CarolinaRunner
I'm not exactly sure how you could calculate a "difficulty" rating for a course unless either:
1) the course was all flat and/or uphill
or
2) we had a formula for the effect downhills have on VO2
I'm sure the uphills would slow a runner much more than the downhills would help a runner. I really like your idea of developing a "grading" system for courses. Maybe we'll come across a formula for VO2 on downhills somewhere.
These formulas can be used relatively well to calculate splits for a race if we're only calculating flat/uphill portions.
Example: Splits for an "even effort" through the first 4 miles of a marathon, where the course is:
2 miles flat
1/2-mile uphill at 3%
3/4-mile flat
1/4-mile uphill at 5%
1/4-mile uphill at 2%
1/4-mile flat
Assuming a velocity of 300m/min on the flat portions, his/her corresponding velocities on the hills would be:
2% = 254.23m/min
3% = 236.2m/min
5% = 206.9m/min
These would have to be converted from metric to English units in order to get mile splits. I'm not going to type all the calculations, but in order to maintain an "even effort" (VO2 of 63.5) the runner would need to run splits of:
Mile 1 = 5:21.9 ~ 5:21.9
Mile 2 = 5:21.9 ~ 10:43.8
Mile 3 = 6:05.3 ~ 16:49.1
Mile 4 = 6:12.6 ~ 23:01.7