Quest for optimal Thrust to Weight ratio (TWR) for launching / first stage rockets

[Kerbal101]

Decided to make an experiment and compile the data for something this basic, yet very important. So, here is it!

 

Craft: stock "Jumping Flea" (Flea booster with MK1), straight launch, variable TWR (adjusted in VAB from data given by KER):

TWR 1.2, highest real altitude: 4100 m  flameout: 3100m
TWR 1.5, highest real altitude: 6200 m  flameout: 4300m
TWR 1.7, highest real altitude: 7200 m  flameout: 4600m
TWR 2.0, highest real altitude: 8000 m  flameout: 4700m
TWR 2.3, highest real altitude: 8250 m  flameout: 4700m
TWR 2.5, highest real altitude: 8320 m  flameout: 4600m
TWR 2.7, highest real altitude: 8350 m  flameout: 4500m
TWR 3.0, highest real altitude: 8350 m  flameout: 4200m
TWR 3.3, highest real altitude: 8350 m  flameout: 4000m
TWR 7.6 (maximum), highest real altitude: 8100 m  flameout: 2100m

 

Explaination:

this means that:
at TWR lower than 2, your craft will be burning fuel fighting the gravity, and
at TWR higher than 2.5, your craft will be burning fuel fighting atmospheric drag.

Enjoy!

 

## Update 2016/09/30

Quick check with Swivel+FL-T400+2xz1k batts+RC001s+Adv.NoseconeA  (2,156 DeltaV) confirms the data:

TWR: 1.7, highest real altitude: 87,600 m  flameout: 31,000m
TWR: 2.2, highest real altitude: 117,500 m  flameout: 31,000m

TWR 2.2:

 

## Update 2016/09/30 - 2

In response to criticism, I decided to make a small "usable" 7 tone "payload" (Payload A). The payload has everything to make orbit, keep in orbit and descend down.
To repeat, this thread about ideal TWR for first stage / launching stage

 

### Payload A, first test

Payload A config: Protective Nose Cone Mk7 + LCR01 RGU + Srvc.Bay 2.5m(3x Z1k batt, 2x SP-L solar panels, 2x MK2-R radial chutes) + Advanced Reaction Wheels, Large + X200-8 Fuel + LV-909 "Terrier"+Rockomax Decoupler.
---
Payload A weight: 7,000 kg
 

This payload will be launched using only one stage - using two ascend methods, using two different TWRs.
The methods:
1) direct climb for statistics:  SAS on, max throttle, ignition.  No Stage 2 disconnect.
2) manual gravity turn:
- 0 degree until 2,5km;
- course to 15 degree(75 on navball) at 2,5km;
- course to 35 degree (55 on navball) on pass 15km;
- course to 55 degree (35 on navball) at 25km;
- course to 75 degree (15 on navball) at 35 km;  (this step was skipped on 2.2 TWR due to atmospheric heat **)
- deactivate if apoapsis reaches 80km, wait until T-45s  (accordingly, this step was much longer on 2.2 TWR)
- burn at horizon line under prograde till end of stage: output stage 1 data
- disconnect stage 1 and finalize burn using stage 2: output payload A in orbit fuel left

will be also noted: out of fuel/flameout for 1st stage (altitude at; horizontal and vertical speeds), amount of fuel left on payload after circularization at 80/80km.

 

#### Payload A (stage 2) - uplifter A (stage 1)

uplifter A  config: (Payload A +) Jumbo 64 tank + RE-M3 Mainsail (+3x launch stability enhancer, start only)
3,218 projected stage 1  DeltaV; 6,370 projected total DeltaV )

[ craft file link ]

Results:

##### Direct climb data
TWR 1.25, highest real altitude: 268,000 m  flameout: 72,000m
TWR 2.20, highest real altitude: 615,000 m  flameout: 69,000m

##### Manual gravity turn data
info: TWR 2.20 appears to compress air higher (hidden aerodynamic center) - thus rocket becomes less stable and either smoother transition between nodes (used here) or additional lifting surfaces required.
TWR 1.25: apoapsis at flameout: 82,000m  periapsis at flameout: -390,000m     Stage 2 80km/80km orbit fuel left:  fuel - 247/360;  LOX - 302/440
TWR 2.20: apoapsis at flameout: 86,000m   periapsis at flameout: -22,000m     Stage 2 80km/80km (90/90km actually) orbit fuel left:  fuel - 340/360;  LOX - 416/440


** apparently there is a room for improvement!  "Engine idling on suborbit ascend equals wasted fuel". This case is free to be tested!
Probable method: throttle down after leaving atmosphere (~28km). Reason: it looks like with TWR 2.2 atmosphere heat prevents efficient acceleration, requiring higher angle of attack. But according to Oberth effect, lower attitude accelerations are more efficient, thus its better to take it slower below.

