The origin of the 30% rule is apparently derived from the automotive engine world (where I have dabbled) and refers to a simplified model of valve lift height to port diameter that doesn't restrict flow. Actual ratios applied depend on engine design dynamics (street vs race; rpm range; bore and stroke; induction and exhaust design, etc), and vary from roughly 25% to 40% (but mostly close to 25%).

The principle behind the rule is that the "curtain area" (imaginary wall area rising from the port circumference up to the valve) should be at least as large as the cross-sectional area of the port in order to avoid flow restrictions. See picture.

How to calculate the ratio. The following example is based on a tonehole with diameter (d) = 30mm, pad height (h) = 7mm (center height, avg height), radius (r), and pi = 3.14:

1) The formula for the "curtain area" is: d * pi * h;

e.g., 30mm * 3.14 * 7mm = 660mm sq

2) The formula for cross-sectional area of a hole is: pi * r^2;

e.g., 3.14 * 15^2 = 707mm

3) Solve for height where curtain area equals hole area: h * hole area / curtain area;

e.g., 7 * 707 / 660 = 7.5mm

When the "curtain area" matches "hole area", the ratio of valve height to hole diameter is 0.25 (or 25%). Let's call this the "25% Rule".

So, The saxophone world's 30% rule seems flawed in methodology and value:

1) Since pad cups tilt open, pad height measured from the high point of pad does not provide a consistent "curtain area" measurement because key cups vary in their tilt; instead, one should measure the center height of the pad (i.e., average height).

2) the 30% figure itself does not appear to be a meaningful value in theory or practice.

That said, nothing here tells us what key pad height is ideal for any given key on a given sax. But I think the "25% Rule" provides a reasoned starting point in key pad height regulation.