A Couple Questions

[Spaced Out]

A couple questions.

1. How much of the total delta-v of my launch vehicle should the 1st and second stages have respectively? (e.g. 1st stage 1/2, 2nd stage 1/2)

2. What is the optimal mass comparison between the two for maximum delta-v? (e.g. 2nd stage is 1/4 the mass of 1st stage)

3. Should I design the 1st stage first or the 2nd stage and build the 1st stage around that?

Edited February 3, 2018 by Spaced Out

[Spricigo]

 

Personally, find much easier to design in reverse order of use. Suppose for example I'm designing a tourist bus to kerbin orbit, first I design(S0) the reentry/landing craft, then (S1) a small stage for circularization and deorbit, (S2)the sustainer stage, (S3) the core lifter and last (S4) auxiliary boosters.

Rather than looking for some 'magic proportions' my goal is that each stages makes his job well without unnecessary costs( be it funds, mass, part count,...). Defenitely, never going for "maximum deltaV" , there is no point to have 6km/s if your mission only require 4km/s and the extra mass, while not being of any use, will affect TWR negatively.

 

[Spaced Out]

55 minutes ago, Spricigo said:

 

Personally, find much easier to design in reverse order of use. Suppose for example I'm designing a tourist bus to kerbin orbit, first I design(S0) the reentry/landing craft, then (S1) a small stage for circularization and deorbit, (S2)the sustainer stage, (S3) the core lifter and last (S4) auxiliary boosters.

Rather than looking for some 'magic proportions' my goal is that each stages makes his job well without unnecessary costs( be it funds, mass, part count,...). Defenitely, never going for "maximum deltaV" , there is no point to have 6km/s if your mission only require 4km/s and the extra mass, while not being of any use, will affect TWR negatively.

 

I am going for an all purpose launcher though for heavy lifting. Any tips for max delta-v that have to do with the topic of my questions? 

Edited February 3, 2018 by Spaced Out

[Snark]

@Spaced Out,

There's not really any single "perfect" answer-- the numbers will vary based on your ship design, such as what kind of engines you're using and so forth.  Here are some broadly useful principles to follow, though:

• Start from the top and build down.  In other words, start by placing the payload of the rocket that you want to go into orbit.  Then add the parts (e.g. fuel tank, engine, etc.) for the final stage.  Then a decoupler, then the stage below that, and so forth.  (I believe this answers your question #3.)  This is what @Spricigo was suggesting, above.
• For an efficient multi-stage rocket, stages get exponentially bigger as you go down.  Pick some number N, typically somewhere in the neighborhood of 2 or 3.  Each stage will generally be about N times more massive than the one above it.  (This is directed at your question #2.)  There's no single answer for exactly what N should be, since it depends on the engines involved, your desired TWR, what sort of ascent profile you use, etc.  But a value somewhere in the 2-to-3 range tends to work pretty well.  You could go higher than 3, too.  Just don't go any lower than 2, typically.
• Don't worry about "dV distribution" (your question #1).  That's because that's a result, not a target.  If you start with your topmost stage, and make each stage below it N times bigger, then the dV-on-each-stage will sort itself out.  And then you just keep adding stages until you get to the total amount of dV you want.
• Design so that each successive stage has lower TWR.  Your initial stage (the one you lift off the launchpad) needs to have the highest TWR, because it's doing a dead lift directly against gravity and needs to overcome that.  Later stages will fire when you're going mostly sideways, i.e. they don't have to fight gravity so much, so you want them to have lower TWR.  You want this both because it means carrying less engine weight (which saves dV), and also because the really high-Isp engines (which are the best way to get lots of dV) generally have low thrust, so being able to get away with low TWR on the upper stages means that you can use the nice high-efficiency engines.

Note that the exponential-progression-of-stages thing I describe above is mainly about single-engine vertical stacks.  If you go with an asparagus configuration, it's tweaked a bit.

[Starman4308]

As with many questions of optimal booster design, there is simply way too much "it depends" and non-analytical math going on to make absolute answers impossible.

In general, what I've heard is that if two stages have similar efficiencies (specific impulse, fuel-to-not-fuel fractions), they should have similar delta-V, and if they're inequal, put more delta-V into the more efficient stage.

In practice: design from the top down, figure out what you need for each part of the mission starting from the last part of the mission.

A good example of this would be designing a Mun lander. For that, I would care more about having the Mun lander have a wide base for stable landing than about the mission having a 100% optimized delta-V distribution.

[Streetwind]

@Spaced Out While wordy, this older post of mine should help you see those questions from a new angle and perhaps answer them yourself

[Foxster]

Lifters are actually easy to build and something that takes a fraction of the time that I put into designing a craft for a mission. For me it has never been worth having a set of off-the-shelf lifters. 

My "process" is:

Build the mission payload i.e. the bit that will set off from LKO. 

Add stages under it until I have about 4K dV to spend on getting the payload to orbit.

The TWR of each lifter stage being close to 1.0 for upper stages and close to 1.5 for those burning in the lower atmosphere and at launch. 

Keep an eye on the isp of the engines being picked to make sure those running in the lower atmosphere are good for this. 

[sevenperforce]

In the real world, it is customary that each stage deliver about the same proportion of dV to orbit.

But everything others here have said is true.

