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# Comparing 1st stages, looking for a metric

## Question

In the context of the Eve 3000 Challenge, it has turned out that the TwinBoar LFB is the best choice for a first stage on Eve. Obviously raw TWR is so worthwhile that it makes up for a poor ISP.

While I could explain the benefits of TWR in many words, I don't know how to quantify it. Is there a way to compare engines that somehow factors in both ISP and TWR? As I'm primarly intersted in Eve lifters, taking off near sea level, this should remove a few variables from the equation. Still, I'm quite clueless as to what I'm looking for.

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It depends somewhat on how long/high the stage is aimed at but I've always liked the (generally Kerbin) SSTO measures.  Presumably you could compare similar 1km Eve quantities or whatever.

Simply: What total mass, therefore TWR, can a given engine lift to a specific altitude.  Nearly all of that mass apart from the engine is going to be fuel, which is where the ISP comes in, so you have a combined TWR/ISP rating.  Conversely, how high can an engine lift a specific payload mass - any mass just being a multiple of that engine+fuel.

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I disagree. The Vector is a superior engine for Eve.

As well as its better performance characteristics you have to understand that Eve craft are about drag.  The Vector being mk1-sized means it has low drag and so does the tanks it's attached to.

The Eve 3000 Challenge is about minimum cost with a large payload, which is where the TwinBoar might win but that is special case that doesn't necessarily apply for most Eve craft. Unless of course you are only designing Eve 3000 craft?

Edited by Foxster
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Eve-3000 requires a hefty payload but that's not the key feature. The important bits are:

• you're optimizing for cost (rather than lowest mass or least delta-V or something)
• use of ISRU makes fuel cheap. You still need enough propellant on the pad to take you to Minmus, but that's a comparatively small one-time fee.

I say the Vector is hardly ever worthwhile. Use Mammoths if you can (that is, if you have enough payload to justify their use), but when even a single Mammoth is too much, there's almost always something more cost-efficient than the Vector.

23 hours ago, Pecan said:

Conversely, how high can an engine lift a specific payload mass - any mass just being a multiple of that engine+fuel.

Ho Hum. Don't know how widely applicable that is, but I find that on my lifters, 1st and 2nd stage have similar sea-level TWRs -- which basically means that the 1st stage has been weighed down with about as much fuel as it can carry.I often think of my stage as a self-propelled external tank.

Would it be reasonable to compare "total impulse delivered from a full fuel load", divided by cost?

This doesn't honestly tell me the contribution of my first stage, as part of the fuel is used in more upstage engines at different ISPs. But does it tell me anything at all, and if so, what?

Edited by Laie

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1 hour ago, Laie said:

I say the Vector is hardly ever worthwhile. Use Mammoths if you can (that is, if you have enough payload to justify their use), but when even a single Mammoth is too much, there's almost always something more cost-efficient than the Vector.

We must be building very different craft and perhaps even on a different planet.

What could you possibly want to get to orbit on Eve that requires a Mammoth?

Edited by Foxster

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6 hours ago, Laie said:

...on my lifters, 1st and 2nd stage have similar sea-level TWRs

Is this a good time to say I've never returned from Eve?

The job of any stage is to accelerate/lift everything else so that after staging 'everything else' starts faster/higher.
Do you want to go faster or higher with your first stage?  Probably higher so, if you know a particular engine can lift a specific mass to X altitude, you know how to lift ANY mass to X altitude (engines & fuel required = required mass / tested mass).  That is - if a particular engine & fuel combination can lift 2t to 3,000m then two of them strapped together can lift 4t to 3,000m.  (NB: Does not say that two of them can lift 2t to 6,000m!)

How useful the metric is is up to you, but you were only asking for a 1st stage metric *shrug*

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9 hours ago, Pecan said:

if a particular engine & fuel combination can lift 2t to 3,000m then two of them strapped together can lift 4t to 3,000m.

Not necessarily on Eve.

That might be true on an airless or thin atmosphere body but on Eve the increased drag of the engines+fuel and coupling parts means you won't get the hoped-for payload doubling.

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4 hours ago, Foxster said:

Not necessarily on Eve.

Good point!  It's only strictly true for vacuum launches

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After mangling data the whole day, I'm not sure if I've come across something profound or just made a hash of it.

