MATLAB program to compute the drag force on a cyclist

Question 1:

Write a Matlab program to calculate drag force against a cyclist.

The factors involved are Velocity, Drag coefficient, Frontal Area, Density of air.

(a) Write a program to plot Velocity vs Drag force.

(b) Write a program to plot Drag Co-efficient vs Drag force.

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Solution:

Drag force is the resistance force generated by the motion of a body through a fluid, such as water or air. Drag force always acts opposite to the direction of the oncoming flow velocity. This is generally the relative velocity between the body and the fluid.

The drag force D exerted on a body traveling through a fluid is given by the below relation,

`F_( D) = 1/2rho CA V^2`

where,

ρ is the density of the fluid through which a body is moving.

C is the drag coefficient, which can vary along with the speed of the body. But typical values range from 0.4 to 1.0 for different fluids (such as air and water).

A is the projected cross-sectional area of the body perpendicular to the direction of flow (that is, perpendicular to v)

V is the speed of the body relative to the fluid.

Drag force being exerted on a car moving with a velocity 'V' is exemplified below.

The various positions of a cyclist are depicted below*.

Fig. 1: The five cyclist positions with frontal area 'A'. (1) sagittal torso angle (2) shoulder angle (3) elbow angle (4) forearm angle (5) hip angle (6) knee angle (7) ankle angle.

For the above-illustrated cyclist positions, below calculations were figured out*.

Fig 2: Frontal area, drag coefficients, and drag area for various cyclist positions.

(a)

%To plot Velocity vs Drag force for a cyclist

clear all

close all

clc

c_d = 0.04; %drag co-efficient of a streamlined body assumed

a = 0.1; %frontal area(`m^2`)

rho = 1.2; %air density(kg/`m^3`)

v = [1:50]; %velocity(m/s)

drag_force = 0.5*rho*c_d*a*v.^2 %drag force(N)

plot(v,drag_force,'color','r','linewidth',1);

xlabel('Velocity (m/s)');

ylabel('Drag force (N)');

title('Velocity vs Drag force against a cyclist with varying velocities');

grid on;

Result:

From the above graph, we can clearly observe that the drag force varies proportionally to the square of the velocity.

(b)

%To plot Drag Coefficient vs Drag force for a cyclist

clear all

close all

clc

c_d = [0.47 0.42 0.82 0.04 0.09];

a = 0.1;

rho = 1.2;

v = 1;

drag_force = 0.5*rho*c_d*a*v.^2;

plot(c_d,drag_force,'color','b','linewidth',1);

xlabel('Drag Co-efficient');

ylabel('Drag force (N)');

title('Plot of Drag Coefficient vs Drag force');

grid on;

Result:

From the above graph, we can clearly observe that the drag force varies almost linearly with the varying values of the drag coefficient.

References*:

Blocken, B., van Druenen, T., Toparlar, Y. and Andrianne, T., 2019. CFD analysis of an exceptional cyclist sprint position. Sports Engineering, 22(1), p.10.

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