Delta-v in Kerbin (and other) atmospheres?

[TheSandDuna]

So I have a question regarding the delta-v equations that are all important to this game. I know a few things about orbital velocities, but what I do not understand is why a certain delta-v in the atmosphere is different than delta-v in a vacuum.

For example, to reach a circular orbit around Kerbin at 80km, you can use the vis-viva equation to find the orbital velocity--> v=sqrt(6.67e-11*5.29e22*(1/680000))=2277m/s. Makes sense, and when I reach that orbit I do get that speed. But delta v is change in velocity so in a vacuum you could accelerate from 0 m/s to 2277 m/s with a delta-v of 2277 m/s. But from Kerbin, you need a delta-v of 4550 m/s to achieve this. Other than drag, what causes this discrepancy, and is there a good (easy) way to calculate the delta-v from the surface of a planet to orbit on planets other than Kerbin?

I'm sure this has been discussed before but any explanation would be great.

Edited February 1, 2014 by TheSandDuna
Answered

[Dave Kerbin]

Gravity and speed, depending on your frame of reference. Atmospheric drag also plays a part.

From the gravity point of view until you are moving 2277 m/s sideways you are still falling on a suborbital trajectory, which means you must somehow prevent yourself from losing altitude and hitting the ground first. So for every second it is taking you to reach 2277 m/s moving horizontally, you must also thrust at least 9.81 m/s vertically to prevent yourself from smacking into the ground.

From the speed point of view 2277 m/s is only the velocity that will keep you in orbit at 80 km. As you lower your altitude the velocity required for orbit increases. So even if you had a special rocket that instantly applied 2277 m/s of acceleration on the launchpad, you wouldn't be at the correct altitude for that velocity to be enough for orbit. So you end up needing additional speed to raise your altitude which circles right back to gravity constantly trying to keep you down.

[MaverickSawyer]

Drag losses, gravity losses, and steering losses are all tracked by MechJeb and Kerbal Engineer Redux. You can pull them up and see what you're losing.

[TheSandDuna]

I haven't used MechJeb butI just started using Engineer Redux, very helpful tools but I think it is good to know where those numbers are coming from before you accept them, so I like to do some calculations by hand if I can.

OK, those answers make sense. But other than watching Scott Manley videos all day, is there any way to decide on a good method for achieving orbit with minimal delta-v losses? It seems possible to just boost vertically straight up to your desired altitude then boost horizontally to a good speed, but that is obviously not as efficient as turning your vehicle until it hits that sweet spot (2277 horizontally) during the ascent.

Usually I just fire at max thrust until I hit 15-20km, then shift over to a 45 degree angle until my apoapsis is around 75km. Then shut down the engines until I am near the edge of the atmosphere and boost horizontally based on my own judgements until I get into orbit. Are there any more exact ways of doing it? Since each vehicle has a different TWR each will have its own optimal maneuvers, I just want to know where to look for some advice to see if I can make interplanetary trips as lightweight as possible.

[Dave Kerbin]

Either with a lot of experience or mechjeb you can fly it 'perfect' by constantly adjusting the throttle and turning to match your ascent speed. But flying straight into an orbit (continuous thrust) is frequently not the most fuel efficient way to do it in KSP because of how the physics work and the unique size and properties of Kerbin. Even in real life some rockets (like the space shuttle) use two burns, a long one to reach a suborbital path, and a second burn at apoapsis (AP) to circularize.

I'm not an expert at getting orbits but I have picked up enough to do it relatively efficiently without having to know a lot of numbers or change the throttle. My method isn't the best possible method, but it is pretty easy to do and gets much better results then going straight up.

First I start with my TWR. With .23 you can tweak the maximum thrust of engines. I take the initial mass of the ship and work out the thrust % so that each stage starts out with a TWR of about 1.44 to 1.5. By preseting my engines like this I can just put the throttle at full and I should avoid drag issues while still wasting as little thrust as possible (the slower you go the more time gravity has to pull you down).

For my ascent I monitor my velocity: At 250 m/s I should be between 10-12km and I should turn 23 degrees east (half way to the next big notch). At 500m/s I should turn another 22 degrees (now at 45 degrees). At 750 m/s I should turn another 23 degrees and be looking at my map and hovering the mouse over the AP to see what it is. At 900-1000 m/s I should turn again to one or two notches before the division between the blue and orange part of the ball and get ready to stop my engines when the AP reaches my goal, which is between 71 km and 80 km depending on how big of a launch vehicle I'm using. Once I've stopped I setup a maneuver node at the AP to circularize my orbit. This should cost about 800 - 1200 m/s, usually closer to 800.

The last burn to circularize doesn't need any tweaking for TWR and can be below 1.5 though you don't want to be too underpowered or you won't have enough time to burn before you start falling back down.

[mhoram]

is there any way to decide on a good method for achieving orbit with minimal delta-v losses?

That is an issue that interests me very much. Currently I use an external tool PSOPT in order to optimize control (thrust and direction) of KSP-rockets for minimal fuel consumption. You can find more infos in this thread.

Edited January 26, 2014 by mhoram

[tavert]

Atmospheric ascent is a difficult optimal control problem that can't really be solved analytically because of the nonlinearities involved. The optimal gravity turn trajectory is craft-dependent. You could look at an idealized rocket with no maximum thrust limit and determine the absolute minimum delta-V ascent trajectory for each planet, but even this would require numerical optimization techniques and wouldn't be of too much practical use.