woodcraft

There's not much flat in my area, so that falls between normal (50'/mile), and quite hilly (100'/mile).

I figure the difference between the two is equivalent to 25%, so 60 miles at 100'/mile is like 75 miles at 50'/mile.

I would think the difference between flat and 70'/mile would be 50%- 60 miles on those hills equals 90 miles flat (assuming no big wind factor).

woodcraft

It would be a 1.3% grade if uniform, and if the OP ended the ride at 35,000' elevation. By that measure an everest ride would be up a 3.5% grade- no problem!

Since we can assume that the OP ended up at the start, the grade would be doubled, and since some would be flatter than the idealized grade, the other parts would be steeper,

so the hills would be ~doubled again.

I know this was not your point but wanted to correct any suggestion that 70'/mile is not really different from flat. Also, the comparison is between a triangle with elevation 35,000' and a triangle with elevation 300', the hypotenuse of both being 500 miles.

asgelle

Only for an out-and-back course. For a loop, there's no telling whether the climbs are steeper or shallower than the descents.

tomato coupe

Isn't the real question "What's the train conductor's first name?"

Mista Sparkle

So this has been bothering me a bit and I wanted a better answer. I decided to go out for a short 100 million mile bike ride over a series of hills with a normal distribution of gradients. I planned my route such that I maintained the same 70’/mile elevation gain as well. I kept my power fixed at an moderate 140 watts, so it did take a while, 6,412,139 hours, 32 minutes, and 43 seconds.

I wasn’t super aero, but I was on the hoods so I was able to maintain a pretty good CdA of .32 for the ride.

Lumping my GP4000SII’s with drivetrain resistance I ended up with a CRR of ~ 0.005.

There was quite a bit of climbing on my out and back ride, 1.3 million miles total, going over a prominence of 1,679,873feet. I stopped by the space station while I was up there.

I then went out and rode another 6,412,139 hours, 32 minutes, and 43 seconds on the flats. Here at 140 watts I maintained 18.9343 mph. It took me a little further, 121,409,261 miles, 567’ 11-1/2” . That was a boring ride.

It is certainly harder to do math while riding.



The fun part here was factoring calculating speed as a function of both power and gradient. I just let wolfram solve it for me, I suppose Matlab could have done the same. I did neglect acceleration as it is conservative, though it would have a small affect on aerodynamic losses. I also neglected the change in air density going up past the space station, but figured this would be close enough.

You could of course use your effort only to go uphill and maybe a bit more aero going downhill, this would bring the difference closer together from the 21% calculated above, but by somewhere in the 3rd significant digit. If you are less aero, the benefit of riding on the flats goes way up, as a result of the extreme speeds you can hit going down a mountain. Bumping CdA to .4 brought the riders something like 2.5% closer to the total difference in time.

If the distribution of gradients becomes pointier (more flats generally but steeper steep sections, the benefit to riding flats goes up somewhat)

tomato coupe

How many gels did you use? Do you get a bulk discount?

indyfabz

The answer is 500 miles, and I’ve ridden plenty of mountains on a fully loaded touring bike.

Mista Sparkle

Yeah, 17099039 gu gels, ~146,000 gallons or roughly 1/3 of a fully loaded 747.

I saved 5%!

Skulking

Did you include all of that weight in the calculations? It seems to me your wattage up hill might be affected by the extra load.

tomato coupe

He didn't carry the gels, he had a 747 for support. Duh.

OP -- Bummer, I had a coupon code for 10% off when purchasing 10M gels that I could have given you.

Drew Eckhardt 

I find 10 miles = 1000 feet, so that would be like 850 flat miles.

https://www.quora.com/In-bicycling-i.../Drew-Eckhardt

10 miles = 1000 feet for me at the same endurance pace. A lower power to weight ratio would make the hills more difficult.

Two rides with the same fitness on consecutive months, 20 mile and 2K foot difference, same Training Stress Score accounting for intensity plus duration, same fatigue, almost the same time and energy.

