Is it more efficient to circularize, or direct to transfer?

[Onigato]

Okay, so from surface to Jool timing is hecka hard, but from KSC to Mun or Minmus, you basically have a pretty decent launch window on a daily basis. Is it more dV efficient to ALWAYS circularize at a LKO altitude and then Hohmann up, or is better to just wait until the paths align, launch on a more vertical path, and go straight into an SOI encounter?

Circularizing at 100km, on a stock Kerbin is about a 4500m/s prospect, depending on aerodynamic cross-section, getting that perfect gravity turn done, not fighting aerodynamic drag from over-thrusting in low atmosphere, etc. Add in about 1080m/s to orbit the Mun, 5580m/s all told, plus landing (I frankly ignore the dV map for that. I can NEVER manage it with minimum fuel.)  

But can it be more efficient to just wait for the Mun to be in a specific phase with the KSC, hold a 45 degree ascent straight through all burns, and just keep burning until you get an encounter?

Generalizing the question, is it more efficient to circularize at 100km and Hohmann to ANY orbit, or just pitch down to 45, hold that until you reach target altitude apoapsis, and then circularize at altitude?

I'm not good enough of a pilot to brute force the question through dozens of flights, I can't manage to get a consistent launch profile twice in a row, much less dozens.

[AVaughan]

In general you reduce gravity losses by circularising over a steeper ascent path.  (You don't need to actually circularise, if you can just continue the gravity turn and continue burning prograde so that you are pitched pitch down to the horizon by around 60km that should be enough to minimise gravity losses).  Also you should be able to reach Kerbin orbit using around 3500 dV, so I assume that the 4500 was a typo.

[bewing]

A direct ascent saves time and (usually) money, and (on rare occasions) fuel. It's also a lot easier to plot out. Some people will try to tell you that it's some tremendous amount less efficient than circularizing + Hohmann, but they are wrong. They will try to tell you that once you have achieved an actual orbit, that gravity losses end, but they are wrong. And especially at the very beginning of career mode, when you don't have maneuver nodes yet -- a direct ascent is a smart way to go.

And the best way to do a direct ascent is just to launch straight up.

If you are trying to do a gravity turn, you want your ship to pitch over a lot further than 45 degrees by the time you are above 35km. Setting SAS to hold prograde is your friend, there.

Edited June 3, 2018 by bewing

[Xd the great]

Well, reaching LKO is more realistic for manned missions, but fuel wise, they should be similar.

Direct ascent saves time though.

[AVaughan]

@bewing I haven't done the math, but testing in sandbox says launching straight up is not the best approach. 

Build the following rocket.  Parachute, mk1 command pod, RT-10 Hammer, decoupler, Kickback srb (thrust limited to 65%), 4 x AV-T1 winglets, launch clamps.  (KER says this rocket has 4330 m/s of dV).   Launching straight up I get an apoapsis of around 12,960 km.  (Of note is the apoapsis keeps decreasing every tick, even after I have left the atmosphere, unless I'm in timewarp.  Not sure what causes this, unless it is loss of numerical precision when ksp is calculating orbit each tick). 

If I launch and then pitch over approx 5 degrees at 20m/s, the rocket will escape Kerbin's SOI.  (Set SAS to prograde after pitching downrange.  This particular turn passes 10,000m at about 60 degrees pitch, and is about 45 degrees pitch at around 40,000m and kickback burnout).  (1.4.3 modded install, but nothing I would expect to affect physics).   Further testing with variations of the above design (reducing fuel in the Rt-10 Hammer) shows that pitching over more aggressively (10 degrees at 15 m/s) is better that the less aggressive turn. 

In the past I've noticed similar behaviour when playing RO/RP-0.  A rocket that could reach orbit, with an apoapsis around of 12,000km, could not reach the same 12,000km apoapsis when launching straight up as a sounding rocket.

[bewing]

33 minutes ago, AVaughan said:

@bewing I haven't done the math, but testing in sandbox says launching straight up is not the best approach. 

 

That's because you are not burning your fuel as rapidly as possible. Vertical launches require max acceleration, because you need to shorten the launch time (and the amount of time that it takes gravity to weaken as you climb) as much as possible -- because that reduces the gravity losses.

