FLOW OVER BICYCLE

AIM:  To calculate the drag force against the cyclist and observe how same frontal area for a cyclist with different position shapes affect the drag.

GOVERNING EQUATIONS:

    The physics behind a cyclist while riding is purely aerodynamics. Aerodynamics is the study of the properties of moving air and the interaction between air and solids moving through it.

    Cyclist will apply more force through the pedals and try and counteract the wind with force, as opposed to changing body position or equipment. When the cyclist hit about 30mph, 90% of his power goes into overcoming air resistance called aerodynamic drag. While riding, the air particles hit the cyclist, gets compressed and spaced out when they flow over him. The difference in air pressure between his front and back creates drag force.

    In cycling, among total resistive forces on the level ground, aerodynamic drag or force is the main resistance opposed to the motion. The optimisation of the aerodynamic drag could be determinant to enhance the cyclist's performance for the same mechanical power output.

    Aerodynamic shapes reduce this pressure drag or drag force by minimizing that difference in pressure and allowing the air to flow move smoothly over his front and reduces the low pressure behind his back.

    Aerodynamics use a number called Coefficient of drag to model all the complex items that affect drag like shape of an object, size and the angle at which the object meets the air. The effective frontal area  represents the position of the cyclist on the bicycle and the aerodynamics of the cyclist-bicycle system in this position

                                            Frontal Area of a Cyclist and Bicycle Experiencing Drag Force 

 Formula:

The major performance parameter in cycling is the displacement velocity of both cyclist and bicycle (`upsilon`, in `m//s`). At constant velocity, the ratio of the mechanical power output generated by the cyclist (P, in W) to the total resistive force (`F`, in N)

                                              `v=frac{P}{F}`

The power output is the quantity of energy output per unit time. At constant speed, the mechanical power output can be assumed to be the sum of the energy used to overcome the total resistive forces. So the aerodynamic drag Force `F_d ,(N)`, is directly proportional to the combined projected frontal area of the cyclist and bicycle(`A_f`, in `m^2`), the drag coefficient(`C_d` , dimensionless), air density(`rho` , in `kg //m^2` ) and the square of the velocity relative to the fluid  (`upsilon_f`, in `m//s` ).

                `F_d =frac{A_fxxrhoxxupsilon_f^2xxC_d}{2}`  

                                                  Where  `rho =1.293 kg//m^3`

Co-efficient of drag varies for different shapes. The values taken here were determined experimentally by placing models in a wind tunnel and measure the amount of drag and the tunnel conditions of velocity and density of air. Drag equation was used to calculate Coefficient of drag,            

                          `C_d =frac{2xxF_d}{A_fxxrhoxxupsilon_f^2}`

OBJECTIVE:

• calculate drag force against a cyclist using Drag Equation.
• To plot the graph between velocity and Drag force, for this we need to calculate different drag forces for different velocities. By taking an array of velocity, `upsilon =[1, 2, 3, 4 , 5]` found the corresponding drag forces and plotting of the graph is done where we get a parabola.
•  To plot the graph between drag force and coefficient of drag. The projected frontal area of each object is taken same for reference and the co-efficient of drag for different shapes are taken as below.

For a Flat plate,  =1.28

For a Prism,        =1.14

For a sphere,       =0.7 to 0.8

For a bullet,         =0.295

For an air foil,         =0.045

Body Of The Content: 

  Software used for coding is MathLab.

% program to claculate the drag force against cyclist
clear all
close all
clc
%Inputs
%drag coefficient dimentionless
c_d=0.8;

% Frontal Area m^2
A_f=0.4;

%Density of Air kg/m^3
rho=1.2; 

%velocity m/s
Vf=2;


%Drag force, Fd
Fd=rho*A_f*Vf^2*c_d*0.5

%plot velocity VS drag force

Vf=[1 2 3 4 5]
Fd=rho*A_f*Vf.*Vf*c_d*0.5

plot(Vf,Fd)
xlabel('Drag Force, Fd (N)')
ylabel('velocity, Vf (m/s)')
grid on

% program to Plot between Drag Force against Coefficient of Drag
clear all
close all
clc

%Inputs
%drag coefficient
c_d=0.8;

% Frontal Area m^2
A_f=0.4;

%Density of Air kg/m^3
rho=1.2;

%velocity m/s
Vf=2;

%Drag force, Fd
Fd=rho*A_f*Vf^2*c_d*0.5;

% plot Drag Force Vs Coefficient of drag

c_d=[1.28 1.14 0.7 0.295 0.045]
 
Fd=rho*A_f*Vf.^2*c_d*0.5
plot(Fd,c_d)
xlabel('Drag Force, Fd(N)')
ylabel('Coefficient of Drag, c_d')
grid on

Results for Drag Force Calculation:

_{Result for Drag Force and Coefficient of Drag:}

 Plot for Drag Force Vs Velocity:

Plot for Drag force Vs Coefficient of Drag:

Conclusion:

       _{The plot for velocity against drag force is a parabola and the function is exponential which explains as the  cyclist rides faster, more the drag force he will observe. To overcome the air resistance drag force, he need to use more power which will be a tough time to a rider.}

       _{The plot for coefficient of drag against drag force is a straight line and the function is linear equation, explains drag force is proportional to Drag. As the shape of the frontal area decreases the drag force also decreases even though the frontal area is same. By this we can say drag force can be reduced by changing frontal position shape of a cyclist. It can be done by changing body position on the bicycle by updating equipment design like providing aerodynamic handlebars, wearing skin tight aero clothing,aero helmets, wheels, frames etc. Dropping handlebars a few cm, can make a big difference in improving aerodynamics because frontal position incurs the biggest aerodynamic drag.}

_{The basic road cycling positions suggestions to ride faster, more efficiently and safer are}

• _{The first is an upright position with hands on top of the handlebars. Here most of the cyclist’s torso is presented to the wind. So it is not expected to be a very aerodynamic position.}
• _{Second position puts the rider’s hands lower on the handlebars call the drops and is a typical racing position both on flat terrain and on the descent.}
• _{Third position is to get more aerodynamic by getting smaller to reduce the area that catches wind. Here he can lower his torso and narrow his hands on the bar.}
• _{The standard time trial position was the fastest, with a more traditional upright riding style creating 20% more air resistance.}