent path is typically what's known as a gravity turn. This involves gaining a certain amount of straight-upward velocity, and then tilting the rocket a certain number of degrees in the desired direction (usually east, and often north or south for polar orbits), waiting for the prograde marker to descend to match the rocket's new "forward" direction, and from that point on following the prograde marker in a smooth curve that minimizes drag. If you have a level 1+ pilot or a good enough probe core, you can turn on SAS and simply set it to the "follow prograde" mode.

And as mentioned by many others everywhere, there is no single, optimal ascent for every rocket. Finding the best gravity turn path for your unique rocket takes trial and error, even when a plugin is doing it (the Gravity Turn launch autopilot is an excellent assistant and/or learning aid if you want to watch how it tries different paths and see what the results are, just be sure that you have the option to 'revert to launch' before using it).

With experience, you'll get more of a feel for what's likely to work well for a given rocket. It depends mainly on two factors: TWR (Thrust to Weight Ratio) and staging. Drag can also be an issue if it's very high (large fairings or a great deal of parts sticking out without a fairing, for instance).

TWR determines how fast your rocket accelerates. If it's not above 1.0, you can't even get off the ground. I prefer to keep the starting TWR in the 1.2 to 1.5 range, and though going higher is an option it could also mean that you have built too much rocket for your payload and might be able to save some money by using a weaker engine. TWR will increase over time as each stage expends fuel, reducing its mass and thus its weight while the amount of thrust (typically) remains constant, resulting in a greater acceleration being felt, peaking right before the fuel runs out.

Staging affects your ascent by typically causing your TWR to change suddenly, usually decreasing quite a bit as your spent first stage's powerful engines and rising TWR are traded for a more efficient but weaker upper stage engine. If your second stage (or third, etc) doesn't have enough TWR you could potentially find yourself falling right back into the atmosphere if your prograde is too low to the horizon and you haven't gained enough horizontal speed yet, especially if the engine is simply too underpowered for the amount of payload it's trying to push. I'd recommend keeping this above 1.0, but keep in mind that sometimes you need to make sure it's showing you the vacuum stats (rather than atmospheric / sea-level) in order to see the right TWR and delta-V figures, as some vacuum-optimized engines (like the Poodle and Terrier) have abysmal sea-level thrust and efficiency (ISP).

How does all this affect your ascent path? If your starting TWR is high, especially if your second stage's is as well, you typically want to make more of a turn away from vertical, and start sooner. If your TWR is low, you want to start later and turn less. Expressing when to start the turn is also often done in terms of your rocket's current speed, such as "start turn at 100m/s" rather than by giving a time or altitude. They're all interrelated along with TWR anyway, and since a high-thrust rocket will gain speed faster than one with lower thrust, using starting speed figures can make it easier to make comparisons and take what you've learned with one rocket and apply it to another.

Finally, it's typically best to throttle back when your time to apoapsis reaches about 50 seconds (in the stock game you have to go to the map view and point at the apoapsis marker to see this, you can right click it to make it stay visible without having to track it with your mouse). Try to maintain that time at 50 seconds so that more of your rocket's thrust is applied later in the ascent when the rocket is aiming closer to the horizon.

The benefits of this are twofold: You waste less thrust on going up, and you delay causing your apoapsis to reach your intended orbital altitude. The sooner that happens, the larger a circularization burn you'll need to finish gaining horizontal velocity. For "getting into orbit" purposes, a larger circularization burn is bad. That's because having to apply more of your horizontal thrust at apoapsis, compared to at a lower altitude, reduces the efficiency of that thrust, costing you more fuel, according to the Oberth Effect. (Basically, you spend more delta-V for the same effect when you do it at a higher altitude.)

It's a bit counter-intuitive, so to put it another way: Applying less thrust during the middle stages of the ascent (when you're aiming more upward) allows you to apply more total horizontal thrust prior to reaching your desired apoapsis height, which saves you from having to apply significantly more thrust at the end of your ascent where that thrust is less effective. The net effect is that you spend less fuel to reach orbit if you throttle back as needed to avoid pushing your time to apoapsis over about 50 seconds until as late as possible in your ascent (often into the 25-50% range, although TWR affects it too).

Edited by Tallinu
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This is a really great read

Edited by Tyko
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8 hours ago, Tallinu said:

This is also a great perspective, overall, but I think it needs a couple of minor caveats.

