Rocket efficiency

[Warzouz]

As I'm waiting for 1.0 to do some serious mission, I was tweaking my current various "first stage".

For my Joolian mission, I had a 500T, but my second stage was too weak so I redesigned it. It ended being much heavier. So I had to redo my first stage too. The full rocket is now a 1130T monstruosity !

It was overfueled and some most of the parts (it was a 13 launches mission assembled around Laythe) used the first stage core to slow down on Jool arrival. Well... overfuelled I said !

I saw various designed stating 15% of payload to orbit efficiency. So I tester my first stage to really know what payload it as able to put to orbit. 200T at 200km with a cost of 2280Cr/T and a payload mass of 15.5%. Seems to be quite average.

So I check other first stage. My previous first stage was able to launch 82T at 100km for a 15.24% and a 2450CR/T.

But my older launcher I used for Duna car launch 63T to 100km orbit at surprising 17.7% payload mass and a 1970Cr/T. It's a very simple design using 1 mainsail and skippers

So my questions : What are your launchers efficiency (discarding reusable ones) and cost per ton ? What do you do to optimize it ? What is you strategy (mutliple launches/single launch) ?

PS :

- Orbit is calculated as nearly no fuel left (less than 100m/s)

- Payload efficiency = Paylod mass / Total rocket mass (including payload)

- Cost/T = Cost of first stage (no payload) / payload mass

[Streetwind]

As a rule of the thumb, the more dV a rocket stage already has, the less efficient it becomes to try and add even more dV to it. Up until about 10x Isp you don't notice this effect very much, but diminishing returns start ramping up noticably above that. Above 15x Isp, more fuel achieves very little.

However, the less dV a stage has, the more stages you need to perform your mission. And every new stage is going to have added cost and added dry mass in the form of decouplers and engines, which negatively impacts your efficiency. So you don't want to make your stages too small, either.

Another thing to keep in mind is that you should be wary of choking your lower stages. If your rocket needs more dV without adding another stage, then it's tempting to add it to the topmost stage, because it adds the smallest amount of mass and cost. But depending on what you just added, you might have unbalanced your rocket stages - the topmost stage gained a disproportionate amount of mass, thus reducing the dV of the second-to-topmost stage. And the top two stages combined also gained mass, reducing the dV of the third-to-topmost stage. And so on. It has a cascading effect that ripples through all stages below the stage you changed, and in a design that has many stages and/or strongly different Isp values between stages and/or is strongly unbalanced, you can accidentally end up with a rocket that has less dV than it had before you started adding fuel! Of course, there is one stage you can always overload to your heart's content without choking anything: the first stage, the bottom-most one. Because there is nothing below it to choke. However, it is also the largest stage, and that means you have to add large amounts of mass and funds to it to achieve the same effect as adding a little bit to the topmost stage. So you need to experiment and see which path is best for you.

My strategies for efficient launchers are thus:

- Do not exceed 10x Isp worth of dV for any given stage to avoid rapidly diminishing returns

- Do not remain below 5x Isp worth of dV in any given stage either, because staging equipment and engines cost mass and money

- All stages should have similar fuel/mass ratios to prevent stage choking

- Lower engine mass can sometimes trump higher Isp because it improves the fuel/mass ratio

- Decide before building if cost efficiency or mass efficiency is more important; they do not always go hand in hand (f.ex. solid booster vs. liquid engine)

Edited April 16, 2015 by Streetwind

[Warzouz]

How do you calculate ISP of a "meta-stage" when you have mutiple engines fireing different durations

My "huge" first stage is

- Small SRB destach first

- Then 8 red tanks with Mainsails

- Then 4 red tanks with mainsails

- then 4 bigger tanks with mainsails

- then the core with clustered engine

Except SRB, all engines have ISP of 360 and descent TWR. DV is just enough to send to orbit 200T

[Streetwind]

Meta-stages aren't properly defined even IRL, unfortunately.

For instance, the Ariane 5 is often called a two-stage rocket, implying a single staging event, even though there's two distinct staging events that happen: the detachment of the solid rocket motors, and the detchament of the core stage. This is despite the fact that the solid rocket motors deliver 14 MN liftoff thrust, and the Vulcain-II engine on the core stage only delivers 1 MN. Clearly the solid motors dominate completely for the duration of their burn. And yet, they're not really counted as their own stage.

You will find this replicated in pretty much every rocket that uses strap-on boosters that fire along with the core stage... even the Delta IV Heavy, which uses extra core stages as strap-on boosters.

The common theme seems to be to simply define everything that ignites together as one stage, even if there are multiple staging events until the last of these parts burns out. To me, that makes absolutely no sense, but hey, I don't make the conventions...

To address you question though:

1.) Sum up the thrust of all your meta-stage's engines

2.) Calculate Thrust * Isp for every engine

3.) Sum up the results of 2.

4.) Divide the result of 3. by the result of 1.

