# Resistance of Air Flow Over a Rider

By Bill Davis – Thanks again for this post Bill.

As a follow-up to hill riding, here is my analysis of aerodynamic issues and wind. It’s kind of long winded (no pun intended), but people write PhD dissertations on this subject.

This analysis starts with the same basic equation that relates power to pedal force and cadence, P=Fx*Vc, where P is power that the rider is expending, Fx is the force on the pedals applied to move the bike in a horizontal, flat direction and Vc is the velocity of the pedals or the cadence in rpm. This equation is fine if there is no air, no friction, no rolling resistance or other forces that slow the rider down. Unfortunately, we live in air and it is not always standing still. Even if it is standing still there are aerodynamic forces that have to be dealt with and they are significant. These aero forces require an adjustment to the equation, as follows

P = Feff*V

where Feff = Fx – Fd, and Fd is the aerodynamic drag force that acts on the bike/rider

Aerodynamic drag comes from 2 primary sources – the pressure due to the frontal area created by the rider on the bike and the resistance of the flow of air over the rider and the bicycle.

The pressure is determined by the “Frontal Area” of the rider/bike as well as the density of the air and the speed at which the rider is moving through the air. If the wind velocity is zero then the aerodynamic drag force is

Fd = .5*ρ*A*Cd*V² ,

where ρ is the density of the air, A is the frontal area of the bike and the rider, Cd is the drag coefficient (an experimentally determined number) and V² is speed of the bike relative to the air that it is traveling through

Some of these parameters can be adjusted to improve performance and some cannot. The density, ρ, of the air is a given parameter that cannot be changed – high humidity will increase drag, low humidity will reduce drag, but for the most part it will change very little while you are riding unless you are on a really long ride that goes through differing climate zones and altitudes (e.g., Breathless Agony). ‘A’ is the area that is projected when looking straight on at the rider on the bike. One reference that I saw stated that this is 65% of the power consumption so pay attention to this. The size of the rider is one parameter, the aero position on the bike is another. Fast bike riders are small and very skinny – that’s why you don’t see linebacker type people or people that are built like me at the Tour de France. The position of the rider is something that you can effect significantly. A rider has three positions that are typically used – on the hoods, in the drops and on the aerobars. By using aerobars or riding in the drops and staying low you reduce the frontal area and hence the drag – I am not certain what the reduction on drag is for aero position vs riding on the hoods, but I would estimate that it is at least a 20% difference. Have you ever noticed how much warmer you are when riding on a cold day if you stay in the aero position vs riding on the hoods – that is the effect of the reduced frontal area. Stay Low and you will improve speed significantly. Cd is the drag coefficient which depends on the geometry, shape of the rider and the bike – it needs to be experimentally determined for a specific rider and a specific bike – this is the number that engineers are trying to determine when they ‘go in the wind tunnel’ and test bikes. V² is the speed at which the rider moves through the air – if there is no wind this speed is the speed of the bicycle – Vb, and if there is wind then it is the speed of the bicycle Vb + the velocity of the wind – Vw, multiplied by the cosine of the direction of the wind angle. The real issue here is that this parameter has that 2 in the exponent which means that the aero force increases exponentially (parabollically exponential) with the speed of the wind and the rider. So now the equation for the pedal force that propels us on level ground with no other resistances becomes

Fx = P/V + .5*ρ*A*Cd*(Vb+Vw*cosine(wind angle direction)²)

for a zero degree head wind the cosine = 1, all other angles up to 90 degrees are less than one and although a 90 degree side wind reduces effective wind velocity to zero, it has other deleterious effects on performance

As for the resistance of air flow over the rider, this can be effected by making the air flow over your body and the bike with laminar flow – this means smooth, non-turbulent passing of air over the surface. There is no such thing as true laminar flow, but wearing very smooth tight fitting clothing has a big effect, aero wheels smooth out the flow, the bike frame and it’s shape reduce turbulence, minimizing or eliminating cables and other non essential things that the air has to pass over will help. So those tight fitting bicycle clothes aren’t just made to show off your svelte physique – they reduce the turbulence that is caused when the air passes over your body.

Unfortunately, I cannot make this long story short and give a simple quantitative example of how aerodynamics increases the load on you pedal force requirements. Simply stated, wear tight fitting clothes, stay in your aeroposition as much as possible and buy a really expensive aerodynamic bike like mine and you should have optimal performance. Also, don’t forget those pointy helmets and aerowheels too.