Calculating Ship Thruster Accel (G) from Watts

[ckirmser]

I'm working on a table for a SciFi RPG to construct ship thrusters. The thrusters have a certain output in watts and I need a formula to figure out how many Gs acceleration for a certain mass of ship can be gained by a certain wattage of energy.

I'm working from;

W = m * d^2 / t^3

Since one gravity is 9.8 m in (1 s)^2, I figure I can just throw in d = 9.8 m and t = 1 s to get the Watts for 1 G. Once I have that, then 2 G is twice the result, 3 G, three times, etc.

But, I am suspect of what results. I get;

W = m * 9.8^2 / 1^3

Or just;

W = m * 96.04.

That just doesn't look right.

Any thoughts?

 

[cmb]

'Fraid it doesn't make sense, because kinetic energy of an object is relative to the frame it is observed in. You have to derive the acceleration by creating a 'force' via some sort of thrust. The power the thrust generates changes according to the frame you measure it in. It is also a function of the velocity and mass of the jet you push out, so that you can achieve a more efficient thrust for a given power into the ejected material if you eject more mass at lower velocity.

You could work out an equivalent 'stationary frame' acceleration of a craft for a given power into the ejected mass (that is, an acceleration assuming you are staring stationary), providing you also state the mass/second of ejected material.

I suspect that may not help because you probably want an inertia-less reaction for your sci-fi ship, but there it is!...

 

[ckirmser]

Well, what I'm working with is one hex is one light second across from side to side and one turn is just under 100 minutes - basically, how long it would take to move one hex at one G.

I actually don't know if the gaming system has any ejected mass - I guess it would have to.

So, then, are you saying that I could toss in an arbitrary value for ejected mass, perhaps increasing the efficiency to account for higher tech levels, but still basically arbitrary?

 

[cmb]

So, then, are you saying that I could toss in an arbitrary value for ejected mass, perhaps increasing the efficiency to account for higher tech levels, but still basically arbitrary?

You could do anything! It is your fiction. But reality might be more interesting than fiction here, because what you can programme in is a tradeoff between a loss of propellant versus a gain in efficiency. You need both propellant and power, and you have to optimise your use of both to achieve whatever the objective is.

You will also drift, so that once you have achieved some speed there is no need for more thrust to cross a space, so you have to decide how much power and propellant you need to keep so that you can slow the ship down again.

 

[ckirmser]

Well, actually, it's not my fiction. I'm coding the ship construction rules from Traveller:2300 and, to make coding easier, I've taken a shortcut that causes a slight problem with thrusters.

In T:2300, ships have a choice of four different power plants; MHD Turbines, Fuel Cells, Fission or Fusion. But, thrusters only work with MHD Turbines. Unfortunately, though the system allows multiple power plants, I've restricted the design sequence to only allow a single type. So, if someone has a fusion power plant, then no thrusters.

So, I decided to allow - sort of - multiple power plants by assigning an independent MHD power supply only for thruster use. For ship construction details, I'd need the MW output of the MHD plant and that output is dependent upon how many watts are needed to move the mass of the ship. So, for example, if it takes 50 MW to move a 6000-ton ship at 1G, then I can use existing formulas to get the specs and fuel needs of a 50 MW MHD plant.

And, the need of the thrusters is not so specific as you suggested. Drifting, for example, would be covered by the skills of the crew, not so much the power of the engines. I mean, if I know how much power is available, then the actual application of that power is up to the devices of the crew. All the pilot - or player - says is, "go there," and the ship goes there in whatever manner the skills in the game dictate.

So, all of this is just to get a MW output, so that I can assign volume, mass and cost.

 

[cmb]

If you are bringing in 'specific fictions', then this clearly isn't the right forum for you. I think there is value in thinking through a fictional proposal to the logical (or illogical) conclusion to see what the 'laws of physics' might permit, but unless you can state how a 'MHD turbine' of 'fuel cell' provides thrust then there is no mileage in this.

