How much deltaV should be in each stage of the launcher?

[guitarxe]

If we have a 2-stage launcher, is there some kind of rule of thumb of how much dV should be in each? Like say a ratio fo 1:2, or 1:3 or something like that? And how high and how fast should your first stage get you, anyway? Or does that all completely depend on the payload or does it not really matter at all?

[regex]

Just depends how you build it.  There's no real hard and fast rule I follow like with RO.  Kerbin is so easy you can do 1+1 launchers no worries.  Maybe I'd say put at least 1km/s in your upper?

[White Owl]

It's totally dependent on which stage(s) you want to reach what orbital height, and how much dV you want to have left over. I don't think there is a simple answer.

[guitarxe]

29 minutes ago, regex said:

Just depends how you build it.  There's no real hard and fast rule I follow like with RO.  Kerbin is so easy you can do 1+1 launchers no worries.  Maybe I'd say put at least 1km/s in your upper?

What makes RO so different that you must follow a rule there in contrast with stock?

[OhioBob]

I've found that dividing the propellant up on an approximate 1:2 ratio works our pretty well.  This generally gives a little more delta-v to the second stage.  Here's a thread in which I've broken down my design method based on a few simple ratios. 

http://forum.kerbalspaceprogram.com/index.php?/topic/136666-a-quick-method-for-designing-liquid-fueled-launchers/

[regex]

4 minutes ago, guitarxe said:

What makes RO so different that you must follow a rule there in contrast with stock?

7.8km/s low orbit velocity as opposed to 2.2km/s.  Launches take longer and require much more delta-V.

[MaxL_1023]

The ratio depends on what TWR you want. If you can get away with a lower TWR on your second stage, you can put more fuel (and delta-v) on it. It depends on what engines you have available, stack size, payload type and ascent profile as well. 

 

Generally, I start with the payload, put propellant+engines until it has a TWR of about 0.8-1 for an upper stage, 1.0-1.2 for the middle stage and 1.25 on the pad for the first stage. How the delta-v balances out depends mainly on what engines you have available and your actual payload size. 

[GoSlash27]

I like 1800 m/sec in the first stage. It may not be the most efficient staging point in terms of raw DV, but it allows staging to occur above 25 km. This means I don't have to worry about aerodynamic issues with the second stage.

Best,
-Slashy

[FullMetalMachinist]

4 hours ago, GoSlash27 said:

I like 1800 m/sec in the first stage. It may not be the most efficient staging point in terms of raw DV, but it allows staging to occur above 25 km. This means I don't have to worry about aerodynamic issues with the second stage.

Best,
-Slashy

I completely agree with this. At that point in the atmosphere you can use a high efficiency vacuum engine, and not lose hardly any thrust due to atmo pressure. 

[Superfluous J]

4 hours ago, GoSlash27 said:

I like 1800 m/sec in the first stage. It may not be the most efficient staging point in terms of raw DV, but it allows staging to occur above 25 km. This means I don't have to worry about aerodynamic issues with the second stage.

Best,
-Slashy

Agreed. It also matches with my own personal rule that - if I'm doing 2 separate lifter stages to orbit - each of them gets about half the dV.

But really in the stock game I far more frequently do my stages in parallel instead of serial, with fuel lines feeding into the inward tanks. Most small rockets only need one such transition, and it's more efficient and you can use all the (lifter) engines at launch.

[Pecan]

Everything else being equal - which it never is - I also think equal dV in each stage is optimal.  Can't remember where I got that from though - mhoram maybe?

The main thing that almost certainly isn't equal though is the relative sea-level and vacuum ISPs of your engines.  Ideally you'd want your upper-stage engine, optimised for altitude, to take over at the point it becomes more efficient than your lower-stage one, optimised for launch.  If your upper engine hasn't got the thrust to carry all the fuel from that point just stick it down on the first.  Most of my launchers now are SSTOs anyway, since it's so easy.  Can't be doing with all that messing about with spaceplanes though.

[GoSlash27]

1 hour ago, Pecan said:

Everything else being equal - which it never is - I also think equal dV in each stage is optimal.  Can't remember where I got that from though - mhoram maybe?

