According to Runner's World (http://www.runnersworld.com/article/0,7120,s6-242-304-311-8402-0,00.html) the number of calories you burn above and beyond your base metabolism by running or walking on flat ground is given by
C = K1 x M x W
where
C = number of calories burned
K1 = 0.63 for running, 0.30 for walking
M = number of miles traveled
W = your weight in pounds - presumably this should include any weight carried on your back as well
There's nothing sacred about this formula but it seems to give reasonable numbers based on my use of it for evaluating my own training progress / goals.
Now of course going uphill one burns more calories. Based on just the work done in raising a weight against gravity, the formula would be
C = K2 x H x W
where
K2 = 0.000324
H = elevation gain in feet
But this assumes the body is 100% efficient at converting calories of "fuel" stored in the body into useful work, which obviously isn't true. How efficient is the human body? Most of the sources I checked suggest something in the 15% - 20% range. Let's take something in between, say 16.66% = 1/6. In that case K2 becomes 0.00194 since you burn 6 times more calories than the gain in potential energy by raising yourself and your pack. Let's round up slightly to 0.002 for simplicity, so the formula becomes
C = K3 x H x W
where
K3 = 0.002
Now if one can consider the horizontal and vertical efforts to be additive (not necessarily a good assumption, if someone has a better formula please do give your testimony):
C = ((K1 x M) + (K3 x H)) x W
One could use this formula or some improved version to estimate one's caloric output. As a criterion for when one is fit enough to consider attempting C2C, one could say:
You should train with a C/Wb of x per week for y weeks to be training enough for C2C
or
You should be able to produce C/Wb of z for n hours continuously to be fit enough for C2C.
where Wb is just your body weight, not including any weight you might carry to increase the intensity of your workout (remember W in the above formulas is your body weight plus the weight you're carrying.)
I'll leave it up to you smart folks to decide what x, y, z and n should be, and how to account for the summer heat, C2C trail conditions, etc.
