ISP Relative to Thrust

[Duxwing]

Dear Forum,

If I have two engines, A and B, and A has a thrust of 1kN and an ISP of 2s, and B has a thrust of 2kN and 1s, then would it logically follow that achieving 2kN of thrust with either A or B would require the same amount of fuel? And is A a 'better' engine if it has an ISP of 3s? Ignore weight, placement, etc.

I ask because when I consider the difference between using one engine and two, I consider the two engines as one. To that end, I take the thrust of a single engine and double it while halving its ISP. For example, my model predicts that three LV-N's produce 180kN of thrust at an ISP of ~233. A single Poodle produces 220kN of thrust at an ISP of 390s. Issues of placement aside, should a single Poodle therefore be substituted for tricoupled LV-N's? Its thrust and ISP both exceed that of the group, so doing so seems logical. However, plenty of builders on this forum use not three but dozens of LV-N's on their spacecraft, so I wonder if my logic holds.

If my hypothesis is correct, then substituting a Skipper for the Poodle becomes profitable if the necessary thrust is even slightly greater than 220kN, and the same for a Mainsail because their ISP's differ only slightly relative to that of the LV-N. But this idea is counter-intuitive when applied to high-flying orbiters: aren't tiny, extremely efficient engines the order of the day in deep space? One could even argue that a single, short burn from a Mainsail would be preferable to many long burns from an LV-N. But I just don't know, so I'll leave my problem to you, the experts.

-Duxwing

[UmbralRaptor]

Achieving 2kN using a pair of engine As will use less fuel than a single engine B.

For any given engine:

Mass flow == thrust / (Isp * g0)

In KSP, g0 == 9.82 N/kg (or kN/Mg)

For multiple engines of the same kind, increase the thrust but do *not* change the Isp. For multiple engines of different kinds, you'll need to take a weighted average, most likely by finding the mass flow of each one, adding it up, and dividing the total thrust by that total mass flow.

eg:

3x LV-Ns produce 180 thrust at 800 s. Mass flow ~= 0.0229 tn/s (2.062 fuel/s, 2.520 oxidizer/s)

1x Poodle produces 220 thrust at 390 s. Mass flow ~= 0.0574 th/s (5.170 fuel/s, 6.319 oxidizer.s)

edit: Demonstration pics:

Edited May 24, 2013 by UmbralRaptor
more info

[numerobis]

Isp is related to the speed at which propellant exits the nozzle, and faster (higher Isp) is better since you get more push from each unit of mass.

No matter how many LV-N engines you have, the Isp doesn't change: a molecule of fuel exits at about 8km/s from your engine even if you add another engine on the other side.

[Duxwing]

Achieving 2kN using a pair of engine As will use less fuel than a single engine B.

When A has an ISP of 2s, or of 3s?

For any given engine:

Mass flow == thrust / (Isp * g0)

In KSP, g0 == 9.82 N/kg (or kN/Mg)

I'm thinking of orbiter applications, not lifter applications--does g0 still matter in that case?

For multiple engines of the same kind, increase the thrust but do *not* change the Isp. For multiple engines of different kinds, you'll need to take a weighted average, most likely by finding the mass flow of each one, adding it up, and dividing the total thrust by that total mass flow.

Ah, OK. I had a hunch that something like mass-flow would be the answer to my question. So fuel+oxidizer use rate is equal to mass flow rate, then? How do I interpret it?

eg:

3x LV-Ns produce 180 thrust at 800 s. Mass flow ~= 0.0229 tn/s (2.062 fuel/s, 2.520 oxidizer/s)

1x Poodle produces 220 thrust at 390 s. Mass flow ~= 0.0574 th/s (5.170 fuel/s, 6.319 oxidizer/s)

[Jason Patterson]

Yes, g0 is a conversion factor, it doesn't matter where you do the math, it will always be Earth's surface gravity. (Aliens wouldn't have chosen the second as the unit of the answer, so they'd have a different constant in its place.)

If by efficient you mean 'least fuel used' then yes, any grouping of engines with a higher average Isp will always use less fuel than any grouping of engines with a lower average Isp for a given amount of thrust. If this is an orbiter though, thrust is pretty far down in the list of features to be considered. Fuel mass, non-fuel mass, Isp, and thereby overall delta-v are far more important once a minimal amount of thrust is available.

[UmbralRaptor]

When A has an ISP of 2s, or of 3s?

If B has an Isp of 1s, either case.

I'm thinking of orbiter applications, not lifter applications--does g0 still matter in that case?

g0 is a constant due to the units used for Isp -- it applies in all situations, independent of current gravity.

Ah, OK. I had a hunch that something like mass-flow would be the answer to my question. So fuel+oxidizer use rate is equal to mass flow rate, then? How do I interpret it?

Fuel and oxidizer units can be treated as volume (in the past they were listed as liters in some menus). Both liquid fuel and oxidizer have a density of .005 units/tonne, making liquid fuel engines relatively simple to get numbers for.

mass flow / density == volumetric flow

Or, units/s == Thrust / (Isp * g0 * ÃÂ)

Stock liquid engines burn 55% oxidizer and 45% propellant (that's what the 1.1 and 0.9 ratios end up amounting to).

So which will achieve 220 thrust more efficiently? The Poodle, or the LV-N? Also: what are "tn/s"?