The main thing that almost certainly isn't equal though is the relative sea-level and vacuum ISPs of your engines.  Ideally you'd want your upper-stage engine, optimised for altitude, to take over at the point it becomes more efficient than your lower-stage one, optimised for launch.  If your upper engine hasn't got the thrust to carry all the fuel from that point just stick it down on the first.  Most of my launchers now are SSTOs anyway, since it's so easy.  Can't be doing with all that messing about with spaceplanes though.

 

2 hours ago, 5thHorseman said:

But really in the stock game I far more frequently do my stages in parallel instead of serial, with fuel lines feeding into the inward tanks. Most small rockets only need one such transition, and it's more efficient and you can use all the (lifter) engines at launch.

^ And as an addendum, vacuum engines should never be staged right off the pad, even in a setup 5thHorseman describes. Their Isp is even worse than SRBs down there, so they waste more mass than is saved by turning them off. They break even around 3.5 km.

Best,
-Slashy

 

[Nich]

2 hours ago, GoSlash27 said:

 

^ And as an addendum, vacuum engines should never be staged right off the pad, even in a setup 5thHorseman describes. Their Isp is even worse than SRBs down there, so they waste more mass than is saved by turning them off. They break even around 3.5 km.

Best,
-Slashy

 

Math!!!! Or link

[AeroGav]

I'm a spaceplane guy not a rocket enthusiast so it's not my strongest area.  I think there is a mathematical formula giving an optimum ratio assuming no gravity or atmospheric drag.

For me it's about which engines perform best at each stage of the ascent.  At the beginning you need high TWR  and good atmospheric ISP.  Gimballing isn't needed because fins are better for steering you aerodynamically.      Above 10km vacuum ISP trumps the atmo rating.   Above 20km gimballing is helpful.   And by the time you're really motoring along, mach 4 +,   orbital effect is cancelling much gravity and you're above the atmospheric drag, you can get away with a lower TWR.

Example early career games I might have a Reliant with some flea boosters for the lower stage.  A Swivel mid stage and Terrier upper stage, for when we're over halfway to orbit.     Late game  I might go with Vector / Dart / Nerv.

Booster stage - goal - 

to get to 240 m/s as fast as possible.

Lower stage - maintain 240 m/s then accelerate through the sound barrier at 10km

Mid stage - high vacuum ISP rating with moderate TWR.  Don't want to get too fast too low but don't want to start falling back.

Upper stage - Once at mach 4 or above 35km we can start to relax.   Even if your TWR is only 0.6 or so until some fuel burns off, you're gonna make it.

[OhioBob]

For a liquid fueled rocket, my basic rules of thumb are,

• The second stage (i.e. upper stage) should have a propellant mass equal to the payload mass*.
• The second stage should have a TWR at ignition of 1.1 to 1.3.
• The first stage (i.e. lower stage) should have a propellant mass equal to twice the payload mass (or twice the second stage propellant mass).
• The first stage should have a TWR at liftoff of 1.3 to 1.5.

Using these guidelines, the second stage will have a mass ratio of about 1.8, and the first stage will have a mass ratio of about 1.7.  The launch vehicle's total Δv will be equal to about 11 times the specific impulse.

Of course, because of the finite number of parts we have to work with, it's not always possible to hit the target numbers precisely.  There is usually some massaging that has to be done, but the above rules are a good starting place.

* In this case, "payload mass" refers to the total mass that mounts to the second stage, which includes decoupler, fairing, etc.  This mass is often greater than the useful payload.
 

Edited April 16, 2016 by OhioBob

[MaxL_1023]

I like to put a first stage which is 4 copies of the second stage arranged radially. It works quite well when you need to lift something heavy with only 1.25m parts. 

[GoSlash27]

6 hours ago, Nich said:

Math!!!! Or link

Nich,

 I'm not sure which part you need the math for, so please pardon my response if it's overkill.

 The point of lighting engines off the pad is so that you're not carrying them as dead weight. If you do this, you can use a little less SRB and save some overall mass/ cost on the launch stage.

 In order for this to save any weight, the mass of the fuel expended by the lit engine must be less than the mass of the propellant that would've been expended by an equivalent SRB. This gets into the other side of Isp that we don't talk about as much.

