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If I understand correctly, the term 'gravity turn' refers to a specific way to turn from the initial near-vertical launch direction to a final tangential orbit direction in an efficient manner. It's described as a relatively small tangential nudge, return to essentially zero angle of attack (or displacement angle - I have asked separately about that) and the trajectory will naturally slowly turn over "sideways" into the tangential direction.

As the Kerbal Wiki wisely teaches us:

Then once a certain altitude is reached, a slight turn is made, called the pitchover maneuver. By turning away from vertical slightly, gravity will pull the velocity vector of the craft down towards that direction and the craft has to tilt to follow it.

In modern, large launch vehicles with sophisticated aerodynamic models, and vectored and throttled thrusts, is the classic gravity turn maneuver still approximated - either by design or coincidence - or is the actual turn the result of such a complex optimization problem that a classical gravity turn per se is no longer recognizable?

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    $\begingroup$ You might want to take a look at this: space.stackexchange.com/questions/6031/… The question is about speed; but the answer cites many relevant materials $\endgroup$ – Antzi Jul 12 '16 at 8:23
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    $\begingroup$ Gravity turn is the minimal AoA maneuver, so still desirable at least through the dense atmosphere. $\endgroup$ – Russell Borogove Jul 12 '16 at 16:07
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    $\begingroup$ Any stretch of time during atmospheric ascent where the rocket isn't vertical and its AoA is near zero is gravity turn by definition. I was hoping Braeunig's Saturn V sim showed AoA in tabulated results, but no luck. $\endgroup$ – Russell Borogove Jul 15 '16 at 15:08
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    $\begingroup$ (Alternately, if it's supersonic and not falling apart, it's probably pretty close to gravity turn. ;) $\endgroup$ – Russell Borogove Jul 15 '16 at 15:12
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    $\begingroup$ @RussellBorogove so it sounds to me like the avoidance of lateral stresses is actually more important in practice than the efficiency of the turn, which is where many descriptions begin. $\endgroup$ – uhoh Jul 15 '16 at 15:22
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Ares I would have flown very close to an ideal gravity turn in the atmosphere. One paper that covers the simplest guidance of pitching it over on an initial azimuth and then flying it with basically zero AoA up until SRB separation is here:

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080048217.pdf

There's another paper here where it finds you can get somewhat better performance in terms of injected mass (if i'm reading it right particularly when considering the envelope of how it could be perturbed by winds) by optimizing the trajectory with a highly constrained aerodynamic bending moment and allowing the AoA to vary from zero as long as the constraint is satisfied (with closed-loop guidance).

https://www.researchgate.net/publication/239415099_Highly_Constrained_Optimal_Launch_Ascent_Guidance

If you look at Figure 9 there the dotted red line is the open-loop gravity turn and the top figure shows it having zero AoA up until about 120 seconds. The blue line is the optimized closed loop guidance which outperforms it. But up until about 80 seconds it looks just like the gravity turn to my eyes...

Other rockets that don't need to be so highly constrained (any rocket other than Ares I) can benefit from flying at higher AoAs. So I believe something like the Falcon 9 would fly pitched up a bit higher to benefit from body lift (the rocket body acting like a wing) up until stress on the structure of the vehicle became a factor (or at some point drag and aerodynamic instability?). But such an ascent is going to look pretty much like a zero AoA trajectory on a naive "eyeball" test (particularly compared to some of my highly non-zero AoA KSP launches).

So I don't know if that helps answer your question at all. Rockets still pretty much fly zero AoA gravity turns more or less. But you can always do better, so they're not flown with perfectly zero AoA gravity turns.

(And I've considered implementing something like the Ares I zero-AoA open loop gravity turn algorithm in MechJeb to deal with optimization of the pitch program for PEG launches, although I don't think I'm going to head that way now)

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    $\begingroup$ This is exactly the kind of answer I was looking for, thanks! $\endgroup$ – uhoh Feb 4 '18 at 6:19
  • $\begingroup$ Per this QA, the lofting of a Falcon 9 is apparent to the naked eye towards the end of the first stage burn: space.stackexchange.com/questions/20916/… $\endgroup$ – Russell Borogove Feb 5 '18 at 3:04
  • $\begingroup$ That looks similar to the AoA curve in the second paper there where the AoA is allowed to deviate after 80 seconds (the F9 shots there are T+90). $\endgroup$ – lamont Feb 6 '18 at 21:48
  • $\begingroup$ If you google "squatcheloid" you can also find some discussions on the allowable envelope of the product of alpha (AoA) times Q (dynamic pressure) or beta (sideslip angle) times dynamic pressure. $\endgroup$ – lamont Sep 30 '18 at 21:13
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Sometimes you just can't get @RussellBorogove to admit that those really helpful comments can become a really a good answer. So until that time comes... I'll temporarily accept this copy/paste answer.

From here:

Any stretch of time during atmospheric ascent where the rocket isn't vertical and its AoA is near zero is gravity turn by definition.

and from here

(Alternately, if it's supersonic and not falling apart, it's probably pretty close to gravity turn. ;)

So a recognizable feature of the general idea of a gravity turn may be the fact that the turn happens without tilting the rocket away from the direction it's moving through the air (very much) with thrust. I think. The added structural mass required to handle side stresses at supersonic speeds are a huge penalty - and if you don't add it, you'd loose structural integrity if you tried to make a substantial turn by vectoring thrust.

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  • $\begingroup$ A better/more thorough answer is always welcome! $\endgroup$ – uhoh Feb 3 '18 at 6:05
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    $\begingroup$ Sometimes my really helpful comments turn out to only tell half the story and I don't realize it until a year later: space.stackexchange.com/questions/20916/… $\endgroup$ – Russell Borogove Feb 5 '18 at 3:05
  • $\begingroup$ @RussellBorogove Well they're always helpful, no matter what else! $\endgroup$ – uhoh Feb 5 '18 at 3:51
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    $\begingroup$ Re ... and its AoA is near zero is gravity turn by definition" Whose definition? A classical gravity turn means thrust is directed along the inertial velocity vector rather than the planet-fixed velocity vector. Angle of attack is measured with respect to the local winds. The Earth's atmosphere more or less moves with the rotating Earth. My take on "gravity turn" is that it's a tautological term. A "gravity turn" trajectory optimizes something such as fuel consumption or mass to orbit. So of course a gravity turn trajectory is the optimal trajectory, by definition. $\endgroup$ – David Hammen Jan 10 at 20:37
  • $\begingroup$ @DavidHammen I see what you mean. Feel free to add an answer here and/or have a look at Angle of attack, or displacement angle? $\endgroup$ – uhoh Jan 11 at 1:33

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