The 3x LV-Ns will use less fuel (as demonstrated) tn/s is tonnes/s (tonnes being by convention the ingame mass units)

[magnemoe]

Isp is related to the speed at which propellant exits the nozzle, and faster (higher Isp) is better since you get more push from each unit of mass.

No matter how many LV-N engines you have, the Isp doesn't change: a molecule of fuel exits at about 8km/s from your engine even if you add another engine on the other side.

However the deltaV or how much you can change your speed goes down then weight of the none fuel part of the ship increases. an point of balance here, you don't want an to slow acceleration, boring to burn for an hour and it also make nodes hard to do.

[Duxwing]

If B has an Isp of 1s, either case.

Why? Wouldn't the burn with B last only half a second, evening out the difference in efficiencies?

g0 is a constant due to the units used for Isp -- it applies in all situations, independent of current gravity.

Interesting! Why is that?

Fuel and oxidizer units can be treated as volume (in the past they were listed as liters in some menus). Both liquid fuel and oxidizer have a density of .005 units/tonne, making liquid fuel engines relatively simple to get numbers for.

.005 units = 1 ton

.005/.005 units = 1/.005 tons

1 unit = 200 tons

A Rockomax X200-8 Fuel Tank carries 800 units of fuel, so it should weigh 800 units * 200 tons / unit or 160,000 tons + Dry Weight, but it doesn't weigh nearly as much. Are you sure that you have the right number of zeros before that five, or the right order of units and tons?

mass flow / density == volumetric flow

So is the flow rate in units the volumetric flow?

Or, units/s == Thrust / (Isp * g0 * ÃÂ)

What is ÃÂ? It isn't p.

Stock liquid engines burn 55% oxidizer and 45% propellant (that's what the 1.1 and 0.9 ratios end up amounting to).

I wonder, why Squad didn't set them at 50-50? The laws of chemistry are no object in a video game.

The 3x LV-Ns will use less fuel (as demonstrated) tn/s is tonnes/s (tonnes being by convention the ingame mass units)

So using 3 LV-Ns is preferable to using 1 Poodle?

-Duxwing

[UmbralRaptor]

Let's see...

While Isp is often expressed in seconds, it's a measure of efficiency, rather than time -- how many seconds one pound of propellant can produce one pound of thrust, or pound(force)-seconds of impulse provided by one pound-mass of propellant. This unit cancellation (lb*s/lb) leaves us with seconds, and is where g0 comes from. If you'll excuse the mixed units, one pound-force acting on one pound-mass accelerates it at ~9.8 m/s².

ÃÂ is the greek letter rho, and commonly used as shorthand for density. I got the units mixed up here, it should be .005 tonnes / liter. (eg: 200 fuel/oxidizer units adds 1 tonne to the craft's mass). The flow rate in units/s is the volumetric flow (or unitmetric? Depends on what assumptions you make on what a fuel unit is) The 45-55 mass split is likely make the propellants sort of like RP-1/LOX.

Whether or not 3 LV-Ns is better than a Poodle is highly dependent on the rest of the craft. There's a large Isp advantage with the nukes, but the overall thrust is still lower, the mass is higher, and the size may be an issue for landers.

[Duxwing]

Let's see...

While Isp is often expressed in seconds, it's a measure of efficiency, rather than time -- how many seconds one pound of propellant can produce one pound of thrust, or pound(force)-seconds of impulse provided by one pound-mass of propellant. This unit cancellation (lb*s/lb) leaves us with seconds, and is where g0 comes from. If you'll excuse the mixed units, one pound-force acting on one pound-mass accelerates it at ~9.8 m/s².

Oh, well, when you put it that way, ISP makes much more sense. Perhaps you ought to edit the Wikipedia article on it; the dang thing left me baffled.

ÃÂ is the greek letter rho, and commonly used as shorthand for density.

Ah, OK. Thanks.

I got the units mixed up here, it should be .005 tonnes / liter. (eg: 200 fuel/oxidizer units adds 1 tonne to the craft's mass).

It's OK.

The flow rate in units/s is the volumetric flow (or unitmetric? Depends on what assumptions you make on what a fuel unit is) The 45-55 mass split is likely make the propellants sort of like RP-1/LOX.

One could define a fuel unit to be the minimum necessary amount of fuel and oxidizer necessary to cycle the engine. And ooooooh, liquid oxygen; the fun that can be had with that.

Whether or not 3 LV-Ns is better than a Poodle is highly dependent on the rest of the craft. There's a large Isp advantage with the nukes, but the overall thrust is still lower, the mass is higher, and the size may be an issue for landers.

The rest of my craft--a Duna lander--will be in two pieces. The first is the support module, which contains RCS, batteries, the engines in question, and a huge load of fuel in detachable tanks. The second is the lander module, which is designed to take two Kerbals down from 50,000m AGL (hereinafter known as Low Dunar Orbit or LDO) to the Dunar surface and back again. Ideally, the lander engines would double as the main engines, but the mass of my original design ran up into the scores of tons, so an extra one or two isn't a huge matter for me. I'm just sick and tired of running out of gas.

-Duxwing

[kahlzun]

If you're running out of fuel, use the NERVAs.

You can land on Duna using them if you need to, it's atmosphere is thin enough they are still super-efficient.