RChung

Yes, but it's complicated unless you're going slowly enough not to worry about aerodynamic drag. If you're going slowly, things are much simpler: each foot of climbing is roughly equivalent to 1/Crr in feet of horizontal distance (a bit less, but this is just a rough ballpark figure). Crr is a number in the neighborhood of 0.005 so 1/Crr is going to be around 1/0.005 = 200; Crr is lower if you're using nice tires, more if you're using Continental Gatorskins. Let's say your tires are commuter tires, so 1/Crr is going to be maybe 150 rather than 200. So each foot of climbing is about equivalent to 150 feet of horizontal travel.

If you're traveling faster then you have to take into account aerodynamic drag so the conversion factor decreases. But let's say you're going slowly. You climbed a 10% hill of 0.2 miles in length, so let's say your hill was 1000 feet long and 100 feet high. So you'd need to travel about 15,000 feet on the flat, so about 3 miles. Give or take. If you go faster, less.

Retro Grouch 

Maybe it matters if you think about your water bottle as being half full or half empty.

livedarklions

I don't think this is just semantics. If I have a climb of 528 feet in one mile followed by a descent of 528 feet over 10 miles, that's a very different level of effort for me than the other way around. I probably won't even notice the 1% grade either climbing or descending.

My long rides are almost always round trips, and I generally want to know which direction is going to have the steepest climbs so I can select a route where I'm not doing most of my tough climbing into the wind. The fact that the average grade for the entire trip will net to zero is a completely useless statistic.

Retro Grouch 

Actually, after thinking about it, I think that you're right. The energy that's required may equal out but, at some point, a hill simply becomes too steep for me to climb.

ofajen

The energetics will be minimized for a flat course. I think, but haven’t done a detailed calculation, that a steep up hill and gradual down slope are energetically better by a slight bit than the reverse.

Actually, I don’t find my argument for that convincing. There may not be a lot of difference in total.

Otto

Milton Keynes

I really think that if someone's only riding 5 minutes at a time, they need to get on the bike and ride more and not worry about mathematical formulas to figure out power going up hills vs. flats.

Flip Flop Rider

there are many factors involved, not just the grade of the road