Delta V Economics

[Empiro]

That's what I had been thinking. Then, I realized that this is not the case. The most efficient IP transfer trajectory from launch will leave your periapsis inside Kerbin. You save the delta-v of working on your periapsis at all, this way.

Happy landings!

This is usually true, and one way to look at it is from the perspective of obtaining enough orbit specific energy for your interplanetary transfer. Since gravity is conservative, it doesn't really matter how your orbit looks, as long as you have the energy you need. Circularization costs you a bit of extra delta-V because for most rocket designs, you coast to AP, which means that you lose velocity as you're waiting, and as we all know, due to the Oberth Effect it means that it will now take more delta-V to get the same amount of orbit specific energy.

Thus, your trajectory and burn may or may not put your PE out of Kerbin, but the savings you get is mostly from the fact that you never stopped firing your engines.

[tsotha]

That's what I had been thinking. Then, I realized that this is not the case. The most efficient IP transfer trajectory from launch will leave your periapsis inside Kerbin. You save the delta-v of working on your periapsis at all, this way.

Happy landings!

This makes no sense to me. Where, exactly, is your Kerbin periapsis when you're on an interplanetary trajectory? Are you saying the instant before you leave orbit your periapsis is inside Kerbin's atmosphere? If so, where is it?

[Kryxal]

This is basically saying that you do mostly all of the transfer burn before you leave the atmosphere ... your periapsis can't be above where you burn from, after all. You just go from a low PE to having it be not far below you and watching the AP go sailing off into the FAR distance, then probably make a small correction burn once you clear atmosphere.

[Starhawk]

This makes no sense to me. Where, exactly, is your Kerbin periapsis when you're on an interplanetary trajectory? Are you saying the instant before you leave orbit your periapsis is inside Kerbin's atmosphere? If so, where is it?

I'm saying that you don't need a trajectory which raises your periapsis outside of Kerbin. You can certainly set up a highly elliptical 'orbit' which has an apoapsis of 82000 km and a periapsis which is still inside the planet Kerbin. If you keep burning, that apoapsis becomes an escape from Kerbin's SOI, and eventually, a transfer to wherever. The point is that it's not necessary to expend any energy on raising your periapsis outside the atmosphere, or even the planet's surface. That is (a tiny amount of) energy you save compared to if you circularize and then start increasing your apo until it becomes your escape.

Happy landings!

Edited March 24, 2015 by Starhawk

[Champ]

I'm saying that you don't need a trajectory which raises your periapsis outside of Kerbin. You can certainly set up a highly elliptical 'orbit' which has an apoapsis of 82000 km and a periapsis which is still inside the planet Kerbin. If you keep burning, that apoapsis becomes an escape from Kerbin's SOI, and eventually, a transfer to wherever. The point is that it's not necessary to expend any energy on raising your periapsis outside the atmosphere, or even the planet's surface. That is (a tiny amount of) energy you save compared to if you circularize and then start increasing your apo until it becomes your escape.

Happy landings!

You are just not considering the fact that you are losing a lot of energy to gravity drag.

Your solution implies you are always burning vertically. This is BAD. Burning horisontally is better.

EDIT : http://en.wikipedia.org/wiki/Gravity_drag#Vector_considerations

This helped me understand why burning horizontally is better. I hope it works for you.

Edited March 24, 2015 by Champ

[Starhawk]

You are just not considering the fact that you are losing a lot of energy to gravity drag.

Your solution implies you are always burning vertically. This is BAD. Burning horisontally is better.

I'm certainly not anticipating a 'burn vertical' trajectory at all. I'm imagining a curve between 'burn vertically' and 'circularize' that would provide the necessary escape velocity while keeping the periapsis inside Kerbin.

Maybe there is not such a trajectory which is more efficient than circularization, but it seems intuitively that it is likely to exist.

Edited March 24, 2015 by Starhawk

[impyre]

I said this in my other posts too... but I'll say it again...

Ejecting from lower orbit is more *efficient*.

Ejecting from higher orbit allows you to take more fuel out of the SOI with you.

Higher orbits are *never* more efficient, I was just offering an alternative perspective of which orbit is "better". This obviously will depend on mission parameters and personal preferences. If efficiency is your top concern, eject from as low as possible. If carrying more fuel and dV with you to the destination (_*at the cost of efficiency*_), then eject from as high as possible.

