LV-N Delta-V: Is this right?

[RocketBlam]

Here is the same rocket with either an LV-N or a LV-909 on the transfer stage. As you can see, the LV-909 has a lot higher D/V (30% more) than the LV-N. I assume this rocket is big and heavy enough that the added weight of the LV-N does not completely reverse its benefits. Is this a MechJeb reporting problem? Because the LV-N seems essentially useless as it is. In fact worse than useless - counterproductive.

ETA: I forgot that the LV-N doesn't use oxidizer any more, so replaced the tanks with just liquid fuel tanks, and it's STILL not as efficient.

Edited May 3, 2015 by RocketBlam

[Superfluous J]

The only thing I can think is it has half the fuel. LV-N only uses liquid fuel now. Swap those tanks with the basic tank of jet fuel, 4 of them total.

Edited May 3, 2015 by 5thHorseman

[Skorpychan]

Weight. The LV-N is a lot heavier now, and the LV-909 is very light and very efficient in vacuum.

[-Velocity-]

Something changed in your staging, it looks like, though I'm not sure what. If you suspect Mechjeb is having a problem, you can always just use the rocket equation, it's very simple.

But also keep in mind that the LV-N really comes into its own when it's running off of a lot of big fuel tanks. If you have it hooked up to a tiny fuel tank (and what you have isn't a lot there), then it will be less of a relative improvement, because it's a VERY heavy, low TWR engine. It's extremely good- the best- for interplanetary transfer vessels, and as a lander engine on low gravity worlds (if you can work your lander around its awkwardly long shape, that is).

[GoSlash27]

RocketBlam,

It's not unusual for the LV-N to deliver worse DV than a less- efficient engine like the LV-909. The ln(Rwd) matters just as much as the Isp. I haven't verified the numbers (I'm feeling especially lazy today), but it sounds about right.

Generally speaking, the LV-N isn't going to be worth using unless you're going really far and you have a pretty large payload.

Best,

-Slashy

[-Velocity-]

The only thing I can think is it has half the fuel. LV-N only uses liquid fuel now. Swap those tanks with the basic tank of jet fuel.

BINGO! That's right! They DID switch the LV-N to liquid fuel only. I haven't progressed far enough in my career yet to acquire the tech yet.

So yea, the reason the delta-V is so horrible for the OP is because he's lugging around a bunch of useless oxidizer.

[RocketBlam]

BINGO! That's right! They DID switch the LV-N to liquid fuel only. I haven't progressed far enough in my career yet to acquire the tech yet.

So yea, the reason the delta-V is so horrible for the OP is because he's lugging around a bunch of useless oxidizer.

I already edited the OP to show that even with all liquid fuel, it's still not as good.

[Mastikator]

The liquid fuel tanks only carry 150 LF, the duo carry 180 + ox.

Look at the weight of both. The 909 weighs 15 tons, the LV-N only weighs 10 tons.

If you make sure they both have the same amount of fuel the LV-N will win, currently it has less than half.

[Superfluous J]

I already edited the OP to show that even with all liquid fuel, it's still not as good.

Then the others are correct: Your ship isn't big enough to see the benefit.

And this is a good thing. It's no longer "SLS engines to launch, 48-7S for small stuff in space, LV-Ns for large stuff in space" anymore. Engines have uses and when you don't use the correct engine for the application, it doesn't do as well.

[FancyMouse]

(Saw your updated rocket)

But see the initial mass difference? 909 rocket 13.4t while LV-N one (the updated one) 10.5t. If you add fuel to LV-N rocket to match 13.4t, this should give you a lot more dV. Remember dV=ln(m1/m0) * Isp * g0. Isp is not the only factor.

[Red Iron Crown]

(Saw your updated rocket)

But see the initial mass difference? 909 rocket 13.4t while LV-N one (the updated one) 10.5t. If you add fuel to LV-N rocket to match 13.4t, this should give you a lot more dV. Remember dV=ln(m1/m0) * Isp * g0. Isp is not the only factor.

This. The LV-N is delivering almost the same delta-V from much less fuel mass (the rocket is 3 tons lighter, and the engine in the lighter one is much heavier). If you equalize the fuel mass, or even equalize the rocket mass, the LV-N's advantage will appear.

[Admiral Regulus]

It's because the LV-N is too massive to see any benefit from the better efficiency.

The Terrier has an Isp of 345 and mass of 0.5, whereas the Nerv is 800 and 3.0. So, the respective delta V's are: 345 * 9.81 * ln([m,full]/[m,empty]) for the 909 and 800 * 9.81 * ln([m,full]/[m,empty]) for the LV-N. This is a pretty complex equation if you're trying to solve for the masses, but if you look at it in terms of the mass ratios, it becomes a little simpler.

