Road Cycling “It is by riding a bicycle that you learn the contours of a country best, since you have to sweat up the hills and coast down them. Thus you remember them as they actually are, while in a motor car only a high hill impresses you, and you have no such accurate remembrance of country you have driven through as you gain by riding a bicycle.” -- Ernest Hemingway

Grade vs. Climb Rate

Old 06-06-05, 08:33 PM
  #26  
TheKillerPenguin
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Originally Posted by eccccyclsm
I'd like to see an "average" cyclist sustain 469 watts up a 6% grade, and a hoss almost 600. Maybe we should consider the reality of our numbers before we throw them around or is this all government work?
You're missing the point. It doesn't matter what numbers are used for power, the relationships should be the same regardless.
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Old 06-06-05, 08:47 PM
  #27  
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Originally Posted by eccccyclsm
I'd like to see an "average" cyclist sustain 469 watts up a 6% grade, and a hoss almost 600. Maybe we should consider the reality of our numbers before we throw them around or is this all government work?
HAHAhaha. The "average" part of that cyclist was the build: 5'10", 165 lbs. Note I used the quotation marks around average, as an average is just a mathematic concept; you can't add people up and divide them out to yield an "average" person.

I am a "hoss", and I've sustained about 575 watts up a 15% grade for about 5 minutes. I promptly fell over and puked, however. That's nearly 3/4 horsepower. Doing it for a whole hour is an entirely different subject.

I don't think it's too unrealistic to think a 165lb rider in good shape on a 20 lb bike could maintain 16mph up a 6% grade. At the Joe Martin Stage Race here in Fayetteville, I watched some guys from Healthnet do a solid 25-26mph up a 1/2 mile stretch of 6.8% avg grade about 20 times, during the Sunday criterium, and after 1 hour + 5 laps they looked pretty beat, but not wasted, and they were off the front by themselves for a good 2/3 of the crit. Yeah, OK, they were pros, and not "average" in the sense you took it, but still, they were doing WELL over the 469 watts required to maintain 16mph, and neither of these guys were 5'10" 165lb; the bigger guy looked like he was 6'3" or so, and about 185lbs, the other was about 6', but probably close to 165.

Maybe we should consider the validity of our criticisms before we toss them around, or is this the line for the government dole?

Seriously though, point taken; nevertheless, while the numbers themselves maybe unrealistic, the relationship between the forces remains constant. Cut them all in half if it pleases you.

Last edited by kandnhome; 06-06-05 at 09:09 PM.
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Old 06-06-05, 09:25 PM
  #28  
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I think you are under estimating the gravitational force here. Although I do think body position on the bike is a bigger factor.
Back to gravity on has to look at how much gravity is pulling down the slop vs in to the ground. If you put a box on a ramp in slowly increase the slop it will over come friction and slide down. Just a thought time for a beer.
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Old 06-06-05, 09:26 PM
  #29  
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I blabbed on about this in another thread; the gravitational component works out as:
Code:
power(W) > total_weight(lb) * vertical_speed(ft/min) / 44.25
vertical_speed = rolling_speed * sin(atan(slope))
Combining the two and fiddling units yields:
Code:
power(W) > total_weight(lb) * rolling_speed(mi/hr) * sin(atan(slope)) * 1.9885
The power requirement is at least linear in vertical speed, and vertical speed varies almost (within 5%) linearly with rolling speed for slopes (grades) between 0% and 30%. This neglects wind, rider posture, chainline, diet, leg hair, horoscope, etc.

-JAB
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Old 06-06-05, 11:36 PM
  #30  
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Several observations. In standard climbs good climbers can stay with great climbers on grades of 4-6% (look at Savodelli on the final climb up to Sestriere, where he lost little time -- about 20-45 seconds-- to the pure climbers Rujano and Simoni) but they tend to have trouble following on the steep slopes (10% as on the prior climb where Savodelli lost 2:27).

At 5% slopes, there is non-trivial wind resistence as well as a little rolling friction, with the wind effect being "quadratic". On slopes of 10% the speeds have dropped enough that the amount of effort overcoming wind resistence is becoming unimportant, especially for us mortals. If efficient long-term pedalling cadence is 90rev/min (I could make arguments why this is the case for a prolonged climb but that is not the primary question here), then a 10% slope is going to run most riders into inefficiently low cadence with most standard gear ratios (although triples help here). If you are having to stand to get enough power to climb the gradient with your gearing, you are becoming less efficient).

On the analytical side: there is a slight difference between the distance up the road relative to the horizontal component (i.e., using the long flat leg is slightly shorter than the hypotenus) and it is possible that differences cited above might rise from this minor distinction which becomes more important as the slope steepens to 10% and more.
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Old 06-06-05, 11:48 PM
  #31  
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Originally Posted by 26mi235
Several observations. In standard climbs good climbers can stay with great climbers on grades of 4-6% (look at Savodelli on the final climb up to Sestriere, where he lost little time -- about 20-45 seconds-- to the pure climbers Rujano and Simoni) but they tend to have trouble following on the steep slopes (10% as on the prior climb where Savodelli lost 2:27).

