A question on climbing

Columbia said:

Okay, bear with me, I'm having trouble putting this into words 🙂

If two riders have different power and weight but have the same power/weight ratio does one have an advantage over the other on different gradients?

Lets assume two riders:
Rider A: 70 kilograms - 280 watts
Rider B: 50 kilograms - 200 watts

So both riders have a ratio of 4 watts for every kilo of body weight.

We'll assume that both riders bikes are weightless 😄 .

On a climb of just 2% would Rider A have an advantage because of his greater power output? I'm really only guessing that weight makes less of a difference on easier climbs.

And on a 10% climb would Rider B have an advantage due to him being lighter. Again, I'm presuming that as a climb gets steeper a riders weight matters more and more.

Provided the riders both have the same power to weight ration they wil both climb the same climb at the same speed. It is not weight or power but the combination of the two that matters in climbing.
Of course I would rather be the heavier more powerful rider since I'd be able to ride away from the lighter guy at the top, down the other side and on the flat.

tafi said:

Provided the riders both have the same power to weight ration they wil both climb the same climb at the same speed. It is not weight or power but the combination of the two that matters in climbing.
Of course I would rather be the heavier more powerful rider since I'd be able to ride away from the lighter guy at the top, down the other side and on the flat.

It's not quite as simple as that... (never is) If you get a hold of a copy of Performance Cycling (google it, I can't remember the author's name right now) you'll find the equations governing the force balance (power at crank = power to overcome aerodynamic drag + power to overcome rolling resistance + power to change height). Obviously in certain cases one or other of the right hand side terms can become more or less significant. E.g on the flat there is no power required to change height, so it is a mixture between rolling resistance and aero drag.

For your rider A (70kg, 280 watts) this results in an approx speed of 21.2 mph versus rider B (50kg, 200 watts) at 19.2mph. (assuming a coefficient of drag that is the same between the two riders, amongst other assumptions). The ratio of aero-drag:rolling-resistance is about 3:1...

Tilting the road will change things!
At 2% gradient, rider A is now putting a majority of his power into overcoming the influence of gravity (39%) versus aero (37%) and rolling resistance (24%) to maintain 17.1mph . The numbers for rider B are 37%, 42% and 22% @ 15.9 mph respectively. All is not created equal.

Above some angle (about 13%!) the two riders' speeds converge (are equal) as about 90%(!) of power is used to overcome gravity.

Anyway, the calcs are all from a megaspreadsheet I put together, but the equations are all in the book (you just need to solve them. Hint: you need to iterate a solution using Newton-Raphson or similar)

Just for fun I plugged in some numbers from the Alpe D'Huez TT - Lance must have averaged just over 500 watts in his 39:41 effort... Woah!!!!

merubeyurubu said:

It's not quite as simple as that... (never is) If you get a hold of a copy of Performance Cycling (google it, I can't remember the author's name right now) you'll find the equations governing the force balance (power at crank = power to overcome aerodynamic drag + power to overcome rolling resistance + power to change height). Obviously in certain cases one or other of the right hand side terms can become more or less significant. E.g on the flat there is no power required to change height, so it is a mixture between rolling resistance and aero drag.

For your rider A (70kg, 280 watts) this results in an approx speed of 21.2 mph versus rider B (50kg, 200 watts) at 19.2mph. (assuming a coefficient of drag that is the same between the two riders, amongst other assumptions). The ratio of aero-drag:rolling-resistance is about 3:1...

Tilting the road will change things!
At 2% gradient, rider A is now putting a majority of his power into overcoming the influence of gravity (39%) versus aero (37%) and rolling resistance (24%) to maintain 17.1mph . The numbers for rider B are 37%, 42% and 22% @ 15.9 mph respectively. All is not created equal.

Above some angle (about 13%!) the two riders' speeds converge (are equal) as about 90%(!) of power is used to overcome gravity.

Anyway, the calcs are all from a megaspreadsheet I put together, but the equations are all in the book (you just need to solve them. Hint: you need to iterate a solution using Newton-Raphson or similar)

Just for fun I plugged in some numbers from the Alpe D'Huez TT - Lance must have averaged just over 500 watts in his 39:41 effort... Woah!!!!

