topic Re: Another SOLVE Block Question in Mathcad

Another SOLVE Block Question

thodij — Sat, 12 Jul 2025 12:52:27 GMT

Good morning, PTC Community:

Objective:

Given circle ID, and fixed value "a" for the equivalent in area & perimeter ellipse, goal seek the value of b.

I am encountering a "These units are not compatible" error. See attached.

Using Mathcad 10.0.1.0.

Your assistance will be appreciated.

Re: Another SOLVE Block Question

thodij — Sat, 12 Jul 2025 13:38:44 GMT

Perhaps, it is not possible to have a circle and a unique ellipse that both have the same area and perimeter.

Re: Another SOLVE Block Question

thodij — Sat, 12 Jul 2025 15:01:48 GMT

Yes, it is impossible to have a circle and ellipse that are both equal in area and perimeter, unless they are both circles!

Correction in the constraints block is attached.

Re: Another SOLVE Block Question

Werner_E — Sat, 12 Jul 2025 18:12:48 GMT

@thodij wrote:

Good morning, PTC Community:

Objective:

Given circle ID, and fixed value "a" for the equivalent in area & perimeter ellipse, goal seek the value of b.

I am encountering a "These units are not compatible" error. See attached.

Using Mathcad 10.0.1.0.

Your assistance will be appreciated.

JT

You cannot add or subtract a length and an area, hence the unit mismatch error.

In the approximation formula for the perimeter of an ellipse you made an error. It should read (a+b), NOT (a*b).

Re: Another SOLVE Block Question

Werner_E — Sat, 12 Jul 2025 17:45:48 GMT

I see that you found your error (a+b) instead of (a*b).

By specifying the values for the circumference and the area of an ellipse, the dimensions of the half axes a and b are clearly defined (except for the order of a>b or a<b).
And if the specifications correspond to those of a circle, then the solution is precisely this circle.
However, this has nothing to do with your original question about the unit mismatch error 😉

Here a demonstration using the 'exact' formula with the elliptic integral.

Input of the function "getAxis" are area and perimeter of the ellipse, output are the lengths of the two half axis a and b.

If the input corresponds to the values of a circle, the result is exactly that circle (a=b).

A circle is the ellipse with the least perimeter by a given area. So if you demand a perimeter too small, the solutions will be non-real.

In the example below the perimeter would have to be at least 35.449 inches to get real solutions.

A solve block does not return non-real solutions if the guess values are real.

To get the non-real solutions you would have to provide non-real guesses:

As you see we also get tiny imaginary parts in the real solutions as well. This is because of numerical inaccuracies, presumable because of the numerical evaluation of the integral, I guess.

Re: Another SOLVE Block Question

thodij — Sat, 12 Jul 2025 17:41:07 GMT

Perfect. Thank you, Werner.

It all makes sense.

Regards,

Joseph T.