Matlab - plot pressure distribution around a circle

super sky

I'm trying to plot the pressure distribution around a cylinder in a uniform flow field, so that the graphic is a circle with the pressure curve around it, like in the image below.

Uploaded with ImageShack.us

I have the equation for the ideal pressure coefficient Cp (which is what I'm wanting to display), and t is the theta values. (See code below)

Then I use the polar function to plot it... polar(t,Cp)... but that starts at the origin, which isn't what I want. I thought it might help if I added the radius of my proposed circle to Cp, but it doesn't. So maybe I need a scaling factor on Cp or something..?

Could someone help me out?
Thanks.

Code:

%%% Flow Around a Cylinder %%%

% Initialise variables
clear all
clc

U = 12;     % Freestream velocity m/s
M = 2;      % Doublet strength
radius = sqrt(M/2/pi/U);    % Cylinder radius
t = linspace(0,2*pi,50);    % Range of theta values
circle = ones(1,50);        % Create vector
circle = radius.*circle;    % Circle of required radius

% Calculations
cp = 1 - 4.*(sin(t)).^2;     % Pressure coefficient
cp_scaled = cp + radius;     % Attempted scaling

% Display graphs
polar(t,cp,'--r')
hold on
polar(t,circle)
hold off
figure
polar(t,cp_scaled,'--r')
hold on
polar(t,circle)
hold off

wgh87

Pretty useless now,

just in case if you ever wonder what was missing

Quote by super sky

I'm trying to plot the pressure distribution around a cylinder in a uniform flow field, so that the graphic is a circle with the pressure curve around it, like in the image below.

Uploaded with ImageShack.us

I have the equation for the ideal pressure coefficient Cp (which is what I'm wanting to display), and t is the theta values. (See code below)

Then I use the polar function to plot it... polar(t,Cp)... but that starts at the origin, which isn't what I want. I thought it might help if I added the radius of my proposed circle to Cp, but it doesn't. So maybe I need a scaling factor on Cp or something..?

Could someone help me out?
Thanks.

Code:

%%% Flow Around a Cylinder %%%

% Initialise variables
clear all
clc

U = 12;     % Freestream velocity m/s
M = 2;      % Doublet strength
radius = sqrt(M/2/pi/U);    % Cylinder radius
t = linspace(0,2*pi,50);    % Range of theta values
circle = ones(1,50);        % Create vector
circle = radius.*circle;    % Circle of required radius

% Calculations
cp = 1 - 4.*(sin(t)).^2;     % Pressure coefficient
cp_scaled = sqrt(cp.^2 + circle.^2); % the missing function

% Display graphs
polar(t,cp,'--r')
hold on
polar(t,circle)
hold off
figure
polar(t,cp_scaled,'--r')
hold on
polar(t,circle)
hold off

super sky

Thanks :)
I never did figure it out, so it was helpful to know in case I have to do it again.

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super sky	Thanks :) I never did figure it out, so it was helpful to know in case I have to do it again.