Launch Vehicle Optimization Test Results

[OhioBob]

I know there have been numerous threads on this topic already, but I have some new test results that I'd like to share.

The test was of a simple two-stage liquid fueled launch vehicle. The first stage was powered by a LFB KR 1x2 "Twin-Boar" Liquid Fuel Engine. The second stage was powered by a RE-I5 "Skipper" Liquid Engine. These engines were selected because my previous v0.90 tests found them to be an ideal pairing for a two-stage rocket. The first stage included four AV-R8 Winglets and the second stage included an Advanced Reaction Wheel Module, Large. Both stages included a Rockomax Brand Decoupler.

The payload was just a dummy mass with a RC-L01 Remote Guidance Unit and Protective Rocket Nose Mk7. The test payload provided good drag characteristics, but not optimum. Actual performance will vary depending on the drag characteristics of your specific payload.

To the first and second stages I added propellant tanks in various sizes and quantities until I found the ideal combination that maximized performance according to three different modes of measurement. First, I found the configuration that resulted in the lowest total Δv. Second, I found the configuration that resulted in the highest payload fraction. And third, I found the configuration that resulted in the lowest cost per unit mass of payload.

The tests were performed using a computer simulation rather than performing test flights within the game. This eliminated unwanted human error and variation in performance. The tests launches were performed under carefully controlled and ideal conditions.

In all cases, the payload mass was found experimentally as the mass that resulted in 100% of the propellant being used to achieve a 75 km circular orbit. The payload includes everything not described above as being as part of the first and second stages. Thus, a fairing, if used, is counted as payload.

The ascent profile consisted of a slow gradual turn beginning after 100 meters of climb. The launch vehicle maintained a constant negative angle of attack throughout the turn. The angle of attack was found experimentally as the angle required to produce the most efficient ascent and to deliver the maximum payload mass to orbit.

My tests show that high thrust-to-weight ratio is best for minimizing the Δv required to attain orbit, while low thrust-to-weight ratio is best for minimizing the cost per tonne of payload. This is because lower TWR is obtained by simply adding more propellant tanks on top of a given engine. The engine is already paid for, so our marginal cost is only that of the relatively cheap propellant and tankage. With more propellant we can launch a heavier payload. It is found that the cost per tonne of payload goes down as more and more propellant is added. Although unit cost goes down, the vehicle becomes less efficient in terms of Δv. We can only add so much propellant before the vehicle becomes so inefficient that unit cost begins to rise.

Below are the results of my simulations. Although there is an almost unlimited number of launch vehicle configurations that you can come up with, the data below might help in establishing some general design guidelines. Note that this is theoretically ideal conditions; actual in game performance is likely to be lower. Cost is for the launch vehicle only, payload is extra.

Optimized for Minimum Δv

First stage:

Dry mass = 11,300 kg

Propellant mass = 36,000 kg

Thrust, sea level = 1866.67 kN

TWR, ignition = 1.90

Stage Δv, vacuum = 1,308 m/s

Turn angle-of-attack = -2.70^o

Cutoff conditions: z = 12.3 km, v = 660 m/s, φ = 40^o

(z = altitude, v = velocity, φ = flight path angle)

Second stage:

Dry mass = 6,600 kg

Propellant mass = 24,000 kg

Thrust, vacuum = 650 kN

TWR, ignition = 1.25

Stage Δv, vacuum = 1,893 m/s

Burn 1 cutoff: z = 42.7 km, v = 2319 m/s, φ = 3.7^o

Burn 2 Δv = 78 m/s

Payload mass = 22,376 kg

Payload mass fraction = 0.2231

Total Δv, vacuum = 3,202 m/s

Δv losses = 669 m/s gravity, 210 m/s drag

Total cost = 33,410

Cost per payload tonne = 1,493
 

Optimized for Maximum Payload Fraction

First stage:

Dry mass = 13,800 kg

Propellant mass = 56,000 kg

Thrust, sea level = 1866.67 kN

TWR, ignition = 1.46

Stage Δv, vacuum = 1,658 m/s

Turn angle-of-attack = -0.86^o

Cutoff conditions: z = 17.9 km, v = 842 m/s, φ = 28^o

Second stage:

