Theatre Design & Technology - Winter 2012 - 56

SteP 2: Work on diAgonALS
The divisor is computed with the following equation:
D = (N1X)(N2Y)(N3Z) + (N2X)(N3Y)(NIZ) + (N3X)(N1Y)(N2Z) -
(N3X)(N2Y)(N1Z) - (N2X)(N1Y)(N3Z) - (N1X)(N3Y)(N2Z)

Wow, what a confusing equation to try to remember. Here
is a trick that might help you figure out how to recreate this
formula without actually remembering all the parts-work on
diagonals. Confused? Look at the color-coded version of the results table below.
N1X = -.435

N1Y = -.381

N1Z = .816

N2X = -.351

N2Y = .282

N2Z = .846

N3X = .470

N3Y = -.059

N3Z = .881

and
D= (N1X)(N2Y)(N3Z) + (N2X)(N3Y)(N1Z) + (N3X)(N1Y)(N2Z) -
(N3X)(N2Y)(N1Z) - (N2X)(N1Y)(N3Z) - (N1X)(N3Y)(N2Z)

Do you see a pattern with the different colors? Look at the
three sets of numbers highlighted in blue. They are arranged
in a diagonal line from the upper-left corner to the lower right
corner. They are your first set of numbers. Replace the variable
names in the equation with their values.
Now, look at the group of numbers highlighted in red.
They also make a diagonal line, just below the blue line (sure,
you have to pick up the stray number at the top of column, but
it follows the pattern). They are the second set. Put these values
into the equation.
Last, look at the green line of numbers. See the pattern?
Put these values into the equation, too.
Now that you have the top line filled in, do the same for the
next three groups of numbers-the bottom line. These three
diagonal rows move from the bottom left corner to the top right
(opposite of the first three groups). See the pattern here?
N1X = -.435

N1Y = -.381

N1Z = .816

N2X = -.451

N2Y = .282

N2Z = .846

N3X = .470

N3Y = -.059

N3Z = .881

D = (N1X)(N2Y)(N3Z) + (N2X)(N3Y)(NIZ) + (N3X)(N1Y)(N2Z) -
(N3X)(N2Y)(N1Z) - (N2X)(N1Y)(N3Z) - (N1X)(N3Y)(N2Z)

By the way, this formula was not included on the last ETCP
Formula Table that I saw (but it could be in a newer one). It sure
would be useful. But if you remember my visual trick-work on
the diagonals-you can create the formula without having to remember what may seem like an interrelated mess of an equation.
Replacing the variables in this formula with the values
from the matrix, we get:
D =(-.435)(.282)(.881)+(-.451)(-.059)(.816)+ (.470)(-.381)(.846) -

Multiplying these six sets of numbers is probably the
most tedious step in computing the load on the bridle legs,
and where most people make mistakes. I recommend that
you ignore the sign of the sets of numbers as you multiply
them (treat them as positive numbers) and apply the sign
(positive or negative) after you do the multiplication. Here is
how you know the sign of the product (result of multiplying
the numbers):
* If there is one negative number in the group, the
product is negative.
* If there are two negative numbers in the group, the
product is positive.
* If there are three negative numbers in the group, the
product is negative.
So, just multiply the three numbers in each of the six
groups as though they were all positive numbers, and then apply the appropriate sign. The results of multiplying these groups
of numbers are:
D = (-.108) + (.022) + (-.151) - (.108) - (.151) - (.022)
or
D = -.518

That was a lot of work for this one number, but you will
need this number in step 3. You will also need one additional
piece of information before you can calculate the load on each
bridle leg-the load being supported by the three bridles. For
this problem, let's say that the bridles are supporting a 500
pound load. The letter F in the formulas below represents this
value. We will call the force (tension) on the bridle legs F1, F2,
and F3, respectively.

SteP 3. CALCuLAting tHe tenSion
Here is the final set of formulas:

()
)( )
)( )

F
F1 = ((N2X)(N3Y) - (N3X)(N2Y)) D
F
F2 = ((N3X)(N1Y) - (N1X)(N3Y) D
F
F3 = ((N1X)(N2Y) - (N2X)(N1Y) D

Fortunately, these formulas are (or were) on the ETCP
Formula Table, so you do not have to memorize them. Let's
plug in the values and compute the loads on the three bridle
legs.

()
)(
)

F
F1 = ((N2X)(N3Y) - (N3X)(N2Y)) D
F1 = ((-.451)(-.059) - (.470)(.282)

500
-.518

F1 = (.026 -.132)(-963.39)
F1 = (-.106) (-963.39)
F1 = 102.12 pounds

(.470)(.282)(.816) - (-.451)(-.381)(.881) - (-.435)(-.059)(.846)

winter

2012

theatre design

& technology

55
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