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Is there a work output formula to compare flats vs hills ?

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Is there a work output formula to compare flats vs hills ?

Old 08-25-21, 03:17 PM
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CheGiantForLife
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Is there a work output formula to compare flats vs hills ?

I am not a real cyclist. I only ride 5 mins to get my lunch. 3rd world commuter.

Today, I rode up a 10% hill that was about .2 miles long.
During this leg burning episode, all I could think was, "I wonder how much flat biking this work is equal to"

Like is 10% for .2 miles the same as riding flat for 1 mile ?
Decline riding is like negative infinity division by zero work.

Is there a conversion factor ?
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Old 08-25-21, 03:23 PM
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Originally Posted by CheGiantForLife View Post

Is there a conversion factor ?
Yes. Miles ridden on the flat = number of pushups divided by number of squats, multiply by the square root of your tire circumference, plus three...
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Old 08-25-21, 03:24 PM
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Yes, but the conversion is complicated. You have to convert the slope of the hill to ASVG (Air Squat Vertical Gain), and the distance to BPE (Bench Press Equivalent). Once you have those numbers, conformal mapping will give you the answer you're looking for.

On edit: Damn, I'm too slow for this sport (online forums).
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Old 08-25-21, 03:27 PM
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Originally Posted by tomato coupe View Post

On edit: Damn, I'm too slow for this sport (online forums).
That's OK. I think the result would be the same number with either formula.
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Old 08-25-21, 03:29 PM
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Here is an example of a calculator. Im sure its not perfect but will give you an idea

https://www.omnicalculator.com/sports/cycling-wattage

Otto
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Old 08-25-21, 03:40 PM
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Yes, the formula is: riding up hills is harder than riding on flat ground.
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Old 08-25-21, 03:43 PM
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100 vertical feet is equal to 1 mile on the flat for basic cyclists and 200 feet for very fit rider. Not talking TdF racers. YMMV
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Old 08-25-21, 03:46 PM
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Originally Posted by ofajen View Post
Here is an example of a calculator. Im sure its not perfect but will give you an idea

https://www.omnicalculator.com/sports/cycling-wattage

Otto
Interesting link, but it does not ask for distance or duration, so how can it calculate work?
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Old 08-25-21, 04:01 PM
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Originally Posted by CheGiantForLife View Post
Interesting link, but it does not ask for distance or duration, so how can it calculate work?
It gives you power, which is the rate at which work is being done. At a particular power output, total work would be power multiplied by time. For example, power (in watts) multiplied by time (in seconds) gives work (in joules). Depending on your particular metabolism, one dietary calorie equates to roughly 4000 joules.

Otto

Last edited by ofajen; 08-25-21 at 04:04 PM.
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Old 08-25-21, 04:03 PM
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This is what power meters do.
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Old 08-25-21, 04:29 PM
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Originally Posted by ofajen View Post
It gives you power, which is the rate at which work is being done. At a particular power output, total work would be power multiplied by time. For example, power (in watts) multiplied by time (in seconds) gives work (in joules). Depending on your particular metabolism, one dietary calorie equates to roughly 4000 joules.

Otto
I see. The variable is then speed. The 2 inclines will have varying speeds.
But, for a constant speed, each 1% of incline is a 10x increase in work.

But, if I plug in wild guess speed estimates, the data makes no sense

15mph at 0% = 100w
3mph at 10% = 100w

No way slow 10% is the same work at easy flat riding
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Old 08-25-21, 05:11 PM
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Bike Calculator
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Old 08-25-21, 05:22 PM
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None of those formulas work unless you ride longer than 5mins!

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Old 08-25-21, 05:35 PM
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Originally Posted by CheGiantForLife View Post
I see. The variable is then speed. The 2 inclines will have varying speeds.
But, for a constant speed, each 1% of incline is a 10x increase in work.

But, if I plug in wild guess speed estimates, the data makes no sense

15mph at 0% = 100w
3mph at 10% = 100w

No way slow 10% is the same work at easy flat riding
Try going 15 mph in a gear so tall you're only turning it at 30 rpm.
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Old 08-25-21, 05:38 PM
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Originally Posted by CheGiantForLife View Post
But, if I plug in wild guess speed estimates, the data makes no sense

15mph at 0% = 100w
3mph at 10% = 100w

No way slow 10% is the same work at easy flat riding
Those numbers are pretty much in line with what I see on my power meter.
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Old 08-25-21, 05:40 PM
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Hills > flats
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Old 08-25-21, 05:44 PM
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Originally Posted by asgelle View Post
Those numbers are pretty much in line with what I see on my power meter.
I bet you two can wear the same kit.
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Old 08-25-21, 06:01 PM
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Originally Posted by CheGiantForLife View Post
I am not a real cyclist.

Seriously. I think you need to ride more and post less. Stop overthinking everything. 😉
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Old 08-25-21, 06:19 PM
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Originally Posted by Reflector Guy View Post
Yes. Miles ridden on the flat = number of pushups divided by number of squats, multiply by the square root of your tire circumference, plus three...
I think the addition of that final plus three is superfluous. But we can argue about it further in this thread.
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Old 08-25-21, 06:57 PM
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Originally Posted by CheGiantForLife View Post
I see. The variable is then speed. The 2 inclines will have varying speeds.
But, for a constant speed, each 1% of incline is a 10x increase in work.

But, if I plug in wild guess speed estimates, the data makes no sense

15mph at 0% = 100w
3mph at 10% = 100w

No way slow 10% is the same work at easy flat riding
Way. See below article for the various terms in the power equation.

Cycling: Uphill and Downhill

The gravity term is giMs, where g is gravitational constant, I is incline, M is combined mass of bike and rider and s is speed of bike.

Put in the SI units carefully amd you will get the right number. I climb at about 300 watts on most hills and about 250 watts will usually be gravity work, but it varies depending upon if its shallow enough that my speed makes the air drag term significant. At 16 mph, I would be needing about 135 watts for the air drag and rolling friction terms.

Otto

Last edited by ofajen; 08-25-21 at 07:01 PM.
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Old 08-25-21, 07:18 PM
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$299 is the conversion rate.
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Old 08-26-21, 01:37 AM
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Two threads because you went up a short hill? Knock it off.
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Old 08-26-21, 02:22 AM
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If you start and finish in the same place for every hill that you struggled up there was a slope for you to coast down.
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Old 08-26-21, 03:22 AM
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Heres another simple calculator to play with that shows distance vs power and energy etc.

Bike Calculator
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Old 08-26-21, 05:05 AM
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Originally Posted by Retro Grouch View Post
If you start and finish in the same place for every hill that you struggled up there was a slope for you to coast down.

Mathematically true, but the grades up can be very different from the grades down. If it's 10 percent going up and 1 percent going down, I don't think I'm going to coast any of that.
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