If I launch exactly the rocket you describe, but eliminate the thrust limiting, I get a Kerbin SOI escape in 2 days and 3 hours. With the exact same amount of fuel. What's your escape time with your bent ascent?

Edited June 4, 2018 by bewing

[AVaughan]

4 hours ago, bewing said:

If I launch exactly the rocket you describe, but eliminate the thrust limiting, I get a Kerbin SOI escape in 2 days and 3 hours. With the exact same amount of fuel. What's your escape time with your bent ascent?

With the kickback still thrust limited, if I start the pitch over at 15m/s I can get a kerbin escape in 2 days 2 hr 25 min.  But the upper stage is getting too close to thermal limits to be comfortable on that ascent profile.  (Red bars about 80% full).

If I remove the thrust limit on the kickback, but pitch the rocket 5 degrees downrange in the VAB, then launch without activating SAS I get 1 day 5 hr 17 mins.  The fins are enough to keep it stable once it gets some velocity.  (Indeed with this much TWR on liftoff I can't pitch downrange enough after launch, so I have to pitch it downrange in the VAB.  Again the upper stage is too close to thermal limits to consider this a comfortable profile).  

I agree that you want to gain as much velocity as early as possible to minimise gravity losses when using a vertically ascent profile, so a low TWR design to test that profile wasn't my best idea.  (It was habit, I tend to use a 1.2 - 1.5 liftoff TWR for most of my rockets).  I think it's possible that by launching downrange I'm able to utilise enough of Kerbin's rotational velocity (about 175m/s at the equator, if my maths is right) to offset my higher atmospheric drag.   (Even if I exit the atmosphere on a trajectory elevated 45 degrees above Kerbin's horizon, I should still be benefiting from about 123m/s of Kerbins rotational velocity).

[Kesa]

On 6/3/2018 at 6:09 AM, Onigato said:

Okay, so from surface to Jool timing is hecka hard, but from KSC to Mun or Minmus, you basically have a pretty decent launch window on a daily basis. Is it more dV efficient to ALWAYS circularize at a LKO altitude and then Hohmann up, or is better to just wait until the paths align, launch on a more vertical path, and go straight into an SOI encounter?
 

A direct ascent is always more Dv efficient than circularisation + transfer burn. This is because both trajectories have the same apoapsis (or ejection velocity, corresponding to your destination), but you make your burns closer to the planet in case of direct ascent (and have a lower periapsis, which only matters if the target trajectory is an ellipse, ie within Kerbin SOI).

Circularisation however lets you plot the perfect launch windows (although your craft won't be able to perfectly fire it due to limited TWR), so it avoids potential losses from an imprecise direct ascent. Direct transfer to Jool is not as hard as it sounds though. You can have one or several probes in very low Kerbin Orbit and plot the transfer for them to have an approximate time as to when to launch your rocket and what velocity you should aim for.

 

Caution, direct ascent is NOT vertical ascent. Vertical ascent is a particular case of direct ascent, and a dubious one.

Using a typical rocket, with TWR < 2 for the most part, you have no choice but to take the same ascent profile as a regular rocket, possibly even flatter, doing a gravity turn, being at 5-30° by 35 km up, and instead of waiting for the apoapsis to circularize, continue accelerating until you're on the transfer trajectory, which is technically a Hohman transfer, but with periapsis lower than 70 km.

That way can use the very same typical crafts you would use for a circularisation + hohman transfer, you just fly them differently.

 

11 hours ago, bewing said:

That's because you are not burning your fuel as rapidly as possible. Vertical launches require max acceleration, because you need to shorten the launch time (and the amount of time that it takes gravity to weaken as you climb) as much as possible -- because that reduces the gravity losses.

Due to gravity, it is always better to go as horizontal as possible, no matter your thrust to weight ratio.

If you want to exit Kerbin SOI with some ejection speed, your direction does not matter. The Vis-viva_equation tells you the speed you need to have at Kerbin's surface, and adjusting launch time allows you to have any ejection angle using any launch angle. So only gravity losses matter.

Using vertical ascent, you'll have gravity losses equal to

Dv/TWR

But using a constant height ascent, your gravity losses will be lesser than

Dv(1-cos(1/TWR)) ~ Dv/2TWR^2 << Dv/TWR

Lesser because you'll be helped by centrifugal forces as you go. And as a bonus, you'll accelerate a bit closer to the planet than with vertical ascent.

