ISP and multiple engines

[Herbert McCheese-Wang]

The Nuclear Engine has a ISP of 800, meaning that 1 litre of 'fuel', (Liquid Fuel and Oxidiser mixed in the ratio 0.9:1.1) be propelled 800 arbitory distance units from the reaction chamber.

If two Nuclear Engines are sharing the same fuel tank, then what is the total ISP, and thrust, of them both?

My thinking currently follows that: 1 litre of 'fuel' must be split between 2 engines for the same ISP, therefore the ISP of each engine is halved, but the thrust is added.

So the engines together would have an ISP of 800, yet a thrust of 100kN.

What would happen if more engines were added?

[Pyre]

ISP would remain the same, thrust would increase based on how many engines you add, and Delta-V would decrease due to the extra mass.

[blizzy78]

Since Isp is a measurement of fuel efficiency, it does not change no matter how many engines of the same type you add.

[Specialist290]

With multiple engines with the same Isp value, the Isp remains the same, and the thrust is directly proportional to the number of engines. This is because the Isp is ultimately a measure of the amount of time it would take to burn a given measure of fuel at a specific rate of thrust, while thrust is a measure of force dependent on the total mass of fuel expended per second. It's not a matter of the fuel being "halved" between the two engines, but more that with twice the total output, the fuel is being used up twice as fast.

However, using more than one engine is slightly less efficient, because unless you add more fuel mass to compensate, you're basically trying to lift a bigger payload with the same amount of fuel. Two engines isn't quite so bad, but for larger payloads there's a trade-off between reducing your burn times to manageable levels and reducing your rocket's delta-v capacity.

[capi3101]

With multiple copies of the same type of engine, 1) Your Isp does not change (it would only change if you had a mix of engines with varying Isps), 2) Your thrust does indeed go up, 3) Your delta-V goes down, on account of the additional constant mass you've added to your rocket.

A good example is my Thunderbolt 7 tug series - I've got three sizes: Standard, Heavy and Superheavy. The Standard has five nukes and one X200-32 tank; it gets about 5,600 m/s without a payload. The Heavy has five nukes and five X200-32 tanks; unloaded, it gets over 12,000 m/s delta-V. The Superheavy is twenty-five nukes and five X200-32 tanks; unloaded, it gets about 6,000 m/s. In each case, the Isp is 800; the Superheavy has the greatest amount of available thrust (equal to a Mainsail; this is the one I intend to take to Moho, incidentally), but all that extra engine mass really cuts into the delta-V (exact same amount of fuel as the Heavy).

[Donziboy2]

I have built small landers for Minmus in the past with nukes and found that it was far better to use a smaller 909 engine then Nerva's. The 909's have a far lower ISP but the large mass savings gave the craft more Delta V with 909's.

[Tiron]

With multiple engines with the same Isp value, the Isp remains the same, and the thrust is directly proportional to the number of engines. This is because the Isp is ultimately a measure of the amount of time it would take to burn a given measure of fuel at a specific rate of thrust, while thrust is a measure of force dependent on the total mass of fuel expended per second. It's not a matter of the fuel being "halved" between the two engines, but more that with twice the total output, the fuel is being used up twice as fast.

However, using more than one engine is slightly less efficient, because unless you add more fuel mass to compensate, you're basically trying to lift a bigger payload with the same amount of fuel. Two engines isn't quite so bad, but for larger payloads there's a trade-off between reducing your burn times to manageable levels and reducing your rocket's delta-v capacity.

IRL, there's two 'versions' of Isp, depending on how the quantity of fuel is specified: If it's given in Mass, Isp is given as a Velocity; if it's given in Weight, Isp comes out as a Time. KSP uses the latter format, as do most real world rockets because it eliminates any possibility of unit confusion.

But yeah, posters above got it right: The Isp rating of an engine is not affected by any other engines attached.

Imagine two identical car engines, attached to the same fuel tank. Turning on the second engine while the first was already running doesn't affect the fuel burn rate or power of the first engine. It just empties the fuel tank faster because now you've got two engines burning it instead of one. But you're also now producing power twice as fast, so it comes out to the same efficiency.

