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, 09:42 AM
  #1  
TheKillerPenguin
Nonsense
Thread Starter
 
TheKillerPenguin's Avatar
 
Join Date: Sep 2004
Location: Vagabond
Posts: 13,575

Bikes: Affirmative

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 700 Post(s)
Likes: 0
Liked 23 Times in 10 Posts
Grade vs. Climb Rate

How does climbing rate interact with the grade of the climb? Does it remain a constant, IE if you can climb 5000ft/hr at 6% you should be able to do the same at any grade, or is there a point where it starts to drop off, depending on your power/weight ratio?
TheKillerPenguin is offline  
Old 06-06-05, 10:21 AM
  #2  
Gonzo Bob
cycles per second
 
Gonzo Bob's Avatar
 
Join Date: Oct 2003
Location: Minnesota
Posts: 1,790

Bikes: Vitus Aluminum, DiamondBack Apex, Softride Powerwing 700, "Generic" Ishiwata 022, Trek OCLV 110

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 2 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
I once looked at this using analyticcycling.com. I calculated "time up a mountain" using various grades and found that grades between 8-10% give the fastest times - thus the fastest climb rates. This, however, was just a theoretical exercise. I don't know if it pans out in the real world.
Gonzo Bob is offline  
Old 06-06-05, 10:26 AM
  #3  
joeprim
Senior Member
 
joeprim's Avatar
 
Join Date: Jan 2002
Location: Northern Neck Tidewater Va.
Posts: 1,688
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by Gonzo Bob
I once looked at this using analyticcycling.com. I calculated "time up a mountain" using various grades and found that grades between 8-10% give the fastest times - thus the fastest climb rates. This, however, was just a theoretical exercise. I don't know if it pans out in the real world.
I'll bet you are right about the existance of a peak climb rate verses % grade. I don't know what the number is and I would think it might vary a little with power to weight ratio, but not as much as the actual rate would vary.

Joe
joeprim is offline  
Old 06-06-05, 10:32 AM
  #4  
KevinF
Keep on climbing
 
Join Date: Apr 2004
Location: Marlborough, Massachusetts
Posts: 2,179

Bikes: 2004 Calfee Tetra Pro

Mentioned: 1 Post(s)
Tagged: 0 Thread(s)
Quoted: 21 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
I've actually looked at this with my GPS on the bike. I found that once the grade drops to 3 or 4% that it's simply too shallow of a grade to get an effective "vertical feet / minute" type number. But from 5% up to about 12%, I found my readings remain remarkably steady at around 3,000 / minute (for a hard but sustainable effort).
KevinF is offline  
Old 06-06-05, 10:58 AM
  #5  
TheKillerPenguin
Nonsense
Thread Starter
 
TheKillerPenguin's Avatar
 
Join Date: Sep 2004
Location: Vagabond
Posts: 13,575

Bikes: Affirmative

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 700 Post(s)
Likes: 0
Liked 23 Times in 10 Posts
It must plateau at some point, like you guys suggest. I would think anything too shallow would take too long horizontally to climb effectively, but in theory at least, wouldn't climb rate stay steady above, say, 5-6%? Since the grade is steep enough so that overcoming horizontal distances isn't a problem, I'd think that most power would be going into gaining vertical distance, and provided your power remains constant, that should mean a static climbing rate no matter the grade.
TheKillerPenguin is offline  
Old 06-06-05, 11:01 AM
  #6  
kandnhome
Unemplawyer
 
Join Date: Aug 2004
Location: The Natural State
Posts: 459

Bikes: 2006 21" Rockhopper

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
This is interesting, so I did some calculations with the help of the kreuzotter calculator.

At 6% grade, a 5000ft/hr climbing rate yields 16mph up that grade for 1hr.

At 10% grade, the same climbing rate yields ~9.5mph over the same hour.

At 15% grade, the same climbing rate yields ~6mph over the hour climb.

As a comparative tool, I calculated the wattages for an "average" cyclist: 165lbs, 5'10", and again for a "hoss" like myself: 6'2", 220bs.

avg cyclist:
6% grade @16mph: 469 watts
10% @9.5mph: 396 watts
15% @6mph: 356 watts

hoss:
6% : 596 watts
10% : 510 watts
15% : 461 watts

So, the avg cyclist sees 16% drop in required wattage output between 6% grade and 10% grade at the same climbing rate, and an 11% drop from 10% to 15%.

