Drag Force Calculation on a Bicycle using MATLAB

AIM:- Drag Force Calculation On A Bicycle Using MATLAB

Governing Equations:-

Drag Equation:-

F_d = `frac{1}{2}`*C_d *A*ρ*V²

Here

F_d is the drag force (SI unit- newton),

ρ(rho) is the density of the fluid (SI unit- Kg/m^3),

V is the speed of the object relative to the fluid (SI unit- m/sec),

A is the reference area (SI unit- m^2), and

C_d is the drag coefficient – a dimensionless number.

Objective:-

1. To calculate drag force on a bicycle
2. To plot graph of velocity vs drag force
3. To plot graph of drag coefficient vs drag force

Drag Force simply means a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

Drag depends on the density of the air/fluid, the square of the velocity, the viscosity of fluid/air and compressibility, the size and shape of the body, and the body's inclination to the flow. In general, the dependence on body shape, inclination, air viscosity, and compressibility is very complex which should characterize the dependence by a single variable. For drag, this variable is called the drag coefficient, designated "C_d." This allows us to collect all the effects, simple and complex, into a single equation.

The drag coefficient is a number which aerodynamicists use to model all of the complex dependencies of drag on shape, inclination, and some flow conditions.

Program 1- To calculate drag force and plot graph of Velocity vs Drag Force

close all
clear all
clc
% a program to calculate drag force on a bicycle
% input values
% dragcoefficient (SI unit- dimensionless number)
C_d=0.8;
% refrence area (SI unit- square metres)
A=0.1;
% density of air(SI unit- kilograms per cubic metres)
rho=1.225;
% velocity range relative to bicycle(SI unit- metre per second)
V=10:50;
% applyingdrag force formula(SI unit- newton)
Fd=C_d*A*rho*V.^2*0.5

plot(V,Fd,"r*")
title("Velocity vs Drag Force")
xlabel("Velocity")
ylabel("Drag Force")
grid on

Result:-

Fd =

Columns 1 through 18

4.9000 5.9290 7.0560 8.2810 9.6040 11.0250 12.5440 14.1610 15.8760 17.6890 19.6000 21.6090 23.7160 25.9210 28.2240 30.6250 33.1240 35.7210

Columns 19 through 36

38.4160 41.2090 44.1000 47.0890 50.1760 53.3610 56.6440 60.0250 63.5040 67.0810 70.7560 74.5290 78.4000 82.3690 86.4360 90.6010 94.8640 99.2250

Columns 37 through 41

103.6840 108.2410 112.8960 117.6490 122.5000

Velocity vs Drag Force Graph:-

Program 2. To plot graph of Drag Coefficient vs Drag Force

Any object moving through a fluid experiences drag - the net force in the direction of flow due to pressure and shear stress forces on the surface of the object.

The drag coefficient is a function of several parameters like shape of the body, Reynolds Number for the flow, Froude number, Mach Number and Roughness of the Surface.

Drag depends on the properties of the fluid and on the size, shape, and speed of the object.

Shape has a very large effect on the amount of drag produced.

Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients.

A flat plate has C_d = 1.28, a wedge shaped prism with the wedge facing downstream has C_d = 1.14, a sphere has a C_d = .07 to .5, a bullet C_d = .295, and a typical airfoil C_d = .045. The drag coefficient for a sphere is given with a range of values because the drag on a sphere is highly dependent on Reynolds number.

Here, the drag coefficient for various shapes are given for same reference area.

Program 2 Coding:-

clear all
close all
clc
% program to plot drag coefficient vs drag force
% input values
% dragcoefficient (SI unit- dimensionless number)
C_d=[1.28, 1.44, 0.47, 0.295, 0.045, 1.05, 0.50];
% naming different values of drag coefficient
label=["Flat plate", "Prism", "Sphere", "Bullet", "Airfoil", "Cube", "Cone"];
% refrence area (SI unit- square metres)
A=0.1;
% density of air(SI unit- kilograms per cubic metres)
rho=1.225;
% velocity relative to bicycle(SI unit- metre per second)
V=2;
% applying drag force formula(SI unit- newton)
Fd=C_d.*A*rho*V^2*0.5

plot(C_d,Fd,"ro-","linewidth",1)
text(C_d,Fd,label)
title("Drag Coefficient vs Drag Force")
xlabel("Drag Coefficient")
ylabel("Drag Force")
grid on

Errors/Mistakes Occured during Programming:-

Solution/Correction to the Errors:-

Result:-

Fd =

0.3136 0.3528 0.1152 0.0723 0.0110 0.2573 0.1225

Drag Coefficient vs drag Force Graph/Plot:-

Coclusion:-

1. As per the graphical representation from Program 1 that is Velocity (V) vs Drag Force (F_d), Drag force (F_d) is directly proportional to square of relative velocity (V²). This means doublingthe velocity will quadruple the drag.
2. As per the linear graph obtained from Program 2 that is Drag Coefficient (C_d) vs Drag Force (F_d), Drag force (F_d) is directly proportional to Drag Coefficient (C_d). Drag Force increases with the increase in Drag Coefficient.(Airfoil having least Drag Coefficient experience least Drag Force whereas Prism having maximum Drag Coefficient amongst all experience maximum Drag Force. )
3. Drag force (F_d) is also directly proportional to Reference Area (A) and Density () as per the Drag Equation.