At 5% slopes, there is non-trivial wind resistence as well as a little rolling friction, with the wind effect being "quadratic". On slopes of 10% the speeds have dropped enough that the amount of effort overcoming wind resistence is becoming unimportant, especially for us mortals. If efficient long-term pedalling cadence is 90rev/min (I could make arguments why this is the case for a prolonged climb but that is not the primary question here), then a 10% slope is going to run most riders into inefficiently low cadence with most standard gear ratios (although triples help here). If you are having to stand to get enough power to climb the gradient with your gearing, you are becoming less efficient).

On the analytical side: there is a slight difference between the distance up the road relative to the horizontal component (i.e., using the long flat leg is slightly shorter than the hypotenus) and it is possible that differences cited above might rise from this minor distinction which becomes more important as the slope steepens to 10% and more.
I agree with you, so it seems that low cadence causing LA buildup in the legs is a major reason as to why climbing rates decrease as grade increases.

As for determining grade, I use the horizontal component of the incline in the rise/run equation, although the difference rarely adds up to anything more than 1% grade change.
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Old 06-07-05, 12:38 AM
  #32  
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Originally Posted by PenguinDeD
I agree with you, so it seems that low cadence causing LA buildup in the legs is a major reason as to why climbing rates decrease as grade increases.

As for determining grade, I use the horizontal component of the incline in the rise/run equation, although the difference rarely adds up to anything more than 1% grade change.
Which means for this problem your typical road bike is terribly overgeared and we are terribly underwatted .
On a 9% grade you are climbing 3749 ft/hr with 250 watts expended spinning 30/27 at 90rpm. Increase to 12% grade and you require 330 watts to spin the 30/27 @ 90rpm, but increase your climbing rate to 4999 ft/hr. Increase to 18% grade, 486 watts, 30/27 @ 90 rpm, climb = 7499 ft/hr. Problem becomes you can't maintain 486 watts for any length of time so in order to climb for any length of time you must gear, question becomes can you keep a bike upright at the speeds gearing would produce to climb 3000ft/hr with little effort? So back to analytic we go and...
To climb 2% at 200 watts, you need 53/24 @ 90 rpm. Speed, 15.7mph, climbing at 1656ft/hr. To climb 12% at only 200 watts and spin 90rpm you'd need a 30/44 and would climb at 3066 ft/hr, speed would be 4.84mph. To climb 18% with only 200 watts of power output at 90 rpm, you'd need 30/65 gearing and you'd climb at a sustainable 3117/hr. At 25% grade with only 200 watts of power output at 90 rpm, you'd need a 30/89 gear combo and your rate of climb would jump to 3154 ft/hr, speed down to 2.39mph. Finally at 40% grade with only 200 watts of power at 90rpm, you'd need a 30/142 gear combo, you'd climb at 3168 ft/hr, but only travel at 1.5 mph, close to tippy time.
Eeek. Just running a few more numbers over at Analytic is scary...I don't have a power meter so I'm not terribly familiar with what us 'average' cyclist can generate and sustain, but I have a feeling 200 watts ain't as easy as I thought it was...

Last edited by Stealthman_1; 06-07-05 at 01:04 AM.
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Old 06-07-05, 09:49 AM
  #33  
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I persume that when we are talking "watts" here, we are talking about power delivered, not energy used to deliver power. Becuase there is inefficiency in out transformation of potential energy (body stores) to delivered effort, there can be a mismatch.

I would think that 200 watts is not too difficult (although it is not crusing at 10 mph on the flats), the value of 500++ in this thread seems quite high, because I thought I remembered Armstrong's numbers being in the 450 range. The short duration of that high wattage might be the reason.

There was a Bicycle omnibook quite a while back that had slopes and speeds and identified some racers.
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Old 06-07-05, 11:16 AM
  #34  
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Originally Posted by Stealthman_1
Eeek. Just running a few more numbers over at Analytic is scary...I don't have a power meter so I'm not terribly familiar with what us 'average' cyclist can generate and sustain, but I have a feeling 200 watts ain't as easy as I thought it was...
I've heard 200 watts thrown around quite a few times as the sustainable output of your average non-competetive cyclist. It's actually a very doable effort for anyone who is not just getting started.
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Old 06-07-05, 03:16 PM
  #35  
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Hills are hard, the steaper the slower.
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Old 06-07-05, 03:30 PM
  #36  
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Originally Posted by PenguinDeD
There are still some unanswered questions though (unless I missed something), and this is the one I'm most confused about.


Basically, this says that the steeper the slope, the higher the climb rate. But why doesn't what happens in real life mirror this? In my experience climbing alone and with others, as grade increases, climbing rate tends to decrease pretty quickly. This must mean that somewhere, we're losing power along the way, but the question is where.

