Yes, I see now. Ignore enough variables and everything becomes simple.

Physics check:

Two general components of that, in addition to m*g*h. One is accelerating the mass. The easiest way to visualize that is the difference in kinetic energy (1/2m v squared, for the two v's). That's how much it took to accelerate to the higher speed. The second part is that the drag is greater at higher speeds - approximately proportional to speed for rolling and drive train losses and the like, but more importantly proportional to the square of the speed for aero drag. Energy (that portion of it) is that drag force times the distance.

But the extra energy he needed to raise his mass up the hill was just m*g*h. It doesn't matter, for that energy, how fast you do it. The confusion here is that Armstrong is more concerned about power than energy, and power is how much energy is used in a given time. So twice as fast uphill takes twice the power, for just lifting the weight. And approaching eight times the power to overcome drag force from the air. If he's going fast enough, and I assume that Armstrong and Ullrich probably were.

But back to OP, the whole reason I brought this up is asking about hills and calorie burn. Bottom line, just add it in for the climbs, the formula I gave earlier, and that produces the (extra for the hill) calories burned. As opposed to flatter rides.

Well, I'm glad you found your mirror. :thumb:

For an interesting look at the factors involved in energy consumption, speed, weight, headwind, grade, etc. this bicycle calculator is pretty interesting:

Bike Calculator

For a given rider and bike going 20 miles with no elevation, what is your guess as which requires more calories: pedaling 20 mph; pedaling 12 mph; pedaling 12 mph against an 8 mph headwind; or, pedaling 15 mph against an 8 mph headwind?

Answer:

1. 12 mph requires the fewest calories... ~359

2. 12 mph against an 8 mph headwind requires about double the calories as 12 mph with no wind, over the same 100 minutes... ~739

3. pedaling 12 mph against an 8 mph is about the same number of calories as pedaling 20 mph with no wind but takes 40 minutes longer.

4. And what about 15 mph with an 8 mph headwind? The ride is 20 minutes quicker than 8 mph with a headwind and 20 minutes slower that 20 mph without a headwind and requires about 200 more calories than either. ~ 931

And, for BONUS points, how does pedaling at 8 mph on a windless day but up a 5% grade compare with the above?


Same 20 miles but 150 minutes. ~1677 calories.


But-- what 20 mile ride requires the most power?


That would be... 20 mph with no head wind (215 watts); going 15 mph against a 8 mph headwind comes in second (203 watts); and, going only 8 mph but up a 5% grade comes in at 3rd (195 watts). 12 mph against a headwind requires more power (129 watts) than 12 mph with no wind (63 watts).


So, what activity uses the most energy per unit of time?


Going up a 5% grade at 8 mph consumes 1677 calories in 150 minutes. However, pedaling 20 mph with no headwind for the same 150 minutes would consume 1,847.5 calories.

Yes and No.

In air (or any fluid) speed is energy expensive because resistance increases proportional to the square of speed. So you get 4 times the resistance riding at twice the speed. Which is why they promote driving 55 vs 65 to save gas.

OTOH - the work done climbing is purely a function of weight and height gained. Speed isn't a factor in work, so fast or slow,the energy used is the same. OTOH - doing the same work in less time requires more POWER, which is something different. Faster riders of the same weight are more powerful, but the energy they consume doing the same task is the same.

Quickie glossary.

Force is what's needed to move a load against resistance (or accelerate it if no resistance).
Work is the product of Force X the distance moved. Energy used is the work done x the efficiency rating.
Power is the work done per time unit, so those who can work faster are more powerful.

More speed uses more energy-- e.g., above:

Going up a 5% grade at 8 mph consumes 1677 calories in 150 minutes. However, pedaling 20 mph with no headwind for the same 150 minutes would consume 1,847.5 calories.

Try this: You decide to do 200 watts on two rides of ten miles. One ride it flat, the other is 5% up for five miles and 5% down for five miles

Plug the numbers into the calculator, keeping the power at 200 watts.

The flat ride burned 348 calories.

The hill ride burned 375 calories climbing, and then 106 calories descending, for 481 total.

But that's kind of a cheat since that the hill ride took longer. Make the time the same and the calories will turn out the same. Yet the calories per mile will be 48 for the hill ride, and 35 for the flat ride!

I'm going to stop geeking out here before someone complains, but playing with the power calculator is always fun.

...a constant 200 watts is the key -- the 200 watts per minute (12,000 Joules -- about 2.857 food calories) in your examples will be the same by definition. Over a given amount of time the energy used will be the same. And, the rider in the examples above cannot do 20 mph on flat ground without expending more energy -- i.e., >200 watts (~215 watts). More speed takes more power... and, will use up more calories.

I wouldn't say we're consistent with riding conditions ... when we head out for a ride, it's anybody's guess what will happen out there.

Strong headwinds are almost always a given, of course ... but there are usually tailwinds too. It's not at all unusual to have winds gusting up around 50 or 60 km/h here and because of the terrain and the fact that we're on an island so we're surrounded by a large body of water, the wind could come from 15 different directions throughout a ride. I only give wind direction on the weather sites a passing glance now because that's just a rough guideline.

These days we could get pouring rain, hail, a touch of snow, sunshine, temps as low as about 0C or as high as about 16C ... all on one ride! All of that all on one ride doesn't usually happen, but there is often quite a variety and we go prepared for anything.

Then there is the terrain. Tasmania is hilly.

And the roads ... sometimes we're on smooth pavement, often we're on quite rough pavement. They don't maintain the roads particularly well here ... doesn't seem to be a priority. We've done many rides where we've felt pretty beat up by the end just simply because the roads have been that rough. And several of our routes are a combination of pavement and gravel. One of the ways they keep the traffic volume down on country roads (and probably keep the maintenance costs down) is to leave several km somewhere in the middle as gravel.

The 100K we do as part of the Audax Tasmania calendar at the beginning of the season (early November), for example, starts with a lovely quiet scenic loop on a rather rough road, with two patches of gravel that total about 7 km. Then there's another lovely quiet scenic loop with a gravel stretch about 3 km long, up a fairly steep hill.



And of course we plan our weekends to do different routes and go different places, so we encounter all sorts of stuff. :)

Just a brief update. On my last ride, a week ago, we did a lot of climbing and I was pathetic. Very close to bonking and generally no energy. The day after, i could barely stay awake. I was exhausted constantly. After some discussion with knowledgeable friends and some contemplation I concluded that it was probable that I had cut carbs too severely. The result was a meltdown in energy and I still wasn't losing any weight. So, I began putting things like bread and potatoes back into my diet. Two things happened. I quickly began to feel better and then I began to lose weight. The weather here has been so hot/humid that we haven't ridden but I continue to feel great and I'm losing weight. I'm now down to 186 lbs.

As it is said, "Fat burns in a carbohydrate fire." Way to go!

Why you shouldn't exercise to lose weight, explained with 60+ studies - Vox......here's something to confuse you even more:

Haven't read the article yet but I was thinking about this today. If you rely on activity to lose weight thane you gain it back with less activity. But, if you lose weight via choice of food and amount, activity becomes something that you fuel with your food choices. It doesn't have a transitory influence on weight but is critical for the proper function of your body.

FWIW....down to 185 this morning. This with no exercise for about 8 days.