Isp*g0= exhaust velocity in m/sec ; "V_e"

T= thrust in kN

m'= mass flow rate in kg/sec

m'=T/V_e

m'*t= mass of fuel expended during launch.

So as you can see, the lower the Isp, the higher the mass of fuel must be expended to produce the same thrust for the same period of time. If you're using an engine with a *worse* Isp than a SRB, it will require more fuel than the SRB would have needed to do the same job. This erases the benefit of lighting it.

The Isp of a vacuum engine doesn't catch up to a SRB until around 3500 m altitude, so it's not worth lighting it before then.

 

 You can confirm this yourself by building a parallel staged booster with a vacuum core engine. Launch it first with the core engine lit, then try again with just the SRBs, turning on the core engine at 3.5km. The second run will leave you with more gas in the tank.

Best,
-Slashy

[Nich]

@goslash27 However this does not account for the fact SRB fuel is cheaper then LFO ( i think) or the fact the your first 1 TWR is paid to the kerbal gravity gods. Worst case serino your rocket has 1 TWR.  if you light your deep space engine with terrible isp you are now accelerating.  On the opposite side if you have 5 TWR your deep space engine has no impact and is just waisting fuel. What is the break even isp TWR.  This gets really complicated when you look at a rhino with a decient atm ISP. Your wasting fuel at 255 now that could be used at 340 later but your getting free acceleration as your lifter has already made the sacrifice to the gravity gods.

Edited April 17, 2016 by Nich

[GoSlash27]

22 minutes ago, Nich said:

@goslash27 However this does not account for the fact SRB fuel is cheaper then LFO ( i think) or the fact the your first 1 TWR is paid to the kerbal gravity gods. Worst case serino your rocket has 1 TWR.  if you light your deep space engine with terrible isp you are now accelerating.  On the opposite side if you have 5 TWR your deep space engine has no impact and is just waisting fuel. What is the break even isp TWR.  This gets really complicated when you look at a rhino with a decient atm ISP. Your wasting fuel at 255 now that could be used at 340 later but your getting free acceleration as your lifter has already made the sacrifice to the gravity gods.

Nich,

 Well... the fact that SRBs are cheaper is why we use them. As for the t/w, you're not liable to ever build a lifter with such dismal t/w that lighting a vacuum engine is going to improve matters. You see, the fuel consumption is constant. It's the *thrust* that varies with Isp, so the vacuum engine isn't adding much thrust... but it's going through a lot of fuel. The break- even point comes when the vacuum engine achieves the same Isp as the SRB.

 If the goal of lighting an engine on the pad is to save weight, then lighting an engine with poor Isp is actually counterproductive, because you have to add fuel for it to waste. The ship actually weighs *more* than it would've if you'd left the engine turned off.

Best,
-Slashy

[Nich]

Oh and the exact answer is 56.7% for a serially staged rocket however this assumes you can perfectly scale your lifter engine, vacuum engine, fuel tanks and decouplers.  It was been a while since I have seen the proof but it might also assume the same starting TWR for 1st and second stage as well the same ISP for each stage.

 

@GoSlash27  I don't think your mass example is quite correct.  If we want to save mass we wouldn't be using SRBs anyways.  Also by that logic we would never want to light the SRBs because the LFO lifter stage always has a better ISP then the SRB.  I did some checking and the terrior does not overtake the swivel until 12.3 km.  So by your logic you would not want to light the terrior until its ISP is greater then the swivels.  In addition we would want to shut off the swivels.  However this would detrimentally affect TWR.  

 

I was more of hoping for some math that shows how TWR is related to dv to LKO.  Unforunitly I do not have excel on my laptop as I am on vacation however I do know off hand that for me TWR of 1 requires 4.6ish km dv to get to orbit, 1.7 requires 3.2ish km dv, and 10ish requires 2.6ish km dv.  I suspect (have no math to support) that if you wanted to do a numerical approximation of the relationship of TWR to dv required to LKO you would want to subtract 1 twr.  However this may only be applicable to the first 10-20km.  In fact the value of TWR to dv to LKO is probably different every 5 km.  