(...)

Absolutely agree!

I suppose that I should have been a bit clearer about that "TTA stability" thing. Although I did worry that I'd end up writing too much.

Indeed, you can only have engines actually firing all the way to orbit if you have a really low TWR towards the end. Also, getting it so that you're literally firing prograde at full power with a stable TTA of 40 seconds or so all the way to orbit is improbable and actually quite dangerous, since it means that you were very nearly too low and too low-powered to make it!
So yes, there's bound to be a fair amount of throttling down in the latter stages, when gravity has very nearly lost the fight but is still hoping to grab you again in a few minutes.
Still, if I find that time-to-Ap is increasing much in the middle of the atmosphere, I generally take that as meaning that my mid/upper-stage engines are overpowered, or my gravity turn too slow (trajectory too high) which in turn suggests that my first-stage engines were overpowered.

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If there was a single perfect trajectory for every rocket, everyone would use it. Figuring out optimal flight profiles is one of the things that is complicated and difficult about rocket science.

That said, there is a flight profile that I typically favour when flying manually.

1. Ascend vertically at the start.
2. When altitude reaches 1km, pitch 5° in the intended direction of travel (usually, this will be East).
3. Continue pitching over another 5° with every kilometer gained, until altitude reaches 10km, at which point you should be pitched 40° relative to the surface (treating the starting pitch as 90°). Now watch your apoapsis.
4. When apoapsis reaches 25km, decrease pitch to 35°.
5. Continue pitching 5° for every 5km added to your apoapsis until apoapsis reaches 40km, at which point your pitch relative to the surface should be 20°.
6. From here, you should be able to point prograde until you reach orbit, if your rocket is well-designed.

This should work for most rockets. It will not necessarily be efficient, but unless you have a low TWR in the early stages of the rocket, it should be sufficient.

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14 minutes ago, Plusck said:

So, the gravity turn has to be:

• at full power at all times (otherwise you could use less engines, saving weight),

[...]

On lift-off, time-to-Ap is necessarily zero and rising. It therefore doesnt help much as you try to start your gravity turn right.
However, it becomes a very good indicator of efficiency when you're at around 8-12km altitude, 45° inclined to the horizon. At that stage, time-to-Ap should be around 30s or 40s or so, climbing slowly before stabilising, then remaining that way until you're nearly in orbit.

[...]

And conversely, if you have a low TWR and time-to-Ap starts falling below about 40s or 35s, you know that you've messed up and are losing vertical speed too fast. It's only recoverable (if at all) by aiming a lot more radially out, meaning a big loss of efficiency.

This is also a great perspective, overall, but I think it needs a couple of minor caveats.

Time to Apoapsis (I'll abbreviate as TTA) isn't necessarily going to stabilize and stop increasing "until nearly in orbit" if you run your engines at full power at all times the way you suggest. In my experience it never stops going up, slowly at first but more rapidly later in the ascent, unless I'm actually taking too sharp a turn and not going to space today after all. If you're taking a high enough turn to make sure you don't burn up or lose excessive amounts of speed to drag, once you start to get into the upper atmosphere TTA can rise quite rapidly, thanks to the increase in TWR as your stages expend fuel. This can happen even if you start with low TWR (around 1.2), as in your engines are just barely strong enough to take off.

Taking a sharper turn isn't necessarily a surefire answer to that, especially if your TWR drops quite dramatically when you stage. It depends on your rocket design and what fraction of your trip to orbit is performed by each stage. In fact, the closer you come to getting all the way into orbit on your first stage (doing so creates a SSTO rocket with any remaining stages as payload), the more you have to throttle back as you get closer to aiming at the horizon in order to avoid pushing your apoapsis up to your target too soon.

Another issue: Being a little too high compared to the most efficient possible gravity turn for your craft is basically safe. Being a little too low can be deadly. Keeping TTA stable toward the higher end of the range gives you more time to correct if it starts dropping (for example, after staging), by aiming slightly above your prograde vector. Doing that is not necessarily the most terrible thing ever in terms of efficiency, as long as you don't have to veer too far off prograde. For example, I've read that real-life rockets often circularize post-apoapsis, which would require just such an orientation.

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As a rough rule of thumb I tend to start my gravity turns at around 1000m aiming to be at 45 degrees by about 10,000m, and continue to flatten off from there.   Probably not the most efficient but it works fairly well for me