Aramis7 said:Let's say that elevation is not significant (500 feet) and that I want to ride the 10K at the same average speed.
Let say that I ride the 10k flat at 20km/h average
If I rode the 10k hilly ride at the same 20 average km/h (faster on the downhill than uphill), will the effort required to do the hilly ride be the same, less or more than the flat?
As frenchyge and RD said, the total work effort required for a hilly ride will be higher than for the flat 10K, if both are ridden at an identical 20km/hr avg.
Just playing with the numbers, believe cruising at 12.4 mph on a level only requires about 70 watts of power. In that case, doing your flat 10K in 30 minutes would require 70 watts for 1800 seconds, for 126kjoules of work. If you add one 500 ft hill, and you and your bike together weigh say 90kg, then climbing 500 ft (~150 meters vertical gain) by itself would add 132 kjoules of work to the course, which exceeds the total energy expended to complete the flat course at 12.4 mph.
Or, looking at the power required, if the hill is a 10% grade, and you climb it at 5 mph, you'll need to put out around 200 watts for over 11 minutes to get to the top. Again, you can see that product of power and time (energy) just for the hill exceeds the total (70 watts x 30 minutes) needed for the flat course.