Four charts, in order:

1. your good ole ISP graph. 'nuff said. Rhino and Poodle thrown in for lulz and giggles.
2. if I weigh down engine X with as much fuel as it can lift at a given altitude, how long will it run with that amount of fuel? The unit is seconds and I think of it as a kind of "actual ISP", insofar as it includes the mass of the engine and tanks. Still very similar to nominal ISP, but the weak/heavy Aerospike slips down quite a bit.
3. Impulse delivered: thrust at altitude multiplied by burntime from chart 2. Pretty useless, this chart mostly tells us that the Mammoth is a vastly more powerful engine than the Poodle.
4. Impulse delivered divided by nominal thrust. I think it's worth a closer look:

This is "if I load down 1kN worth of engine X with as much fuel as it can carry at \$altitude, how much of an impulse will it deliver until it burns out?" and it's kinda-sorta "ISP squared" because at higher altitude you can both load more fuel and make more of it. However I've come there by multiplying actual thrust at altitude with burn time at altitude, then dividing by the engine's nominal thrust. So the unit is "seconds" and I don't quite know what to make of it. Overly Specific Impulse, perhaps? I know the underperforming Aerospike from experience, though, so I think this chart is providing some actual insight.

Paging @OhioBob: sorry to bother you, but can you tell me what I did there?

And finally, the graph I originally set out to do, which is "impulse delivered divided by cost":

Including fuel and everything, three LFBs are about as expensive as a single Mammoth but actually give you more of a push before they burn out. The chart extending to 10km and beyond is probably meaningless, though: a fully fueled LFB may outperform the Mammoth at any altitude, but getting to altitude in the first place won't be cheap.

It may seem silly to measure Eve performance against the roll-out cost on the launchpad, but with ISRU this becomes quite practical: most Eve lifters can single-stage to Minmus and top off their tanks for the voyage to Eve.

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On 12/22/2018 at 7:25 PM, Laie said:

In the context of the Eve 3000 Challenge, it has turned out that the TwinBoar LFB is the best choice for a first stage on Eve almost any challenge that scores heavily on cost.

Corrected this for you.

The conclusion is valid for that particular challenge, because it focuses on cost. The Twinboar is simply a ridiculously cost-effective engine in a lot of circumstances, Eve just being one of them.

When it's all about bang for buck, the Twinboar is way out of the stock 'balance', there isn't really any competition. Corrected for the fuel and dry mass of the included Jumbo tank, it's less than 7000 funds per 'engine', but with a comparable TWR and ISP to the much more expensive Mammoth or Vector. Nothing even comes close to that RoI in stock.

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16 hours ago, swjr-swis said:

Corrected this for you.

Heh.

Small nitpick though, it's nowhere as as cheap or efficient as you say. 11,250 funds, and ISP a bit short of the Mainsail. Until now I mostly thought of it as the Mainsail's more powerful and less efficient cousin, assuming that these two would about cancel each other.

OK, on Eve they don't because up to 10km their ISPs are virtually indistinguishable. Still, ISP is way, way worse than the Mammoth's. Call me stupid, but that sheer TWR can make up for it to such a degree came as a surprise to me.

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1 hour ago, Laie said:

Small nitpick though, it's nowhere as as cheap or efficient as you say. 11,250 funds, and ISP a bit short of the Mainsail.

It is exactly as cheap as I said. Stock game, all default settings: Twinboar - 17000 funds wet, 14062 funds dry. Even without adjusting for the (dry) cost of the integrated Jumbo fuel tank this is already down to 7031 funds per 'engine'. Dry cost of a Jumbo is 2812, subtract even a fraction of that from the dry cost of the Twinboar, and as I stated, its price per 'engine' drops to under 7000 funds.

I'll concede that the raw Isp is lower than either, but I did say 'comparable', not equal. I disagree at calling a 5.0-5.3% difference 'way way worse' in any kind of comparative or numerical analysis.

Now, in the specific case of optimizing for cost, seeing how cheap fuel mass is compared to engine mass (a factor of roughly 19-28!), the massive 60-75% difference in cost per 'engine' between the Twinboar and either Mammoth or Vector becomes an overwhelming factor, relegating the marginal Isp advantage of those two to a side note.

Look at it from another angle: the price difference between the Twinboar and either Vector or Mammoth buys the Twinboar a margin of roughly 1.3 Jumbo tanks of LFO per 'engine'. The Twinboar could guzzle fuel like there's no tomorrow and still come up on top. That price gap all by itself makes all the difference when optimizing for cost.

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But then again, the lack of a node on the bottom is a huge drawback, that I think is worth several thousand funds at least.

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1 hour ago, bewing said:

But then again, the lack of a node on the bottom is a huge drawback, that I think is worth several thousand funds at least.

