need a mathematician

[jischr]

Riding 14 mph today into a 15 mph headwind with 20 mph gusts got me to wondering. Given the energy expenditure to ride a flat 4 miles into the wind, what is the equivalent energy output in terms of distance up a 12% grade with no wind? If possible presume everything else is equal. Anyone have an answer?

[54ny77]

a lot. :banana:

[Peter P.]

This web site might help. Just plug in the numbers...

Analytic Cycling (http://www.analyticcycling.com/QCHome_Page.html)

[bcgav]

Punch some numbers into http://bikecalculator.com/

[Ken Robb]

My under-educated guess would be that to calculate extra power required for overcoming headwinds one would have to no the coefficient of drag and the frontal area of the entire vehicle as ridden. Hills are easier to calculate for extra required power because the biggest variable is weight. But then I am a retired real estate broker and I don't even play a doctor on tv. :)

[joosttx]

~7 mph difference off the top of my head. (I have a Ph.D. But am in marketing so everything is an educated guess at best for me these days)

[rounder]

My under-educated guess would be that to calculate extra power required for overcoming headwinds one would have to no the coefficient of drag and the frontal area of the entire vehicle as ridden. Hills are easier to calculate for extra required power because the biggest variable is weight. But then I am a retired real estate broker and I don't even play a doctor on tv. :)

You are being modest.

Tell us. If it were a car, what would it be like. Could you calculate it, or would you just have to feel it.

[dustyrider]

I was just trying to figure how something like this would work...windy days of spring.

[Ken Robb]

You are being modest.

Tell us. If it were a car, what would it be like. Could you calculate it, or would you just have to feel it.

At my age I'm happy to be able to feel anything. :banana:

[rounder]

Thanks Ken. When I started clicking around here (Serotta Forum), you were buzzing around teaching M3 driving, etc. Most likely, no one here could have kept up with you, or these days still kept up with you.

[F150]

I see a power meter in your future, sir.

[bcgav]

42

[wallymann]

you're talking energy, mass, distance, velocity, vectors, friction, etc...thats not mere math, that's physics.

anyway, check out analyticcycling.com as others have suggested...and its as easy as pie.

Riding 14 mph today into a 15 mph headwind with 20 mph gusts got me to wondering. Given the energy expenditure to ride a flat 4 miles into the wind, what is the equivalent energy output in terms of distance up a 12% grade with no wind? If possible presume everything else is equal. Anyone have an answer?

[Louis]

thats not mere math, that's physics

Hmmm, I wonder what mathematicians would say to that... ;)

[Michael Maddox]

Hmmm, I wonder what mathematicians would say to that... ;)

We'd say that's arithmetic, not math.

[roydyates]

Riding 14 mph today into a 15 mph headwind with 20 mph gusts got me to wondering. Given the energy expenditure to ride a flat 4 miles into the wind, what is the equivalent energy output in terms of distance up a 12% grade with no wind? If possible presume everything else is equal. Anyone have an answer?

It depends on what you weigh. The "equivalent energy output" is less for a heavy guy and more for a light guy. Their frontal areas are roughly similar so the extra power required to ride into the headwind is comparable for the light guy and the heavy guy. However, the extra power required for climbing is a lot more for the heavy guy.

[mg2ride]

Riding 14 mph today into a 15 mph headwind with 20 mph gusts got me to wondering. Given the energy expenditure to ride a flat 4 miles into the wind, what is the equivalent energy output in terms of distance up a 12% grade with no wind? If possible presume everything else is equal. Anyone have an answer?

Depends GREATLY on how fat and wide you are.

With an increasing weight to width ratio the distance of uphill will go down.

I think

[oldpotatoe]

I was just trying to figure how something like this would work...windy days of spring.

Rather ride in the rain than in the wind.

[Kirk Pacenti]

https://www.youtube.com/watch?v=4ZfpwfQ58Ds

[Mikej]

That's a problem that would have a very high number of variables. And yes, as pointed out earlier, physics.

[ultraman6970]

Remember there was a coefficient of energy needed to increase your speed for 1 mile given x mph winds. You need to find that equation, but remember that at some point to go from x to y speed you needed like double of power to be able to make it, the issue is that besides wind in front of you, as faster you go that wind speed increase too. PITA calculation for sure.

And there was something similar for climbs, IMO the restitution coefficient in the tires is not even a big factor unless you want to be anal about it.

If it works, dutch riders since they dont have climbs they train against the wind.

[marciero]

We'd say that's arithmetic, not math.

Indeed, the math is straightforward. Varying forces, for example, would require calculus, but still...

[dustyrider]

Rather ride in the rain than in the wind.

Any day! The worst was dodging the tumble weeds traveling faster than me in the opposite direction...it was like they were laughing at me.
The really "funny" part is I commute into work headed east and the wind in the morning comes out of the east, care to guess which way the wind comes from in the afternoon on my westerly commute home?


I brought the OP question up to a few friends today and the consensus was that I would need to collect data without a head wind. The variables discussed seemed manageable, but they were rambling out, and drawing, some pretty interesting formulas. Maybe I'll play around with the links provided 1st...

[OtayBW]

Physics is the phenomena. Math is the language.

[Louis]

Math and Particle Physics tats:

(I think the Physics geeks have more to choose from, but the Math geeks could also show spirals...)

http://blogs.discovermagazine.com/loom/files/2010/07/Boise-Euler440.jpg

https://s-media-cache-ak0.pinimg.com/736x/a2/b4/d5/a2b4d5b57c2947282a68a4ed6019038a.jpg

[Michael Maddox]

Indeed, the math is straightforward. Varying forces, for example, would require calculus, but still...

Thank you. We pure math grads have to step up, on occasion.

A low-order differential equation is HARDLY mathematics, people. :banana:

[MadRocketSci]

in its simplest form,

0.5*air density*speed_relative_to_air_on_flat_road^3*Cd*fr ontal area = rider_weight*d(elevation)/dt

if you know values for all those in consistent units (except Cd which is dimensionless) then bobs your uncle.

for best results use a wind tunnel to find your own Cd*frontal_area, and go slow during climbing so aero drag is negligible...otherwise put it in on the right side as well

yeah, in this model there's barely anything that counts as "math"....

[mtechnica]

It depends on your aerodynamic profile, ambient temperature, elevation, and probably other factors.