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Any science nerd here work out the work equivalence formula for incline vs. flat ?

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Any science nerd here work out the work equivalence formula for incline vs. flat ?

Old 07-27-22, 02:29 PM
  #26  
GhostRider62
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Originally Posted by livedarklions
Also a lawyer, so yeah.

Not a physicist here, but I'd have to think that would vary with grade. It's a lot easier to climb a foot at 1% grade than it is to climb the same foot at 25% grade. If the grade gets steep enough, it becomes actually impossible.
My simple model breaks it down to two components. the X and Y. X = distance and Y = elevation. Since my power output is fairly constant, I treat them independently and since most climbs are at least 5% and the speeds relatively low, linear approximations work for old fat people like me. Let's say you have 30 miles to get somewhere, you might think that two hours but if that 30 miles adds 3,000 feet of elevation gain, you might have an additional hour of riding to account for the additional 3,000 feet of elevation.
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Old 07-27-22, 02:56 PM
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Using the watts formula from KerryIrons, I looked at what speed 200 watts buys me at various inclines and made some assumptions and approximations, like, no wind, total weight 200 lbs, rolling coefficient of .005 to make the math tidier.

As you would expect, the air drag term is still dominant at very small inclines but soon we move to the part where the speed drops and it’s all the gravity term. Even as soon as 1% and 18 mph, the two terms are similar.

200W gets me about 21 mph on the flat. The first three percents of grade each. cost me about 3 mph at 18, 15 and 12 mph. 4% is about 10 mph, 6% is about 7.5 mph and 10% is about 4.7 mph. At the higher inclines, you can see the product of grade (%) and speed (mph) leveling off and approaching about 50. At 300W, that product will approach 75.

Otto
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Old 07-27-22, 02:58 PM
  #28  
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Originally Posted by livedarklions
Wrong. There's no reason you can't get as much training stress from a lighter bike, one simply adjusts gears, routes, payload, and speed. And if you really want to do it with weight, carry something on your bike.

Want to do the math? How much faster do you have to ride a bike that's 5 pounds lighter in order to equalize the resistance that's being overcome? Please be sure to include drag in your calculations.
You are wrong and don't have a clue what the others are saying. Try reading about training zones and focus on energy systems. Stress was used to denote the effect metabolically. Not the stress of weight. The original research related to bicycling was about 1991 with Coyle and Coggan who I believe was his post grad student at the time. The effect of higher intensities places a much higher training stress than the same work done over longer period of time despite having the same energy expenditure. This is beyond refute. The weight lifting example was a simple way to communicate that concept and was not a bad one.
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Old 07-27-22, 03:10 PM
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A 2 hour ride at 50% of FTP is not the same stress as 1 hour at FTP.

One is a TSS of 100 and the other is a training stress of 50. Half the stress despite both burning the same calories (energy)

https://www.trainingpeaks.com/learn/...mance-manager/
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Old 07-27-22, 03:20 PM
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I was going to post some witty comment in regard to the title and the insinuation that a group of people sitting around on a computer and posting about riding a bike on the interwebz was rather stereotypical.....and then all the nerds showed up.

/dang
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Old 07-27-22, 03:20 PM
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at 6 minutes and 40 seconds they show something like you may be looking for
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Old 07-27-22, 04:29 PM
  #32  
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Originally Posted by GhostRider62
Admit that this is a rough way to look at a ride.

So, we're both randonneurs. Let's say I have a 200K with 7,500 feet of climbing. The distance takes me around 6:15. The elevation takes me about 2:15. So, it is going to be a little under 9 hours with controls. If it is a flatter course like in southern NJ or Florida. It is going to be under 7 hours.

On a 300K recently, there was about 11,500 feet of climbing. I rode hard and did under 13 hours. About 20 mph for the distance or about 9 hours and a little under 4 hours for the climbing.

Where it gets tricky is on a long ride like a 1200k because of fatigue and 100 feet might be more like a mile after the first day or so. I predicted my PBP time within 30 minutes with this approach with slight modification, I ignore short shallow hills and because they will be steam rolled.

Note: This back of the envelope is for my upright. The bent is more like 25 mph on the flats and less elevation per hour. I wear the same kit on my upright, so, the aerodynamics are about the same on any brevet. The bent aerodynamics are in another world so to speak. Again, just a rough way for an approximate equivalency, It can be important if there is a control at the top of a mountain......I just barely made the second control out West due to a big climb and several riders just missed it. I knew based on elevation that it would be tight and rode hard, just barely making it.