Dry mass = 6,600 kg

Propellant mass = 24,000 kg

Thrust, vacuum = 650 kN

TWR, ignition = 1.10

Stage Δv, vacuum = 1,597 m/s

Burn 1 cutoff: z = 42.3 km, v = 2348 m/s, φ = 2.5^o

Burn 2 Δv = 51 m/s

Payload mass = 29,576 kg

Payload mass fraction = 0.2275

Total Δv, vacuum = 3,255 m/s

Δv losses = 765 m/s gravity, 152 m/s drag

Total cost = 37,160

Cost per payload tonne = 1,256
 

Optimized for Minimum Payload Unit Cost

First stage:

Dry mass = 16,300 kg

Propellant mass = 76,000 kg

Thrust, sea level = 1866.67 kN

TWR, ignition = 1.21

Stage Δv, vacuum = 1,953 m/s

Turn angle-of-attack = -0.25^o

Cutoff conditions: z = 21.9 km, v = 927 m/s, φ = 23^o

Second stage:

Dry mass = 6,600 kg

Propellant mass = 24,000 kg

Thrust, vacuum = 650 kN

TWR, ignition = 1.03

Stage Δv, vacuum = 1,464 m/s

Burn 1 cutoff: z = 42.4 km, v = 2362 m/s, φ = 1.6^o

Burn 2 Δv = 39 m/s

Payload mass = 33,784 kg

Payload mass fraction = 0.2156

Total Δv, vacuum = 3,416 m/s

Δv losses = 968 m/s gravity, 118 m/s drag

Total cost = 40,710

Cost per payload tonne = 1,205

 

Edited December 21, 2015 by OhioBob
fixed formatting

[GoSlash27]

^ Exactly.

Optimizing for minimum DV is a fool's errand. You need to have a rough idea of the DV requirement for planning purposes, but the object is to orbit payloads with a minimum of fuss and expense.

Efficient SSTO spaceplanes waste a ridiculous amount of DV to drag, but they ship the payload to orbit more cheaply and reliably than anything else this side of hyperediting.

Brawndo IV

Launch mass: 123.1t

Launch cost: $99,271

Payload mass: 39t

Payload fraction: 32%

Recovery cost: $89,826

Cost per tonne: $242

Total DV = 5,200 m/sec

And of course, there are better SSTO designs.

Best,

-Slashy

Edited September 15, 2015 by GoSlash27

[NathanKell]

Now *that* is what I love to see! Great job!

I especially like the way you broke it down into the three cases, and also broke down the losses into gravity and drag. I'd be very interested to see you run a similar setup, except with some strapons, since SRBs remain quite cheap and the vast majority of gravity losses occur early.

EDIT: In fact since KSP engines throttle, you could get away with STS/SLS style boosted sustainers.

[AbhChallenger]

Any suggestions on when or when to not use "moar boosters" ? Specifically soilds as I do not like to use asparagus.

[OhioBob]

Any suggestions on when or when to not use "moar boosters" ? Specifically soilds as I do not like to use asparagus.

Asparagus staging has its place, but I favor solids as well.

I haven't come up with a good set of guidelines for using solids (at least nothing that I can back up with data). What I've done in the past is to go with a two-stage liquid fueled launcher as my first option. However, when I'm caught between two engines options - for example, a Skipper is too small and a Mainsail is too big - I go with the smaller option and supplement it with solid strap-on boosters to get my liftoff TWR where I want it.

[OhioBob]

NathanKell said:

I'd be very interested to see you run a similar setup, except with some strapons, since SRBs remain quite cheap and the vast majority of gravity losses occur early.

I'll have to work on that.

NathanKell said:

EDIT: In fact since KSP engines throttle, you could get away with STS/SLS style boosted sustainers.

I can think of several configurations:

(1) Two-stage liquid core, thrust augmented with SRBs. SRBs and liquid stage both ignite at liftoff. (Atlas V)

(2) Single stage liquid core with SRBs. SRBs and liquid stage/sustainer both ignite at liftoff. (Space Shuttle)

(3) Single stage liquid core with SRBs. SRBs ignite at liftoff, liquid stage is air-lit after SRB burnout. (Titan III)

I'm not sure which option is most effective. Option #1 is quite popular on Earth, but the Δv requirement to get to orbit in KSP is low enough that I doubt a second liquid stage is necessary. And I'm concerned that option #3 may not provide enough steering. That makes me lean toward option #2.