The LV-N is only more efficient if the following holds true:

[m,full,909]/[m,empty,909] < ([m,full,LV-N]/[m,empty,LV-N])^2.3188

So, if, with the 909, you have a mass of 2 t initially and 1 t after the burn, you'll have more delta V than you would if you add the nuclear engine. If, however, you have a mass of 3 t at start and 2 t at the end of your burn, you'll be better off with the LV-N. In general, the more fuel you're burning, the more beneficial it is to use the LV-N. You'll get more use out of your fuel, so with longer burns you're saving more. However, the LV-N weighs a lot. So, if you have a small amount of fuel on your vessel, a lighter engine will help you more than a higher efficiency engine. A heavy engine behind a heavy fuel tank doesn't change the mass significantly, but a heavy engine behind a light fuel tank makes a world of a difference.

[AaronLS]

RocketBlam,

It's not unusual for the LV-N to deliver worse DV than a less- efficient engine like the LV-909. The ln(Rwd) matters just as much as the Isp. I haven't verified the numbers (I'm feeling especially lazy today), but it sounds about right.

Generally speaking, the LV-N isn't going to be worth using unless you're going really far and you have a pretty large payload.

What is "In(Rwd)"?

But yeh good point about "really far/really large". A better ISP isn't everything. For small loads a smaller engine, even if less efficient, is sometimes better.

Consider if you are carrying 2 tons of fuel, and had one engine which weighed 5 tons but had a 400 ISP for a total 7 ton rocket, and considered a 1 ton engine instead with 200 ISP. If I understand ISP, then the second engine requires twice as much fuel to do the same amount of work. Adding 2 tons of fuel but swapping the 5 ton engine for a 1 ton engine puts your new total at 5 tons. So you are going to do the same amount of work, but your rocket is 28% lighter and thus you'll get more deltaV for the same amount of work. It's also going to be cheaper and more maneuverable.

[FancyMouse]

What is "In(Rwd)"?

But yeh good point about "really far/really large". A better ISP isn't everything. For small loads a smaller engine, even if less efficient, is sometimes better.

Consider if you are carrying 2 tons of fuel, and had one engine which weighed 5 tons but had a 400 ISP for a total 7 ton rocket, and considered a 1 ton engine instead with 200 ISP. If I understand ISP, then the second engine requires twice as much fuel to do the same amount of work. Adding 2 tons of fuel but swapping the 5 ton engine for a 1 ton engine puts your new total at 5 tons. So you are going to do the same amount of work, but your rocket is 28% lighter and thus you'll get more deltaV for the same amount of work. It's also going to be cheaper and more maneuverable.

That's L, not I. It's the Log function with base e.

And no, you don't need twice fuel. You need less. Assume we can ignore fuel tank container mass. 2t fuel, 5t engine, 400 Isp results in ln(7/5)*400*g0 dV. A 200 Isp engine with 1t own mass will need x tons of fuel to achieve the same dV where x satisfies ln((x+1)/x)*200*g0=ln(7/5)*400*g0. This x is 1/0.96, which is about 1.04, which is less than 2.

If you really mean physics term "work" (which I don't think is the case), then the formula is more complicated and depend on your current velocity.

[GoSlash27]

What is "In(Rwd)"?

But yeh good point about "really far/really large". A better ISP isn't everything. For small loads a smaller engine, even if less efficient, is sometimes better.

Consider if you are carrying 2 tons of fuel, and had one engine which weighed 5 tons but had a 400 ISP for a total 7 ton rocket, and considered a 1 ton engine instead with 200 ISP. If I understand ISP, then the second engine requires twice as much fuel to do the same amount of work. Adding 2 tons of fuel but swapping the 5 ton engine for a 1 ton engine puts your new total at 5 tons. So you are going to do the same amount of work, but your rocket is 28% lighter and thus you'll get more deltaV for the same amount of work. It's also going to be cheaper and more maneuverable.

AaronLS,

ln(Rwd) is the natural log of your wet/ dry ratio.

The Isp is straightforward. 2 otherwise equal engines, the engine with twice the Isp will create twice the DV. But when they're not equal, the ln(Rwd) comes onto play.

Any rocket is engine, fuel, tanks to hold the fuel, and payload. Everything except the fuel is the dry mass, while all of it together is the wet mass.

In the case of the LV-N vs. the LV-909, the 2 1/2 tonnes that is engine in the LV-N can be 2 1/2 tonnes of fuel and tankage for the LV-909. So if the payload is relatively small, the LV-909 can actually produce more DV for the same mass than the LV-N despite it's lower specific impulse.

This also holds true for small DV budgets (such as circularizing in LKO). There's no point in lugging a 3 tonne engine + fuel all the way up if a less- efficient engine can do the job with less than 3 tonnes total mass.