 

Edited September 30, 2016 by Kerbal101
added unthrottled, because why not.

[Streetwind]

The reality is more complex than this, unfortunately.

For starters, gravity losses still greatly outweigh atmospheric drag at TWRs even above 3 for typical rockets - and this counts double for straight-up launches! You can prove this by making more complex tests with vessels that actually go to orbit. Yet your findings appear to contradict this. What is going on? The answer was already given in the text: those other vessels go to orbit, yours doesn't. You merely found a solution that applies to a vessel that climbs to 8000 meters altitude. That solution does not apply to an orbital launch vehicle, which flies the whole ascent trajectory. In that case, even though the trajectory flattens out and thus reduces gravity losses over time, the added initial speed gives you so much of a bonus across the entire ascent that it ends up saving fuel despite spending extra at launch! It's all a question of building and carrying early speed into the thinner parts of the atmosphere.

Another thing to consider is the ballistic coefficient, which is a number that describes the relationship between cross section and mass. Your test vessel has a fairly large cross-section (the full 1.25m diameter) with almost nothing behind it (only a flea, which is even empty of fuel for half the flight). Such a craft loses a lot more to aerodynamic forces than a much heavier orbital rocket, which has a full two-stage stack plus payload, as well as the thrust to drive it, behind that same 1.25m cross-section. It's like the difference between a single train car running into a wall, or a whole freight train running into the same wall. The single car will likely be stopped, or at least slowed down a lot; the full train won't even register a change in speed.

Ultimately, the question of "what is the optimal TWR to launch this at" depends a lot on each individual rocket and its individual flight profile. As annoying as this is - it's the unfotunate reality, outside of which you can make only vague, general statements.

Two such statements that the community has worked out, by the way, are: "If you optimize for lowest dV to orbit, make the pointiest rocket possible and launch with the highest TWR possible", and "if you optimize for payload to orbit, TWR greater than 2 is typically not useful because you're carrying too much engine where you could instead be carrying payload". Yes, lowest dV to orbit and highest payload to orbit are in fact not the same goal, but rather two partially exclusive goals. There's even a third one, which is lowest cost to orbit, which requires yet another different setup.

Edited September 29, 2016 by Streetwind

[Kerbal101]

19 hours ago, Streetwind said:

The reality is more complex than this, unfortunately.

Thank you!  Correct me, but I think you misread the topic title

Also, I would welcome some reproducible data   I like reproducible data  

[Gaarst]

32 minutes ago, Kerbal101 said:

Thank you!  Correct me, but I think you misread the topic title

Also, I would welcome some reproducible data   I like reproducible data  

Reproducible data for this would be 1) extremely hard to obtain, 2) utterly useless.

Finding the optimal TWR for a launch requires you to evaluate path integrals of your drag and gravity losses. Besides being stupidly difficult to get, the results you could find would only be valid for this launch profile and rocket, changing your rocket or trajectory would completely change them.

[Kerbal101]

2 hours ago, Gaarst said:

Reproducible data for this would be 1) extremely hard to obtain, 2) utterly useless.

Finding the optimal TWR for a launch requires you to evaluate path integrals of your drag and gravity losses. Besides being stupidly difficult to get, the results you could find would only be valid for this launch profile and rocket, changing your rocket or trajectory would completely change them.

I welcome any input!

[John Cochran]

Attempting to optimize the first stage booster while performing a suboptimal launch is pretty much an exercise in futility. Also a few statements in your posting indicate an incomplete understanding of a few terms.