Another factor is whether you ride at the same output from ride to ride. I tend to ride at a certain HR and it corresponds to a certain power (zone 2). If I am fit and healthy, this power starts at a certain level and declines as time goes by and unless it is very hot, this decline is also fairly predictable.
I think such a formula can actually be pretty accurate within a certain range of parameters, once developed for a certain person based on their particular performance factors. I suspect, however that it would fall apart a bit when the climbing is not distributed in the way it is on courses from which the formula was developed. On a bent in particular, climbing accrued on little hills typically proceeded by little downhills would create a larger ft per mile equivalency than when the climbing is gained through long and steep mountain climbs. My last two rides illustrate this. The ability to create very different types of routes around here has defied the creation of a single formula. I do know my moving averages seem disproportionately slower when I have to do ridge climbs as opposed to battling a large number of smaller hills down in the valleys.

My two sample rides were both on bents, and at a zone 3 pace. The relatively low aero drag and high intensity of those rides compared to the assumptions built into your formula are surely distorting factors. I think it makes sense that those two things would lower my ft to mile number, comparatively.

None of that accounts for very long events where things can be even more variable, as you suggest.

Last edited by Steamer; 07-27-22 at 04:38 PM.
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Old 07-27-22, 04:49 PM
  #33  
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In some ways the elevation gain calculation works better for bents. The linear approximation for slower speeds would move the curve to the right. However, small hills on a bent can be obliterated and my back of the envelope estimation does not work well, which is why I completely deduct elevation gains on short, shallow hills for a bent.

A famous ultra racer was quoted as saying 1 mile = 100 feet of climbing. That got me thinking. I had wanted to break 8 hours on a PA 200k but never did it (walking across the Delaware river bridges 4-6 times is another factor) and started to think how much power and energy are needed to raise my body up the hills. Climbing is slow speedwise, so, wind isn't much a factor. The individual factors like power and weight vary from rider to rider. Of course, I am also talking about riding solo. I had looked at a couple of the top 5 finishers at PBP and their climbing times, realizing I needed to lose 15% of my weight or gain 15% more power to stand a chance of sucking wheels. There really isn't any practical application. VAM is slightly different and gear towards professionals who ride much faster on hills to the extent drafting actually helps. When tired, 100 feet might feel like more than a mile. When Lael blew by me on a climb, I quickly calculated she had almost 3 full days on me just on climbing ability alone. That made me sad.
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Old 07-27-22, 05:42 PM
  #34  
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Originally Posted by GhostRider62
You are wrong and don't have a clue what the others are saying. Try reading about training zones and focus on energy systems. Stress was used to denote the effect metabolically. Not the stress of weight. The original research related to bicycling was about 1991 with Coyle and Coggan who I believe was his post grad student at the time. The effect of higher intensities places a much higher training stress than the same work done over longer period of time despite having the same energy expenditure. This is beyond refute. The weight lifting example was a simple way to communicate that concept and was not a bad one.
You guys are having different conversations but are on the same general side. He's talking in the context of the idiots that say that a heavier bike makes for a better workout while you guys are talking about TSS, CTL, ETC, LOL, WTF, BBQ.
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Old 07-27-22, 06:24 PM
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Originally Posted by GhostRider62
You are wrong and don't have a clue what the others are saying. Try reading about training zones and focus on energy systems. Stress was used to denote the effect metabolically. Not the stress of weight. The original research related to bicycling was about 1991 with Coyle and Coggan who I believe was his post grad student at the time. The effect of higher intensities places a much higher training stress than the same work done over longer period of time despite having the same energy expenditure. This is beyond refute. The weight lifting example was a simple way to communicate that concept and was not a bad one.
Uh, huh, where did I say anything about varying time? I'm making the very obvious point that if you go faster for the same effort on another bike, you increase the distance to maintain the same effort over the same amount of time. I very clearly said increasing resistance increases effort per MILE, I would hope you would recognize that that is a measure of distance, not time.

Track back the thread a couple posts to see what I was reacting to. The variable determining the intensity of the workout is your effort and the quote I was initially "corrected" for with weight lifting nonsense was agreeing with caloso's statement that 250 watts for a minute was the same intensity whether it was on a heavy bike or a super light bike. You'll notice that I said you could do the exact same intensity on the lighter bike as on the heavy. The weight lifting analogy doesn't fit because it doesn't refute at all that one minute at 250 watts is the same effort and intensity no matter what bike.

