But going back to the cost of BTU of heat produced. If we look at efficiency, we would have to say 100% efficient cooking would be a fuel that passes 100% of it's energy to the work of cooking the food with 0% lost to transient heat. OK, that is not possible, so we look at what does it cost me to cook my eggs and bacon in the morning and what other factors can I apply to it?
I assumed any energy lost to transient heat while cooking (i.e. heating the air and your cabin instead of the food) would be the same for electric or propane. Since it scales the same for both types of stoves, it's not a factor. Either propane is 100% efficient and a gas generator is 25% efficient. Or propane is 50% efficient and a gas generator is 12.5% efficient. It's a 4:1 ratio either way.
That changes at the dock as you have to get into some pretty high KW rates to exceed the cost of propane. Ours is currently .12 per KW hour. Plumbed natural gas is almost always cheaper, thus the strong argument for gas @ home. So, dock is less, generator is more.
That's a very good point, but I was trying to keep this in terms of a fuel efficiency standpoint to avoid bogging my post down with math. To convert it to cost efficiency, you need to multiply by the $ per BTU (or kWh). Or probably what's more accessible to most people, ($/gal) / (BTU/gal). The rough BTU/gal of various fuels are:
Diesel: 139,000 BTU/gal (1.39)
Gasoline: 124,000 BTU/gal (1.24)
Propane: 91,000 BTU/gal (0.91)
Nat Gas: ~1050 BTU/ cu ft (0.0105)
If diesel is $4/gal, gasoline $3.50/gal, Propane is $3/gal, and natural gas is $12 per 1000 cu ft, then you're paying:
Diesel: ($4/gal) / (1.39) = $2.88 per 100,000 BTU
Gasoline: ($3.5/gal) / (1.24) = $2.82 per 100,000 BTU
Propane: ($3/gal) / (0.91) = $3.30 per 100,000 BTU
Nat Gas: ($0.012/cuft) / (0.0105) = $1.14 per 100,000 BTU
Which explains why nobody is racing to build a propane-powered boat (it contains less energy per dollar than gas or diesel). Divide by the efficiency and you get:
Diesel = $2.88 / .35 = $8.22 per 100,000 BTU used for heating
Gasoline = $2.82 / .25 = $11.29 per 100,00 BTU used for heating
Propane: $3.30 / 1.00 = $3.30 per 100,000 BTU used for heating
Nat Gas: $1.09 / 1.00 = $1.09 per 100,000 BTU used for heating
Electricity from shore power can be generated from many sources. Hydro in particular is dirt cheap to produce (2-3 cents/kWh). Even the coal plants the power company operates are 45%-55% efficient, with their gas furnaces exceeding 60%. So shore power electricity is a lot cheaper per kWh than from running your own generator. This is the same thing that makes the economics of electric cars work. Electricity is actually a terrible way to power a car (fuel => combustion => generator => electricity => power line => car battery => motor => move car, compared to fuel => combustion => transmission => move car). But the power company's generators are a lot more efficient than your car engine, and coal/nat gas is a lot cheaper than gasoline. And as a result the cost of the electricity needed to drive an electric car 1 mile ends up being about 1/3rd what it would cost in gasoline.
If we convert a typical 11 cents/kWh to the same units as above (29.3 kWh per 100,000 BTU), we get:
($0.11/kWh) * (29.3) = $3.22 per 100,000 BTU used for heating
So shore power does slightly edge out propane for heating. Normalizing these against propane, you get:
Nat Gas: 0.35x
Shore power: 0.98x
Substitute your own local prices for the different fuels into the math above to find out how they stack up locally. The math is just straight multiplication and division so goes into a spreadsheet easily. (Bear in mind the efficiency figures for diesel and gasoline are rough averages, so diesel is probably more like 2-3x more expensive than propane, and gasoline 3-4x more expensive.)