My review of the 30% Rule for pad height; perhaps someone will find it useful. In the saxophone world, a common rule or assumption about key pad heights is: a pad height (measured at high side of pad) of 30% of the tonehole diameter is (approximately) a height below which pitch and tone will start to be affected, and above which there is no effect.
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 crosssectional 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 crosssectional 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.
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 crosssectional 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 crosssectional 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.
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