Vertical ascent requires huge TWR in order to be viable, which means taking off from a small body where you happen to have high TWR already, or using a dedicated craft, with heavy, expensive engines. It is the easiest direct ascent to plot though and possibly easier than circularisation if you can't use manoeuver nodes or equivalent.

Constant height ascent can be done even using a non overpowered craft and requires many times less overpowering than vertical ascent if you want to reduce the gravity losses to near zero.

If the body you take off has an atmosphere, or if your target is in the SOI of the body you take off from, vertical ascent may or may not have a small additional edge to compensate.

If the body has any rotational speed, it is a big pro for horizontale ascent, although I expect retrograde horizontal ascent to still beat vertical ascent for ascent burn of more than 30s on most bodies in terms of Dv efficiency.

Finally, IRL, engines are significantly more powerfull than stock ones, compared to their mass and size, so using modded engines, including low tech realistic ones, it can be quite easy to push your TWR in the tens of G's where gravity losses no longer matter, without building an expensive pancake whose mass is mostly engines, so that's one more points in favor of the viability of vertical ascent (but such powerful engines don't necessarilly have the best Isp).

 

I am not sure what to think about 45 ° direct ascent, it seems to me that it misses both the efficiency of a mostly horizontal direct ascent and the simplicity of a vertical ascent. Maybe  it's as good as you get trying to do an horizontal ascent if your first stage is too powerfull, but then I think you would gain from toning the first stage down and adopting a flatter trajectory.

 

TL;DR :

Direct ascent is a bit more efficient than circularisation in theory, but harder to get right. With very few exceptions, horizontale (once atmosphere is cleraed) (direct) ascent is strictly more efficient than verticale (direct) ascent but harder to get right (and more efficient than any non horizontale ascent). Vertical ascent requires a dedicated crafts with high acceleration.

Edited June 4, 2018 by Kesa

[Tyko]

something else to consider....if you circularize first and then do your transfer burn you can take the time to optimize your transfer maneuver. A direct launch can be optimized too, but it would take a lot more planning and precise timing/flying to hit your optimal transfer from the launch pad.

[Onigato]

Cool. So, as I'm understanding, it CAN be more efficient to direct launch, but the timing and ascent profile has to be fairly narrow (a few minutes and degrees of angle for Mun/Minmus, potentially seconds and arc seconds for things outside Kerbin SOI) to pull it all off with a dV neutrality, and even tighter to get a dV savings.

Cool! It's probably best if I circularize for my Duna shots, just for timing and the fact that the optimal window for Duna isn't great for three dozen or so direct launches, but now I don't feel as weird about my never ending "Bang! Zoom! Straight to th' Mun, Alice!" launches.

[Snark]

On 6/3/2018 at 9:22 PM, bewing said:

If I launch exactly the rocket you describe, but eliminate the thrust limiting, I get a Kerbin SOI escape in 2 days and 3 hours. With the exact same amount of fuel. What's your escape time with your bent ascent?

On 6/4/2018 at 3:04 AM, AVaughan said:

If I remove the thrust limit on the kickback, but pitch the rocket 5 degrees downrange in the VAB, then launch without activating SAS I get 1 day 5 hr 17 mins.

I tried it, and gave the rocket a smidgeon more than 5 degrees in the VAB (less than10, though-- that's way too much).

Was able to get SOI escape in 1 day 4 hr 41 mins from burnout.

It's also worth noting-- if we're comparing "go straight up" against "do a gravity turn"-- that this particular test is stacking the deck heavily in favor of go-straight-up.  Yes, the gravity turn won out by quite a bit even so... but this wasn't a terribly realistic test, and for "typical" rockets, the difference is much more dramatic.

What do I mean when I say that the test @AVaughan proposed here "stacks the deck" in favor of vertical ascent?  It's because this rocket has an unrealistically high TWR.  It's literally nothing but engine, other than that little command pod.  The TWR of this rocket got way higher than normal KSP rockets do.

Why does this matter?  Well, the reason that vertical ascent is worse than a gravity turn is that it incurs more gravity losses.  Gravity losses are real, and they're big.  One way to mitigate them is to have higher TWR:  the higher the TWR, the lower the gravity losses.

