[TheForge] formula for figuring taper volume

[Brian Hall]

This is the formula I use for figuring the volume of a
taper. You then figure out how long a piece of parent
stock you need to equal that volume. This is a nice
formula because it doesnt matter what the cross
sectional shapes are because the calculation is based
on pre-calculated areas of those shapes.

Stuff to pre-calculate:
   A1= cross secional area of the start of the taper
   A2= cross sectioal area of the point of the taper
   L= the desired length of the taper

remember to have all in the same units!

Volume of the taper=
0.333 * (A1 + A2 + (squareroot(A1*A2)) * L

Heres an example. You want to taper .75" squarestock
to
 .25" squarestock over 8". How many inches of the .75"
steel do you need?

A1=0.75*0.75= 0.5625in2
A2=0.25*.025=0.0625in2
L=8in

0.333*(0.5625in2 + 0.0625in +
(sqrt(0.5625*0.0625))*8in

 =0.333*(0.5625in + 0.0625in2 + 0.1875in2)* 8in
 =0.333 * (0.8125in2) * 8in
 =0.271in2 * 8in
 = 2.16in3

So now use algebra to figure what length of 3/4in
square steel equals 2.16in3

 0.5625in2(X) = 2.16in3
 X=2.16in3/0.5625in2
 X = 3.84 inches I usually only deal with 8ths and
very occasionally with 16ths of an inch so I would
need 3and7/8inch of 3/4" square to make the taper

Good Luck - I know this is computationally a pain... I
only use it on big tabers when length is critical such
as tapered table legs.

Brian

ps I did'nt check my math so forgive any errors.

  




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