I'm a bit lost at this argument, unless you're making fun of me and I'm missing it.

There are so many ways to trivially solve the 'lacking' bottom node that I have to believe you are making a joke. A radially attached truss piece (25 funds) or empty NCS cone (256 funds) comfortably offset between the engine bells, for example. Or if you want to be fancy about it: an upside down fairing on the top node, offset to move its top interstage node below the engine, for a few hundred more. Or since the context is about a lifting stage large enough to push 3000 ore to Eve orbit, the bottom node would be provided by the core return vehicle the Twinboars will be radially attached to, for zero net cost. What are we talking about here?

In more general terms, since we were comparing cost-effectiveness of top-tier TWR lifter engines, there is no function (and thus no worth) for a bottom node at all - these engines are supposed to be the first to light up.

If we're going to calculate net worth based on a general list of pros and cons, I still don't see the Twinboar losing:

• Mammoth doesn't have a bottom node either, plus it's not radially attachable (Twinboar is).
• Mammoth and Vector are heavier per engine than the Twinboar.
• At less than half the price per engine of either Mammoth or Vector, the Twinboar already comes with an integrated and filled Jumbo tank of LFO. Let's not forget this one particular little point.

We'd have to penalize its cons in a very biased manner compared to the pros to really make the Twinboar lose out on any calculated net worth.

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@swjr-swis: cost per engine bell, seriously? I wonder where the Ant Drive would end up if I'd made a chart on that metric...

I guess you've only been looking at LFB/Vector/Mammoth where each bell amounts to 1MN of thrust, but I'm not convinced the LFB really plays in that league. Perhaps on Kerbin it does (as I said, I've been undervaluing TWR all those years). Yet when I said that ISP was much worse I was thinking of Eve. Strictly on performance data it cannot compete in any way. Only when you factor in cost does it start to draw about even (which I take more as a sign of low price, rather then superior performance.

However, the performance gap narrows with altitude, and bang for the buck quickly outpaces the Mammoth. Which is probably the reason why it's worthwhile to use a *lot* of LFBs, not only for a brief initial push, but as a full first stage lasting to 5+km of altitude, and airspeeds on the order of 300m/s (those two go together).

While I don't take drag optimization to the same degree as Foxster, it still pains me to see a half-dozen short and stubby boosters attached to my rocket as it goes towards mach 2. But with LFBs, that's actually worthwhile. Bang for the buck indeed.

@bewing: All things considered the LFB *is* a gas-guzzler after all, it only works so well because it can carry more gas to begin with -- so for all the guzzling you still get more oomph out of a LFB stack compared to Mainsail or even Mammoth. Doubly so if part of that fuel isn't actually used in the LFB, but asparagus-fed into more efficient engines. But still, it requires a lot of propellant to perform it's magic. Lifting the engine plus fuel by any other means than under it's own power is bound to become expensive pretty damn quick.

No, I don't think it's lack of an attachment node is an actual problem.

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37 minutes ago, Laie said:

cost per engine bell, seriously?

You did ask for a comparison 'factoring in both ISP and TWR', yes? I guess I could've ignored that the ratios between the engines correlate almost perfectly to the number of bells, and make my little analysis that much more difficult to follow by referring every time to a 'generic totally-not-based-on-an-approximate-Vector unit-of-engine'. I'm not sure that would've helped any.

50 minutes ago, Laie said:

I'm not convinced the LFB really plays in that leagu﻿e.

I agree; that was rather my point. The Twinboar leaves them way behind in the league of cost-effectiveness, even when adjusting for the differences, as shown. Hence the not-so-surprising dominance of that engine in the Eve 3000 challenge, or any situation scoring for cost.

39 minutes ago, Laie said:

Only when you factor in cost does it start to draw about even (which I take more as a sign of low price, rather then superior performance.

Well, at least you do recognize the underlying reason, if still denying the extent. Small steps.   Note though that I in no way argue anywhere that the Twinboar is either more efficient or has superior performance, in any other way, other than cost-effectiveness (although adjusted for engine mass by recalculating through a totally-not-based-on-an-approximate-Vector unit-of-engine <breathe>, its TWR is slightly better than either Mammoth or Vector).

Anyway, I don't really want this to turn into some type of argument. You expressed puzzlement with certain outcomes, and I know how annoying it can be to have the answer to something dangling just out of my reach, so I did some numbers to explain why those outcomes are not so surprising, since it seems perfectly obvious to me. That's all. I hope you find your answers.

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