>> 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...   ;-) 


I'd say that you should start with the simple formula for a linear
increase.  Anyone should be able to come up with:

(shortest + longest)*N/2

(You all have learned this in school, haven't you? -- Sorry: I needed
this ...)

In your case, (10"+24")*88/2 = 34"*44 = 1496" = (Can't you go metric?!?)
= 124.66666666666666666' = let's say 125'.

Two pieces of information show that the linear increase is not okay:

* You estimate that you need 150' -- and because you are a professional,
you are probably right.

* You measured an increase of 1/2" from tube to tube. But with 88
tubes and a shortest tube of 10", the longest would then be around
10+88/2 = 54", instead of the 24" you told us -- a _huge_ difference!
So I guess that the shorter tubes' lengths increase faster.

Short of doing a statistical analysis of quite a few tracker tubings,
I would suggest to multiply the formula's result with a correction
factor of, right now, 1.2, so that we end up with

(shortest + longest)*N/2*1.2

or, for 88-tubed stacks,

(shortest + longest)*44*1.2

which, for your tubes, is 149.6'

(Do you see how _precise_ a formula can be?  You must have guessed
wrong with your 150'.   ;-)  ).

In later times, you could make a list of correction factors based
on the stack manufacturer: maybe some provided more space, so that
more "mathematically increasing" tubing can be used.  Others need
more comical turnarounds, further destroying the nice formulae...

Notice that the formula above is very dependent on only two tube
lengths, so if they are somehow "odd" or you measured wrong, you'll
end up with a very wrong result.  Maybe a more reliable idea would be
to measure the four longest tubes (2 on the left, 2 on the right) and
the four shortest tubes (all in the middle, probably) and then compute

    (sum of all 8 lengths)*N/8*1.2

or, for 88 tubes and a fixed correction factor of 1.2,

    (sum of all 8 lengths)*13.2

This should average out any gross mis-measurements.  (And if you believe
that 13 is an unlucky number, you can now blame it on the formula if
you ordered too little tracker tubing ... but note that it's actually
13.2, i.e., about 1.5% more).

Regards
Harald M. Mueller