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Feasible dV for a single-stage mothership


AlpacaMall
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I'm making a reusable mothership for those long, interplanetary trips. Playing with (among other mods) OPM and USI-LS.

For a NERV-powered mothership, how much dV can I expect to be able to pack in the mothership's single stage? 

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11 hours ago, AlpacaMall said:

I'm making a reusable mothership for those long, interplanetary trips. Playing with (among other mods) OPM and USI-LS.

For a NERV-powered mothership, how much dV can I expect to be able to pack in the mothership's single stage? 

OPM doesn't really directly affect the capability of vessels; it only extends the boundary for long-term missions.  USI-LS does change the capability of vessels by increasing the necessary life support payload (and thus reducing the available payload for other things that you might have wanted to take).  The amount that it affects depends on how many Kerbals you're taking, what kinds of amenities you have for them, and the difficulty settings for the mod.

As others have said, there are no easy answers, but we might be able to rough out a solution space based on the kinds of things that you might want to do with such a vessel.

First, I will assume that you will have enough Nerv engines to give a thrust-to-weight ratio of 0.2, and this is simply for the sake of your own sanity.  The Nerv has a thrust of 60 kN, so 0.2 TWR means a maximum weight of 300 kN per engine.  Take out the gravitational acceleration (TWR is a ratio of Kerbin weight unless specified otherwise) and that leaves 30 tonnes per engine (30.6 if you want to be more precise).  Out of that 30 tonnes, 3 are the engine itself.  Out of the remaining 27 tonnes, you can choose to use the Mk. 3 short fuselage, up to 12 Mk. 1 fuselages (though you won't actually want to use all 12), or you can add engines and divide a larger tank between them.

Let's say that you use 10 Mk. 1 liquid fuel fuselages.  That's 22.5 tonnes in tankage and propellant.  20 tonnes is in the propellant.  Add 3 tonnes for the engine, and that leaves 4.5 tonnes for assorted other stuff.  That's a payload fraction of 15%.  That's a lot less than I'd like for a long-term mothership, but reusability eats into payload fraction with a certain ill-tempered voraciousness.  If you need more payload, then add another 10-tank + Nerv engine module, and you'll have 9 tonnes of payload to use.  The delta-V for such an arrangement (which is a wet/dry ratio of 3) will be 8,619 m/s.

With no payload (or control, but this is just playing on paper), the wet/dry ratio is 4.636 and the available delta-V would be 12,034 m/s--but none of it would be useful.  Therefore, you can go from 8,619 m/s for a fully-loaded rocket up to something approaching 12,000 m/s for an unloaded rocket.  More payload than the maximum reduces the TWR to unacceptable levels, and less payload than just the propellant tanks and engine is not possible.  Those are the boundary conditions for this design.

Let's say, instead, that you want to use three Nervs and one Mk. 3 long fuselage.  That tank is 57.14 tonnes (50 of which is propellant), and the engines add nine tonnes to that for a total of 66.14 tonnes out of a total target mass of 90 tonnes, thus leaving 23.86 tonnes for whatever else you want or need.  That leaves a potential payload fraction (again, only on paper) of 26.5%.  The total wet/dry ratio is 2.25.  The delta-V of such a rocket works out to be 6,362 m/s.  Unloaded, the delta-V is 11,066 m/s.  Again, you can't actually achieve that, but it shows the maximum available range if you should choose to have a higher TWR with a partially-loaded rocket.

Please note that I'm not certain that you can keep your Kerbals alive and sane with USI-LS for an OPM-scale trip with only 24 tonnes of available payload for life support.  And, of course, using that much payload for life support leaves you with none for the actual mission.  On the other hand, the propulsion module (1 tank + 3 engines) is a beautifully low part count, so you can multiply it easily.

On the gripping hand, you could always send probes.  Probes are cool.  Remember, Mars is the only planet known to be inhabited entirely by robots.

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It depends entirely on how much of your mothership is fuel. That percentage will be determined by other design considerations, such as how low an acceleration rate you're willing to put up with and how much mass you're willing to launch into orbit.

 Sorry, no simple direct answers on this one.

Best,

-Slashy

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According to the rocket equation, dV = 9.807 * ISP * ln(wet mass/dry mass).

All those values are known in KSP- the fuel fraction (wet/dry) of most fuel tanks is 9; spaceplane parts like the Mk3 LF tanks are a bit less, Mk0 fuselages gives a higher mass ratio but they’re very small and trying to build an interplanetary ship using literally thousands of those will kill your PC. ISP for the NERV is 800 seconds. Add those in and you get dV = 9.807 * 800 * ln(9) = 7845.6 * 2.197 = 17238.5m/s. That’s the best you can do for a single stage with NERVs, but the TWR with one engine will be abysmal and in reality the weight of engines, crew pods and other miscellaneous bits and bobs will increase the dry mass and so decrease the delta-V.