This gives you the meta-stage's average Isp. At least, until the next staging event. Because when the types and numbers of running engines change, then the result of this calculation changes as well.

For proper dV estimates, you should treat your meta-stage as a series of discrete stages - even if all of these discrete stages happen to ignite together. Tools like Kerbal Engineer Redux actually take care of this (and the average Isp calculation) for you already. A stage like you described would show up in KER as a series of consecutive stages with small dV values, step-by-step decreasing thrust, and short burntimes (which actually equal time between staging events).

[Warzouz]

I didn't noticed KER gives the average ISP. I'll look into it.

What I call Meta-Stage is a launcher

- The first meta-stage is meant to put it's payload to orbit.

- The second meta-stage is meant to push the lander/return vehicle to it's target celestial body.

Usually I design my "meta-stage" in classic KSP aparagus where all engines works together.

My first heavy 200T "meta-stage" has 5 stages

My second meta stage for Jool has 3 stages (dumps empty tanks and engines)

I find easier to design this way becaus each meta-stage has a task of it's own, thus specific DV requirement.

[Yakky]

My efficient launch strategies:

1. Don't let your first stage thrust-to-weight ratio get too low. You want to accelerate up to terminal velocity as rapidly as possible -- ideally the instant you take off. Don't forget that every ten seconds you shave off your initial vertical ascent profile saves you nearly 100 delta-V by reducing your gravity losses. (But this is only true when you're moving significantly slower than terminal velocity. Above terminal velocity, you lose efficiency from the air resistance.) I've seen massive spacecraft with huge but nearly choked first stages that can just barely get things moving -- in such cases, there are huge rewards to spamming a bunch of initial cheap boosters to get things up to terminal velocity quickly.

2. It's OK to have a low(er) thrust to weight ratio in your upper stages, and this can often save a lot of engine mass. Depending on your trajectory, a TWR of as low as 0.6 on the final orbital insertion stage can work. Don't lug a heavy Kerbodyne/Mainsail/Skipper engine up to orbital velocities unless you absolutely need the performance later. Every bit of mass you can shave off your upper stages has cascading benefits.

3. This is even more true for interplanetary stages. Be patient and use one tiny engine. Do multi-pass orbital boosts to escape orbit.

4. Enter the lowest possible parking orbit. Don't waste fuel climbing higher than 75 km, and make sure your trajectory follows a smooth gravity turn. (Your optimal trajectory shape will depend on stage performance and whether or not you use FAR.)

Also FWIW I find the Kerbal Engineer mod to be extremely helpful in understanding stage performance. It shows you you delta-V, thrust-to-weight ratio, and mass for each stage.

Edited April 16, 2015 by Yakky

[Warzouz]

My first stage (launcher to orbit) as usually a TWR around 2 all the way up. This allow to have a shallow angle in upper atmosphere and get a better gravity turn.

My second stage TWR is usually around 0.5, but I'm not too easy with that. For instance, my previous second stage had only 3 LVN for a 38T max payload. The TWR was 0.25 I think. I redid it with 4 fixed LVN and 4 dumpable LVT30. This allow to have a high TWR at start. It's less efficient, but I get some kind of variable TWR and ISP by toggling engines.

Further more, the design of the second stage allow it to fire, event if the first stage core has fuel left (and have not beeing dropped).

My Joolian payloads were largely under 200T (more like 90T), that's why the first stage had plenty of fuel left after reaching orbit.

[Norcalplanner]

Optimizing for payload mass ratio is different from optimizing for rocket mass or for cost. Mainsail and big S1 SRBs are my favorite combination for cost- effective medium-heavy loads. You can see this technique with my LPC station over in the Grand Orbital Space Station Challenge thread. There was also a good thread on efficiency a while ago - don't recall the name though.

Edited April 16, 2015 by Norcalplanner

[OhioBob]

So my questions : What are your launchers efficiency (discarding reusable ones) and cost per ton ? What do you do to optimize it ? What is you strategy (mutliple launches/single launch)

I outline my design method in the following post:

http://forum.kerbalspaceprogram.com/threads/107763-Designing-Launch-Vehicles?p=1678756#post1678756

The guidelines I give are for stock aero. If you use NEAR/FAR, then I would disregard.

For very small launchers, say those for payloads of 5-10 t, I rarely get payload fractions greater than about 0.14. Almost all of my mid-sized launchers give a payload fraction right around 0.16. For my larger designs, say for payloads ≥75 t, the payload fraction is usually about 0.18. Of course these payloads fractions are the maximum that can be achieved. I'm often lifting a payload that is a little smaller than what a particular rocket can theoretically lift.

Cost varies considerably depending largely upon how many solids I use. My cost can vary anywhere from about 1500 to 3000 funds per tonne of payload. The median cost for my mid to heavy launch vehicles is about 2100 per tonne of payload (not counting the cost of the payload itself).