As we just showed in the test here, even a rocket with a really really high TWR is still going to pile up quite a few gravity losses, which is why the time-to-escape-SOI here for vertical ascent (2d3h) is fully 40% worse than the best reported gravity-turn time.

But with a more "typical" rocket (i.e. one with a significant payload) that's not engine), the difference becomes much starker.  The physics says so, and also practical experiment in KSP says so.  For an excellent discussion on this topic, check out @bewing's very well-stated experimental problem from this thread a couple years back:

This was a test that involved a "typical" KSP rocket that wasn't all engine, and the results turned out to be very dramatically different for the two cases:

On 8/16/2016 at 8:51 AM, Snark said:

Clearly the OP's expectation turned out to be not just wrong, but dramatically wrong:  gravity turn was not just better than vertical ascent, but a lot better (by a factor of more than three).

 

It's worth noting, though, that everything I've said here pertains to "vertical ascent versus gravity turn", which is not what the OP of this thread was asking, so it's a bit of a side issue:

On 6/2/2018 at 9:09 PM, Onigato said:

Generalizing the question, is it more efficient to circularize at 100km and Hohmann to ANY orbit, or just pitch down to 45, hold that until you reach target altitude apoapsis, and then circularize at altitude?

That question is more about "which is better, a gravity turn with a single burn to Ap, or a gravity turn to LKO and then a second burn to Ap".

The answer, as has been discussed above, is:  technically speaking, the "direct ascent" (single burn) is more efficient.  However, how much more efficient is going to depend on circumstances.  If your target Ap is high enough that you need to get fairly close to escape velocity to raise your Ap that far-- e.g. if you're going to the Mun or beyond-- then the difference is going to be pretty small.  Theoretically you save dV due to improved Oberth benefit, but the amount saved will be fairly tiny, because the relative difference in altitude between "I hit orbital velocity at 40 km" versus "I hit orbital velocity at 100 km" just isn't all that much.

What really ends up mattering the most, in my experience, is how precise you need your trajectory to be.

For example, suppose you just want to loft a satellite to a 30,000 km circular orbit.  In that case, it doesn't matter which direction you launch in, because you're not trying to rendezvous with anything-- you're just trying to raise your Ap to 30,000 km, and you don't care what longitude your Ap happens to fall at, because you're just going to be circularizing there anyway.  So in a case like that, where precise navigation doesn't matter, you might as well just do a direct ascent; there's no reason not to.  You could circularize too, if you wanted to-- it would be slightly worse, though not much-- but circularizing wouldn't offer any benefit at all.

But to take a very different case, suppose you want to go to Mun orbit.  That means you do care about navigation, because it's not enough simply to raise your Ap to 12,000ish km; you actually have to do it in the right direction to get a Mun encounter.  Furthermore, you want to fine-tune the encounter so that you have a relatively low Pe over the Mun, because that's going to be the most efficient place to do your burn to brake into Mun orbit.

In that case... my experience has been that in practice, it ends up being more efficient to circularize first, because that makes navigation more precise, and that particular situation is one where precise navigation can make a significant difference in dV.  On direct ascent, it's hard (for me, anyway) to precisely hit a target.  But if you circularize, it's a lot easier, because then you can plop down a maneuver node and tinker with it at your leisure to get an optimum trajectory.  Circularizing in that case does lose a small amount of dV compared with direct ascent... but (in my experience) it more than pays for itself with the dV savings from precise navigation.

 

So, the TL;DR is:

• Direct ascent (with a good gravity turn and mostly-horizontal burn) is slightly more efficient that circularizing, but for most cases, the savings is too small to make much practical difference.  And navigation is a lot more precise and easy if you circularize-- which, depending on the mission, might provide considerably more dV benefit than the smidgeon that's lost.
• Doing a gravity turn and a mostly horizontal burn (whether you're doing direct ascent, or circularizing in LKO) is a lot more dV-efficient than just accelerating straight up.

Of course, how much you care depends on play style.  For example, the vertical ascent certainly is simple and low-hassle-- maybe it's worth it to you, even though it's less dV efficient.  If you'd rather just strap on more boosters to save the navigation hassle, nothing wrong with that.