Edited December 21, 2015 by OhioBob

[Red Dwarf]

I dunno. My gut says the third option would be best in terms of hassle reduction. It would be cheaper for sure, especially if you designed it along the lines of the Ares 1: cheap, efficient, and easy to escape from if the ascent goes bad. You'd be limited in terms of payload mass, but your definitely not obligated to use just one.

[Warzouz]

Setting a nice TWR mostly depends on your vehicle structure

- Setting it too low and you'll have a hard time flying it straight

- Setting too high and you may flip quicker or even blow. Adding wings will make it go straight, but gravity turn would be harder.

I find those considerations much more significant than dV fixing.

[selfish_meme]

I dunno. My gut says the third option would be best in terms of hassle reduction. It would be cheaper for sure, especially if you designed it along the lines of the Ares 1: cheap, efficient, and easy to escape from if the ascent goes bad. You'd be limited in terms of payload mass, but your definitely not obligated to use just one.

Apparently the Ares 1 was several times more expensive than the Falcon 9. It pained me to find that out especially after just putting so much work into my replica.

[mhoram]

Great results!

May I ask what software did you use for the simulation?

[More Boosters]

Apparently the Ares 1 was several times more expensive than the Falcon 9. It pained me to find that out especially after just putting so much work into my replica.

You should take into consideration that it never got to mass production which tends to reduce costs.

[selfish_meme]

You should take into consideration that it never got to mass production which tends to reduce costs.

I'm not sure the estimated cost per launch of the Ares was 1 billion, compared to 59 million for the Falcon 9, it only took half the payload, but you could launch more than 10 Falcon's for the cost of an Ares 1. Anyway I think we have derailed the thread enough.

[DancesWithSquirrels]

I toss together variants on a few fairly simple launchers for most stuff, with the assumption that the payload can handle the last 50-100 m/s for circularization, dropping the booster to reenter:

* LV-45 2nd stage with two KD-25's as first stage (with a payload of Mk1, service bay, FL-T400, and Terrier for LKO rescues).

* Skipper core with SRBs (generally lighting the Skipper at medium thrust along with the SRBs).

* Mainsail core (lit at launch, hence 1.5 stage) with a pair of onion staged (fuel pipes to the core) liquid boosters on 2x or 3x LV-30s.

* Rhino 1.5 stage core with lots of KD-25's boosting.

I put drogue and lots of Mk-2R chutes on the cores, staged for separation and with fairly high pressure settings (.45, .5 respectively), and generally recover the cores with 50% payback.

I generally don't even bother with subassemblies for these, as they are really quick to slap together - and I just add fuel/SRBs for a particular payload until I get about 3700 m/s for launch.

[OhioBob]

May I ask what software did you use for the simulation?

It's just an Excel spreadsheet. I've tried some different things over the years but, in the end, I've found that Excel is the easiest to work with.

[NathanKell]

I agree that SLS/ArianeV style is probably best for KSP if you're using solids. Titan/old-SLS style makes some sense, but doesn't seem right for KSP given the low burn times of solids, you'll be air-lighting rather early both in terms of altitude and horizontal velocity, and unless your core has so high a TWR that you're wasting mass on engine, you'll lose back some of the gravity losses you avoided earlier.

For that style, though, it's worth considering using verniers (24-77s probably) for TVC during SRB phase.

[Fearless Son]

Any suggestions on when or when to not use "moar boosters" ? Specifically soilds as I do not like to use asparagus.

I found that SRBs are good for those low thrust-to-weight ratio rockets, where you need a cheap way of imparting some extra starting acceleration on the first stage, something to get it to cruising ascent speed without spending an inordinate amount of liquid fuel just getting off the ground.

That said, I find it a good balance of cost and efficiency that, rather than using liquid fuel boosters, I just use radially-mounted drop tanks that feed into the main engine. Gives me extra liquid fuel to burn in the lower atmosphere, then I can jettison them when empty to save fuel. It also helps me lower the center of mass in the lower stage, which helps keep the rocket stable. Stabilizing fins on the drop tanks help that stability too, as well as causing the tanks to angle away from the rocket's hull when they detach due to their individually asymmetric drag.

[OhioBob]

I agree that SLS/ArianeV style is probably best for KSP if you're using solids. Titan/old-SLS style makes some sense, but doesn't seem right for KSP given the low burn times of solids, you'll be air-lighting rather early both in terms of altitude and horizontal velocity, and unless your core has so high a TWR that you're wasting mass on engine, you'll lose back some of the gravity losses you avoided earlier.