The Hoss sees a drop of ~14% from 6% to 10%, and a drop of 10% from 10%to 15%. Pretty close to the avg cyclist.

So this raises another question: given a certain wattage output for the hour, can the same rider achieve different climbing rates (ft/hr) on different grades? Gonzo Bob says his calculations at analyticcycing.com show 8-10% to be the best for climbing rate, so we'll test the 10% slope at the wattage output for the 6% grade (469W for the avg cyclist, 596W for the hoss):

Avg cyclist @ 469W on a 10% slope: 11.1mph, for a 5860ft/hr climbing rate
same cyclist @ same W on a 15% slope: 6177ft/hr climbing rate (hmm...)

Hoss @ 596W on a 10% slope: 11.0mph, 5808ft/hr climbing rate (note: 600W for an hour sounds pretty impossible to me, i don't know)
Hoss @ same W on 15% slope: 7.7mph, 6098ft/hr climbing rate.


Now, what the hell all of this means, I leave to someone else (I've been up for close to 40 hours now -- don't ask), but there are a few of the relationships between climbing rate and % grade.

Have fun.
kandnhome is offline  
Old 06-06-05, 11:05 AM
  #7  
my58vw
Meow!
 
my58vw's Avatar
 
Join Date: Sep 2004
Location: Riverside, California
Posts: 6,025

Bikes: Trek 2100 Road Bike, Full DA10, Cervelo P2K TT bike, Full DA10, Giant Boulder Steel Commuter

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
At a given power rate (wattage) you will climb at a certain feet/hour, no matter the grade. This does not change between differences in grade, etc. Now there will come a point where you can not develop enough wattage to be able to climb the hill (i.e. falling backwards) which for me occurs at hills greater than 15% incline.

10% at 8 MPH vs say 6% at 14 MPH, you are going the same vertical distance, but just covering less ground...
__________________
Just your average club rider... :)
my58vw is offline  
Old 06-06-05, 11:06 AM
  #8  
TheKillerPenguin
Nonsense
Thread Starter
 
TheKillerPenguin's Avatar
 
Join Date: Sep 2004
Location: Vagabond
Posts: 13,575

Bikes: Affirmative

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 700 Post(s)
Likes: 0
Liked 23 Times in 10 Posts
Wow, thanks for the data!

So this means that since climbing rates actually drop off at higher grades, that for some reason riders lose wattage going up these climbs. Wonder why that is?
TheKillerPenguin is offline  
Old 06-06-05, 11:12 AM
  #9  
kandnhome
Unemplawyer
 
Join Date: Aug 2004
Location: The Natural State
Posts: 459

Bikes: 2006 21" Rockhopper

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by my58vw
At a given power rate (wattage) you will climb at a certain feet/hour, no matter the grade. This does not change between differences in grade, etc. Now there will come a point where you can not develop enough wattage to be able to climb the hill (i.e. falling backwards) which for me occurs at hills greater than 15% incline.

10% at 8 MPH vs say 6% at 14 MPH, you are going the same vertical distance, but just covering less ground...

Actually, and I think the calculations I did above reflect this: if you are going 16mph at 6% grade to have the same climbing rate as you would going 9.5mph at 10% grade, you are expending more watts. The confounding variable I think you are leaving out of the equation is wind resistance (as speed decreases, so does the resistance, but geometrically as opposed to linear), so as you head up hill (and your speed decreases), more of your wattage is being converted to the vertical component vector, as less is being robbed by the horizontal (wind) component vector. I think that's the trend reflected by the increasing climb rates as slope increases, and the decreased wattage requirements as slope increases given a constant wattage.
kandnhome is offline  
Old 06-06-05, 11:16 AM
  #10  
kandnhome
Unemplawyer
 
Join Date: Aug 2004
Location: The Natural State
Posts: 459

Bikes: 2006 21" Rockhopper

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by PenguinDeD
Wow, thanks for the data!