I prefer smaller rockets because very large ones can become difficult and sluggish to control. The biggest launcher that I've saved as a stock design is capable of lifting 93 t. Anything bigger than that and I start using multiple launches and in orbit assembly and refueling.

- - - Updated - - -

My second stage TWR is usually around 0.5, but I'm not too easy with that. For instance, my previous second stage had only 3 LVN for a 38T max payload. The TWR was 0.25 I think. I redid it with 4 fixed LVN and 4 dumpable LVT30. This allow to have a high TWR at start. It's less efficient, but I get some kind of variable TWR and ISP by toggling engines.

I generally like to design my upper stage TWR based on the ÃŽâ€v of my ejection burn. I try to limit the duration of my burn to about 5 minutes so that my sweep angle is not too large. If I have to deliver only 1000 m/s ÃŽâ€v, then my average TWR can be at low as 0.34. On the other hand, if I have to deliver 3000 m/s ÃŽâ€v, then my average TWR must be 1.02. It can be hard to obtain a TWR that high with big payloads using LV-N engines, so I've been know to break my rule on occasions. As Yakky said, when you have a high ÃŽâ€v and a low TWR, you can always do multi burns through successive periapsis passages.

- - - Updated - - -

To address you question though:

1.) Sum up the thrust of all your meta-stage's engines

2.) Calculate Thrust * Isp for every engine

3.) Sum up the results of 2.

4.) Divide the result of 3. by the result of 1.

That's close but incorrect. The steps should be:

1.) Sum up the thrust of all your meta-stage's engines

2.) Calculate Thrust / Isp for every engine

3.) Sum up the results of 2.

4.) Divide the result of 1. by the result of 3.

In other words,

Isp = ΣF / (ΣṠ* g)

[mhoram]

A while back (V0.23) I held a payload-fraction to orbit challenge.

Top contributers managed to get payload fractions of over 20%.

My current Lopac lifter family has payload fractions of around 16-18% if I recall it correctly.

While the focus of that lifter family was a low partcount, it came out with a reasonable payload fraction too.

Main construction ideas behind the larger Lopac lifters:

- Asparagus staging for better utilization of engines in comparison to serial staging (Also see Temstar's post)

- High ISP engines in later stages (like LV-N or KR-2L). These Engines burn the whole time so their high ISP helps to reduce the amount of needed fuel.

- For the vertical ascent part I initially tried to take as many engines as necessary to keep the ship near terminal velocity, but this method was replaced by the strategy of starting with a (Kerbin-Surface)-TWR of ~1.4-1.5 and reducing it with each stage until a (Kerbin-Surface)-TWR of ~0.5 in the final stage. The reason for this change was that by experimentation I came to the conclusion that using more fueltanks and less engines made for more efficient lifters with less parts.

Costs per ton is something I would improve by using jet engines or solid fuel boosters.

[NathanKell]

If you stage during the 'meta-stage' it gets more complex.

Basically, you know dV = ln(wet/dry) * g0 * Isp.

Further, you know burn time: fuel mass * g0 * Isp / thrust_at_that_Isp.

Now, if you have boosters, you need to do it in (# of stage events) steps. Let's take a simple example, a 2 minute core stage with 1 minute of boosters. Thrust 1500 for the core and 215 for the boosters, Isp 310 for the core and 305 for the boosters.

You know that after booster separation you've burned half your core fuel. So:

dv1 = ln((core_wet + boosters_wet) / (boosters_dry + core_dry + 1/2 *core_fuel)) * (1500*310+430*305)/1930 * g0

dv2 = ln((core_dry + 1/2 *core_fuel) / dry_core) * 310 * g0.

Total dV = dv1 + dv2.

[OhioBob]

(1500*310+430*305)/1930

That's the same method of I_sp calculation that Streetwind gave, which is incorrect.

Specific impulse is given by,

I_sp = F / (á¹Â*g_o)

When we have two different engines with different Isp, we must set F equal to the total thrust and á¹ equal to the total rate of mass flow. That is,

I_sp = ΣF / (Σá¹Â*g_o)

Mass flow rate is found by simply rearranging the I_sp equation,

á¹ = F / (I_sp*g_o)

Substituting the above for á¹Â, and cancelling out g_o, we get

I_sp = ΣF / Σ(F/I_sp)

On the other hand, your (and Streetwind's) equation can be written as,

I_sp = Σ(F*I_sp) / ΣF

Let's take your example but with a small change. Since the I_sp you have chosen are so similar, the two methods while yield nearly the same number. Instead of 305 s for the I_sp of the boosters, let's call it 250 s.

Your method yields,

I_sp = (1500*310+430*250)/1930 = 296.63 s

The correct method yields,

I_sp = 1930/(1500/310+430/250) = 294.27 s

The difference is not huge, but it is certainly significant.

[Warzouz]

Well I understant why KER mod has some difficulties handeling deltaV calculation on my design...