I'm working on an analysis of the 1.02 engines to highlight which engines are best for common scenarios to help with this sort of problem.

Best,

-Slashy

Edited May 4, 2015 by GoSlash27

[AaronLS]

Ah I recognize it as natural log now. I didn't expect a formula in that sentence.

And no, you don't need twice fuel. You need less [...] to achieve the same dV.

Sorry I should have bolded "thus you'll get more deltaV". I didn't say you need twice the fuel to achieve the same dV. I was of the understanding that you need twice the fuel to generate the same impulse since Isp is impulse per unit fuel. Since the resulting build is lighter and the impulse is the same, then you can say with certainty that it will generate a greater dV, and therefore I agree that you can reduce the fuel load if you simply want the same dV.

Either, way we both determined that the lighter engine, despite being less efficient, was the better choice in that scenario. You did so by calculating the exact fuel needed to achieve the same dV and seeing that the result required less fuel, and I did so by calculating the fuel needed to obtain the same impulse and seeing it was lighter(which in turn means it would generate greater dV). Perhaps my approach is wrong though, and I arrived at that by pure coincidence.

[Meithan]

As people pointed out already, the comparison in the OP is a bit unfair because the fuel/total masses are different, and because the LV-N now only consumes liquid fuel so it's better to use fuel-only tanks.

Waiting for someone (or the man himself) to recompute tavert's engine efficiency charts, I prepared a few of my own, which I present below.

tl;dr: if you don't care about a potentially tiny TWR, a single LV-N will outperform a single LV-909 for any payload heavier than 5 tonnes and for desired ÃŽâ€v's larger than 2000 m/s; see this graph:

If you prefer to avoid 30-minute burns, the LV-N is the better choice up to a TWR of 0.5; see this other post.

---

Intro

This is meant to give an approximate analytical perspective on the debate of LV-909 vs. LV-N as interplanetary transfer stage engines. I do this by computing the total ship mass required to yield a desired ÃŽâ€v for a specified payload mass. The "ship" is considered as one engine + fuel + fuel tanks to hold it + payload.

Assumptions:

• Only one LV-909 or one LV-N, so no restriction on TWR. Both engines now have a thrust of 60 kN, which is not much for an interplanetary ship, so TWR considerations will be important; see my next post for an updated calculation.
  
• Single-stage ship. As we all know, dropping mass on the way yields higher ÃŽâ€v values, but I'm keeping it simple here.
  
• Propellant quantity is treated as a continuous value, so tanks are considered infinitely divisible. While this is not realistic, one could approximate this in practice by using a large numbers of small tanks (at least for LFO tanks; for LF only there are fewer options).
  
• For the LV-909 I'm assuming a fuel-to-empty tank mass ratio (my "alpha") of 8 (i.e., 8 tonnes of fuel per tonne of empy tank mass), corresponding to most LFO tanks. For the LV-N fuel-only tanks, I'm using a value of 6, the value for the Mk 2 tanks. The Mk 3 tanks have a better ratio of 8.3, even better than LFO tanks, so choosing this value would only make the case better for the LV-N.
  
• "Payload" is defined as everything that is not the engine, fuel or tanks, so it includes stuff like structural elements as well as the proper payload.
  
• Engine stats used: LV-909: Isp=345 s, mass=0.5 t; LV-N: Isp=800 s, mass=3.0 t (vacuum Isp used)
  

---

Results

With a bit of algebra, we find that for a given desired ÃŽâ€v and using the parameters of these two engines, the total ship mass for a desired payload mass is given by:

where

is the fuel-to-empty tank mass ratio, which states how many tonnes of fuel you get for each tonne of dry tank mass (the more, the better).

Before we get to the graphs, let me take a detour to mention an important point: the fact that we're considering the mass of the fuel tanks in the calculation basically imposes a maximum achievable ÃŽâ€v for any engine, which depends on its Isp and the value of α of the tanks:

For the LV-909 and assuming α=8, this turns out to be ÃŽâ€vmax = 7,444 m/s, which means that for anything close to or beyond this value, a single-stage ship using an LV-909 is impossible. For the LV-N and assuming α=6, the limiting value is ÃŽâ€vmax = 15,287 m/s.

Now to the graphs. I've plotted the total ship mass vs. desired ÃŽâ€v for payload masses of 5, 10, 20 and 50 tonnes. For any desired ÃŽâ€v, the lower curve indicates the more efficient engine of the two, since it achieves that ÃŽâ€v with a smaller total ship mass (which includes its own mass and the fuel mass it needs). The vertical blue dashed line indicates the ÃŽâ€v limit for the LV-909 at ~7450 m/s. The last image shows 2D map of the regions where each engine is a better option, like tavert did.