So this means that since climbing rates actually drop off at higher grades, that for some reason riders lose wattage going up these climbs. Wonder why that is?
As I kind of postulated in my response to my58vw, I think the inverse is true; climbing rates increase directly proportional to %grade, and wattage requirements drop due to the speed decrease. The removal of the drag vector increases the efficiency of the translation of power to movement, yielding higher climbing rates. However, I'm presupposing that the kreuzotter calculator accurately accounts for the gravity vector, and its changing direction as slope increases.
kandnhome is offline  
Old 06-06-05, 11:26 AM
  #11  
my58vw
Meow!
 
my58vw's Avatar
 
Join Date: Sep 2004
Location: Riverside, California
Posts: 6,025

Bikes: Trek 2100 Road Bike, Full DA10, Cervelo P2K TT bike, Full DA10, Giant Boulder Steel Commuter

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by kandnhome
As I kind of postulated in my response to my58vw, I think the inverse is true; climbing rates increase directly proportional to %grade, and wattage requirements drop due to the speed decrease. The removal of the drag vector increases the efficiency of the translation of power to movement, yielding higher climbing rates. However, I'm presupposing that the kreuzotter calculator accurately accounts for the gravity vector, and its changing direction as slope increases.
That can not be true either...

At typical climbing speeds wind resistance is not nelgable but is not such a big factor... why do you think there are very few pacelines up steep hills (unless you are a pro)? Think about this... to climb faster you must counteract the forces going down the hill... i.e. gravity at a different rate. The force vector for gravity does not change but the direction of the rider does and the percentage of the gravity vector that is in the same direction and the riders travels increases as he goes steeper... in laymans terms it is harder to climb steeper hills.

You use more wattage to climb at the same speed up a steeper hill at the same speed. Our speed drops on long hills because if you are riding at lactic treshold you are not going to produce any more watts, so you slow down. We can get alot more complicated than this (I spend a whole quarter studying dynamics and wind resistance computer aid calculations) but the basics are at climbing speeds you end up with approx. the same elevation change for each hill with simular methods...

Now if you sprint up the hill or go anaerobic, etc, things will change but we are talking a nice steady multiminute climb.
__________________
Just your average club rider... :)
my58vw is offline  
Old 06-06-05, 11:53 AM
  #12  
kandnhome
Unemplawyer
 
Join Date: Aug 2004
Location: The Natural State
Posts: 459

Bikes: 2006 21" Rockhopper

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by my58vw
That can not be true either...

At typical climbing speeds wind resistance is not nelgable but is not such a big factor... why do you think there are very few pacelines up steep hills (unless you are a pro)? Think about this... to climb faster you must counteract the forces going down the hill... i.e. gravity at a different rate. The force vector for gravity does not change but the direction of the rider does and the percentage of the gravity vector that is in the same direction and the riders travels increases as he goes steeper... in laymans terms it is harder to climb steeper hills.

You use more wattage to climb at the same speed up a steeper hill at the same speed. Our speed drops on long hills because if you are riding at lactic treshold you are not going to produce any more watts, so you slow down. We can get alot more complicated than this (I spend a whole quarter studying dynamics and wind resistance computer aid calculations) but the basics are at climbing speeds you end up with approx. the same elevation change for each hill with simular methods...

Now if you sprint up the hill or go anaerobic, etc, things will change but we are talking a nice steady multiminute climb.
I took a couple years of calculus and physics classes during my undergrad stuff, but that was years ago, so sorry if I'm not making sense

I understand what you're saying about gravity: as the slope increases, the angle at which the force of gravity is exerted more closely approaches the opposite of the direction of forward movement (riding straight up a wall is the extreme of this trend, as gravity is working 100% against the direction of forward movement). This is what slows you down, and why a given wattage at a steeper slope yields less speed; but we're not talking about speed here, we're talking about climbing rate, which is just the vertical component of the speed vector [edit: to be more precise, I mean velocity, as speed is a directionless vector]. I'd have to get into a bunch of trigonometry to really explain this, so please excuse me for not doing it. I can't remember it that well.

At a given wattage, as I've shown above, your speed will decrease as slope increases (6%=16mph, 10% (at same wattage)= 11mph). However, at that given wattage, your climbing rate will increase as slope increases, precisely because speed decreases. The rate of increase of the (component) force of gravity (as slope increases) is less than the rate of increase of the force of wind resistance (as speed increases). [an example of this can be seen at analyticcycling.com's site, under "Forces on Rider by Source" using default rider/bike/etc variable values]. For example, the force of gravity roughly triples going from a 3% grade to a 10% grade, while the force of the wind resistance caused by doubling one's speed from 18km/h to 36km/h increases by a factor of about 5.

