Well sir I have been schooled by a sharper mind.Primary, yes. Singular, no.The compression ratio is the primary and singular dynamic that requires the electrical energy and ampere load of the dual battery setup to crank.Cold is an afterthought.
The inherent reason the diesel engine "cranks hard" in the cold is entirely due to the high compression ratio and in turn the high combustion temps needed for ignition.
Glow plugs serve to aid in the combustion process...block heaters aid to serve in assisting the "overcoming" of the compression process by either heating the oil or by heating the coolant which aids in heating the block, thus heating the overall engine platfom and oil which aids in the compression process.
It's by far better to use a block heater to aid in the compression process than it is to use glow plugs or combustion starting aids.
In short, it's better to turn the engine over a few times to allow for proper lubrication of all components than it is to "amplify" the ignition and combustion process with starting aids before the engine is actually "lubed" and warm enough to handle.
END STATE: It's all about compression.
Let's separate this into two starting factors: starter electrical load and length of time to start.
It is correct to say that the primary driver of starter electrical load is compression. Work must be done on the gas to compress it, which is the mechanism by which its temperature is increased. Whenever you compress a gas, it gets hot. The heat generated is energy that ultimately came from the battery - it just went through several conversions to end up as an increase in gas temperature. The higher the compression, the higher the temperature achieved, and the more energy required from the battery. Other losses in that system are negligible in comparison. That much is straightforward.
The nuance comes in on the length of time to start, which has a strong dependence on temperature. There are two types of compression at play: adiabatic compression and isothermic compression. In purely adiabatic compression, there is no heat lost during the compression of the gas. During purely isothermic compression, all of the heat generated by the compression work is lost (so that the temperature does not increase, hence the term "isothermic," which means "same temperature").
Of course, nature does not operate at extremes, and compression in a heat engine cannot be purely adiabatic and it cannot be purely isothermic. Whenever you have a thermal interface between two things that are at different temperature, there is heat flux, so you cannot compress gas in a vessel and have it retain ALL of that energy. Some energy is always lost to the vessel, and the amount of that energy depends on the difference in temperature between them.
When you have a metallic vessel that is a good conductor of heat, it is going to cause differences in your compression process based on its temperature. When that vessel is very cold, it is going to start pulling heat out of your compressed gas as soon as you start to compress it. So, the ending temperature of your gas is going to be lower than it would be were the vessel hot. If the vessel is cold enough, it can pull enough heat out of your compressing gas to prevent it reaching the auto-ignition point of your air-fuel mixture. Now, the autoignition temperature of an air-fuel mixture varies WILDLY according to many factors. Experimental data from the University of Washington suggests that the air-fuel mixture in a diesel motor needs to be 1000-1100F for auto-ignition.
So, how do we get to 1000-1100 degrees F?
Let's assume our ambient conditions are T1 = 253 Kelvin (-20C, darn cold), P1 = 100 kPa (normal atmospheric pressure), and our cylinder has an open volume V1 =0.625L and a compressed volume of V2 = 0.039L (16.2 compression ratio). Let's also assume we have a perfect adiabatic compression process with no heat loss, and that "air" is just an 80/20 mix of Nitrogen and Oxygen. This diatomic gas as a known polytropic process exponent of 1.4.
The process equation for this compression is P*V^1.4 = C where C is a constant. We can compute this constant C from our initial conditions for P1 and V1, and thus C = 3.268 Pa * m^1.4
We can then calculate P2 (the compressed pressure) from the same equation using the new volume. P2 = C / V2^1.4 = 3.268 / (0.000039m^3)^1.4 = 4.86 MPa
So, now we know the open, uncompressed pressure P1 = 0.1MPa and the compressed pressure P2 = 4.86 MPa.
Now we need to know how hot the gas got when we compressed it. We can find it using the ideal gas law, PV = nRT. From our initial conditions we know P1, V1, and T1, so we can compute nR (both n and R are constants) from those. nR = PV/T = 0.247.
Now, we can use the same equation to find T2 = P2 * V2 / 0.247 = 4.86MPa * 0.000039m^3 / 0.247 = 768 Kelvin = 923 Fahrenheit
So, did we get hot enough for auto-ignition? No. We didn't, so we need to do one of three or four things:
1) pre-heat our intake are by approximately 80-180 degrees
2) put something hot in the cylinder so that at least some place the fuel goes is above the auto-ignition temperature (glow plug)
3) put something in the cylinder that instantaneously discharges at least the ignition energy of the mixture (spark plug)
But wait, there's more. Let's make it even HARDER to get this mixture going. We're trying to reach the auto-ignition temperature of an air-fuel mixture, but when the diesel fuel is injected, we don't yet have an air-fuel mixture. We have an air-fuel suspension. The liquid fuel must first evaporate in order to arrive at an air-fuel mixture. The liquid itself may also auto-ignite, but the evaporation process is going to start immediately. Anyone who has ever broken a sweat knows that evaporation is a very efficient cooling process, because evaporating a liquid takes a lot of heat. Add to this the cold metal of the combustion chamber, and you've got two very effective mechanisms for lowering the final temperature of your compression stroke before fuel ignition takes place. I don't have time to go through all of that math right now but suffice it to say we arrive at our 4) heat up the metal so that it does not cool your compressed air as much. Block heaters have other benefits (such as decreasing viscosity of the oil so that it flows more easily once the engine is started), but the starting benefit is through reducing the heatsink action of the combustion chamber / increasing the compression temperature of the air-fuel mixture during start.
Out of time...
I read your post four times and, I must say, was thouroughly impressed.
I ran over the estimated calculations and, in doing so, realized I may be bested?....."deditionem I" my friend and well done.