Lesson14-Tension on Three-Point Bridles

Rigging Math

(Made Simple)

A Primer by

Delbert L. Hall, Ph.D.

ETCP Certified Rigger

ETCP Recognized Trainer

Lesson 14: Tension on Three-Point Bridles

     Although calculating the lengths of thee-point bridles is relatively simple, calculating the load on each bridle is more “involved.”   While the math is not complicated, there are several steps. And because each step involves numerous operations that use a lot of numbers, it is very easy to get confused and make mistakes. Since just one mistake can throw off everything, calculating the loads on the bridle legs can be a tedious task, but not an impossible one.

You will, of course, need the bridle lengths that you computed above, but that is just a start; you will need three more formulas (or sets of formulas). Each formula is a “step” in calculating the tension on the legs. In the first step you will create a formula matrix, which makes it easy to remember. These formulas calculate nine values that will be needed in steps 2 and 3. Let’s get started.

Step 1:

The matrix looks like this:

Write out these formulas, substitute the X, Y and Z values from the coordinate table, and the L dimensions (bridle lengths) which you calculated earlier, and calculate the results.   The results of this set of equations are:

N1X = -.435       N1Y = -.381       N1Z = .816
N2X = -.351       N2Y = .282       N2Z = .846
N3X = .470          N3Y = -.059       N3Z = .881

These results will be used to compute a divisor number in step 2, below. This divisor, D, will be used in the final set of equations.

Step 2:

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

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

and,

Do you see a pattern with the different colors? Look at the three sets of numbers highlighted in Yellow. 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 Magenta. They also make a diagonal line, just below the Yellow 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 Bright 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?

BTW, this equation was not included on the last ETCP Formula Table that I saw (but it could be on a newer one). It sure would be useful. But if you remember my “visual trick,” you can create the formula without having to remember what may seem like an interrelated mess of an equation.

Replacing the variables in this equation with the values from the matrix, we get:

        D = (-.438)(.282)(.881) + (-.451)(-.059)(.816) + (.470)(-.381)(.846)
- (.470)(.282)(.816) – (-.451)(-.381)(.881) - (-.435)(-.059)(.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 (positive) numbers in each of the six groups and them apply the 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 the final step, below. 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 equations below represents this value. We will call the force (tension) on the bridle legs F1, F2 and F3, respectively. So, here is the final set of equations:

Step 3:

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.

The results of your calculations may vary slightly from the ones above (but not by much – less than one pound) based on how many places to the right of the decimal you extend each number, so do not be confused if your results are not exactly as above.

Conclusion

Calculating the lengths of the three bridle legs was pretty easy, but calculating loads on the three bridle legs was a LOT of potentially frustrating work. Computing these loads with a rigging app like RigCalc, for Android and iPhones, is definitely a LOT easier. Still, there are times when you might have to calculate this by hand.

Practice is the only way to become proficient at doing math problems such as these, so create some problems and work them. Be careful; most math mistakes are just foolish errors. Use a rigging app to check your answers. Happy calculating.

Worksheet

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