I'll accept your apology for putting words in my mouth about time now.
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Old 07-27-22, 06:33 PM
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Originally Posted by GhostRider62
A 2 hour ride at 50% of FTP is not the same stress as 1 hour at FTP.

One is a TSS of 100 and the other is a training stress of 50. Half the stress despite both burning the same calories (energy)

https://www.trainingpeaks.com/learn/...mance-manager/

You appear to be refuting a point no one made.
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Old 07-27-22, 07:30 PM
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Originally Posted by KerryIrons
Power to ride a bicycle can be calculated pretty accurately with a well known equation:horse power = [Vg*W(.0053 + %G/100) + .0083(Va^3)]/375

calories/hr = [Vg*W(.0053 + %G/100) + .0083(Va^3)]*7.2

watts = [Vg*W(.0053 + %G/100) + .0083(Va^3)]*2

where Vg is ground speed, Va is speed through the air (includes head/tail winds), W is bike + rider weight in lbs., and %G is grade in per cent. The factors listed here (0.0053 for friction + rolling resistance and 0.0083 for aerodynamic drag) are obviously not absolute. They will vary with efficiency of the tires and drive train, and with the aerodynamics of the bike + rider combination. Both of these assume a racing position on a racing bike. A clunker bike or a more efficient riding position will change these numbers, which are averages anyway. Power to overcome friction and gravity is proportional only to rider weight and ground speed. Power to overcome wind drag is proportional to the cube of the air speed. For reference, 1 hp = 2700 calories (because of human metabolic efficiency of 24%); 1 calorie = 0.276 watts; 1 hp = 746 watts. Here, all calories are kg-calories, or "food calories."

Analyticcycling.com allows you to put your numbers into a calculator and get numbers out. There are other calculators out there but some of them are pretty inaccurate. They often estimate significantly high calories burned.
I don't think you can equate 1 calorie to 0.276 watt, because "calorie" is a unit of energy and "watt" is a unit of power. I'm not sure how it affects your equation
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Old 07-27-22, 07:52 PM
  #38  
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Originally Posted by Road Fan
I don't think you can equate 1 calorie to 0.276 watt, because "calorie" is a unit of energy and "watt" is a unit of power. I'm not sure how it affects your equation
It looks like he meant to say “calorie/hr”, and he just left off the “/hr“ in the places you mention.

Otto
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Old 07-27-22, 09:39 PM
  #39  
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Originally Posted by CheGiantForLife
For example, 1 minute up a 6% grade is equal to X minutes on a flat grade.
If not specifics, has anyone ever come up with a "Rule of 72" style rule of thumb approximation?

with or without the gulf clubs?
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Old 07-28-22, 04:42 AM
  #40  
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So let's take the comparison between a flat ride workout vs. hilly seriously. As discussed above, there's no reason why either will require a more intense effort than the other. One can adjust their speed and gearing to make it as intense as possible or, as ghostrider points out, with less training stress, and that's true on flats or hills. Where I think the workouts are going to be systematically different is that the geometry of the rider on vehicle is different. Obviously, when going uphill, the front wheel is higher than the rear wheel, and the rider is between them. On a df frame, it's not uncommon for people to adopt a completely different position, standing or otherwise, on the hills. Depending on how much you do this, this will translate into working different muscles and/or working the same muscles differently.

Last edited by livedarklions; 07-28-22 at 04:52 AM.
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Old 07-28-22, 05:28 AM
  #41  
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Originally Posted by livedarklions
You appear to be refuting a point no one made.
I was trying to help you not be the laughing stock.

Last time I do that.
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Old 07-28-22, 05:30 AM
  #42  
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Originally Posted by livedarklions
Uh, huh, where did I say anything about varying time? I'm making the very obvious point that if you go faster for the same effort on another bike, you increase the distance to maintain the same effort over the same amount of time. I very clearly said increasing resistance increases effort per MILE, I would hope you would recognize that that is a measure of distance, not time.

Track back the thread a couple posts to see what I was reacting to. The variable determining the intensity of the workout is your effort and the quote I was initially "corrected" for with weight lifting nonsense was agreeing with caloso's statement that 250 watts for a minute was the same intensity whether it was on a heavy bike or a super light bike. You'll notice that I said you could do the exact same intensity on the lighter bike as on the heavy. The weight lifting analogy doesn't fit because it doesn't refute at all that one minute at 250 watts is the same effort and intensity no matter what bike.