 

I am going to have to think about it but I dont think it is as simple as mass wasted.  Maybe it falls more to mass used vs dv gained (after subtracting gravity losses).  So assuming 5 engines, 1 terrior, 2 swivels, 2 thuds.  We then need to look at the ratio of actual dv gained vs mass used.  Then we need to look at the ratio of terrior on vs terrior off.  When this ratio is greater then 1 it means having the terrior on gets us more dv.  I think this could be set up rather easily numerically in a spread sheet (GGAAHAHAHAHHHH I want my computer) for a pure vertical launch however when a gravity turn thrown and aero drag gets thrown in it become extremely complicated. 

Edited April 17, 2016 by Nich

[Superfluous J]

On 4/16/2016 at 11:35 AM, GoSlash27 said:

^ And as an addendum, vacuum engines should never be staged right off the pad, even in a setup 5thHorseman describes. Their Isp is even worse than SRBs down there, so they waste more mass than is saved by turning them off. They break even around 3.5 km.

This is very very true. Actually one of the main considerations for me to decide between staging in serial or parallel is the type of engines I'm going to be using in space. Frequently for large craft, I just use a few Rhinos in space and their atmo I_sp is good enough to use right off the pad. At least, I think that's true. I've not done the math. As is typical of me

Edited April 17, 2016 by 5thHorseman

[Plusck]

2 hours ago, Nich said:

Oh and the exact answer is 56.7% for a serially staged rocket however this assumes you can perfectly scale your lifter engine, vacuum engine, fuel tanks and decouplers.  It was been a while since I have seen the proof but it might also assume the same starting TWR for 1st and second stage as well the same ISP for each stage.

 

@GoSlash27  I don't think your mass example is quite correct.  If we want to save mass we wouldn't be using SRBs anyways.  Also by that logic we would never want to light the SRBs because the LFO lifter stage always has a better ISP then the SRB.  I did some checking and the terrior does not overtake the swivel until 12.3 km.  So by your logic you would not want to light the terrior until its ISP is greater then the swivels.  In addition we would want to shut off the swivels.  However this would detrimentally affect TWR.  

 

I was more of hoping for some math that shows how TWR is related to dv to LKO.  Unforunitly I do not have excel on my laptop as I am on vacation however I do know off hand that for me TWR of 1 requires 4.6ish km dv to get to orbit, 1.7 requires 3.2ish km dv, and 10ish requires 2.6ish km dv.  I suspect (have no math to support) that if you wanted to do a numerical approximation of the relationship of TWR to dv required to LKO you would want to subtract 1 twr.  However this may only be applicable to the first 10-20km.  In fact the value of TWR to dv to LKO is probably different every 5 km.  

 

I am going to have to think about it but I dont think it is as simple as mass wasted.  Maybe it falls more to mass used vs dv gained (after subtracting gravity losses).  So assuming 5 engines, 1 terrior, 2 swivels, 2 thuds.  We then need to look at the ratio of actual dv gained vs mass used.  Then we need to look at the ratio of terrior on vs terrior off.  When this ratio is greater then 1 it means having the terrior on gets us more dv.  I think this could be set up rather easily numerically in a spread sheet (GGAAHAHAHAHHHH I want my computer) for a pure vertical launch however when a gravity turn thrown and aero drag gets thrown in it become extremely complicated. 

I think GoSlash27's example is correct. The mass of an SRB is basically "free" mass: the SRB provides thrust and then all of its mass is dropped. This is not true for the fuel for vacuum engines unless you put that extra fuel into a drop-tank (and calculate exactly how much fuel should go into that drop-tank to get your vacuum engine up to a decent ISP). The trouble is that with the terrible thrust of vacuum engines, a vacuum engine is barely capable of lifting itself, let alone lifting its own fuel with a TWR equal to the TWR of the rest of the ship.

Basically, to know whether an engine should be lit, or dumped, you need to know its effective TWR compared to the ship's TWR. That's easy for an SRB: its TWR on its own is always going to be higher than the ship it's attached to. It's trickier for a liquid fuel engine since the mass of the engine, fuel and fuel tankage are part of the ship itself. 