I'm planning to test a few different options, however I don't want to go overboard with it because it takes a lot of time to run through all the optimization iterations. I'll probably pick two or three viable candidate configurations and leave it at that.

For that style, though, it's worth considering using verniers (24-77s probably) for TVC during SRB phase.

I've considered doing something like that. I've never had a problem controlling small solids using reaction wheels, but I've had trouble steering big launchers unless I've had at least one gimbaled liquid engine. I'm not sure I really need to worry about it for the tests that I'll be performing. My tests are strictly a theoretical exercise focused on trying to find the optimum TWR etc. Control/steering is an in game problem that requires a practical solution. There is no guarantee that the optimum configuration revealed by the computer simulations will be a practical design that can be reliably controlled.

- - - Updated - - -

I found that SRBs are good for those low thrust-to-weight ratio rockets, where you need a cheap way of imparting some extra starting acceleration on the first stage, something to get it to cruising ascent speed without spending an inordinate amount of liquid fuel just getting off the ground.

I have frequently used SRBs in this manner.

That said, I find it a good balance of cost and efficiency that, rather than using liquid fuel boosters, I just use radially-mounted drop tanks that feed into the main engine. Gives me extra liquid fuel to burn in the lower atmosphere, then I can jettison them when empty to save fuel. It also helps me lower the center of mass in the lower stage, which helps keep the rocket stable. Stabilizing fins on the drop tanks help that stability too, as well as causing the tanks to angle away from the rocket's hull when they detach due to their individually asymmetric drag.

I think drop tanks may be a very practical solution for a low TWR launcher. One thing that I didn't discuss in my opening post is that as we stack more and more propellant tanks, the launch vehicle becomes more and more slender. The "optimized for minimum payload unit cost" design has an extremely high slenderness ratio. I suspect that it would be very wobbly in flight. Using drop tanks would significantly reduce the slenderness and make the vehicle more stable and structurally sound.

[Archgeek]

Also lots of fun, plopping fuel tanks cross-fed into the core atop or amongst one's SRBs, with throttle and thrust limiters set such that the droptanks run out just as the SRBs do, allowing them to be staged off at once.

[OhioBob]

EDIT: THIS POST HAS BEEN MODIFIED TO REMOVE THE AV-R8 FINS FROM THE TEST VEHICLE. THEY ARE SHOWN IN THE IMAGE BUT NOT INCLUDED IN THE TEST RESULTS.

As suggested earlier in this thread, I tested a launch vehicle with solid rocket motors. I only tested one design, which is shown below:

I wanted a design that made extensive use of solids so we could really see how much of a difference it made in comparison to an all-liquid design. As you can see, I went with six SRBs. Two of the six are set to 100% thrust and burn out after about 42 seconds. The other four SRBs are set to 50.5% thrust and burn out after about 84 seconds. The center sustainer engine is a "Skipper". All engines and motors ignite at liftoff. The top propellant tank is just ballast to simulate a payload (the propellant is not used).

Although I've test flown this vehicle in the game, the data that I report here is from the same computer simulation used when recording my opening findings. The results should be comparable. In the game, the test vehicle flew well and was easy to control.

This time I didn't bother optimizing for Δv because I see no practical reason why anyone would want to do so. There was very little difference between the payload fraction optimized and the cost optimized versions - the cost optimized version had just one small additional propellant tank. (The picture shows the payload optimized version.)

It is no surprise that with the lower performing solid propellant, the payload fraction of the SRB launcher is significantly less than that of the all-liquid design. I am surprised, however, to discover that the SRB launcher is more expensive per tonne of payload. One of the main reasons for this appears to be because of the large amount of "extras" needed, such as decouplers, nose cones, struts, etc. If we add up the cost of just the propellant, tanks, engines and SRBs, then the SRB launcher is less expensive - 917/t vs. 1035/t.

The fleet of launchers that I used prior to version 1.0 typically delivered payloads to orbit less expensively when solids were used. I assume the results that I'm now seeing are due to the rebalancing that has taken place since v0.90. Of course, it's also likely that a more cost effective SRB design can be found than the sample tested here.