I'll accept your apology for putting words in my mouth about time now.
Pretty much everything you wrote was incorrect WRT to training stress. You want to stay ignorant, fine.

No apology.
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Old 07-28-22, 06:44 AM
  #43  
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Originally Posted by GhostRider62
Pretty much everything you wrote was incorrect WRT to training stress. You want to stay ignorant, fine.

No apology.
Guy. He wasn't making a comment on training stress. He was simply saying that, if two bikes have slightly different resistance, for whatever reason, you'll go slightly different distances for the same effort at the same duration.
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Old 07-28-22, 09:47 AM
  #44  
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Thank you for not insulting my intelligence.

Originally Posted by livedarklions
Because bicycles aren't weights being lifted so the analogy is completely wrong--the differences in resistance between the lighter and heavier bikes are not so significant as to affect the effects of resistance meaningfully. This is more like comparing lifting 198 pounds 11 times to lifting 200 pounds 10 times, but that's not even true as you'll see below.

You aren't the first person to misapply weightlifting logic here, Start with the fact that the differences in weight between bikes are likely small in comparison to the gross weight of the rider and the bike, and that the bike is actually a machine designed to minimize the vertical lifting of the weight and to maximize the advantages of forward momentum and you'll soon realize that the analogies are more confusing than they are helpful.

Also, for that matter, riding in a higher gear, or riding faster add resistance (both mechanical and wind).. Increased weight also just adds resistance. And as pointed out repeatedly, if you really want your resistance in the form of weight, just carry something heavy on your light bike.
I kind of expected a "cycling is not weightlifting" response. I appreciate your trying to refine my example to more accurately reflect a comparison to cycling. I think they are more comparable than many folks assume. I've lifted weights for training, but am not a "bodybuilder". Among those who are, it is known that many more repetitions with lower weights builds definition, a more obvious shape to the muscles. Fewer repetitions with much heavier weights builds strength. I was reminded of this when I started riding again - after several months I could see much more definition in my legs when they flex or move, even though my legs are still skinny. So, I don't think comparing 'workouts' in the two activities is so far-fetched.

I also realize that you can get more resistance by using a higher gear, and I think it is a good idea to do exactly that on occasion, for training purposes, to help build strength, just as it is good to use lower gears, to improve pedaling form. Just because there is a second way to do things doesn't make the first one wrong, but I would agree that banging around on a clunker won't give one the good pedaling form that is so beneficial to longer, harder efforts. I would also say that there is a big difference in feel between extra weight on the body and extra weight on the bike, but agree that it doesn't matter in terms of energy expended.

The biggest workout benefit in my experience, in terms of equipment choice while training, comes from heavier wheels. There is no good, practical way that I know of to mimic their effect while training, especially when you are riding with others. Every time you have to catch a wheel, or try to build a gap, you are getting a better workout than if you had ridden your lighter wheels, and a better workout than any others who are riding lighter wheels as well. Switching to light wheels for the race is a bit like taking off your heavy backpack after a long hike. You almost feel like you could fly!

Racers riding light wheels while training should save them for racing, and train on heavier wheels, by a pound or more, each. This will get them more in the long run than saving a few more grams with super-light racing wheels.

In my opinion, of course. Thanks for respecting it.
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Old 07-28-22, 12:42 PM
  #45  
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Originally Posted by ofajen
It looks like he meant to say “calorie/hr”, and he just left off the “/hr“ in the places you mention.

Otto
Maybe that was his intent - I don’t know.
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Old 07-28-22, 01:02 PM
  #46  
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Originally Posted by GhostRider62
I was trying to help you not be the laughing stock.

Last time I do that.
Man, you are completely full of crap. I defy you to cite anything I said that remotely resembles an assertion that "a 2 hour ride at 50% of FTP is the same stress as 1 hour at FTP." Nothing.I wrote suggests anything like that. I'm just saying 1 hour at FTP on a heavy bike is not intrinsically a "better workout" than 1 hour at FTP on a light bike. You want to actually explain why that is wrong, I'll respect that, but nothing you've said has anything remotely to do with that assertion. .

Again, all I'm saying is that if you are putting out the same effort for the same duration of time, it doesn't matter whether the resistance you are overcoming is due to speed (drag), gearing, or weight. You aren't lifting the bike, there's nothing special about weight..