Also, to clear up an earlier misconception, ***if you are refuelling and trying to simply take as much fuel out of the SOI as possible for a given vehicle size*** the orbit with the greatest stored energy is absolutely the best. This means the orbit with the greatest orbital period (as the energy associated with any orbit is directly proportional to orbital period) will afford you the greatest advantage. Since the SOI is in the shape of a sphere, this orbit will be a circle right at the edge.

Also... this method assumes you are refuelling (or the vehicle is already full) once the vehicle reaches the parking orbit... if you are ejecting without refuelling, the lowest orbit is always best.

- - - Updated - - -

I'm certainly not anticipating a 'burn vertical' trajectory at all. I'm imagining a curve between 'burn vertically' and 'circularize' that would provide the necessary escape velocity while keeping the periapsis inside Kerbin.

Maybe there is not such a trajectory which is more efficient than circularization, but it seems intuitively that it is likely to exist.

Such a trajectory does indeed exist... it will be a hyperbolic path with the periapse within the planet.

Edited March 25, 2015 by impyre

[Kryxal]

That circle may or may not be better than launching from LKO. It's about how much of a savings the Oberth effect gives vs. how much of a savings starting with the higher energy gives.

[TheXRuler]

*snip*

Also, to clear up an earlier misconception, ***if you are refuelling and trying to simply take as much fuel out of the SOI as possible for a given vehicle size*** the orbit with the greatest stored energy is absolutely the best.

Also... this method assumes you are refuelling (or the vehicle is already full) once the vehicle reaches the parking orbit... if you are ejecting without refuelling, the lowest orbit is always best.

I'm sorry, I must admit I completely misunderstood you. If you are refueling in the parking orbit then of course the highest possible is the best.

My explanation was assuming that the mission was to be done with a minimal amount of funds.

Edited April 8, 2015 by TheXRuler

[Brainlord Mesomorph]

Your best bet for Kerbin escape is a highly elliptical orbit w/ your Pe as your ejection angle.

(see the tutorial in my sig)'

[impyre]

@Kryxal and TheXRuler:

I'd have to do some math, but I'm certain there's a point of local maxima where the benefit of higher orbit is maximized and losses from giving up the Oberth effect are minimized... especially since the Oberth effect is proportional to v squared, and total orbital energy is proportional to orbital period. Since this is the case, there must be a point where one function stops dominating and the other picks up the lead. It may be that the best of both worlds is indeed to establish an extremely elliptical orbit with a very low periapse and as high an apoapse as you can manage, and then refuel in that orbit right before doing the ejection burn... although the elliptical orbit will likely make rv'ing a pain in the neck. And thanks TheXRuler, sorry if I was impatient.

[impyre]

On doing a bit more research and reading... the conclusive answer is that for an arbitrary vessel, *having just been refuelled in a pre-set orbit*, the orbit that will allow the vessel to leave kerbin and reach the destination with the most dV possible can be described as:

1) as eccentric as possible (though this can making rendezvous more difficult)

2) having as low a periapse as possible

3) having as high an apoapse as possible (without escaping).

This doesn't consider the cost of fuel spent for the purpose of refuelling said vehicle, it's concerned only with how much fuel that vehicle is able to leave with after the refuelling and ejection burn. Of course, having a disposable transfer stage renders the entire conversation a moot point... since the payload will get intercept without spending any fuel that way also... but it basically works exactly the same way.

As a side note, the advantage gained from increased speed during burns does begin to generate smaller returns after a point due to reduced propulsive efficiency at speeds higher than exhaust velocity... although I'm not sure if KSP considers this at all. At speeds below the exhaust velocity, increases in speed improve efficiency due to both Oberth effect and increasing propulsive efficiency... once vehicle speed exceeds exhaust speed, propulsive efficiency begins to drop again. The Oberth effect probably dominates the equation both above and below exhaust speed though. Propulsive efficiency is related to the amount of propulsive energy you get from a given mass of fuel. So if exhaust speed is 3500m/s, and you aren't moving at all, the spent fuel is getting a large portion of that energy (and being accelerated in the retrograde direction)... if you're already moving at 3500m/s exactly, then the fuel leaves out going 3500m/s to your relative retrograde... but it's speed relative to the parent body will be almost nothing (you kept all the kinetic energy gains). If your vehicle's speed was 5km/s, the exhaust particles would be moving with the same prograde (relative to parent) as your vehicle, and still have 1500m/s kinetic energy left over... that's energy you can't use now.