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It's clear that the LV-N becomes the better choice very quickly: already at only 5 tonnes of payload it outperforms the LV-909 for any ÃŽâ€v larger than 2000 m/s. That's not a lot: it's not sufficient for a round trip to low Mun orbit unless aerobraking is heavily used for the return.

From the last plot we confirm that the LV-N dominates for all but the lightest ships (< 5 tonnes) and for most useful interplanetary ÃŽâ€v figures (> 2000 m/s). But as mentioned previously, this does not consider the TWR of the resulting ship, and these solutions with a single engine might not be practical (pushing a 100 t ship with a single LV-N yields 0.6 m/s^2 of acceleration).

Edit: I made some corrections since the thrust of the engines is not as high as I initially thought. Main results remain unchanged, but see my next post for the full analysis including TWR.

Edited May 4, 2015 by Meithan

[Red Iron Crown]

That's some fine rocket science, Meithan, have some rep.

I bet the chart changes if you consider ion engines, seeing as your figures ignore TWR.

[Wanderfound]

That's some fine rocket science, Meithan, have some rep.

I bet the chart changes if you consider ion engines, seeing as your figures ignore TWR.

OTOH, the new solar panels make Ions rather impractical in the outer system. Looks like the nukes are still the king of interplanetary.

[Red Iron Crown]

OTOH, the new solar panels make Ions rather impractical in the outer system. Looks like the nukes are still the king of interplanetary.

Interestingly, a fuel-cell powered ion drive can work anywhere and still deliver an effective Isp of about 1200s.

[Wanderfound]

Interestingly, a fuel-cell powered ion drive can work anywhere and still deliver an effective Isp of about 1200s.

How many cells per ion?

[Red Iron Crown]

One of the larger fuel cells can drive two ion thrusters, see this thread for some more info.

Edited May 4, 2015 by Red Iron Crown

[Whirligig Girl]

Basically, sometimes, if you have a light enough rocket, a lighter rocket engine will be more efficient than a more efficient one. If you had a huge amount of fuel, (Jumbo-64s with oxidizer removed) you would probably get more delta-v from the LV-N

[Meithan]

That's some fine rocket science, Meithan, have some rep.

I bet the chart changes if you consider ion engines, seeing as your figures ignore TWR.

Indeed, the previous charts ignore TWR and it can be an important consideration since these engines don't provide a lot of thrust. I've included a minimum TWR restriction to the analysis (by asking my program to increase the number of engines in each case until the restriction is met).

Edit: Charts recalculated using correct thrust values.

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For TWR up to 0.4 (about 4 m/s^2 of acceleration), the previous result holds: the LV-N is generally the better choice for ÃŽâ€v's larger than about 2000 m/s and payloads heavier than 5 tonnes.

For TWR of 0.5-0.6, the breakeven point moves to higher ÃŽâ€v's and becomes less sensitive to payload mass (the masses of the engines are starting to become dominant). Also, a region of no solution at high ÃŽâ€v appears (to the right of the charts). This is because the LV-909 can't yield more than 7400 m/s and the solution with the LV-N would require a ridiculous amount of engines (I've limited the code 100 engines).

For a TWR of 0.8 and beyond, the LV-N is too heavy to provide efficient solutions, and the LV-909 wins where a solution is possible.

---

I think the bottomline is that the LV-N's efficiency makes it the better choice for TWRs up to about 0.5; beyond this it's just too heavy to satisfy the TWR restriction efficiently and the LV-909 is the only practical choice. Of course, the more sensible solution to this problem is to drop stages on the way.

I've done missions to Jool with a TWR of 0.25 (with 6 LV-Ns and a total ship mass of 130 tonnes) and it's perfectly practical. It's all about whether your mission profile can work with long burns (on the order of 10 minutes).

If you're curious as to why the jaggedness in some of these charts, it's because the number of engines changes suddenly to satisfy the TWR restriction. I've included the last chart to better visualize the effect: it's clear how the additional LV-N added at a ÃŽâ€v of 2200 m/s temporarily makes it a worse choice than the LV-909. Those 3 tonnes hurt!

Interestingly, a fuel-cell powered ion drive can work anywhere and still deliver an effective Isp of about 1200s.

I saw that thread. The new solar power scaling is definitely making things interesting for ion drives. I've been wanting to crunch the numbers on that, but I really should get to work for now .

Edited May 4, 2015 by Meithan

[phunk]

FYI, I'm pretty sure Mechjeb is having some issues calculating dV in 1.0.x, on multiple occasions I've noticed it telling me the current stage has more dV than the burn I was about to perform, only to have the tanks run dry well before the burn completed.