Let's look at this a bit more, as I see you have now copied and pasted this in several places.
An overview of the process by which the simulation programs calculate port length is as follows:
- Calculate the effective length L_{EFF} of the port based on box volume, box tuning frequency and port cross-sectional area A.
- Calculate the actual length of the port L_{ACT} using an end correction whose value is proportional to the square root of the port cross-sectional area A. This formula has the form:
L
_{ACT} = L
_{EFF} - k * D
where k is the end correction factor and D is the diameter of the equivalent cylindrical port having cross-sectional area A.
Now, it's been observed that using this equation with k = 0.732 gives incorrect port lengths, and the error results in a port that's usually too long. The
website to which you previously linked shows errors between calculated and actual length, but does not establish the
why.
For the sake of argument, let's assume your hypothesis is correct, namely that this error is solely due to an error in the end correction factor k. That is, assume there is a value k
_{RIGHT} giving the correct length L
_{RIGHT} and a value k
_{WRONG} giving a wrong length L
_{WRONG}. This leads to the following:
L
_{RIGHT} = L
_{EFF} - k
_{RIGHT} * D
L
_{WRONG} = L
_{EFF} - k
_{WRONG} * D
Let's compute the percent error in length as follows:
percent error in length = (L
_{RIGHT} - L
_{WRONG}) / L
_{RIGHT} * 100
In the subtraction of the numerator, L
_{EFF} drops out, and the error term in the numerator only depends on the equivalent port diameter D. The result is this:
percent error in length = (k
_{WRONG} - k
_{RIGHT}) * D / L
_{RIGHT} * 100
For a given port area, the numerator does not depend on port length at all. If the port area is constant, the numerator is constant also. That means the percent error in port length would be inversely proportional to the correct port length if this hypothesis were true. Now look at the
web site with the data in the table titled "Results, un-damped box". The percent error in port length is almost constant (with actual lengtth / calc. length going from 0.81 to 0.83 as the port length varies by a factor of 3). In the case of 10 cm and 20 cm port lengths, the percent error is the same.
So assuming the data of that web site is correct, the "incorrect end correction" hypothesis fails. So yes, there is an error between computed and actual port lengths, but the assumption that this is due entirely to the end correction factor leads to a contradiction.