I don't think KSP models propulsive efficiency (or at least kerbal engineer redux doesn't) because the dV readouts don't seem to change with velocity. Unlike gains from the Oberth effect (which don't change a vessel's dV but the amount of energy gained from a given amount of spent dV) gains from changes in propulsive efficiency (since it deals almost exclusively with kinetic energy[at least in lower orbits]) should probably be noticeable in the dV readouts.

[Empiro]

Your rocket continues to get greater benefits at greater speeds from the Oberth Effect regardless of how it compares to the exhaust velocity. In your example, you're correct that exhaust is travelling at 1500 m/s, which is a great amount of kinetic energy, but consider how much kinetic energy it had before it was burned, when it was moving at 5000 m/s. Compare it to the kinetic energy of 3500 m/s to 0 m/s. The conservation of energy means that this lost energy has to be made up somehow (it is gained by the rocket).

Edited March 30, 2015 by Empiro

[Red Iron Crown]

Exhaust velocity is relative to the rocket, it doesn't matter how fast the rocket is moving, both in KSP or in real life (assuming non-relativistic velocities IRL). The rocket moving faster than exhaust velocity is irrelevant and does not reduce efficiency one whit.

[Khazar]

I have couple questions about dV but they focus more on launching and getting to orbit, hope they fit in this topic.

At image below I have marked 2 points.

http://imgur.com/2CRhXWr

Point nr 1 is the alt where I start gravity turn. Point number 2 is where I burn to circularize.

When designing heavy and complex craft it’s sometimes hard choice between having more dV and TWR (most often by adding more boosters) or keeping decent stability (placing them in more and more awkward places). Because of that I sometimes end up not daring to start gravity turn until I’m over 20-25k alt, (so the point nr 1 is much higher than it’s supposed to be), and then at point nr 2 I have to accelerate more and faster. I wonder what’s more efficient ? How much I could save performing “perfect†gravity turn, and would it outweigh extra power provided by extra boosters ). I don’t need numbers, just wonder if one of the options is obviously better than other or are they around equal.

Also, would I save some reasonable amounts of dV If I would have high TWR at point nr 2, so my circularizing burn would be very short ? Would that be worth carrying all those engines all the way ?

Let’s consider 2 profiles :

1. I keep TWR between 1.1-2.0 at most of the time and I drop some engines whenever I exceed TWR 2.0 so I get lighter. I cost’s me less fuel to reach point 2 but it needs to be at lower alt (because I need to burn for longer time to circularize)
   
2. I keep TWR between 1.1-2.0 only by reducing throttle and I don’t drop any of my engines (only empty fuel tanks) so when I reach point nr 2 I have high TWR so circularizing burn would be a short one, and happening almost entirely at AP. After I have stable orbit, I drop extra engines to reduce weight for rest of the mission.
   

What would be more efficient ? Same as above, no numbers needed.

[Superfluous J]

When designing heavy and complex craft it’s sometimes hard choice between having more dV and TWR (most often by adding more boosters) or keeping decent stability (placing them in more and more awkward places). Because of that I sometimes end up not daring to start gravity turn until I’m over 20-25k alt, (so the point nr 1 is much higher than it’s supposed to be), and then at point nr 2 I have to accelerate more and faster. I wonder what’s more efficient ?

Turning early is more efficient. If you simply can't turn early then you'll waste more dV, and therefore more fuel, which of course you must carry with more boosters which makes your rocket more unstable which means you'll need more dV ... And the circle continues.

How much I could save performing “perfect†gravity turn, and would it outweigh extra power provided by extra boosters ). I don’t need numbers, just wonder if one of the options is obviously better than other or are they around equal.

Turning at about 10km and burning at a 45 degree angle until your periapsis is around 80-100 is more efficient than turning at 20km, and far more efficient than turning at 30km. I don't know the numbers and you didn't ask but it is.

Also, would I save some reasonable amounts of dV If I would have high TWR at point nr 2, so my circularizing burn would be very short ? Would that be worth carrying all those engines all the way ?

No. You are again much better off doing a proper gravity turn so you don't need to do a long circularization burn, and you therefore don't need the engines to do it quickly.

1. I keep TWR between 1.1-2.0 at most of the time and I drop some engines whenever I exceed TWR 2.0 so I get lighter. I cost’s me less fuel to reach point 2 but it needs to be at lower alt (because I need to burn for longer time to circularize)
   
2. I keep TWR between 1.1-2.0 only by reducing throttle and I don’t drop any of my engines (only empty fuel tanks) so when I reach point nr 2 I have high TWR so circularizing burn would be a short one, and happening almost entirely at AP. After I have stable orbit, I drop extra engines to reduce weight for rest of the mission.
   

