Tailwind and speed difference
- Thread starter koger
- Start date
no definitely not and even with no rolling resistance accounted for ...koger said:
I think some folks are confusing equal aero "drag" with equal aero power
let's drop Crr, drivetrain resistance - everthing except aero drag. Power for the cyclist to travel at speed Vg in headwind Vw on flat terrain will be:
P(v) = Vg x (0.5 x rho x CdA x (Vg + Vw)^2)
or to simplify P(v) = constant x Vg x (Vg+Vw)^2
So if the baseline is 200W and 6 m/s on a flat, windless course
constant = 200W / (6*(6+0)^2) or 200/6^3 or 0.926 (implying a hideous CdA BTW! ~ 1.55)
P(v) with -4 m/s tailwind will be
P(v) = 0.926*Vg*(Vg -4)^2 and for 200W solving for Vg yields 8.92 m/s not 10 m/s
If you start off with a more typical road bike CdA around 0.40, 200W with no Crr will provide a baseline speed of 9.41 m/s. Add 4m/s tailwind and the resulting speed at 200W will be 12.25 m/s or a delta of 2.85 m/s (vs 4 m/s).
Adding Crr back into the mix, road bike CdA 0.40, mass 85kg and Crr 0.004, 200W should provide 8.92 m/s. Add -4 m/s tailwind and the speed rises to 11.61 or a delta of 2.69 m/s (vs 4 m/s).
So it's not linear to start with considering aero drag/power only. You never gain the entire tailwind in bike speed. Add in Crr to the mix and you gain even less.
I think that's about it ... it's not nuclear engineering
.
Is Crr constant for any speed?What is the formula for Crr calculation?Iam bad in fysik/and English/.rmur17 said:no definitely not and even with no rolling resistance accounted for ...
I think some folks are confusing equal aero "drag" with equal aero power
let's drop Crr, drivetrain resistance - everthing except aero drag. Power for the cyclist to travel at speed Vg in headwind Vw on flat terrain will be:
P(v) = Vg x (0.5 x rho x CdA x (Vg + Vw)^2)
or to simplify P(v) = constant x Vg x (Vg+Vw)^2
So if the baseline is 200W and 6 m/s on a flat, windless course
constant = 200W / (6*(6+0)^2) or 200/6^3 or 0.926 (implying a hideous CdA BTW! ~ 1.55)
P(v) with -4 m/s tailwind will be
P(v) = 0.926*Vg*(Vg -4)^2 and for 200W solving for Vg yields 8.92 m/s not 10 m/s
If you start off with a more typical road bike CdA around 0.40, 200W with no Crr will provide a baseline speed of 9.41 m/s. Add 4m/s tailwind and the resulting speed at 200W will be 12.25 m/s or a delta of 2.85 m/s (vs 4 m/s).
Adding Crr back into the mix, road bike CdA 0.40, mass 85kg and Crr 0.004, 200W should provide 8.92 m/s. Add -4 m/s tailwind and the speed rises to 11.61 or a delta of 2.69 m/s (vs 4 m/s).
So it's not linear to start with considering aero drag/power only. You never gain the entire tailwind in bike speed. Add in Crr to the mix and you gain even less.
I think that's about it ... it's not nuclear engineering
yes within reason of course typical Crr ranges from around 0.002 to 0.008 on the track and road to much higher for mountain bike tires and surfaces (don't have any data for that).luban said:
not for the calculation of Crr per se but the power required to overcome rolling resistance is:
P = Vg x m x g x Crr
Vg= bike ground speed in m/s
m = total mass of bike, rider and kit
g = gravitational constant ~9.81
Crr = unitless coefficient of tire/surface rolling resistance
rmur17 said:
Thank you for your great post. I have one question though, where did you find the equation? I found this at http://en.wikipedia.org/wiki/Drag_(physics)
P(v) = 0.5*rho*v^3*A*Cd
Could you tell me what I missed?
Thanks again
I'm too old to remember where!koger said:
re that equation it's for calm conditions only - if you take 'my' equation and the factor Vg*(Vg+Vw)^2 .... set Vw to 0 and you get Vg^3 or simply v^3 as in the equation above.