Last edited by kandnhome; 06-06-05 at 12:01 PM.
kandnhome is offline  
Old 06-06-05, 12:18 PM
  #13  
Brillig
Bananaed
 
Brillig's Avatar
 
Join Date: Feb 2003
Location: Philly-ish
Posts: 6,426

Bikes: 2001 Lemond Nevada City (only the frame remains)

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by KevinF
I found my readings remain remarkably steady at around 3,000 / minute (for a hard but sustainable effort).
3000 feet per minute?

Gentlemen, we have our next Tour de France winner here.
__________________
If once a man indulges himself in murder, very soon he comes to think little of robbing; and from robbing he comes next to drinking and Sabbath-breaking, and from that to incivility and procrastination.
- Thomas De Quincey
Brillig is offline  
Old 06-06-05, 12:43 PM
  #14  
my58vw
Meow!
 
my58vw's Avatar
 
Join Date: Sep 2004
Location: Riverside, California
Posts: 6,025

Bikes: Trek 2100 Road Bike, Full DA10, Cervelo P2K TT bike, Full DA10, Giant Boulder Steel Commuter

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
I guess what we have to look at is if the component of gravity and compare it to wind resistance which is greater at the same wattage.

There are so many factors to discuss here... not just wind resistance and gravity... just take a moment and think of friction, slope of the road, even little things like temperature, wind itself etc. For example on my Sierra Climb for the first .2 miles there is always a nasty crosswind coming off the "mountain" as you go through it. After you are sheltered by the hills you can use more power to overcome the hill vs the wind. There are so many factors...
__________________
Just your average club rider... :)
my58vw is offline  
Old 06-06-05, 02:52 PM
  #15  
TheKillerPenguin
Nonsense
Thread Starter
 
TheKillerPenguin's Avatar
 
Join Date: Sep 2004
Location: Vagabond
Posts: 13,575

Bikes: Affirmative

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 700 Post(s)
Likes: 0
Liked 23 Times in 10 Posts
Yeah, but I was assuming all things (including power output) were constant.

What's weird is on a 9% grade I climb at about 4000ft/hr, and on a 11-12% grade it falls sharply to 3400ft/hr. That's a pretty dramatic drop in climbing rate, and something's gotta account for it.

Unless I was just having a bad day, which could be too.
TheKillerPenguin is offline  
Old 06-06-05, 04:20 PM
  #16  
Stealthman_1
12 2005 DC Finishes
 
Join Date: Oct 2003
Location: Folsom, Ca
Posts: 455

Bikes: 1998 Cannondale V1000, 2001 Specialized Sirrus Pro, 2004 De Rosa King

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
The gravity vector is inconsiquential as compared to the decreased wind resistance at low angles of climb (<20%). Gravity is always linear and wind is what squared (?), however at some point, without gearing to offset the changes, the extra wattage available due to decreased wind resistance will not overcome the increased wattage required to overcome gravity. It looks like this happens around 25 to 30% for an average cyclist. 10 to 20 % grade is only a 5 degree change in angle from an initial 5 degree angle. Pull out a protractor (do they still exist?? ) and tell me how much an effect gravity is here. Switch directions in just a 5 mph wind and the effect is very noticable. The friction component should be negligible for this excersize up to probably 75 degrees (WAG). Provided you had the gearing you could climb anything.
Stealthman_1 is offline  
Old 06-06-05, 04:28 PM
  #17  
KevinF
Keep on climbing
 
Join Date: Apr 2004
Location: Marlborough, Massachusetts
Posts: 2,179

Bikes: 2004 Calfee Tetra Pro

Mentioned: 1 Post(s)
Tagged: 0 Thread(s)
Quoted: 21 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by Brillig
3000 feet per minute?

