Program to calculate Aerodynamic Drag Force against Cyclist by Using MATLAB.

Aim: To write a Matlab program to calculate drag force against a cyclist.

Objective:

1. Write a program to plot Velocity vs Drag force.
2. Write a program to plot Drag Co-efficient vs Drag force.

Factors involved:

• Velocity: It is defined as displacement over time.
• Drag coefficient: It is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.
• Frontal Area: The total resistance offered by the vehicle is the product of the frontal area and drag coefficient.
• Density of air: The density of air or atmospheric density, denoted ρ (Greek: rho), is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature, and humidity.

- The expression for Drag Force:

- Different positions of cyclist:

MATLAB Program:

1) Program to plot Velocity vs Drag force:

Here the values of the Frontal Area and Co-efficient of drag are considered to be constant and the value of Velocity is considered to be in the range of 1 m/s to 35 m/s.

Program:

%Program to calculate the drag force of a bicycle and plot Velocity vs Drag Force
close all
clear all
clc

%Inputs
%Drag coefficient 
C_d = 0.6; 

%Frontal Area (m^2)
A = 0.4;

%Density (kg/m^2)
rho = 1.2;

%Velocity (m/s)
v = linspace(1,35,10);

%Drag force (N)
F_d = 0.5*rho*A*v.^2*C_d

%Plotting: Velocity vs Drag Force
plot(v,F_d,'linewidth',2);
xlabel('Velocity (m/s)');
ylabel('Drag Force (N)');
title('Velocity vs Drag Force')
grid on;

Output:

Graph:

Result:

• As the velocity increases, the drag force increases with V²
• This effect may be negligible in case of low-velocity objects, but in case of high-speed objects such as aircraft jets, the drag force is considerably high which needs to be dealt with.
• A high drag force causes high fuel consumption.

2) Program to plot Drag Co-efficient vs Drag force:

Here velocity is considered as constant whereas the values of Frontal Area and Drag Co-efficient are taken from the following table

Program:

%Program to calculate the drag force of a bicycle and plot Drag Coefficient vs Drag Force.
close all
clear all
clc

%Inputs
%Drag coefficient 
C_d = [0.626 0.638 0.655 0.655 0.670]; 

%Frontal Area (m^2)
A = [0.374 0.370 0.339 0.423 0.460];

%Density (kg/m^2)
rho = 1.2;

%Velocity (m/s)
v = 7;

%Drag force (N)
F_d = 0.5*rho*A.*C_d*v^2

%Plotting: Drag Co-efficient(with respect to area) vs Drag Force
plot(A.*C_d,F_d,'color','r','linewidth',2);
xlabel('Drag Co-efficient w.r.t Area');
ylabel('Drag Force (N)');
title('Drag Co-efficient w.r.t Area vs Drag Force')
grid on;

Output:

Graph:

Result:

• Drag Force increases linearly with Drag Co-efficient.
• C_d is not a constant but varies as a function of flow speed, flow direction, object position, object size, fluid density, and fluid viscosity.
• For certain body shapes, the drag coefficient only depends on the Reynolds number, Mach number and the direction of the flow. For low Mach number, the drag coefficient is independent of Mach number. Also, the variation with Reynolds number within a practical range of interest is usually small, while for cars at highway speed and aircraft at cruising speed, the incoming flow direction is also more-or-less the same. Therefore, the drag coefficient can often be treated as a constant.

Conclusion:

• From Velocity vs Drag Force Graph, we can say that as the speed of the cyclist increases as the drag force increases in an exponential manner and varies with V²
• From Drag Co-efficient vs Drag Force Graph, we can say that the larger the frontal area, the more the drag co-efficient which in turn increases the drag force.
• Hence in order to reduce the drag force, the frontal area must be as low as possible.

Thus, the Matlab program is written to calculate drag force against a cyclist.

References:

- Aerodynamic analysis of different cyclist hill descent positions.

https://www.sciencedirect.com/science/article/pii/S0167610518305762?via%3Dihub