I guess the only 'datum' to which one might ascribe a calculated power is if someone were to invent a 'light drive' that worked by emitting photons as the propellant. For a single photon we would have an energy of hc/L whilst the momentum is h/L. So I suppose that'd end up as 1/c kgm/s for 1 J input. So to get a 6000 tonne ship to 1 m/s would take 6000c J of energy. Expending enough energy for [10 m/s]/s would therefore be 60,000c W = 18 terawatts. I guess 'light drive' isn't very efficient, and goes to show that for efficiency you really want to use the most propellant mass, ejected at the lowest velocity, but obviously you can only do that for so long! You have to balance your stock of propellant with your power source, and how far you want to get!

 

[ckirmser]

No, I think it's the right forum. I want a taste as close to "reality" as possible - that's the basic tenet of the Traveller series; everything has a lineage that can be traced to current technologies with minimal fudging.

I was getting some results in the terrawatt range, too, and thought I was doing something wrong. But, then I thought, maybe I'm getting that huge number because I was putting in the size of a hex and the length of a turn. I said to myself, "Self, all you need is just an acceleration of 1 G. The distance and time doesn't matter, since 1 G is 9.8m/s^2."

Basically, I figured I could set m = 1 and s = 1, divide by 9.8 to make it Gs, et voila! Or, so I thought.

I looked at the equation for Watts and that it was W = m * d^2 / t^3. I saw that I could take out acceleration, a = m/s^2, giving me W = m * d / t * a.

If I slapped in m = 1, t = 1, which would give me a = 1, and then divide the answer by 9.8, that'd give me the watts required for an acceleration of 1G. But, when I put those numbers in I got m / 9.8 as the watts required; different than what I got in the figuring shown in the first post.

So, it may be that I'm trying to do something that can't be done with what I have and that's why I'm having this difficulty.

I'll have to look up some technical specs on current ion drives and see about extrapolating something reasonable from that data.

But, thanks for your help; it may not be what I was looking for, but it was what I wanted; an answer.

 

[cmb]

So sorry, it looks like I mistook tonne for kg up there. So it should have read 18 petawatts!

 

[cjl]

I guess the only 'datum' to which one might ascribe a calculated power is if someone were to invent a 'light drive' that worked by emitting photons as the propellant. For a single photon we would have an energy of hc/L whilst the momentum is h/L. So I suppose that'd end up as 1/c kgm/s for 1 J input. So to get a 6000 tonne ship to 1 m/s would take 6000c J of energy. Expending enough energy for [10 m/s]/s would therefore be 60,000c W = 18 terawatts. I guess 'light drive' isn't very efficient, and goes to show that for efficiency you really want to use the most propellant mass, ejected at the lowest velocity, but obviously you can only do that for so long! You have to balance your stock of propellant with your power source, and how far you want to get!

Since rockets tend to be limited to the amount of fuel they can carry onboard, their efficiency is typically expressed as the impulse they can obtain from a given quantity of propellant, rather than a given quantity of energy. So, for the greatest efficiency, you want the smallest possible propellant mass ejected at the highest possible velocity.

 

[cmb]

for the greatest efficiency, you want the smallest possible propellant mass ejected at the highest possible velocity.

That's not the greatest power efficiency. 'High impulse' relates to the overall mission capability - e.g. in satellite thrusters you have 'free energy' (solar power) but cannot afford to throw your propellant away, so 'efficiency' is then one of 'mass efficiency' [high impulse] rather than 'energy efficiency' [which is maximised with lowest impulse].

Momentum is mv, whereas energy is 1/2.mv^2, so to get the 'most [energy] efficient' amount of momentum, you use the lowest velocity and the highest mass.

It's the same reason gliders with high aspect wing spans are more efficient than fighter jets with tiny ones - the glider pushes more air down (more mass, lower speed) to achieve its lift than a fighter jet of equivalent mass with a small wingspan.

 

[AlephZero]

As #10 says, in real physics there is no direct link between power in watts and thrust. Thrust is equivalent to change in momentum, not change of energy. For example a jet engine on a typical airliner that moves a large amount of air relatively slowly is much more fuel efficient than a military jet engine that moves a small amount of air very fast, but there are good reasons for not wanting to put a 10-foot-diameter engine on a jet fighter!

You might be better forgetting about "power" and comparing your various engines in terms of amount of fuel availabe and a "thrust per amount of fuel burned" number. That would be combining the real physics of "different types of engine + different types of fuel" into one quantity that makes sense in the game.