The Delta-V of the rocket however *will* be reduced by the second engine. Delta-V stands for 'Change in Velocity', the greek letter delta (which looks rather like a triangle, but we don't have that on our keyboards so we just type it out) stands for 'Change', and 'V' is short for 'Velocity'. Delta-V is one of the most important things on a rocket. It indicates how much it's able to change its speed. Changes in speed are required for every single type of maneuver (even just changing directions is classed as an acceleration), so Delta-V measures how much movement you're able to accomplish. Extra Mass decreases Delta-V because of the extra inertia that has to be overcome.

Practically, in some circumstances the Delta-V reduction doesn't matter: During a launch, if you don't have enough thrust, all the Delta-V in the world won't save you from falling back into the body you're launching from. Thrust will. More thrust can also actually IMPROVE efficiency during a launch by reducing drag and gravity losses, potentially by more than the Delta-V cost of adding engines (or using less efficient ones with higher thrust and/or lower weight).

Edited August 16, 2013 by Tiron

[Herbert McCheese-Wang]

Wow, so it turns out, that each engine should have it's own fuel tank.

This will change my designs alot, thanks for tour help.

[SRV Ron]

Wow, so it turns out, that each engine should have it's own fuel tank.

This will change my designs alot, thanks for tour help.

Not necessary. They can all use fuel from one large tank. I have even set those up with drop tanks for interplanetary designs.

You should consider the efficiency with the extra 1.75 tons of the LV-N compared to the less efficient but far lighter LV-909. For landers, the LV-909 is the far better choice as the extra weight of the engine for landing becomes a liability. For interplanetary maneuvers, the LV-N becomes more desired due to its much higher efficiency on the long burns needed on those missions.

Edited August 17, 2013 by SRV Ron

[capi3101]

Wow, so it turns out, that each engine should have it's own fuel tank.

This will change my designs alot, thanks for tour help.

Actually, it works best if they all feed from a single tank (or single set of tanks). I didn't explain that about the Thunderbolts; sorry. With the Heavy 7, all five engines feed off the central tank. The four outboard tanks use fuel lines to feed in, and so they all drain first. The 'bolts are meant to be reusable, so they have no provision for dumping off the empty tanks (which would help with thrust/acceleration). A better system than what I have would probably utilize radially mounted docking ports; dump off the side tanks when they're empty, put new ones on when you get back to Kerbin. Of course, that has it's own issues...

Moar fuel does not necessarily equate to moar delta-V. Before the 'bolts, I had a design where each system had its own tank; it didn't give me nearly as much delta-V and it unnecessarily ramped up the part count drastically.

[tavert]

IRL, there's two 'versions' of Isp, depending on how the quantity of fuel is specified: If it's given in Mass, Isp is given as a Velocity; if it's given in Weight, Isp comes out as a Time. KSP uses the latter format, as do most real world rockets because it eliminates any possibility of unit confusion.

Nope. Specific impulse as time is a historical convention because the conventions we use today in rocket science mostly came out of the US. Weight changes with location, Isp doesn't. It's really introducing more unit confusion than it solves, to be honest. You can think of specific impulse as thrust times time divided by weight-at-standard-gravity of propellant, but that's a mouthful. I prefer thinking of specific impulse in this way: first measure the "effective exhaust velocity" which is thrust times time divided by mass of propellant, but express it in units of pound-force seconds per pound-mass (or equivalently kilogram-force seconds per kilogram). Specific impulse in seconds is this quantity, multiplied by one pound-mass per pound-force (or one kilogram per kilogram-force) just to convert the units to seconds without changing the numerical value. The unit conversion of one pound-mass per pound-force is equal to one over the standard acceleration due to gravity, which is a constant that comes entirely from the units.

[Arkalius]

Isp in seconds does have a meaningful (if less-than-useful) interpretation. If a motor would output a constant thrust equal to the weight at sea level on Earth of some particular quantity of propellant, the Isp in seconds is how long that motor would be able to provide that thrust given that quantity of propellant. So, for example, that nuclear engine could provide, say, 1 kN of thrust for 800 seconds if it had about 102kg (a mass that weighs 1 kN at sea level on Earth) of reaction mass to work with.