by Stephen Herrick

Suppose a Diablo Cyclist wanted to train hard enough that he/she could start at a point exactly 15 miles from the summit of Mt Hamilton (say at Amy’s Rancheria,) ride to the top, and then return exactly the same way and have an average speed of 15 miles per hour upon his return.

He/she goes out as hard as he can, and checks his cyclometer as he makes the turn at the observatory before heading back down. He’s got an average speed of 7.5 miles per hour so far.

At what average speed will he need to ride the descent back to the start in order to finish with his target goal of 15 miles per hour for the compete out-and-back?

Well, it’s a trick question really. He can’t get his average up to 15 miles per hour unless he can teleport instantaneously back to the start.

Here’s the deal. Average speed is determined by the distance you travel, divided by (per) the time you take to do it. However, if you average ½ of your target speed over ½ of your distance, you use up all the time you’ve allotted yourself to complete the entire trip already.

Plug in some numbers, and it gets easier to see. It’s exactly 15 miles from the start to the summit, so an out and back would be a total of 30 miles. If you want to finish the whole round trip with an average speed of 15 miles per hour, you have to complete the ride in 2 hours. But if you average 7.5 miles per hour for the first 15 miles, then you’ve already taken two hours!

Or, for the mathematically inclined, d (distance) / t (time) = v (velocity or average speed)
Flip that around you get, d/v=t.
But, 1/2d / 1/2v also = t.

Try something actually doable for all you daredevil descenders. Say you start at the same point 15 miles from the top, and you’ve got the same goal of 15 mph average, so you have 2 hours to complete the ride. You check your cyclometer at the top and you’ve got a respectable 10 miles per hour.

Okay, it took you one and ½ hours to climb to the summit (15 miles at 10 miles per hour, congratulations.) Now you’ve got to make the return 15-mile trip in ½ hour. That requires an average speed of 30 miles per hour. Watch it on the hairpins!

But say you get to the top and you’ve got an average of 8 miles per hour. Well, riding 15 miles at 8 mph means it took you 1 hour, 52 minutes, and 30 seconds to get there. Remember, to average 15 mph you have to complete the trip in 2 hours, so now you have only 7 and ½ minutes left to get down. Let’s see, 7.5 minutes to go 15 miles would require an average speed of 2 miles per minute, or 120 mph! I don’t think you’re going to make it.

The moral of the story is; you can almost never recover your average speed after climbing up a long hill merely by descending the other side.