I’m looking for the work flow of how to create a volume by revolving a variable area trapezoid around the z axis. I have a formula for the area of the trapezoid and it is a function of the radial distance from the origin. Both the height and this radial distance vary with the angle of revolution.
The figure immediately below shows the elliptical path that the rotation takes. Because the trapezoid area varies with the angle of revolution, the path traced in the x-y plane is an ellipse and not a circle. The figure below shows the path in the x-y plane:

This next figure shows the x-z plane which shows the variable-area trapezoid at phi = 0 degrees and phi = 180 degrees. The rotation occurs around the vertical axis that goes through the point "S". Notice the large reduction in area of the trapezoid.
The radial line length, p, to the ellipse edge is given by,

where is a constant value as are w and R. At = 45 degrees and R = 0.0006, w = 0.0007908.

What I am trying to do is to verify an equation that I have developed for calculating this volume. I want to make sure that my equation, in fact, produces the volume of the revolved variable-area trapezoid. The area of the trapezoid is given by

and h is given by:

where B is a constant and is a constant where p is evaluated at = 90 degrees. For the values of , w and R given above, B = 0.867.
The volume then is given by,

The next figure shows an incremental volume diagram which is then integrated as in the equation immediately above,

And so the final result should look something like the blue portion of each drawing below. How would I go about implementing this in Matlab?I’m looking for the work flow of how to create a volume by revolving a variable area trapezoid around the z axis. I have a formula for the area of the trapezoid and it is a function of the radial distance from the origin. Both the height and this radial distance vary with the angle of revolution.
The figure immediately below shows the elliptical path that the rotation takes. Because the trapezoid area varies with the angle of revolution, the path traced in the x-y plane is an ellipse and not a circle. The figure below shows the path in the x-y plane:

This next figure shows the x-z plane which shows the variable-area trapezoid at phi = 0 degrees and phi = 180 degrees. The rotation occurs around the vertical axis that goes through the point "S". Notice the large reduction in area of the trapezoid.
The radial line length, p, to the ellipse edge is given by,

where is a constant value as are w and R. At = 45 degrees and R = 0.0006, w = 0.0007908.

What I am trying to do is to verify an equation that I have developed for calculating this volume. I want to make sure that my equation, in fact, produces the volume of the revolved variable-area trapezoid. The area of the trapezoid is given by

and h is given by:

where B is a constant and is a constant where p is evaluated at = 90 degrees. For the values of , w and R given above, B = 0.867.
The volume then is given by,

The next figure shows an incremental volume diagram which is then integrated as in the equation immediately above,

And so the final result should look something like the blue portion of each drawing below. How would I go about implementing this in Matlab? I’m looking for the work flow of how to create a volume by revolving a variable area trapezoid around the z axis. I have a formula for the area of the trapezoid and it is a function of the radial distance from the origin. Both the height and this radial distance vary with the angle of revolution.
The figure immediately below shows the elliptical path that the rotation takes. Because the trapezoid area varies with the angle of revolution, the path traced in the x-y plane is an ellipse and not a circle. The figure below shows the path in the x-y plane:

This next figure shows the x-z plane which shows the variable-area trapezoid at phi = 0 degrees and phi = 180 degrees. The rotation occurs around the vertical axis that goes through the point "S". Notice the large reduction in area of the trapezoid.
The radial line length, p, to the ellipse edge is given by,

where is a constant value as are w and R. At = 45 degrees and R = 0.0006, w = 0.0007908.

What I am trying to do is to verify an equation that I have developed for calculating this volume. I want to make sure that my equation, in fact, produces the volume of the revolved variable-area trapezoid. The area of the trapezoid is given by

and h is given by:

where B is a constant and is a constant where p is evaluated at = 90 degrees. For the values of , w and R given above, B = 0.867.
The volume then is given by,

The next figure shows an incremental volume diagram which is then integrated as in the equation immediately above,

And so the final result should look something like the blue portion of each drawing below. How would I go about implementing this in Matlab? volume MATLAB Answers — New Questions

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