[GoSlash27]

I do it like @Snark suggests. I assume 1,700 m/sec per stage and go from there. I may adjust the final DV distribution to minimize partially- filled tanks.

Upper stage: 1,700 m/sec, 0.7 t/w minimum
Lower stage: 1,700 m/sec, 1.4 t/w minimum. If the lower stage uses SRBs, then I reduce the t/w min to 1.2.

Best,
-Slashy

[Snark]

@Spaced Out,

Here's a working example of these principles in action.  The example below is by no means intended to be "optimal" or "best"-- it's just a simple demonstration of a reasonably efficient design that works pretty well.

As with any rocket, we start with the payload, the thing that we actually want to get where it's going.  For purposes of this example, I'll take a fairly basic small-space-station design:

There we go, holds 7 kerbals, has power, docking port, antennas.  The specific design doesn't matter here much-- the rest of the example below would work with any payload that's roughly this size and shape.  So this is basically just a placeholder.

...Okay, that's the payload.  It weighs in at a bit over 7 tons.  So the first thing we need to decide is, what kind of fuel tank + engine we put on that for the uppermost stage.  Well, one handy rule of thumb is "go for a mass ratio of roughly 2:1", i.e. make the fuel load approximately as big as the payload.  So, we've got a 7-ton payload, so a fuel tank that holds 8 tons of LFO seems reasonable.  Since this will be the top stage, we don't need to worry about TWR much, so we'll pick the lightest, most efficient engine that fits conveniently in our stack.  This is a 2.5m stack, so we'll put a Poodle on it.

There we go.  Just stick a fuel tank and Poodle under it, with a nosecone on top for aerodynamics during launch.  17.885 tons, has 2030 m/s of dV.  So, time for the next stage.  Let's double the fuel tank size and move up one notch in engine thrust.  So we'll add a 16-ton tank and a Skipper.   Let's add a reaction wheel too, for convenience (not strictly necessary).

So now our total mass is 39.485 tons.  This stage has 1630 m/s of dV.  for a total of 3660 m/s.  That's easily enough to get this to LKO all by itself at this point, with a couple hundred m/s of dV left over.  But since we're working this as an example, let's keep going, shall we?

Okay, let's double again.  Last stage was 16 tons of fuel, so let's make this one 32, and we'll take the engine up one more notch, to a Mainsail.

82 tons altogether.  This stage has 1380 to 1500 m/s of dV, depending on which Isp value you use (vacuum or atmo).  In reality, it'll be somewhere between those two.  Let's say 1400 to be conservative.  It has a TWR sitting on the pad of 1.7, which is reasonable.  (Can go lower, can go higher, it's a matter of taste and on what sort of ascent trajectory you like.)  So, with this in place, we now have a total of 5060 m/s, or about 1600 above what we need to get to LKO.  That's enough for a one-way trip to Duna orbit, or a one-way landing on the Mun, or a round-trip to Mun orbit.

Let's say we want to keep going.  Well, we double again, that's 64 tons.  Probably don't want to be too much taller at this point or it'll start getting all floppy-noodly on us, so perhaps it's the time to start expanding radially.  So, for example, we could stick a couple of side boosters on, like this:

Note that I only put Skippers on them, not a Mainsail.  That's because we don't really need a higher TWR at this point-- 1.7 was already pretty aggressive.  If we had put a Mainsail on each of those boosters, the booster would have an inherent TWR of over 3, which would raise our overall TWR even higher than the 1.7 it's already at.  Whereas with a Skipper, each of the radial boosters has an inherent TWR of just under 1.5, pretty close to what we have already (which was somewhat more than we need), so that's plenty for us.

Note that I'm assuming that all three engines are firing off the pad.  I've set up asparagus staging, here.  I simply toggle the radial decouplers' "enable fuel crossfeed" option on.  This means that as the ship lifts off the pad, the three engines (including the Mainsail in the middle) will completely drain the radial tanks before touching the center tank's supply at all.  This is nicely efficient.  It just means that I simply watch the radial fuel tanks' content as it climbs, and stage the boosters away as soon as those tanks run dry.

Anyway, adding those boosters raises the overall mass of the ship to 161 tons, with a launchpad TWR of just under 1.6.  The dV for the radial boosters is roughly 1500 m/s.  This also means that the stage just above-- i.e. the lone Mainsail, after jettisoning the boosters-- will get close to its maximum 1500 m/s, since that stage won't start until the ship is already well over 10 km high, so at that point the Mainsail will be getting close to its vacuum Isp.  So, this raises the overall dV of the ship up to somewhere north of 6600 m/s, or about 3200 m/s above what's needed to get to LKO.  With that sort of dV budget, it could do a Mun landing and return with fuel to spare, or get to orbit of pretty much any planet in the solar system except Moho.

Just now did a quick test launch of the ship, and it made it to 100 km circular orbit with the Skipper's tank nearly full.

As I've said, this doesn't even try to be an "optimal" design.  For example, as currently designed, it gets nearly to orbit before activating the Skipper, and at that point the Skipper is way overpowered for any further burns. Heck, even that top-most stage is overpowered-- the Poodle gives the final stage a TWR higher than 1 even with full tanks, which is way more than it needs.

But it works well enough, it's easy to build, it's reasonably efficient, and it's a reasonable illustration of the general principles of how building a multi-stage ship works, even if the details will vary from case to case.