Need a Math Wiz

Hi All,  I'd like to impose on those who are good at math to come up
with a formula for determining how much trackerbar tubing is required
for the tubes between the trackerbar and the stack.  Since the exact
distance from the trackerbar to the stack varies from manufacturer
to manufacturer, it seems to me that the formula only has a couple
of constants.

First is the spacing of the nipples on the stack.  Due to normal width
of an upright piano, the nipples are almost always spaced at 1/2-inch
intervals.  Typically, this means that all 88 nipples on the stack fit
within a space of 48 inches (there is a little blank space at the
breaks in the scale).

Second, by virtue of the 9-holes per inch spacing of the holes in the
bar, all 88 nipples fit within a space of 10 inches.

The two main variables in the formula have to do with the physical
distance between the trackerbar and the stack and the arc of the
tubing.  Normally, figuring out the proper length of the shortest tube
is as simple as taking a flexible ruler (or string) and measuring the
distance.  Figuring out the longest length is somewhat more difficult,
especially if the tubing is missing.  However, in most cases, that
distance can also be easily measured.

So, assuming that you know the shortest length, the longest length, and
the other two constants, is there an easy formula for figuring out how
much tubing will be required?  Mind you, it doesn't have to be extremely
accurate.  A general formula will do.  It would just be nice to have a
formula where you could plug in a few numbers and come up with an
answer.

As an example, I measured the shortest tube and it is 10".  The longest
tube, 'drooping' correctly, is 24".  Measuring a few subsequent tubes,
I found that they increased in length just less than 1/2" per tube.
So, how many feet of tubing will I use?  I guess it will be about 150
feet (based on prior experiences), but a formula would be nice!

Musically astute, but mathematically challenged...  ;-)

John A Tuttle
Player-Care.com
Brick, New Jersey, USA

By the way, I will give credit to the creator of the easiest formula
on the "Tubing" page at Player-Care...  :-))

 [ http://www.player-care.com/tubing.html  -- Robbie