First, the Oberth effect has only an indirect relationship to low altitudes. It is far closer related to velocity. To illustrate, take a look at the formula for kinetic energy.

e = 0.5 * m * v²

Notice the v² component. Now compare the values of the (v+1)² - v² for various values of v. For instance, with a v of 0, you get 1. If v is 10, you get 21, 100 gets you 201, a 1000 gives you 2001, etc. The larger the value of v, the greater the difference between (v+1)² and v². So, the higher your initial velocity, the greater the increase in your kinetic energy for the same increase in your velocity. Now at which point in your orbit is your velocity the highest? At periapsis.  Hence the Oberth effect in that burning at periapsis gives you the most efficiency for your burns.

Now, the mention of energy is quite important in getting to orbit. For any given orbit, the total of the gravitational potential energy and the kinetic energy of your craft is a constant. As your velocity decreases (meaning your kinetic energy decreases), your gravitational potential energy increases (meaning your altitude increases). So to achieve orbit, you need to increase your orbital energy to a high enough level and in the correct proportions for the desired orbit. You do this by changing your velocity by burning propellant. There are three axis which you can make velocity changes. They are prograde/retrograde, normal/anti-normal, and radial/anti-radial. Of those three axis, only a prograde/retrograde vector will change your orbital energy. The normal/anti-normal vector changes the orientation of your orbit, and the radial/anti-radial changes the shape of your orbit. This means that any expenditure of fuel to change your velocity vector in other than the prograde direction is wasted energy. Burning in a non-prograde direction is inefficient and you can do better.

Now, of course, there are practical concerns that may mandate that your insertion into orbit isn't completely efficient. Such constraints are the TWR or your rocket, the atmosphere, thermal heating, etc. There are also three loss mechanisms for loss during a launch. There's gravity drag, atmospheric drag, and vector losses (see above about burning in a non-prograde direction). You want to minimize the sum of all those losses during launch. The gravity drag can be reduced by burning at right angles to the local gravity vector. The atmospheric drag is reduced by streamlining and getting into thinner atmosphere. And the vector losses is reduced by minimizing any off prograde velocity changes. Because of all that, the most efficient launch is one where you start your gravity turn as soon as possible and then perform a purely prograde burn, reducing your thrust as your altitude increases, eventually tapering off the zero when you reach your desired orbit. During the entire burn you keep the time 'til you reach apoapsis some small constant number of seconds (40 is about right). If you use too much thrust, what will happen is you'll have a highly elliptical orbit when your apoapsis reaches the desired altitude. And then when you circularize, you're going to have make an extremely large off-prograde burn (see vector losses above). Additionally, your burn is going to happen when your velocity is fairly low (see Oberth effect above) making for even more loss of efficiency. The ideal launch will get your craft traveling close to horizontal with your velocity just above orbital velocity for the altitude you're currently at so your orbit gradually grows larger. This makes your burns happen while traveling at a high velocity (see Oberth effect) and the burn will be constantly prograde (see vector losses) and your vector will be at near right angle to the local gravity vector (see gravity losses). But that pesky atmosphere and the heating and drag effects tend to prevent perfect efficiency. You take care of that by increasing the time until apoapsis which means you're burning a bit more than optimal so your altitude increases faster. This will increase your gravity losses since you're further away from the ideal right angle, but it does get you out of the atmosphere faster so you decrease your atmospheric drag faster and get out of the heating effects before you explode.  

[Kerbal101]

@John Cochran first, thank you very much for taking time in writing a consistent post about the perfect orbital climb.

However the true goal for this quest is finding the optimal TWR for first stage on Kerbin, and making it as hands-on and as quantitatively measurable (values) as possible. As you wrote: "... perform a purely prograde burn, reducing your thrust as your altitude increases... ", but without mentioning with what TWR exactly. Because the "burning" is not a "1 and 0", "on and off" state, but is defined primary by a thrust-to-weight value.

Furthermore, the optimum (optimal) is seen as a balanced value between perfect and average, because both of extremes waste either pilot (concentration stress when steering) or propellent resources.
And the goal is approached with optimizing "one parameter at a time" (here, TWR) rather than trying to take on them all once (drag profile, lift profile, their static and dynamic balance, twr, thrust profile, ascend profile). That would indeed be futile.

Hence the ("perfection of an") orbital insertion trajectory (vector loss) from surface is not touched and left on the consciousness of the pilot.
Specifically you write that ("Burning in a non-prograde direction is inefficient and you can do better.") which is an axiom, especially because in KSP there is no visual guidance for "perfect prograde".
The orbit is simply defined/locked as a smallest possible stable orbit with any degree of inclination (80/80km in the tests) and just kept same across test.