Gentlemen, we have our next Tour de France winner here.
AIGH! Minutes, hours... I was never all that good with that "time" concept.
KevinF is offline  
Old 06-06-05, 06:41 PM
  #18  
Gonzo Bob
cycles per second
 
Gonzo Bob's Avatar
 
Join Date: Oct 2003
Location: Minnesota
Posts: 1,790

Bikes: Vitus Aluminum, DiamondBack Apex, Softride Powerwing 700, "Generic" Ishiwata 022, Trek OCLV 110

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 2 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by my58vw
At a given power rate (wattage) you will climb at a certain feet/hour, no matter the grade. This does not change between differences in grade, etc.
I disagree. With shallow grades, the speeds will be higher and more of your watts will go to fighting air resistance rather than increasing your elevation. Take the example of a 1% grade vs a 10% grade. To climb 1000m with a 1% grade, you have to ride 100km. For a 10% grade, you have to ride only 10km. You can't ride 10 times faster up a 1% grade than up a 10% grade so your climb rate will be lower on the 1% grade.
Gonzo Bob is offline  
Old 06-06-05, 06:57 PM
  #19  
fujiacerider
Senior Member
 
Join Date: Sep 2003
Posts: 524
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
my58IQ,
I almost congratulated you on making a worthwhile post, as you at least seem to be following the conversation, if nothing else. However, your horrendous grammar once again made an appearance. No congrats for you.

Cole
fujiacerider is offline  
Old 06-06-05, 07:34 PM
  #20  
boyze
Senior Member
 
Join Date: Sep 2004
Posts: 328
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by PenguinDeD
Yeah, but I was assuming all things (including power output) were constant.

What's weird is on a 9% grade I climb at about 4000ft/hr, and on a 11-12% grade it falls sharply to 3400ft/hr. That's a pretty dramatic drop in climbing rate, and something's gotta account for it.

Unless I was just having a bad day, which could be too.
I think it works out. At 9% and 4000/hr and assuming the majority of the resistance is gravity and you maintain a constant engine wattage the 11% climb would simply be (9/11)*4000=3273
boyze is offline  
Old 06-06-05, 07:36 PM
  #21  
TheKillerPenguin
Nonsense
Thread Starter
 
TheKillerPenguin's Avatar
 
Join Date: Sep 2004
Location: Vagabond
Posts: 13,575

Bikes: Affirmative

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 700 Post(s)
Likes: 0
Liked 23 Times in 10 Posts
Originally Posted by Stealthman_1
The gravity vector is inconsiquential as compared to the decreased wind resistance at low angles of climb (<20%). Gravity is always linear and wind is what squared (?), however at some point, without gearing to offset the changes, the extra wattage available due to decreased wind resistance will not overcome the increased wattage required to overcome gravity. It looks like this happens around 25 to 30% for an average cyclist. 10 to 20 % grade is only a 5 degree change in angle from an initial 5 degree angle. Pull out a protractor (do they still exist?? ) and tell me how much an effect gravity is here. Switch directions in just a 5 mph wind and the effect is very noticable. The friction component should be negligible for this excersize up to probably 75 degrees (WAG). Provided you had the gearing you could climb anything.
Yes, wind is squared, gravity is linear. So what you are saying is that climbing rate should plateau until the gearing of the bike runs out?

Another factor that VW brought up but didn't expand upon is the influence of the body on climbing, as in a person's LT and aerobic capabilities and how they affect the plateau. It would seem to me that given one is sitting, eventually if one's LT isn't well developed, the plateau will not extend to steeper grades, IE one's climbing rate will drop off.

So the consensus so far is as follows:
-shallower grades require more Wattage to climb at the same rate as higher grades, due to wind resistance
-as a grade becomes steeper, speed decreases, and therefore so does wind resistance, freeing up more watts for climbing. This is where one's peak climbing rate will be located
-eventually, the gearing of a bike runs out, and because of that the plateau drops.

There are still some unanswered questions though (unless I missed something), and this is the one I'm most confused about.
Originally Posted by kandnhome
Avg cyclist @ 469W on a 10% slope: 11.1mph, for a 5860ft/hr climbing rate
same cyclist @ same W on a 15% slope: 6177ft/hr climbing rate (hmm...)
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?
TheKillerPenguin is offline  
Old 06-06-05, 07:38 PM
  #22  
kandnhome
Unemplawyer
 
Join Date: Aug 2004
Location: The Natural State
Posts: 459

Bikes: 2006 21" Rockhopper

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by fujiacerider
my58IQ,
I almost congratulated you on making a worthwhile post, as you at least seem to be following the conversation, if nothing else. However, your horrendous grammar once again made an appearance. No congrats for you.

Cole

fujiacerider, you make a characteristically uncalled-for personal attack, and contribute nothing to this thread. If I had my way, there'd be nothing for you, or those like you. No air, no space, no life. Useless.

Back on topic: Very good, simple illustration of the point I was trying to make Gonzo Bob.
kandnhome is offline  
Old 06-06-05, 07:39 PM
  #23  
TheKillerPenguin
Nonsense
Thread Starter
 
TheKillerPenguin's Avatar
 
Join Date: Sep 2004
Location: Vagabond
Posts: 13,575

Bikes: Affirmative

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 700 Post(s)
Likes: 0
Liked 23 Times in 10 Posts
Originally Posted by boyze
I think it works out. At 9% and 4000/hr and assuming the majority of the resistance is gravity and you maintain a constant engine wattage the 11% climb would simply be (9/11)*4000=3273
i'm so confused. Is the answer really that simple?!
TheKillerPenguin is offline  
Old 06-06-05, 08:03 PM
  #24  
kandnhome
Unemplawyer
 
Join Date: Aug 2004
Location: The Natural State
Posts: 459

Bikes: 2006 21" Rockhopper

Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
Originally Posted by PenguinDeD
i'm so confused. Is the answer really that simple?!
I don't think so. I think this is just some convenient mathematical coincidence. Here's a question for boyze: why isn't the ratio 11/9 for 4888ft/hr? How did you arrive at the 9%/11% * climbing rate (at 9%) formula?

At 9% grade, every 100ft forward = 9ft up; 4000ft up in 1 hour = 44444 ft forward / 5280 ft = 8.417mph

At 11% grade, every 100ft forward = 11ft up; 4000ft up in 1 hour = 36363 ft forward / 5280 ft = 6.887 mph

For a 165lb rider + 20lb bike, 8.417mph up a 9% grade requires 316 watts. That same rider + bike at 6.887mph up an 11% grade requires 308 watts.

So, given boyze's assumption of constant wattage, the climb rate up the 11% slope MUST be faster than that up the 9% slope, because less wattage is expended going up the steeper slope at the exact same climb rate.

Boyze also decided to neglect the force of gravity as constant between the two slopes (it's not, but as Stealthman pointed out, the force of gravity opposite the direction of forward movement at these slopes is negligible). If the force of gravity were constant between the two slopes, the wattage requirement for the above calculations for the 11% slope would be even smaller, because the Kreuzotter site (where I got those wattage numbers from) does account for gravity.

So, sorry PenguinDeD, no, I don't think it's that simple.


edit/update: I was just sitting around thinking about what would account for all the anecdotal data of decreased climb rates at more severe slopes despite the theoretical data indicating increasing climb rates at more severe slopes, and a little light went on: as slope increases, body position on the bike changes, altering geometry of pedal stroke (and accordingly the muscles used to effect the pedal stroke), and also (possibly-not certain here) altering the range over which force can be applied to the pedal (the effective pedaling range). On flat ground the effective pedaling range (discounting the relatively small force from pulling up/back on the pedals on the backside of the stroke) is somewhat less than 180 degrees, probably closer to 140 or 160 or so; as you move around on the bike up a slope, that effective pedaling range may be decreased even further.

The sum of these altered geometries may mean 1) less power can be delivered as compared to flatter ground because of the use of other (smaller/weaker/less trained) muscles, and the decreased use of the bigger/stronger/more trained muscles; and 2) the power must be delivered over a shorter effective range, leaving the average wattage output over the entire pedal stroke the same, but the peak wattage output through the arc of the shorter pedaling range higher, forcing riders to back off to lower wattages to avoid crossing into anaerobic activity.

Just some thoughts, maybe way off.

Last edited by kandnhome; 06-06-05 at 08:32 PM.
kandnhome is offline  
Old 06-06-05, 08:27 PM
  #25  
eccccyclsm
Junior Member
 
Join Date: May 2005
Posts: 18
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)
Likes: 0
Liked 0 Times in 0 Posts
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?
eccccyclsm is offline  

Thread Tools
Search this Thread

Contact Us - Archive - Advertising - Cookie Policy - Privacy Statement - Terms of Service

Copyright © 2018 MH Sub I, LLC dba Internet Brands. All rights reserved. Use of this site indicates your consent to the Terms of Use.