It could just be that LT's dictate that that power can't be held over steeper grades simply because the aerobic system can't keep up with the increased Lactic Acid buildup over shorter distances, but this is just a theory on my part.

Ideas?
Whatever the theoretical possibilities, there are artificial limits placed on this exercise by our equipment. That is - few people have the combination of sufficient strength and proper gearing to make a steady ascent up a 20% grade. on a really steeply geared bike (probably would have to be a trike to keep balance at ultra-low speeds) you may be able to achieve the theoretical constant.

this is a long way of saying, the real world is interfering with our damn science, here!
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Old 06-07-05, 03:31 PM
  #37  
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just saw stealthman's post, which I second.
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Old 06-07-05, 06:35 PM
  #38  
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I'm very confused, by all this babble, could'nt it just be said that it takes more effort to climb 500Metres at 10% than it does to climb 500Metres at 6%.
No trig or anything needed, it is harder because it is steeper. So obviously more effort is required to maintain speeds
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Old 06-07-05, 06:47 PM
  #39  
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Originally Posted by gabdy
I'm very confused, by all this babble, could'nt it just be said that it takes more effort to climb 500Metres at 10% than it does to climb 500Metres at 6%.
No trig or anything needed, it is harder because it is steeper. So obviously more effort is required to maintain speeds
I think technically the 500M at 6% takes more effort, as you have to travel farther to reach the same altitude. It's been a year since I was in physics, but from what I remember it winds up multiplying the effort needed, but it spreads it out over so much greater a distance that it feels easier.
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Old 06-08-05, 01:02 AM
  #40  
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Originally Posted by gabdy
I'm very confused, by all this babble, could'nt it just be said that it takes more effort to climb 500Metres at 10% than it does to climb 500Metres at 6%.
No trig or anything needed, it is harder because it is steeper. So obviously more effort is required to maintain speeds
No, that is not the message here. At 6%, if you are fast, you are still getting an effect from wind resistance that adds to the effort so that climbing 500m implies doing more work. However, if you are not very fast or if you increase the slope some, the speed will drop enough that the "speed squared" effect of wind resistance will drop out of the picture empirically. At this point, getting steeper runs into the power and minimum cadence factors, at which point you are probably climbing vertically at the greatest rate.

When I was racing, I think that my fastest rates of vertical climb were on sections of about 10% (1600 feet vertical in 18 min at the end of a climb totaling 4500 feet in a little over an hour. You probably cannot climb that rapidly, so a 7-8% slope might max out your climbing rate.
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Old 06-08-05, 06:53 AM
  #41  
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Originally Posted by jab
power(W) > total_weight(lb) * rolling_speed(mi/hr) * sin(atan(slope)) * 1.9885

The power requirement is at least linear in vertical speed, and vertical speed varies almost (within 5%) linearly with rolling speed for slopes (grades) between 0% and 30%. This neglects wind, rider posture, chainline, diet, leg hair, horoscope, etc.

-JAB
Thanks JAB. (though I think it's W/unit time, and whats the conversion factor at the end?)

Anyway, this should quell all the confusion here...elegantly simple
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Old 06-11-05, 06:29 PM
  #42  
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Very interesting discussion, but I am lost on much of it. I went over to analytical cycling and did some playing with numbers. I don't know how to create a table for easier reading, but this is what I came up with:


Scenario A: 2.75 m/s, about 6 mph, GI returned was 35,
Scenario B: 2.50 m/s, about 5.5 mph, GI returned was 31
Scenario C: 2.25 m/s, about 5 mph, GI returned was 28
Scenario D: 2.00 m/s, about 4.5 mph, GI returned was 25
Scenario E: 1.80 m/s, about 4 mph, GI returned was 22

WATTS NEEDED
Slopes: 2%, 4%, 6%, 8%, 10%, 12%, 14%
Scenario A: 078, 141, 203, 266, 329, 391, 454
Scenario B: 071, 128, 184, 241, 298, 355, 412
Scenario C: 063, 114, 166, 217, 268, 319, 370
Scenario D: 056, 101, 147, 192, 238, 283, 329
Scenario E: 049, 088, 128, 168, 208, 248, 289

Interesting relationships:
--dropping 3GI drops .5 mph
--each 3GI drop drops wattage by about 10%

Interesting observations:
200w power @35GI can handle 6% slopes at 6 mph
200w power @22GI can handle 10% slopes at 4 mph [assuming they can keep balance]

300w power @35GI can handle 9% slopes at 6 mph
300w power @22GI can handle 15% slopes at 4 mph

My conclusions
1. If you can't generate 200w and have slopes greater than 10%, you need a bent trike
2. If you can increase your power from 200 to 300w, you can drop 4 gears [13GI].

This also explains the range in lowest GI touring riders say they are comfortable with.
Some say they need 29Gi, others say need 24GI, a few need 19GI. Rider with inclinometer reported 27GI was ok for 12% grade.

At the other end of the spectrum, some SF riders are reporting hills of 26%. That would require 526 watts. No wonder they walk those hills.

Food for thought....
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