Effect of Velocity and Drag coefficient on Drag force in Tour de France Bicycle race

Objective

To calculate the drag force against a cyclist

Introduction

Drag is a force acting opposite to the relative motion of any object with respect to a surrounding fluid. The drag force can exist between two fluid layers or a fluid and a solid surface.

• At sea level and at 15°C , the density of air is 1.225 kg/m³.
• A typical cyclist presents a frontal area of 0.3 to 0.6 metres squared depending on position.
• On a racing bicycle the average speed is around 40-45 kmph on the flats and 35-40 kmph on montainous terrain

The values of drag coefficient based on the position of the cyclist is given below:

Matlab Code to Calculate the Drag Force against a cyclist during a bicycle race

The following matlab code is used to study the influence of drag coefficient and velocity on drag force in Tour de France bicycle race.

case 1: Velocity vs Drag_Force

% To plot velocity vs Drag_force
frontal_area=0.5;% The frontal area is chosen as 0.5 from the given range
density=1.225; % Density of air at 15 degree celsius
c_d=0.88; % drag_coefficient
velocity=linspace(0,14,100) % The velocity data is taken for Tour de France bicycle race and is in m/s
Drag_force=0.5*c_d*frontal_area*density*velocity.^2 % Drag_force formula
plot(velocity,Drag_force,'color','b','linewidth',3)
xlabel('velocity (m/s)')
ylabel('Drag force (N)')
grid on

The drag force increases by 4 times if the velocity increases by 2 times. The drag force is proportional to the square of velocity. Hence at higher velocity the cyclist will experience more drag force. To reduce this effect the cyclist has to change his position to reduce the drag coefficient which reduces the drag force.

case 2: c_d (Drag_coeff) vs Drag_Force

% To plot drag_coefficient vs Drag_force
frontal_area=0.5;% The frontal area is chosen as 0.5 from the given range
density=1.225; % Density of air at 15 degree celsius
c_d=linspace(0.5,1,100) % c_d value based on cyclist position
velocity=12 % terminal velocity in m/s
Drag_force=0.5*c_d*frontal_area*density*velocity^2
plot(c_d,Drag_force,'color','r','linewidth',3)
xlabel('c_d (Drag coeff)')
ylabel('Drag force (N)')
grid on

The drag force varies linearly with the drag_coefficient at terminal velocity. For lower drag_coefficient values the cyclist will experience lower drag force.

Hence Bicycle races need high velocity which cannot be compromised. However the drag_coefficient can be reduced by aerodynamically designing the cycle and changing the cyclist position.