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physics:fluid-dynamics-drag

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UNDER CONSTRUCTION

Have any of you cycled against 40mph headwind? Is it even possible? If 90% of resistance to moving forward, is wind resistance, then you would have to be able to average 36mph in still air, to be able to make forward progress. I have cycled through a tropical storm, where I was moving very, very slowly, and there was water lapping the bottom bracket. What would it take to not make any progress at all?

https://youtu.be/3JaEJUlGxyk

Aside from spokes spinning into the wind, I don't see a difference in drag between a 20mph direct headwind, and rider moving through still air at 20mph. However, the following equation from http://www.kreuzotter.de/english/espeed.htm disagrees with this belief.

Speed & Power Calculations from another site, that I am challenging

The following equations take into account all of the relevant resistance components: Rolling friction including the dynamic (speed-dependent) rolling friction, air drag including the influence of wind speed, mechanical losses, and uphill/downhill forces.
 
 
PRider's power
VVelocity of the bicycle
WWind speed
HnnHeight above sea level (influences air density)
TAir temperature, in ° Kelvin (influences air density)
gradeInclination (grade) of road, in percent
β(“beta”) Inclination angle, = arctan(grade/100)
mbikeMass of the bicycle (influences rolling friction, slope pulling force, and normal force)
mriderMass of the rider (influences rolling friction, slope pulling force, and the rider's frontal area via body volume)
CdAir drag coefficient
ATotal frontal area (bicycle + rider)
CrRolling resistance coefficient
CrVCoefficient for velocity-dependent dynamic rolling resistance, here approximated with 0.1
CrVnCoefficient for the dynamic rolling resistance, normalized to road inclination; CrVn = CrV*cos(β)
CmCoefficient for power transmission losses and losses due to tire slippage (the latter can be heard while pedaling powerfully at low speeds)
ρ(“rho”) Air density
ρ0Air density on sea level at 0° Celsius (32°F)
p0Air pressure on sea level at 0° Celsius (32°F)
gGravitational acceleration
FrgRolling friction (normalized on inclined plane) plus slope pulling force on inclined plane


 
 

Air density via barometric formula:
Air density via barometric formula
 
 
Rolling friction plus slope pulling force:
Equation for rolling friction force and slope pulling force
 
 


|Power:
Equation for the required human power |


 
 
Speed:
In order to solve this Power equation for Velocity V, we write it in the implicit form
Equation for the required human power
so we can use the cardanic formulae to obtain the solutions:
If a2 + b3 ≥ 0: Velocity equation
If a2 + b3 < 0 (casus irreducibilis; in case of sufficient downhill slope or tailwind speed): Velocity equation (casus irreducibilis)


|with
Expression "a" of the velocity equation
and
Expression "b" of the velocity equation|

Discussion

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physics/fluid-dynamics-drag.1464276977.txt.gz · Last modified: 2016/05/26 10:36 by marcos