The best solution is to use lots of engines and asparagus staging, draining fuel from a series of radially mounted tanks in turn and dropping them once they’re empty. Get used to long burn times, splitting burns with periapsis kicks where possible to reduce cosine losses (burning in a direction that isn’t directly pro/retrograde) and frame rates that aren’t so much frames per second as seconds per frame, but it’s feasible to build a single ship that can carry a crew and landers to visit every planet and moon in the stock solar system in one trip, without refuelling.

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Posted (edited)

Realistically, you are going to be looking at 6000-8000 if you want to have a reasonable fraction of your craft be payload, and also want a sane twr (0.1-0.2, bellow this and direct burns to Eeloo or Jool become a real pain in the ass even with periapsis kicks, you will end up spending extra dv both on the transfer burn itself, and on correcting for the inaccuracy).

Edited by Lt_Duckweed
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i agree with @Lt_Duckweed, 6000-10000 is the realistic value, depending on how much of your ship is payload.

and with Nervs, it is most efficient to keep TWR between 0.1 and 0.2. Below that, you'll lose more in cosine losses than you gain in saved mass. Above that, your engines will add so much mass, it won't be convenient no longer to use them.

I once made a ship powered only by nervs to land on Vall; it weighted 500 tons, and it had 24 engines, for a total of 72 tons, the majority of its dry weight. I later calculated that if I made the ship chemically powered, and I swapped out 24 nervs for 4 wolfhounds, the ship would have the same TWR - actually even a bit better, because it'd have the same thrust for a lower mass - and it would have actually had more deltaV, because the reduction in weight would have compensated for the lower Isp.

 

It has to be pointed out that, especially if you use some smart gravity assists on the moons, you should not need a huge amount of deltaV. My current mothership is also made for OPM planet hopping, and it's dragging around a third of its dry mass in mining equipment because I'm using mods that make mining more realistic - and, hence, more difficult. I also have to land it whole on planets, so I have some chemical engines to push twr to 0.5 during take off and landing. i only have roughly 4000 m/s of purely nuclear propulsion once I am in orbit - exact value depending on how much chemical fuel I need to keep in storage for the next landing. And I expect it should be enough; a Urlum-Neidon transfer will be a lot cheaper than a direct Neidon transfer from Kerbin. at least I hope it will be enough, I invested a lot of time in that mission

with your 6000-10000 m/s, you should be more than fine.

 

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Thanks for the replies everyone! Looking at my last ship, my 0.4 TWR was probably overkill and what made it harder to go higher. 

On 7/5/2021 at 2:44 AM, jimmymcgoochie said:

The best solution is to use lots of engines and asparagus staging, draining fuel from a series of radially mounted tanks in turn and dropping them once they’re empty.

Do drop tanks noticeably improve dV over normal tanks, or are you talking about full tank+engine disposable stages? I could probably add some docking ports to mount detachable tanks on, but I'm not sure if it's worth the effort and all the debris left in space.

 

On 7/5/2021 at 9:03 AM, king of nowhere said:

It has to be pointed out that, especially if you use some smart gravity assists on the moons, you should not need a huge amount of deltaV.

The farthest out I've been so far is Jool, and even with a free capture and return from the moons, it still cost about 2.5k to get there; without aerobraking on the return trip, it would probably be 5k for the round trip, before maneuvers there. For the outermost planets, wouldn't the requirement be even higher? Or are you talking about some other way of getting there and back?

On 7/5/2021 at 9:39 AM, Zhetaan said:

Let's say, instead, that you want to use three Nervs and one Mk. 3 long fuselage.  That tank is 57.14 tonnes (50 of which is propellant), and the engines add nine tonnes to that for a total of 66.14 tonnes out of a total target mass of 90 tonnes, thus leaving 23.86 tonnes for whatever else you want or need.  That leaves a potential payload fraction (again, only on paper) of 26.5%.  The total wet/dry ratio is 2.25.  The delta-V of such a rocket works out to be 6,362 m/s.  Unloaded, the delta-V is 11,066 m/s.  Again, you can't actually achieve that, but it shows the maximum available range if you should choose to have a higher TWR with a partially-loaded rocket.

I think I'll probably aim for this; four parts engine per 24 tons payload seems pretty good.

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1 hour ago, AlpacaMall said:

The farthest out I've been so far is Jool, and even with a free capture and return from the moons, it still cost about 2.5k to get there; without aerobraking on the return trip, it would probably be 5k for the round trip, before maneuvers there. For the outermost planets, wouldn't the requirement be even higher? Or are you talking about some other way of getting there and back?

