Charting Gravity's influence on Climbing?

[DirtyWorks]

Another modeling question: We as cyclists know that when climbing much of the effort goes to defeating gravity.

I'm looking for a chart something like the power/speed chart of defeating air resistance, except charting power on one axis and rise/run on the other axis.


I'm not a physics person, so I'm not sure how to search for such a graphic or table of data.

 

[Eshnar]

Another modeling question: We as cyclists know that when climbing much of the effort goes to defeating gravity.

I'm looking for a chart something like the power/speed chart of defeating air resistance, except charting power on one axis and rise/run on the other axis.


I'm not a physics person, so I'm not sure how to search for such a graphic or table of data.

not sure what you're asking exactly. If you want a Power/gradient graphic (which is what I understood), I think it wouldn't mean much, as the two are not straightforwardly correlated (force/gradient are correlated quite easily, but to convert force to power, you need to know the speed... so you should probably take a few token speeds. It can be done ofc, but not sure how valid it would be EDIT: or you could estimate the actual speed riders have while riding those gradients)

 

[JayKosta]

In most simple terms the grade doesn't matter - as long as wind drag is small enough to be ignored.

What is important is the amount of vertical rise, and the length of time it takes.

Do the same rise in 2x the time means that 1/2 of the power (watts) is needed.

Jay Kosta
Endwell NY USA

 

[DirtyWorks]

Eshnar,

All good questions. I'm looking for what percentage of power is used to defeat gravity at a given gradient.

I stumbled upon this very nice interactive model:http://www.gribble.org/cycling/power_v_speed.html

I can change gradient and the portion of a given speed that is dedicated to defeating gravity is nicely represented.

What it does graph nicely is all power for most cyclists goes to defeating gravity at a 6% incline. The model agrees with my limited calculations of my own performance on nearly flat course well.

BUT, it seems to me, a cyclist would need to generate far more than 300w riding 20 Kmh on a 6% grade. Maybe I'm wrong because I've never followed quantizing cyclists with great interest.

Right now, I'm only seeking a loose mathematical model that's sort of accurate.

 

[DirtyWorks]

In most simple terms the grade doesn't matter - as long as wind drag is small enough to be ignored.

What is important is the amount of vertical rise, and the length of time it takes.

Do the same rise in 2x the time means that 1/2 of the power (watts) is needed.

Jay Kosta
Endwell NY USA

I found this: http://alex-cycle.blogspot.com/2013/08/resistance-is-futile-even-for-mtb.html

The infographic seems pretty close to what I'm looking for. The blue curve is 300 Watts output as speed at increasing gradients, what percentage of Watts is used to defeat gravity at various gradients.

Is the infographic roughly correct? I don't quantize cycling so I don't know how good a model it is.

At this point, I realize I didn't ask the right question, but the replies helped me get to what I was actually looking for.

 

[Eshnar]

Eshnar,

All good questions. I'm looking for what percentage of power is used to defeat gravity at a given gradient.

Now THAT's clear. Ok.
I thought you were looking to somewhat theoretical gravity-only scenarios, but since you're talking about percentages you take into account drag and rolling too.

I stumbled upon this very nice interactive model:http://www.gribble.org/cycling/power_v_speed.html

I can change gradient and the portion of a given speed that is dedicated to defeating gravity is nicely represented.

What it does graph nicely is all power for most cyclists goes to defeating gravity at a 6% incline. The model agrees with my limited calculations of my own performance on nearly flat course well.

BUT, it seems to me, a cyclist would need to generate far more than 300w riding 20 Kmh on a 6% grade. Maybe I'm wrong because I've never followed quantizing cyclists with great interest.

Right now, I'm only seeking a loose mathematical model that's sort of accurate.

Don't have a graph, but it shouldn't be too hard to make one (when I have some time)
The mathematical model is fairly easy.

the rider has to overcome three forces:
- gravity, which is expressed as
Fg=m*g*cos(angle) where m is the mass of everything (rider+bike), g is the free fall acceleration constant and the angle is... the angle of the road;
- rolling friction, which is expressed as
Fr=m*g*r*sin(angle) where r is the rolling friction coefficient(depends on materials);
- drag resistance, which is expressed as
Fd= d*v^2 where v is the speed and d is the drag coefficient (depends on the shape of the exposed surface)

Hence, considering that the power can be calculated as P=F*v, where F is the total force applied and v is the very same speed of the rider, we can get this object:
P=m*g*cos(angle)*v + m*g*r*sin(angle)*v + d*v^3

as you may notice, the percentage of the power spent to overcome gravity over the total is:

Pg/P = m*g*cos(angle)*v / (m*g*cos(angle)*v + m*g*r*sin(angle)*v + d*v^3) = m*g*cos(angle) / (m*g*cos(angle) + m*g*r*sin(angle) + d*v^2)

That means, it still depends from v.
You can try to play with the values and see what you get, or else you could, as mentioned earlier, use actual speeds of actual riders on each gradient.

EDIT: the site you linked looks good. I have no reason to believe there's anything wrong in that, but I didn't look carefully :V

 

[Eshnar]

even better, you could establish a fixed, reasonable power value and estimate the percentage from there (with power fixed it's a piece of cake)

 

[Alex Simmons/RST]

I found this: http://alex-cycle.blogspot.com/2013/08/resistance-is-futile-even-for-mtb.html

The infographic seems pretty close to what I'm looking for. The blue curve is 300 Watts output as speed at increasing gradients, what percentage of Watts is used to defeat gravity at various gradients.

Is the infographic roughly correct? I don't quantize cycling so I don't know how good a model it is.

Yes, it's correct, and based on the validated mathematical model of the physics of cycling:
http://www.academia.edu/239368/Mart...cycling_power._J_Appl_Biomech_1998_14_276-291

and is pretty much what most online websites that provide such calculations use (often without attribution).

Of course the model output is only as good as the input assumptions used, IOW the exact speed from power (or power from speed) values for any individual will vary with different values for air resistance, rolling resistance, rider mass, wind velocity, drive train efficiency and power output.

The main point of that chart is to show the general trend in the split in energy demand factors at various gradients, and of course to show how speed declines at same power with increasing gradient.

 

[Le breton]

I found this: http://alex-cycle.blogspot.com/2013/08/resistance-is-futile-even-for-mtb.html
......

Didn't you realize that the blog in question belongs to our very own ALEX (Simmons)?