Another factor which is perhaps smaller than the difference you mention on the flats but which is a consideration nonetheless is heat dissipation versus height. Imagine first the 70 kg rider being 5 ft tall (152 cm). Now imagine the 70 kg rider being 6 ft tall (183 cm). As a 5 footer, his skin surface area is going to be smaller than it will be as a 6 footer at the same weight. His average limb and trunk thickness will be greater as a result. Therefore, he will have a reduced capacity to dissipate heat compared to the taller but same weight rider. This will make the most difference at the steepest climbs where wind resistance is not a factor and heat convection is minimized.

I think Eddy Merckx' fanaticism about keeping his weight down helped him most by allowing him to stay much cooler than he would have otherwise.

If you hold power output the same, of course they will both ride at virtually the same speed. It's just that when you consider that power output is also a function of heat dissipation, it will not hold constant. If you overheat, you will slow down and so will your power output. The same rider will ride slower when overheated even though he is capable of maintaining if his temperature does not escalate.

Jeez, I'm usually scientificaly minded, but man, I've had to read these last couple of posts 3 times to get the drift. 🙂

So, basically (and this is what I gathered so if I got this wrong please tell me) my presumtion was correct, but it has to get very steep (+13%) for the smaller guy to get his advantage?

Columbia said:

Jeez, I'm usually scientificaly minded, but man, I've had to read these last couple of posts 3 times to get the drift. 🙂

So, basically (and this is what I gathered so if I got this wrong please tell me) my presumtion was correct, but it has to get very steep (+13%) for the smaller guy to get his advantage?

Correct! The extra power number for rider A will be an advantage on teh flat and a decreasing advantage uphill as the slope increases... until an angle is reached where there is no more advantage. At that point (13% in your case) the identical power/weight ratio mean they'll both climb at the same speed.

merubeyurubu said:

It's not quite as simple as that... (never is) If you get a hold of a copy of Performance Cycling (google it, I can't remember the author's name right now) you'll find the equations governing the force balance (power at crank = power to overcome aerodynamic drag + power to overcome rolling resistance + power to change height). Obviously in certain cases one or other of the right hand side terms can become more or less significant. E.g on the flat there is no power required to change height, so it is a mixture between rolling resistance and aero drag.

For your rider A (70kg, 280 watts) this results in an approx speed of 21.2 mph versus rider B (50kg, 200 watts) at 19.2mph. (assuming a coefficient of drag that is the same between the two riders, amongst other assumptions). The ratio of aero-drag:rolling-resistance is about 3:1...

Tilting the road will change things!
At 2% gradient, rider A is now putting a majority of his power into overcoming the influence of gravity (39%) versus aero (37%) and rolling resistance (24%) to maintain 17.1mph . The numbers for rider B are 37%, 42% and 22% @ 15.9 mph respectively. All is not created equal.

Above some angle (about 13%!) the two riders' speeds converge (are equal) as about 90%(!) of power is used to overcome gravity.

Anyway, the calcs are all from a megaspreadsheet I put together, but the equations are all in the book (you just need to solve them. Hint: you need to iterate a solution using Newton-Raphson or similar)

Just for fun I plugged in some numbers from the Alpe D'Huez TT - Lance must have averaged just over 500 watts in his 39:41 effort... Woah!!!!

The question was about climbing speed for two riders with the same power to weight ratio. You cannot quantify air resistance since you don't know what height width or position they have and you can't quantify rolling resistance since you don't know the tyres and pressures that each is using. They could easily have the same aerodynamic properties but be at different weights, you can't tell that from the question.
It is a simple power to weight question and you only need simple newtonian mechanics to solve it.

tafi said:

The question was about climbing speed for two riders with the same power to weight ratio.

and was answered with this in mind...

tafi said:

You cannot quantify air resistance since you don't know what height width or position they have and you can't quantify rolling resistance since you don't know the tyres and pressures that each is using. They could easily have the same aerodynamic properties but be at different weights, you can't tell that from the question.

Yes, but you can certainly make ASSUMPTIONS rather than IGNORING the aero effects. As has been discussed, the relative contributions of the aero and gravitational factors CHANGE as the incline changes, so ignoring the aero effect is out and out misleading.
The assumption that the frontal area and coefficient of drag of the two riders is the same is not a bad one... certainly much better than ignoring it.

tafi said:

It is a simple power to weight question and you only need simple newtonian mechanics to solve it.

