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Elliptical Pressure Distribution Function

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Nicolas Wilding
Nicolas Wilding on 5 Nov 2021
Answered: Yash on 21 Feb 2024
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.

Answers (1)

Yash
Yash on 21 Feb 2024
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!

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