And I'm sorry, but are you saying that the weightlifting example has anything to do with FTP? I don't think I'd be concerned with someone else being the laughing stock after committing such a howler. .

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Old 07-28-22, 01:21 PM
  #47  
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Che really trolled you guys...
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Old 07-28-22, 01:33 PM
  #48  
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Originally Posted by Fredo76
I kind of expected a "cycling is not weightlifting" response. I appreciate your trying to refine my example to more accurately reflect a comparison to cycling. I think they are more comparable than many folks assume. I've lifted weights for training, but am not a "bodybuilder". Among those who are, it is known that many more repetitions with lower weights builds definition, a more obvious shape to the muscles. Fewer repetitions with much heavier weights builds strength. I was reminded of this when I started riding again - after several months I could see much more definition in my legs when they flex or move, even though my legs are still skinny. So, I don't think comparing 'workouts' in the two activities is so far-fetched.

I also realize that you can get more resistance by using a higher gear, and I think it is a good idea to do exactly that on occasion, for training purposes, to help build strength, just as it is good to use lower gears, to improve pedaling form. Just because there is a second way to do things doesn't make the first one wrong, but I would agree that banging around on a clunker won't give one the good pedaling form that is so beneficial to longer, harder efforts. I would also say that there is a big difference in feel between extra weight on the body and extra weight on the bike, but agree that it doesn't matter in terms of energy expended.

The biggest workout benefit in my experience, in terms of equipment choice while training, comes from heavier wheels. There is no good, practical way that I know of to mimic their effect while training, especially when you are riding with others. Every time you have to catch a wheel, or try to build a gap, you are getting a better workout than if you had ridden your lighter wheels, and a better workout than any others who are riding lighter wheels as well. Switching to light wheels for the race is a bit like taking off your heavy backpack after a long hike. You almost feel like you could fly!

Racers riding light wheels while training should save them for racing, and train on heavier wheels, by a pound or more, each. This will get them more in the long run than saving a few more grams with super-light racing wheels.

In my opinion, of course. Thanks for respecting it.

Wow, that's a really interesting response about the heavier wheels! Thank you!
Obviously, if you say x provides a better workout for you, I have no business disagreeing with it because "better" is a subjective term. I think when we say that, we're really saying "I perform a better workout on this piece of equipment than that one". I'm not a racer, but I could see how what you're saying might work for some of them, while others may want to train to be just as fast as they can be on the equipment they're going to race. Keeping in mind that increasing your speed on a lighter bike is really just swapping one form of resistance for another, I suspect that the benefits of the wheel swap are probably more motivational than reflecting actual muscle development, but you're the one actually doing it and I have no experience doing that, so I will defer. I'm going to disagree with your assertion that "racers should" only because I don't think either of us are in a position where we should be prescribing or not prescribing this for other people.

"Better" also means more suited for my purposes in a workout. I'm a high gear masher, so I'm very aware I have relatively huge calf and thigh muscles as a result of that high resistance style of pedaling. Where I think the weightlifting analogy breaks down though is where going really fast requires overcoming a much higher amount of air resistance than going slower, so I don't think pedaling a fast rolling bicycle on flat ground is as qualitatively different from pushing a heavy bicycle at slower speed as lifting two very different weight amounts.

Oh, and thanks for not being disagreeable for disagreeing. It was really a pleasure to read your post, and the discussion is fun,

Last edited by livedarklions; 07-28-22 at 01:39 PM.
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Old 07-28-22, 01:52 PM
  #49  
livedarklions
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Originally Posted by GhostRider62
Pretty much everything you wrote was incorrect WRT to training stress. You want to stay ignorant, fine.

No apology.

In other words, you tried to show me up but you got nothing.
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Old 07-28-22, 08:26 PM
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Back to the original question, if you take a 160 pound biker riding 22 pounds of bike and gear at 225 Watts, he/she will cover around 10.25 miles in 30 minutes (per an online bike speed/power calculator). If that same biker goes up a steady grade, once the grade gets above around 6% the speed drops such that it is mostly about simply overcoming gravity. And at the same power output he will climb between .51 miles (6% grade) and .57 miles (15% grade). So call it .54 miles.

So for that particular scenario of power output, biker/bike weight, and grades above 5'ish%, .54 miles of climbing is kind of like 10.25 miles on the flats. The relationship will change a lot with rider weight and some with power output.

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Last edited by DaveLeeNC; 07-28-22 at 08:31 PM.
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