... however, ignoring important terms in these simple mechanics is not going to help your case.

The conclusions to draw:
- on the flat, the higher power rider A has the advantage (assuming their aero position is similar to that of rider B)
- on the easy inclines, rider A still will climb FASTER
- at some level of incline (13% in this case), speeds will drop such at aero effects are insiginificnat with respect to power to overcome gravity, thus the twe riders will then climb at the same speed.

Oh, so the lighter rider wont have any advantage, even at gradients over 13%.

Thank you for answering that, merubeyurubu. 🙂

Columbia said:

Oh, so the lighter rider wont have any advantage, even at gradients over 13%.

Thank you for answering that, merubeyurubu. 🙂

Yep, at that power/weight level. So, rider B needs to work on power!! 😉

tafi said:

Of course I would rather be the heavier more powerful rider since I'd be able to ride away from the lighter guy at the top, down the other side and on the flat.

But you're assuming he's more powerful because of his wattage output. What if the higher wattage rider is putting out more power because he has to, and the lower wattage rider is putting out less power because he doesn't have to? Who said both riders are putting out 100%? 😉

I think I would rather be the lighter rider, because over a long, long ride, I would be conserving energy on all the climbs, so I wouldn't bonk as soon. Besides, you can ride more and get stronger, buy you can't always lose weight.

Interesting thread .. but lets keep this simple .. bcs there is no such thing as a linear power curve for a cyclist .. (and for engine) .. are we talking of Max sustainable power output without getting in the blowout zone or average output.. ???

Just a comment .. did not want to discredit what was said.

Cheers

Columbia said:

Oh, so the lighter rider wont have any advantage, even at gradients over 13%.

Thank you for answering that, merubeyurubu. 🙂

Sticking with the Newtonian calc's, the lighter guy will still have an advantage, because he will be able to accelerate away from the bigger guy. The mass comes in twice - once in terms of the gravitational force you have to overcome, but again because acceleration is net force/mass. Once they both settle back to a steady pace, the little guy will stay ahead.

Columbia said:

Oh, so the lighter rider wont have any advantage, even at gradients over 13%.

Thank you for answering that, merubeyurubu. 🙂

Is this actually correct for any distance? I could be wrong but I believe that the lighter rider will gain advantage as the distance increases beyond a certain point. this is partially because taxing the muscular system will give out much sooner than taxing the cardiovascular system. Am I wrong on this?

There are no massive monkeys in those marathon runners' rank. How does that translate into cycling? With those long stage races, the sprinters seemed to do pretty well after 250km of flat stage. Could it all be explained by the energy savings through drafting in cycling?

rob of the og said:

Sticking with the Newtonian calc's, the lighter guy will still have an advantage, because he will be able to accelerate away from the bigger guy. The mass comes in twice - once in terms of the gravitational force you have to overcome, but again because acceleration is net force/mass. Once they both settle back to a steady pace, the little guy will stay ahead.

No, they have the same power to weight, same acceleration.

11ring said:

No, they have the same power to weight, same acceleration.

how about the 'ability to take a whole lot of suffering' factor?

the mind, imo, overcomes much more 'if' given the will and chance!

the OP is right.. if he's still around he posted in 2004...

on the 2% hill the larger rider will have an advantage and on the steeper climb the lighter rider will have an advantage... but not because of there weight.

on the 2% hill speed will be faster and aerodynamics will be more important roll (power to frontal area is relatively more significant than power to weight on the 2% climb)

larger riders have a better relative ratio of power to frontal area than smaller guys.. mass or volume goes up as the cube but frontal area is only going up as the square... think of the riders as cubes:
small rider: 2x2x2, density of 1, power : weigth of 4 --> small rider has a mass of 8, frontal area of 4, power = 32 --> power : frontal area = 8
larger rider: 4x4x4, density of 1, power : weigth of 4 --> larger rider has a mass of 64, frontal area of 16, power = 256 --> power : frontal area = 16

these number are obviously more extreme to demonstrate the effect... and doesn't take into consideration the length of the hills were anarobic capacity could play a huge role and nullify all of this on short hills (e.g. Boonen on 1-2 km cobbled climbs)... but on longer hills probably at least 5 kms+ the smaller rider will have a relative advantage the steeper the pitch of the climb because the steeper the climb the slower the speed and the more power to weight matters in relation to frontal area to weight...