However, it is not too difficult to guesstimate: if you have an 18t ship with an atmospheric TWR of 1.5, and you have an unlit Terrier on that ship, and assuming it'll take you 40s to get to 10km (which is 2/3 of the time it would take if TWR remained constant). If you lit the Terrier, it would burn 141.6 units of LFOx in 40s, so let's round that down to an FL-T100+Oscar+raidal decoupler+fuel line, or 0.8625 tonnes = 8.46kN weight. Sea-level thrust is 14.78kN, giving a "contributed" TWR of 1.7 for a lit v unlit Terrier for the 40s following launch, using an additional drop-tank. 

So there you have it: as long as the Terrier was going to be there anyway, and you drop the tanks containing the fuel that it uses, then it (just barely) makes sense to light it on the launchpad under those conditions. Since the ship weighs 18t, it must have a total thrust of 264.9kN off the launchpad. Lighting that Terrier added 14.78kN, but added weight (for 8.46kN), so it contributed a total of 2.3% to thrust, with a net contribution (difference between 1.7 and 1.5 TWR) of 1.8kN or 0.7%...

However, if you don't have a separate drop-tank, you either have to take the total ISP of the ship into account to see what dV losses you made, or compare fuel+tank masses before and after that first 10km ascent. To get 265kN off the launchpad and up to 10km you need a trio of Hammers (45% thrust-limited) with an ISP of 170. Actually we don't care about their ISP since we'll ditch them shortly after 10km (they'll burn out at about 50s... so shortly after 10km). Three Hammers weigh 10.7t, so rest-of-ship must be 7.3t. That leaves second stage a bit heavy but manageable for a single Terrier. Assuming 1.5t payload and 0.5t engine leaves 5.3t fuel tanks, or FL-T800+T100+Oscar, which is neat since we used the last two getting up to 10km with the Terrier lit. Teh rocket equation tells us that we have a difference of about 794 m/s delta-v depending on whether the T100+Oscar are full or empty.

I would have liked to do the calculation for the amount of dv gained by having the Terrier lit up to there, but it's getting late and I'd hazard a guess that a contribution of 0.6% (net) to 2.3% (gross) to thust over 40s is not going to amount to much. A rough calculation seems to suggest something like 200m/s if very generous. So if we fire the Terrier without changing the rocket by adding drop-tanks, we lose about 600 m/s from what was originally going to be about 4.5k dv (again, a ballpark figure).

 

As for the precise maths to relate TWR to dv to LKO: I think it would be horrendously complicated. Basically, for each increment of time, you need to determine the orbit from your radius (i.e altitude +600km), angle and speed, then add thrust and subtract drag and resample to get your new orbit, angle, speed, then recalculate remaining fuel, mass, ISP and therefore thrust, then add that thrust and subtract drag to get your new orbit and you're back to resampling again... And you'd have to use a reasonably short resampling period to get a decent result.

So while I'm sure that there is a possible function that would take all that into account, I'm pretty sure that the only feasible solution would be to sim it, which boils down to playing KSP...

[CSE]

@Nich If you really love your spreadsheets, it's just about feasible to include the gravity turn.

You know your upward velocity and so you can predict your time to apoapsis. (Working in the frame of the rocket and treating the centrifugal acceleration as real may help.) Derive your rocket's pitch angle from your t_ap, so that as TWR and centrifugal force components increase and gravity decreases, you pitch over further to stop your t_ap overshooting. Step the calculation until you're horizontal and at orbital velocity.

Twenty or so columns should lay out all the calculation steps nicely, and then just fill down the page with time steps. The really nice part of this model/simulation, rather than a compact formula, is that it's then quite easy to include staging events.

Edited April 19, 2016 by CSE
(spelling)

[numerobis]

@GoSlash27: with low TWR you lose efficiency, so there's a tradeoff. At launch, gravity loss increases as 1/(TWR-1).

So the ideal can include low-Isp off the pad, and turning them off when you start moving.

Fun fact about vertical flight: the speed at which apoapsis grown under thrust depends on your thrust directly, but also on the *product* of thrust and speed. The faster you're climbing, the less you need to push to keep apoapsis rising. The analysis is pretty simple if you ignore the reduction in gravity; tacking on horizontal flight makes it pretty complicated; and drag, forget it.