Cycling Aerodynamics – An Introduction

Aerodynamics are an important consideration for cycling, but ‘aerodynamic’ is a buzzword for cyclists. There is this silent allure to the word and to the concept:

  • “That bike is so aero”
  • “I only race with an aero helmet”
  • “He looks so aero in that position”
  • “Are those wheels aero enough for the price?”

For every research paper on cycling aerodynamics there is a marketing associate convincing you THIS helmet is the key to victory. Let’s try to understand aerodynamics better so we can better sift through all this ‘aero info’ in our way.

Aerodynamics Basics

Air is 78% nitrogen, 21% oxygen, and ~1% other gases; all of these elements have mass. When we try to move through non-moving mass, we have to push it out of the way. Applying a force to a mass to push it out of the way takes energy. The sum of the forces to push each molecule out of our way is the drag force. In a flat event, drag forces can account for 95%+ of the forces resisting a cyclist’s forward movement. The goal of aerodynamics in cycling is to reduce this drag force as much as possible.

Drag Force

The engineering equation for drag force is:

\text{Drag} = \frac{C_d\rho V^2 A}{2}

Where Cd is the coefficient of drag, ρ (“rho”) is the density of air, V is the relative velocity between the air and the object, and A is the frontal area of the object. As cyclists, we can’t control the density of air, but the we can, to a certain extent, control the other three areas.

Power

We also know that the power required to pedal is:

\text{Power} = \text{Force} * \text{Velocity}

So the power required to overcome a drag force is:

\text{Power} = \text{Drag Force} * \text{Velocity}\\ \text{Power} = \frac{C_d\rho V^2 A * V}{2}\\ \text{Power} \propto V^3

The key lesson here is that the power required to overcome drag scales cubicly with velocity. This is why it’s so hard to attack and get away; to speed up from 25mph to even 27mph requires 26% more power! Another way to think of this: if we want to go twice as fast, we need to increase power by 8x.

If we rearrange the equation such that velocity is the dependent variable:

\text{Veloctiy} = \sqrt[3] \frac{2*\text{Power}}{C_d\rho A}

The key points from this equation are: if we reduce Cd by 27% then we only see a 3% increase in velocity. Also, a decrease in frontal area of 27% also nets us only 3% improvements in speed.

Another note to make: for these aerodynamics equations, the variable V for velocity is the relative velocity between the object and the air/medium around it. As a result, the same values will be obtained from a static object in high velocity air as a high velocity object in static air. This phenomenon is the reason wind tunnels work, as the rider is static, but the air is flowing at a high speed to simulate the motion of a cyclist riding down a flat road.

Flow – Laminar and Turbulent

Another key principle of aerodynamics is the idea that the air molecules directly touching the object are the same speed as the object. As we observe molecules further from the surface of the object, the speed approaches the average speed of the air. This layer of air is called the boundary layer. Sometimes the boundary layer produces a laminar flow.

Laminar flow is characterized by smooth flowing air and it is relatively efficient. Turbulent flow is just as you expect, hectic. The flow is less predictable, erratic, and produces significantly more drag. The likelihood of an object producing turbulent flow increases as speed increases and this is an important consideration for engineers as they try to design the most efficient bicycles/helmets/wheels.

Controlling Laminar to Turbulent Flow Transition

One technique is to control the transition from laminar to turbulent flow. Sometimes, objects will transition from laminar to turbulent on their own, without much pattern. If texture, such as a slight bump, is added to the object, it can force the flow into turbulence at that point. Forcing turbulent flow in a controlled way can be more efficient than uncontrolled turbulence.

On this topic, it was popular for a time to have dimpled helmets, under the belief that they would improve aerodynamics by reducing turbulent flow. Golf balls have dimples because it changes the local aerodynamics and allows them to fly further. The purpose of the dimples is to change the pressure in a rotating body, but… aero helmets don’t rotate, so there is actually minimal advantage to dimpled helmets. The trend has since largely been abandoned by the industry.

Human Aerodynamics

The position of a rider accounts for 65-80% of the total drag on the system. It is by far the most important factor to tune to improve your ability to fight the wind. It has been shown that reducing the height of a rider is significantly more important than reducing the width of a rider. Tuning a cyclist properly for aerodynamics is difficult because an overly aggressive position reduces the rider’s ability to produce power. It doesn’t matter how aero you are if you can’t ride your bike hard.

A picture of the inside of the MIT wind tunnel. Wind Tunnels of this size can be used to learn about cycling aerodynamics.
The MIT wind tunnel. Cycling aerodynamics can be measured in wind tunnels. The MIT Cycling Team has done experiments and optimizations in their wind tunnel. Source.

Bicycle Wheel Aerodynamics

Wheels are of special interest for aerodynamicists because they offer an opportunity to see significant improvements in aerodynamics. The main benefits of deep dish aero wheels is that there is more control of the turbulent flow around them and the decrease in length of the spokes.

For a spinning wheel, each spoke must push through the air to continue spinning. For a longer spoke, the speed of the end of the spoke near the tire is higher and we know power increases cubicly with speed. As a result, longer spokes are significantly less efficient because they travel at a higher speed at the outer edges. Bladed spokes, internal spoke nipples, and wheels with fewer spokes can help reduce the detrimental effects of spoke aerodynamics.

With all these benefits, there is some tradeoff. The issues with deep dish aero wheels includes a reduction in stiffness with some rider’s rubbing their rim brakes during sprints. Other concerns are a decrease in durability and an increased chance of irreparably damaging the wheels in a crash. There are performance detriments in response to an attempt to cheat wind.

Aerodynamics of Other Cycling Equipment

If the rider accounts for 65-80% of the drag and wheels account for another significant portion, what about shoes, helmets, skinsuits, gloves, etc? Let’s demonstrate with the example of helmets. For any given aero helmet lineup from the same year, we see differences in drag of about 10% and we also know that a helmet accounts for 2-8% of the total drag of a cyclists. So at best, we reduce the total drag on the system by 0.8%.

But remember, speed is related to cube root of drag. So the improvements in speed are even smaller, something like 0.27%! So while your friends are arguing over which aero helmet to purchase, you should just buy some aero helmet and move on to training more. It is important to use equipment specifically designed for an aerodynamic advantage, but which brand? It doesn’t matter, as long as the equipment is somewhat modern.

Unless you are a true time trialist who has absolutely maxed out your body’s ability to produce power over your given discipline’s length, cycling aerodynamics don’t matter beyond ensuring you have decent equipment. Every race I’ve been in has been determined by the strength of the rider, not their equipment.

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