I assume you are going to use isru, because you mentioned your mothership being reusable. So, with 2.5k you go to jool, refuel on pol, then go on sarnus, refuel on eeloo....

even if you can't/won't refuel on every planet, there are workarounds. In my case, using kerbalism, I can't refuel around jool because all the viable planets are either enveloped by killer radiation belts, or they lack the water needed to make rocket fuel. But I can reach Jool with approximately 1500 m/s from Ike, deploy the various landers, and return to ike with about as much, especially using a couple gravity assists and aerobraking on the way back.

as for going to the outer planets, it is indeed more expensive to get there... if you are starting from kerbin. I haven't yet been there, but going from a planet to another nearby is much cheaper than going all the way from kerbin. in the stock game, you need about 1500 m/s to reach Dres, 2000 to get to Jool, and 2100 to arrive to Eeloo. Plus, for the two dwarf planets, 1500 m/s of intercept speed.

but for a dres-jool you only need 750 m/s, and for a jool-eeloo starting from pol, you can manage with as little as 600 m/s. intercept speeds starting from kerbin are very high because the starting and final orbit are very different, but going between two close planets, you have similar orbits and much lower intercepts. Finally, the further from kerbol you are, the cheaper it is to manuever.

So, assuming you go to a gas giant, refuel on a moon, then move to the next, it's going to be fairly cheap.

if instead I assumed wrongly, and by "reusable" you mean "go to the outer planet, return to kerbin, gets refueled by a dedicated tanker in LKO", then yes, for the outer planets I would not want to do it with less than 5000.

 

Oh, when you say "mothership", i also assume that you are going to stop the mothership in a high jool orbit, or perhaps orbiting Pol, and will deploy smaller landers to go places. Because it's much cheaper that way. If you want to put your mothership in low orbit of every moon, yeah, the cost is going to increase.

Perhaps I really AM making too many assumptions based on how I conduct those missions.

 

P.S. Assuming this second case, where you are going to receive dedicated refueling missions in LKO but will require a lot of deltaV, and you would not be amiss to drop tanks, then I can suggest looking at my "Bolt" mothership (linked in my signature, "kerbalism grand tour at hard level (Bolt/Nail)") as a good example on how to stack drop tanks in a reusable way. Meaning that the refueling mission can resupply you with new drop tanks.

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Posted (edited)
7 hours ago, AlpacaMall said:

Do drop tanks noticeably improve dV over normal tanks

Yes.  However, the savings are modest enough that the choice between efficiency and rocket complexity is a serious one, and there are compelling arguments on both sides.

Here's an example:  Let's say that you have a 45-tonne rocket being pushed by one Nerv.  That's a bit low on the TWR scale (it's only about .136) but that's fine.  We're not looking for good burn times here.

Let's say that our fictional rocket is bearing two Mk. 3 liquid fuel short fuselages.  That's 14.29 tonnes per tank when full, of which 12.50 tonnes is propellant.  Let's also assume that the rocket is built with reuse in mind--meaning docking ports rather than decouplers on the tanks--so that adds .2 tonnes (for a Clamp-O-Tron Sr.) to each tank.  It also adds .2 tonnes to the main vessel, but we can ignore that because we're not staging away that port.

A 45-tonne Nerv rocket with 25 tonnes of propellant when full, provided that you run it until it's empty as a single stage, has a mass ratio of 2.25 and a delta-V of 6,362 m/s.

Let's say that, instead, we opt for a two-stage operating paradigm.  The first stage is a 45-tonne Nerv rocket with 12.5 tonnes of propellant, a mass ratio of 1.38, and a delta-V of 2,553 m/s.  Then we stage away the 1.99-tonne empty tank and docking port, leaving us with a 30.51-tonne Nerv rocket with another 12.5 tonnes of propellant.  This rocket has a mass ratio of 1.69 and a delta-V of 4,135 m/s.

Thus, the total for the two-stage design is 6,688 m/s.  That's 326 m/s over the single-stage design (that's more than 5%), and all of it comes from not needing to push around an empty propellant tank.

However, 5% may not be worth it to you, especially when you consider that replacement tanks need to be sent up from Kerbin (or recovered somehow--likely for a lot more than 326 m/s) and it means sacrificing your potential propellant load until you can get those replacements.  For a one-off rocket, that makes a lot of sense.  For a reusable rocket (that only operates in space--launch platforms are a different matter), it makes less sense.  If you plan on ISRU, depots, or other tricks to resupply, then the tank is more valuable than the propellant savings.  You ought to be familiar with that side of planning:  you can save propellant by not sending Kerbals, too, but the capsule is more valuable than the propellant savings of not sending one, so it goes on the mission.  In like fashion, when refuelling is a part of the mission, the empty tank technically becomes part of the mission payload rather than parasitic mass.

