energy is generally measured in Joules.

http://en.wikipedia.org/wiki/Energy#Measurement

Force is in Newtons F = mass*acceleration according to Newton’s Law. Power = Force*distance/time OR Power = Fv. In order to translate force into power you’d have to know the Force of what you are trying to solve and the velocity.
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In a situation like your question 20 tons of water = 20,000kilograms multiply this by gravity 9.8m/s/s. This would give you 196 000Newtons of force. You don’t have a distance or time, so this way is pretty useless. The only other way is to translate into another formula where P = Energy/time. Choosing potential energy will give you the equation Pe = mass*gravity*height. Again though this is useless as you do not know the height. Is there anymore to the question? You can only get to output and input once you know your final values.

Without getting heavily into the mathematics: Force is how a mass is affected by acceleration (F=ma); power is the time rate at which work is done (P=F/a), work being a product of force and displacement (W=Fs). The key difference between force and power is a time factor,

OK, let me clarify. I have 46 tons of lifting force at the bottom of the ocean, say 1000 ft. down. How many (and which) equations will I have to do and plug in to figure out how much power it could produce if I fill it full of air and let it rise?

You would need to use 3 equations.

(If you need to know which 3, continue reading, if not, ignore this part)

F(net) = ma
P = Fd/t / Since P = Energy/time you can use mgh = Penergy as well.
Efficiency = Output/Input x 100%

Part of the problem here is a misuse of terms. Mass is not force. What you are really descibing is potential energy convertible to kinetic energy, Also the potential energy of bouyancy is variable with depth. So it actually involves more than three equations and includes vector and possibly tensor calculus. The simplest, but only very roughly accurate, way to describe your example is the potential energy of mass and position. But this is like a 46 ton rock at the top of a 1,000 foot cliff, bouyancy is only roughly equivalent to this.In buoyancy problems, the gravitational constant doesn’t work the same way as a rock falling from a cliff. It’s not a simple “plug in” equation,

I shoulda known. If it were easy it would have been done by now.

No, It has been done. It is a method used for lifting sunken ships to the surface. But the physics involved is complex. BTW, there is also a potential power in the temperaure difference between ocean depths and is being tapped on a relatively small scale now, called Ocean Thermal Gradient, If Stirling-cycle engines can be brought to their potential this can be a major energy source for electric power production.

But the temperature gradients involved in a Stirling engine are a bit much. I mean, they generally don’t do well in the power/weight or power/volume departments so it’d be a bit tricky to make one practical for an automobile.
Besides, if the Tesla Model S can’t sell well despite being faster/quicker than many sports cars, what makes you think a Stirling engine would be commercially successful? And isn’t that what Detroit is all about; commercial viability?

@jerv Agree. The Stirling-cycle will only be practical, if ever, as a stationary power source. I was describing Stirlings in that context only. I think right now that the intermediate term automotive solution will be pure electric, hybrids and biodiesel/second generation alcohol fuels. I’ve gone that direction personally; running my old M-B on B100 and converting a ‘64 VW pickup to electric

@stranger_in_a_strange_land – It sounds like you and I will need to have a private talk sometime.
Sadly, on my budget I doubt I’ll even be able to salvage forklift components to convert my old Corolla, and even if I could, I wouldn’t be able to afford Lithium-ion, can’t get NiMH thanks to Chevron, so that means lead-acid and short-range since an old Corolla can’t carry much weight.

Sorry, guys—what’s the distinguishing characteristic of a Stirling-cycle engine?

BTW, thanks for all the answers, everyone!

A Stirling cyle engine is a heat engine that more or less directly converts heat into motion. One problem with it is tapping the power generated without interfering with the motion process itself.It’s principle is the cyclic compession and expansion of a working fluid, an external heat source being employed. Wikipedia has a good illustration in their article “Sterling Engines” but some of the documentation in the article is rather weak. I’m going to rectify that when I can find the time.