Carrying engines you're not using is bad. If you have 4 engines and are running at 3/4 throttle you're essentially carrying a useless engine into the air. Throw it away and your rocket is instantly more efficient. So therefore #1 is better.

Also, keeping the TWR under 2 after launch isn't that important. You want your TWR to be just enough to keep you at atmospheric efficiency up to 13-15km, and after that it can be as high as you want, really, though at that point TWR is less important because if you do a proper gravity turn, you can have TWR as low as 0.75 or so and still be perfectly fine.

[Empiro]

Beginning the gravity turn so high up is going to cost you quite a bit of extra delta-V, no doubt about it. I recommend that you try it out by launching a small rocket and seeing how much delta-V you have left after getting into orbit using each method. I estimate that the difference will be 500-800 m/s, which is pretty significant, all things considered.

Even very large rockets can turn if given enough control and enough stability via struts, so you might be able to simply make minor tweaks to your design.

Your circulation burn doesn't need to have high TWR at all, because as long as your velocity is close to horizontal and you're thrusting along that direction, there is very little loss from gravity drag. Therefore, you should drop your engines whenever possible.

[Khazar]

Turning at about 10km and burning at a 45 degree angle until your periapsis is around 80-100 is more efficient than turning at 20km,

I forgot to mention that I have FAR installed, gravity turn is not that simple like in stock.

Even very large rockets can turn if given enough control and enough stability via struts, so you might be able to simply make minor tweaks to your design.

The worst thing is that boosters like to hit engines or other parts of the rocket. The more horizontal i would go the higher chance they would hit something. That's the key factor I don't like to turn too early. I prefer to wait at least until I drop first stage of boosters. I guess it might be not worth to bring them at all if so.

[Superfluous J]

I forgot to mention that I have FAR installed, gravity turn is not that simple like in stock.

Oh jeez then I take all that back. You're doing it 100% completely wrong

You want a TWR around 1.2-1.4 on launch. You want to start your gravity turn in the first km or so, when you're going somewhere between 50 and 100m/s. Others may be able to use math and physics to know exactly when to turn, but for each rocket I just test it a few times to see when to turn. You should almost never need to burn more than 5-10 seconds at apoapsis to circularize and you should never, ever need to worry that your gravity turn will cause stress on your rocket. Literally you should tap the control to the east so it tips like 5 degrees, and the rest should happen (mostly) automatically.

The worst thing is that boosters like to hit engines or other parts of the rocket. The more horizontal i would go the higher chance they would hit something. That's the key factor I don't like to turn too early. I prefer to wait at least until I drop first stage of boosters. I guess it might be not worth to bring them at all if so.

There is a bug in stock with radial decouplers that causes stuff to hit the center stack when it shouldn't. Fixing this bug with the Stock Bug Fix mod could alleviate some of your troubles.

Edited March 31, 2015 by 5thHorseman

[Khazar]

Oh jeez then I take all that back. You're doing it 100% completely wrong

You want a TWR around 1.2-1.4 on launch. You want to start your gravity turn in the first km or so, when you're going somewhere between 50 and 100m/s. Others may be able to use math and physics to know exactly when to turn, but for each rocket I just test it a few times to see when to turn. You should almost never need to burn more than 5-10 seconds at apoapsis to circularize and you should never, ever need to worry that your gravity turn will cause stress on your rocket. Literally you should tap the control to the east so it tips like 5 degrees, and the rest should happen (mostly) automatically.

Well I knew that instead of stock 0/45/90 profile in FAR it should be smooth 0-90 turn, but didn't know that I need to start it so soon. I just have finished assembling my main craft, so I won't be doing large launches in the nearest future, just small satellite carriers and things like that so I can start turning since launch (I wander how much fuel have I wasted putting this ship into orbit as I have did it)

There is a bug in stock with radial decouplers that causes stuff to hit the center stack when it shouldn't. Fixing this bug with the Stock Bug Fix mod could alleviate some of your troubles.

hehe I have installed this fix just couple days ago, (wanted to prevent eva ejections) and I have noticed that radial decouplers seemed to work much better but I thought it was just because the smaller size of launching craft. Nice to know that.

[Empiro]

In FAR, I've also noticed that sometimes there is a linkage failure between the decouplers and the boosters you're decoupling, so I strut the decouplers to the boosters. After that, even without the stock fix mod (which I don't use), separatrons should be enough to get your boosters safely decoupled no matter what the orientation of your rocket is.