Here are the test results:

Optimized for Maximum Payload Fraction

Strap-on SRBs:

Number of SRBs = 6

Inert mass = 1,675 kg each, 10,050 kg total

Propellant mass = 6,150 kg each, 36,900 kg total

Rated thrust = 250 kN sl, 300 kN vac per each

Thrust limiter = 2 each at 100%, 4 each at 50.5%

Burn time = 2 each at 42.2 s, 4 each at 83.6 s

Burnout, 1^st group: z = 4.85 km, v = 271 m/s, φ  = 68^o

Burnout, 2^nd group: z = 17.25 km, v = 618 m/s, φ  = 35^o

Core stage:

Dry mass = 8,600 kg

Propellant mass = 40,000 kg

Thrust = 568.75 kN sl, 650 kN vac

Burn 1 cutoff: z = 40.9 km, v = 2342 m/s, φ  = 3.1^o

Burn 2 Δv = 64 m/s

Total launch mass = 114,957

Total liftoff thrust, sea level = 1,573.75 kN

Liftoff TWR = 1.40

Payload mass = 19,407 kg

Payload mass fraction = 0.1688

Total Δv, vacuum = 3,440 m/s

Δv losses = 854 m/s gravity, 180 m/s drag

Total cost = 26,722

Cost per payload tonne = 1,377

Optimized for Minimum Payload Unit Cost

Strap-on SRBs:

Number of SRBs = 6

Inert mass = 1,675 kg each, 10,050 kg total

Propellant mass = 6,150 kg each, 36,900 kg total

Rated thrust = 250 kN sl, 300 kN vac per each

Thrust limiter = 2 each at 100%, 4 each at 50.5%

Burn time = 2 each at 42.2 s, 4 each at 83.6 s

Burnout, 1^st group: z = 4.30 km, v = 236 m/s, φ  = 75^o

Burnout, 2^nd group: z = 16.3 km, v = 509 m/s, φ  = 45^o

Core stage:

Dry mass = 9,100 kg

Propellant mass = 44,000 kg

Thrust = 568.75 kN sl, 650 kN vac

Burn 1 cutoff: z = 42.6 km, v = 2363 m/s, φ  = 1.6^o

Burn 2 Δv = 40 m/s

Total launch mass = 120,216

Total liftoff thrust, sea level = 1,573.75 kN

Liftoff TWR = 1.335

Payload mass = 20,166 kg

Payload mass fraction = 0.1677

Total Δv, vacuum = 3,514 m/s

Δv losses = 963 m/s gravity, 146 m/s drag

Total cost = 27,522

Cost per payload tonne = 1,365

 

Edited December 22, 2015 by OhioBob
fixed formatting

[Pecan]

Are not all the 'extras' of which you speak also needed for disposable liquid-fuel boosters?

If you're comparing core + SRBs to core-only it's not really the same test. How do SRBs compare to LF(O)s in a similar configuration.

(My view has generally been that SRBs aren't worth it in that, once you need/want boosters you're better off with the controllability and longer burn-time of LFO. Since you're coming from the opposite view I'll be pleased to be proved wrong)

[OhioBob]

Are not all the 'extras' of which you speak also needed for disposable liquid-fuel boosters?

If you're comparing core + SRBs to core-only it's not really the same test. How do SRBs compare to LF(O)s in a similar configuration.

That's a valid point. But then again, one of the advantages of liquids is that we don't need to employ a radial attachment configuration. We always have the option to go to a "Mainsail" or "Twin-Boar" and use an in-line arrangement. With solids the largest option available has a sea level thrust of 594 kN. If we need more than that, we've got no choice but to add moar boosters.

[Pecan]

Applause and accolades for testing and reporting what you can anyway :-)

There's always more options than can be fully explored; that's what's kept us here for so long, after all.

[OhioBob]

There's always more options than can be fully explored; that's what's kept us here for so long, after all.

You got that right. There's almost no limit to what can be imagined.

[sardia]

I'm not sure what this implies for our space program. Am I just too tired to get it? What's the cheapest and reliable way to get a payload to space via rockets?

[NathanKell]

sadia: It doesn't imply anything for real life space programs, other than the baseline takeway that "efficient" can mean any one of a number of things, and that "lowest dV to orbit" is not the same as "lowest cost/kg to orbit." Certainly the costs in KSP bear literally no resemblance to real life, let alone the ascent path, payload fractions, etc.

If you mean what it implies for our *kerbal* space programs, then, well, OhioBob just demonstrated fairly well that in 1.0.4 it's no longer the case that solid+sustainer is cheaper than 2stage liquid.