Edited by Zhetaan
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On 7/12/2021 at 10:49 AM, W2D2 said:

I’d guesstimate approx. half is feasible with a payload and a TWR of just under 0.5. So aim for 8k-10k dV.

Unfortunately, it doesn't work that way.  You're seriously overestimating the performance of this engine.  I can show you why:  we can work though the delta-V calculation backwards to get an idea of whether your guess is feasible for a vessel.

Let's say that we want your guesstimated values, and since I like calculation, I'll cover both ends of your range.

For 8,000 m/s of delta-V with a Nerv, we need a wet-to-dry mass ratio of 2.772.

Spoiler

Δv = Isp * g0 * ln (mwet / mdry)

Δv = 8,000 m/s
Isp = 800 s (for a Nerv)
g0 = 9.80665 m/s2

Δv / (Isp * g0) = ln (mwet / mdry)
eΔv / (Isp * g0) = mwet / mdry

e8000 / (800 * 9.80665) = mwet / mdry
e8000 / 7845.32 = mwet / mdry
e1.0197 = mwet / mdry
2.7724 = mwet / mdry

This requires a propellant mass that is 1.772 times that of the dry rocket, or a wet rocket that is 63.9% propellant.

Spoiler

mwet = mpropellant + mdry

mwet / mdry = (mpropellant + mdry) / mdry
mwet / mdry = (mpropellant / mdry) + 1
mwet / mdry - 1 = mpropellant / mdry

If we set the dry mass to 1 dry rocket mass, then the equation simplifies to:

2.7724 - 1 = mpropellant / mdry

1.7724 = mpropellant

... in units of dry rocket masses.  1.7724 / 2.7724 * 100 = 63.9%

To have .5 thrust-to-weight, this rocket would need to push no more than 12.24 tonnes per engine.

Spoiler

The Nerv has a thrust output of 60 kN, and .5 thrust-to-weight ratio gives a maximum of 120 kN weight.  Solving for the mass against standard gravity, that results in 120 kN / 9.80665 m/s2 = 12.237 tonnes.

3.00 of those tonnes are taken up by the engine itself, 7.82 tonnes are in the propellant, and the propellant tank takes up another .87 tonnes for a total of 11.69 tonnes.  That leaves .55 tonnes, or 550 kg, for remaining payload, and of course does not account for the fact that there is no propellant tank that offers exactly 7.82 tonnes.  One can string together multiple engine modules to keep the same overall performance and increase the payload, but that is the shape of the problem.

For 10,000 m/s of delta-V, it works out that you need a wet-to-dry ratio of 3.58 and an attendant propellant mass of 2.58 times the dry rocket, or 72.1%.  At .5 thrust-to-weight ratio, that means that you're still limited to 12.24 tonnes per engine, but now 8.83 tonnes are taken up by propellant, .98 tonnes are taken up by the tank for that propellant, and 3.00 tonnes are in the engine.  That adds up to 12.81 tonnes, which is over-budget and leaves no room for payload.  You may certainly choose to have a lower thrust-to-weight ratio, but it is not possible to combine the Nerv engine with a propellant load to have a .5 thrust-to-weight ratio and 10,000 m/s of delta-V.

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I think NERV is the go-to engine for the stage of the game when all your missions are Duna and Eve. For the other planets, and especially OPM planets, you need better tech.

My Trans-Joolian explorer cruiser is based on the Near Future engines, namely the 2.5 m plasma engine. The engine is fueled by 12 tanks of Lithium and powered by two nuclear reactors, which gives it the delta-V capacity of 10000 m/s fully loaded and fueled while being able to produce NERV-like acceleration around 0,2 G. The nuclear reactors like to play thermal tricks and occasionally explode if you leave them on during a timewarp. So I designed a "Reactor Safety System" based on a KAL-1000 which starts the reactors and deploys extra radiators when you throttle up the plasma engine, and stops them when you kill thrust.

Edited by ave369
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On 7/5/2021 at 11:03 AM, king of nowhere said:

I once made a ship powered only by nervs to land on Vall; it weighted 500 tons, and it had 24 engines, for a total of 72 tons, the majority of its dry weight. I later calculated that if I made the ship chemically powered, and I swapped out 24 nervs for 4 wolfhounds, the ship would have the same TWR - actually even a bit better, because it'd have the same thrust for a lower mass - and it would have actually had more deltaV, because the reduction in weight would have compensated for the lower Isp.

 

I’m with @king of nowhere, I often find that using LF+OX engines I actually come out even, or sometimes even ahead in terms of DV.   Especially if a surface landing is planned.

Like others have said, the theoretical DV attainable with Nervs is much higher, but with a practical ship that actually has a payload I usually find 6,000 - 8,000 DV is as good as I can get.  I often end up with more like 5,000, because I want to carry more payload without adding a ridiculous amount of fuel storage.  

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