The step-by-step description of orbital insertion was created as a necessary step rather than part of the goal, in order to address the criticism that the "vertical ascend alone does not cut it". It should not be the subject of optimization here. Thus it should be irrelevant factor as the ascend trajectory (gravity turn) is left purposely same (so long its practically possible to execute) for every test object for the sake of comparability.

Likewise the shape/drag properties for the subject (drag loss) are kept same by using the same craft in the test group. The case where pilot uses some different craft is addressed by using the most basic, typical, yet a drag efficient craft: either a nose cone with basic engine, or a sharp angled fairing (encasing the functional sample payload) with decoupler, fuel tank and an engine.

Finally, the test is done only on Kerbin, thus the gravity loss is likewise same between tests. Of course, planets/moons with higher/lower gravity will cause optimal TWR to be higher/lower.

 

The only thing modified/tested is the "TWR of 1st stage at launch with 100% thrust value" and (optionally) "actual thrust value applied at any point of the climb" (as a percentage of throttle reduction).

That said, the testing craft is attached and I very much welcome any reproducible TWR/thrust setting/limit (static - as a thrust limit in VAB, and especially the dynamic one - as throttle value during ascend) with would improve the demonstrated scores using the attached craft and following specified ascend profile. If anyone considers mentioned value to be incorrect, feel free to link me the craft where, say, first stage (preferably long one) TWR 1.5 would be more efficient in fuel use, than TWR 2.2 when following the same ascend pattern.

[Starman4308]

I think his point is that rocket ascent parameters exist in a very high-dimensional space (as in: many, many, many variables), and that trying to optimize just one parameter is an exercise in futility, and leads one to draw misleading conclusions, as the optimal value of any given variable is dependent on every other variable. You can crack one problem easily holding all others fixed... and then you move on to the next parameter, and the next, and the next, and return to TWR, and find you've got to reoptimize it because now you've changed everything else that led to the initial conclusion!

[Kerbal101]

On 10/31/2016 at 3:03 AM, Starman4308 said:

I think his point is that rocket ascent parameters exist in a very high-dimensional space (as in: many, many, many variables), and that trying to optimize just one parameter is an exercise in futility, and leads one to draw misleading conclusions, as the optimal value of any given variable is dependent on every other variable. You can crack one problem easily holding all others fixed... and then you move on to the next parameter, and the next, and the next, and return to TWR, and find you've got to reoptimize it because now you've changed everything else that led to the initial conclusion!

So, you don't play KSP because there are many ways to build rocket or plane or rover or base or lander?

 

There is really only one parameter important for first stage. Its fuel economy. Because until there is fuel, everything else is not important
And TWR is big part of fuel economy.

Of course, one can reduce drag, fly in better profile, work on thrust changes - but all this is useless, if the rocket is not ascending or ascending poorly. And its not ascending because of bad TWR.

 

I really feel forward to someone improving the results of the test vehicle.

[wumpus]

On 10/30/2016 at 10:03 PM, Starman4308 said:

I think his point is that rocket ascent parameters exist in a very high-dimensional space (as in: many, many, many variables), and that trying to optimize just one parameter is an exercise in futility, and leads one to draw misleading conclusions, as the optimal value of any given variable is dependent on every other variable. You can crack one problem easily holding all others fixed... and then you move on to the next parameter, and the next, and the next, and return to TWR, and find you've got to reoptimize it because now you've changed everything else that led to the initial conclusion!

I'd say you are overthinking things.  Some 'hard problems' lend themselves to simple rules of thumb: it isn't really possible to determine the exact split of delta-v between stages, but equal amounts of delta-v in each (assuming no stage is recovered) is a great place to start.  Additionally, TWR of the first stage is relatively trivial to control (assuming a stage 3 launchpad in career), just keep adding kickers [SRB-KD25k] until you hit the "magic number".

In practice, so far experience has shown the "optimal launch TWR" as 1.2.  Personally, I find that hard to believe and have done similar experiments leading me to believe it is close to 2.0 (maybe slightly less), but I have yet to match the efficiency of these 1.2 TWR craft.  Experimental Proof: