# Hill climbing speeds



## flanman (Jul 7, 2006)

Let's say that I can average about 11 mph on a 7% gradient. What speed should I expect on a 9% or a 5%? Is thare a good rule of thumb or equation?


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## Mark McM (Jun 18, 2005)

*General rule of thumb*



flanman said:


> Let's say that I can average about 11 mph on a 7% gradient. What speed should I expect on a 9% or a 5%? Is thare a good rule of thumb or equation?


At climbing speeds, air resistance and rolling resistance are minimized, and the majority of your power goes to lifting your mass up the hill. Power is defined as force times velocity, so when working against the force of gravity (a vertical force), your vertical velocity will be roughly proportional to your power divided by your gravitation force (weight).

Percent grade is defined as rise over run, so vertical velocity is equal to horizontal velocity times percent grade. At type climbing grades, your velocity up the grade (the tangent of the angle) is very close to your horizontal velocity, so you can use your ground speed for the horizontal speed.

So, if you are going 11 mph up a 7% grade, your vertical velocity is (11 mph) x (0.07) = 0.77 mph. This vertical speed will remain roughly constant at different grades for the same power output (if you know your total weight, you can also calculate the power from the weight times the vertical velocity.) To figure out the horizontal speed at different grades, you just have to divide the vertical velocity by the percent grade. So, on a 9% grade you'd be going (0.77 mph) / 0.09 = 8.55 mph, and on a 5% grade you'd be going (0.77 mph) / 0.05 = 15.4 mph.

Of course, there are other factors and variables that will affect the actual speed, but gravity, weight and power are the predominant variables, so you can get a pretty good estimate by setting power output to weight x vertical velocity.


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## Fixed (May 12, 2005)

*better*



flanman said:


> Let's say that I can average about 11 mph on a 7% gradient. What speed should I expect on a 9% or a 5%? Is thare a good rule of thumb or equation?


better than a rule of thumb: www.analyticcycling.com Have fun!


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## GearDaddy (Apr 1, 2004)

*Here's a formula*

Someone once posted an interesting formula that estimated power output in watts. It goes like this:

P = 2 * ( V * W ( .0053 + G/100 ) + .0083 V^3)
where: P = power (watts)
V = velocity (MPH)
W = weight (lbs.)
G = gradient (percentage)

The .0083 is a weighting factor that estimates resistence based on using a "normal" time trial setup.

So, 11 MPH up a 7% gradient with a weight estimate of 155 lbs using this formula would come out to about 415 watts (that's huge!). At 10 MPH it would come out to be about 350 watts.

Try out your numbers on this to see what sort of velocity gets you the same power output on different gradients.


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## Kerry Irons (Feb 25, 2002)

*Plugging and chugging*



GearDaddy said:


> So, 11 MPH up a 7% gradient with a weight estimate of 155 lbs using this formula would come out to about 415 watts (that's huge!). At 10 MPH it would come out to be about 350 watts.


I have no idea how you came up with 415 watts, because with the numbers you list, it's 280 watts at 11 mph.

To the OP, in this range of grade and speed, its about 1 mph for every 1% change in grade. So 9% grade is 2 mph slower, and 5% grade is 2 mph faster.


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## GearDaddy (Apr 1, 2004)

Kerry Irons said:


> I have no idea how you came up with 415 watts, because with the numbers you list, it's 280 watts at 11 mph.
> 
> To the OP, in this range of grade and speed, its about 1 mph for every 1% change in grade. So 9% grade is 2 mph slower, and 5% grade is 2 mph faster.


Ooops, you're right. I think I accidently used an 11% gradient instead of a 7% gradient. Anyway, the formula seems to give a pretty good estimate.


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## homebrew (Oct 28, 2004)

All these estimates factor a steady power output. Climbing a steeper grade requires a higher wattage according to my powertap just to keep moving. I can keep say 300 watts for X amount of time on a 7% grade but does not mean I can climb an 11% grade at 300 watts. I may go to 400 watts or more. I may have to get out of the saddle and may therefore reduce cadance. Increase grade also brings increased fatigue. IMO these estimates are very qustionable in the real world.


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## Fixed (May 12, 2005)

*gearing?*



homebrew said:


> All these estimates factor a steady power output. Climbing a steeper grade requires a higher wattage according to my powertap just to keep moving. I can keep say 300 watts for X amount of time on a 7% grade but does not mean I can climb an 11% grade at 300 watts. I may go to 400 watts or more. I may have to get out of the saddle and may therefore reduce cadance. Increase grade also brings increased fatigue. IMO these estimates are very qustionable in the real world.


My guess is that gearing matters. For any formula to work, I think it would have to assume the same efficiency at the various speeds and grades, which means having gears available so that you can have the same cadence for the same power at any given speed or grade. I know that my efficiency falls way off when I'm "geared out" or riding fixed gear. Now, that said, I'm not sure "power" (watts) goes up with steeper grades, but torque sure does, when standing and mashing. 

Part of your example may be the desire not to drop below a certain arbitrary speed, let's say 7 mph, for example, no matter the grade, so you apply disproportionate power as it gets steeper to stay above that speed. Seems to be so with me, anyway.


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## Dwayne Barry (Feb 16, 2003)

"For any formula to work, I think it would have to assume the same efficiency at the various speeds and grades, which means having gears available so that you can have the same cadence for the same power at any given speed or grade. I know that my efficiency falls way off when I'm "geared out" or riding fixed gear. Now, that said, I'm not sure "power" (watts) goes up with steeper grades, but torque sure does, when standing and mashing."

I don't think you mean "efficiency", as most studies of efficiency show just the opposite, i.e. cyclists retain their normal efficiency or even become more efficient as cadence drops below normal (or they show we become less efficient as cadence gets above ~100rpm). I think what you mean is that you can not maintain your typical power when cadence falls below your normal range?


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## Sub (Feb 13, 2004)

I would like to figure out how much power I average on a particular hill climb. That formula looks complicated...Hill is 3.25 miles, average gradient of 7.8% and I averaged 10.3 mph. I weigh 160 lbs and my bike is a tank, 19-20 lbs. Who wants to do the math? I've looked at analytical cycling but there isn't a setup to figure out power I don't think.


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## SilasCL (Jun 14, 2004)

Here's the formula for you: =2*(10.3*180*(0.0053+7.8/100)+0.0083*10.3^3)

327 watts is the number I get


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## Sub (Feb 13, 2004)

SilasCL said:


> Here's the formula for you: =2*(10.3*180*(0.0053+7.8/100)+0.0083*10.3^3)
> 
> 327 watts is the number I get



Not to bad i guess? Took me 18:39 which is 15 seconds off the known record on the climb. What is a good power to weight for a cat 3? This works out to 4.48 watts/kg.


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## Mark McM (Jun 18, 2005)

*Steeper grades don't require more power*



homebrew said:


> All these estimates factor a steady power output. Climbing a steeper grade requires a higher wattage according to my powertap just to keep moving. I can keep say 300 watts for X amount of time on a 7% grade but does not mean I can climb an 11% grade at 300 watts. I may go to 400 watts or more. I may have to get out of the saddle and may therefore reduce cadance. Increase grade also brings increased fatigue. IMO these estimates are very qustionable in the real world.


I don't think are looking at this correctly. There is no reason that you need more power to climb a steeper grade - you just go slower at the same power. If you find that you have to stomp on the pedals out of the saddle just to keep the pedals turning, it means that you are over-geared - not that you need more power. I've done the Mt. Washington Hill Climb several times (7.6 miles at an average 12% average grade), and I put out only about to 250 Watts to move 180 lb. of rider and bike up the hill. However, I do it in a very low gear (20x23) and move at a slow speed (5.5 mph).

By the way, this is what gearing is all about - matching a rider's power, pedal force and cadence to a particular grade. With very low gearing, you can climb very steep grades with only a small power output - you just go slower.


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## Mark McM (Jun 18, 2005)

*Analytic Cycling*



Sub said:


> I would like to figure out how much power I average on a particular hill climb. That formula looks complicated...Hill is 3.25 miles, average gradient of 7.8% and I averaged 10.3 mph. I weigh 160 lbs and my bike is a tank, 19-20 lbs. Who wants to do the math? I've looked at analytical cycling but there isn't a setup to figure out power I don't think.


On the Analytic Cycling web page, on the right panel click "Static Forces on Rider" and select "Power, give Speed".


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## bianchi77 (Jul 15, 2008)

what kind of training for improving the climbing capability ?
Is static bike training could help ? 
The indicator is the power that dissipated while trained using it..??


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## homebrew (Oct 28, 2004)

Best training for climbing is climbing. Once your base is well established try some hill sprints both seated and standing. Allow for plenty of recovery. Keep your bodyweight down but not to the point you drop power. Climbing is all power to weight and maybe 3% technique. I spend at least a week every spring up in the mountains near Boone NC. After riding in Boone everything else looks pretty flat.

This is an old post. I looking at my reply I will confirm that in my world yes, you do need more power to climb, just look at any rider after a long climb, they are hurting. Gears only do so much. Granted that 8% is not very steep but when the grades are double digit you will notice it more even without a power meter


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## bianchi77 (Jul 15, 2008)

homebrew said:


> Best training for climbing is climbing. Once your base is well established try some hill sprints both seated and standing. Allow for plenty of recovery. Keep your bodyweight down but not to the point you drop power. Climbing is all power to weight and maybe 3% technique. I spend at least a week every spring up in the mountains near Boone NC. After riding in Boone everything else looks pretty flat.
> 
> This is an old post. I looking at my reply I will confirm that in my world yes, you do need more power to climb, just look at any rider after a long climb, they are hurting. Gears only do so much. Granted that 8% is not very steep but when the grades are double digit you will notice it more even without a power meter


So the best train is climbing on the steepest mountain as possible..and get use to it..
Static bike can help too, can't it ?
Reduce my weight is also help, currently I'm 177cm 65 kg, should I reduce my weight ?


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## iliveonnitro (Feb 19, 2006)

Sub said:


> Not to bad i guess? Took me 18:39 which is 15 seconds off the known record on the climb. What is a good power to weight for a cat 3? This works out to 4.48 watts/kg.


That's really good. Like, really, really good.


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## Mr. Jones (Jul 4, 2006)

homebrew said:


> This is an old post. I looking at my reply I will confirm that in my world yes, you do need more power to climb, just look at any rider after a long climb, they are hurting. Gears only do so much. Granted that 8% is not very steep but when the grades are double digit you will notice it more even without a power meter


I think there are two different ways of looking at this. Gears will get you up the hill, you need improved power to go faster (at some point there is some minimum power to keep the bike upright, assuming you don't want a virtual trackstand). There are a lot of people here that are very content to say that they've gone up a famous climb, and have no desire to race up the climb. If you want to go faster, power is the only thing that is going to do it for you.


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## BassNBrew (Aug 4, 2008)

bianchi77 said:


> So the best train is climbing on the steepest mountain as possible..and get use to it..
> Static bike can help too, can't it ?
> Reduce my weight is also help, currently I'm 177cm 65 kg, should I reduce my weight ?


I'm going to disagree to an extent homebrew even though I love his choice of riding location. As he states, it's mostly about power to weight ratio. That can be built up anywhere including a trainer. The actual hill comes handy because it gives you a goal to shoot for and if you stop pedaling there are consequences. Riders from FLA and the Carolina coasts frequently do well at the Assualt on Mt. Mitchell w/o riding significant hills.

Regarding your weight question I've got two answers for you. 1) Only you can determine your ideal performance weight. How the heck can people on a messageboard answer this. 2) Assuming you're a chick, yes you need to lose wieght. Your ass looks big in that dress.


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