I have a degree in chemical engineering and we study this not just in pipe flow but in a fluidized catalytic bed and when you will lose catalyst out the chimney. In my chemical engineering studies we have never treated particle speed versus wind speed differently.
According to Galilean invariance you should get the same wind resistance in any frame of reference. It is only relative. Think about this we are spinning and rotating around the sun.
Wind resistance is the net. 30 mph in still air is exactly the same as 5 mph in 25 a mph head wind.
Gearing make this possible but that is not the stated question. The question is regarding wind resistance alone does:
30 mph (speed) + 0 mph (wind) = 5 mph (speed) + 25 mph (head wind)
The answer is yes they are the same. The proof is Galilean invariance.
Put 30,0 and 5,25 into this calculator. Both sets of numbers give same relative velocity (30) and the same WATTS.
FLO Cycling - How Velocity Affects Drag
When calculating drag, velocity is not simply the speed at which you
are travelling on your bike. Velocity is the combination of the speed
at which you are travelling on your bike and the velocity of the wind.
This combination of velocities is know as relative velocity.
In this example the cyclist is travelling at 15mph and the wind is
travelling in the opposite direction at 5mph. The relative velocity
is therefore equal to...
Rider Speed - Head Wind
(15mph) - (-5mph) = 20mph
Drag Forces in Formulas
The power required to overcome the total drag is:
P = Ftotal v where v : velocity in m/s
The formula for air resistance strictly applies only with no wind. With any wind the vector sum of wind due to motion of the bicycle plus true wind is to be taken instead of v;
refers to forces acting opposite to the relative motion of any object
moving with respect to a surrounding fluid
v is the speed of the object relative to the fluid
u, is the flow speed of the object relative to the fluid
proportional to the square of the relative flow speed between the
object and the fluid
v is the speed of the body relative to the fluid
Drag Force and Drag Coefficient
U is the relative velocity of the fluid with respect to the particle
If you drop a rock the terminal speed from gravity should be exactly the same as the wind speed from a fan it takes to hold it in air.
If the third V in power V³ is ground velocity and not relative velocity I am not finding any reference that states that. Let's assume that is true:
Vs1 is velocity still
Vs2 is velocity in wind
Vw is velocity of wind
Vs1^3 = (Vs2 + Vw) * (Vs2 + Vw) * Vs2
Vs1^3 = (Vs2^2 + 2*Vs2*Vw + Vw^2) * Vs2
Vs1^3 = Vs2^3 + 2*Vs2^2*Vw + Vw^2*Vs2
if Vs1 = 30 and Vw = 25 then Vs2 = 16
Able to ride 16 mph into a head 25 mph wind does not seem right to me but I am just not so sure anymore
The only possible difference is wind is slightly disturbed so it is going to have some turbulence. But at even a small speed you are into turbulent flow (Reynolds number).
Because of the gusting and turbulent nature of wind it will feel faster than the sensation of riding in still air.
Assume 30 net mph is 600 watts