Actually what I listed is a very simple version that applies only to direct headwinds and tailwinds. Add in a 'yaw angle' and the math is a little messier -- though the concepts exactly the same.
I would also like to see the derivation of that equation, because it looks fishy to me.
I think the correct equation (for wind directly behind the rider) and ignoring all effects except aerodynamic drag is:
Power = 0.5 rho V**3 A Cd (as said by another poster)
where: rho is density, A is area, Cd is drag coefficient, and V is the speed of the bike relative to the air.
(And I am a nuclear engineer).
I think the correct equation (for wind directly behind the rider) and ignoring all effects except aerodynamic drag is:
Power = 0.5 rho V**3 A Cd (as said by another poster)
where: rho is density, A is area, Cd is drag coefficient, and V is the speed of the bike relative to the air.
(And I am a nuclear engineer).
Which equation are referring to as being fishy? So, you saying that this is nuclear engineering?Yojimbo_ said:
Canadian P.Eng here graduated with a 'specialization' in Electrical in '86.Yojimbo_ said:
I'm old and cranky most days and I stand by my math. Period.
Unless corrected by a true expert of course
. Where are the true boffins when you need them????Hey you're not in charge of installing backup safety pumps at Chalk River are you?
Me too. You must use the same reference point for all velocities, whether that's the ground, rider, air, or an observer. Rick's equation uses the ground as the reference point for the rider velocity Vg, and the air as the reference point for the drag force (ie, by subtracting Vg and Vwind *before* squaring the terms) calculation. If the drag force is a function of the body's speed relative to the air, then the drag power is a function of that same relative velocity.Yojimbo_ said:
Consider the case where a rider is standing stationary in the face of a 10mph wind. The rider is still expending energy to resist the force of the wind, despite the fact that she is not moving relative to the ground. There is still a frictional energy transfer taking place because of the relative motion.
If you use (Vg + Vw) in place of the first Vg in Rick's equation, you do indeed get 10m/s for Vg in the example of a -4m/s wind, since the example neglects the other sources of friction.
oh dear. try again ! look up the definition of mechanical work !!!frenchyge said:
on a simply practical basis - haven't you folks noticed that headwinds don't slow one down proportionally to headwind speed and the opposite for tailwinds? Does a say 10 m/s headwind stop you folks in your tracks? !!!
I'm honestly shocked at the lack of understanding here ...
Aero drag is the shear force between the fluid and the body. The drag is the frictional force parallel to the flow and the distance is the length of the body over which it flows. Makes no difference whether the object is moving through stationary air or the air is moving against a stationary body -- only the frame of reference has changed.rmur17 said:
By 'proportionally', you don't mean linearly, do you? I don't believe anyone has stated that the aero drag power is other than a cubic function, and that the total power includes that plus some other factors.rmur17 said:
so you stand by this statement that the only reason the bike speed won't reach 10 m/s is because of the increase in the force/power to overcome Crr?frenchyge said:
Go into analytic cycling or another proven bike speed/power calculator, set Crr to zero and run thru some examples.
The difficulty I'm having is believing that a cyclist without rolling resistance who is experiencing a 1 m/s relative wind is expending 50 times more power while riding at 50 m/s than at 1 m/s (assuming the wind is much stronger in the second case so that the relative wind remains 1 m/s in her face).rmur17 said:
Additionally, I have difficulty believing that a bird or plane flying against a strong headwind but making no speed over ground is doing no work and expending no power.
Your equation above would indicate that both of those examples are true, and maybe they are. I'll have to think about it some more once the post-race delirium wears off.
the 1st example is correct but the 2nd is not ... the bicycle's frame of reference is the ground whilst clearly for the airplane or bird that makes no sense.frenchyge said:
Anyhow, go back and look at the Martin, Coggan et al formula and simplify it to the case(s) at hand. for pure head/tail winds. I stand by P_aero (v) = 0.5*rho*CdA *Vg*(Vg+Vw)^2
