Elliptical Pressure Distribution Function

Hi everyone,

I am simply trying to have a number, called "Pressure Factor", to be between 0 and 1 but with a specific distribution. I would like it to start at 1, then go towards 0 as x increases but in an elliptical fashion, like the ideal spanwise lift distribution on an airplane wing. Can anyone help?

Thanks.

Answer 1

[Yash]

Hi,

You can obtain an elliptical distribution for your "Pressure Factor" using the equation of an ellipse. Here's the code that generates the desired distribution:

x = linspace(0, 1, 100);  % Range of x values
a = 1;  % Semi-major axis of the ellipse
b = 0.5;  % Semi-minor axis of the ellipse

pressureFactor = sqrt(1 - (x/a).^2) * b;  % Elliptical distribution

plot(x, pressureFactor)
xlabel('x')
ylabel('Pressure Factor')
title('Elliptical Pressure Factor Distribution')

In this code, x represents the range of values from 0 to 1. The a and b variables determine the shape of the ellipse. The equation sqrt(1-(x/a).^2)*b calculates the pressure factor based on the elliptical distribution formula. Finally, the code plots the pressure factor against the x values as shown below:

You can adjust the values of a and b to modify the shape of the elliptical distribution according to your requirements. Hope this helps!