126 miles, 8,400 vertical feet, 10:12 moving out of 11:27, 399 TSS, .59 IF, 4070 kj.
May 200km Sunnyvale - Santa Cruz - Pescadero - Sunnyvale - Drew Eckhardt's 125.5 mi bike ride
May 200km Sunnyvale - Santa Cruz - Pescadero - Sunnyvale

104 miles, 10,250 vertical feet, 9:55 moving out of 11:41, 392 TSS, .57 IF, 3639 kj
June 100 miles long, 2 miles up - Drew Eckhardt's 104.3 mi bike ride
06/26/16 Sunnyvale to Davenport

126 miles, 8,400 feet:


104 miles, 10,250 feet:

Cyclist0108

You biked right by my house in that second one.

pdlamb

I spent an afternoon playing with analyticcycling.com a few years ago, trying to figure out how much climbing it takes to use as much energy as riding a mile, and came up with a similar answer -- 100-150 feet of climbing (and subsequent descent) roughly equates to a mile of flat riding. Fun way to make up for decades without having to answer a physics test problem. Interesting that you (Drew) have some power meter data that comes up with a similar answer.

Of course, the devil's in the details. What's a good average for aerodynamic coefficient of drag, equivalent area, and rolling resistance (tire type and pressure)? How much do you weigh? (Less, now! which probably means I'd have to climb more.) How far can you coast for "free"? I can never get good experimental evidence on coasting, because I start pedaling near the bottom of a good descent to keep my speed up as long as possible.

Stop signs at the bottom of a big hill are evil. Discuss.

indyfabz

A mile is a unit of linear measure. If two cyclists each ride 500 miles, they will have both ridden 500 miles, regardless of terrain or any differences in terrain between the two courses ridden.

If you want to know if there is a way to compare the energy expended between flat and hilly miles, then ask that.

Koyote

Unless you are presenting a convincing answer that is based in physics and evidence, I don't know how you can reach this conclusion. (And yes, I have ridden plenty of mountains; and no, I wouldn't base my answer on something so subjective as my "feeling.") But, given that the person riding on flat terrain will likely have a higher average speed - and hence higher average CdA - I suspect that the answer is not quite what you think it is.

This.

asgelle

Speaking of not being quite what you think it is ...

Mista Sparkle

This is good stuff.

When I have some time, I'll run through my model, I have a feeling that some of the in consistencies in real world power from dealing with gradient will play a bit of a role. However it looks that the largest contributor to the difference is that it just isn't feasible to blast down mountains at full speed all the time, so breaking will reduce your average speed to power, as it is essentially negative work.

Of course the answer in a vacuum is that they are the same.

indyfabz

Lookey what I found:

https://www.bikeforums.net/general-c...tion-gain.html

Koyote

I wasn't reaching any definitive conclusion, and am quite happy to be educated!

woodcraft

Illustrating my thoughts in post #26 ,

here's a comparison of two recent rides as per Strava- 2 weeks apart, under Covid slacker casual conditions...

Ride A: 38 miles, 4,455', 160 WAP, 1614 kj, 12 mph avg.

Ride B: 38 miles, 2,192', 154 WAP, 1243 kj, 15.3 mph avg.

The flatter ride was group of two & the hillier was solo.

woodcraft

I think he's referring to that CdA is a coefficient- does not change with speed.

Koyote

That's what I figured. But I still wonder if my supposition is correct, generally.

woodcraft

I can always put out higher watts on hills than the flats, so not IME. Maybe it's what you're used to.

CargoDane

I'd rather cycle 35 miles on the flat than going up a mountain for half of it from an energy expendature point - even if there's downhill on the half. I will certainly be more busted on the mountain route, whereas on the flats, 35 miles is nothing. Of course, I'd probably take the mountain route because it's more fun, but I'll be more busted at the end. I don't know the math of this as there are various parameters we don't know, but hilly country is harder than flat routes.

I figure that going up hill makes my muscles work closer to max output, thus become tired quicker. Of course, I could do the same with wind resistance and get plenty of workout that way, but I rarely go so fast on the flat that I get the same resistance as going up hill. Maybe I should get a taller gear.

WhyFi

This is such a dumb rabbit hole. From now on, when someone asks me, "how far did you ride today?" I'm going to answer, "2994kj"