**How to
find the Unknown Length of a Guy Wire**

**by N4UJW
Hamuniverse.com**

**It is late
and you are sitting at your desk and in the middle of planning
your new tower project or antenna support and your getting all of the
materials, parts, accessories list, etc together so you can dig deep into
your bank account for the needed money to purchase all of the needed
supplies.**

In your excitement you
realize you just can't wait to get that antenna support mast or that
tower you just acquired high in the air so your signal will travel the
earth and beyond.

**In your planning stage
you have looked over your proposed tower or mast site and found the
ideal place in which to "plant" it in the ground and you know how high it
will be when it is installed.**

**Now you ask
yourself where to put the guy wires for it on the ground...you walk
around the area and pick some good locations for each of them hopefully
conforming to recommended safe installation procedures. In your
observations, you realize that each guy wire will have to be a different
length due to obstructions and Murphey's Law getting in the way. It never
fails, Murphy is always looking over our shoulders and picking
on us as ham radio operators!**

**Ok now, stand back
Murphey...each guy wire has to go in a specific location whether "Murphey"
likes it or not and you know how high the tower or support mast, pole, etc
is so then it hits you... and you ask yourself....how long will the guys
have to be for the locations I have picked out? I don't want to have to
buy more guy wire than I need. After all, my wife says I am
cheap!**

**You look at the tower,
pole, mast etc and your location for the guy wire at ground level and
say....well the mast is 50 feet tall, so the length at the location of my
first guy has to be at least as long as the mast is high
but a bit longer...but how much longer will it have to be due to the
angle of the guy coming off of the tower if it is 70 feet away?
See the example drawing below for our proposed setup and to get the answer
to our question in our fictitious installation.**

**In
our example above, the tower is 50 feet from the base to the top
guy**

attachment point and the distance to the first guy is 70 feet...how
long is the guy wire!

**Back to our school
days!**

Here is where the Pythagorean
theorem, **that was proven
by an ancient Greek named Pythagoras, (call sign unknown and he is
SK), comes into play for our
purpose.**

**Pythagoras proved mathematically.... that for a
right triangle with legs A and B, and a "hypothenuse" C that these
formulas will work every time for us to find our unknown guy wire
length:**

**Get your calculator out,
the simple one with 4 functions plus square root. No, you don't need a
scientific calculator...get the one that you use to balance your
checkbook. If you don't have a calculator, use the one at the top of this
page when the guy gets done with it! GRIN!**

Now referring to the
drawing above, Leg A or B in the formula below can be
either the height or the distance from the base of the tower or mast. Yes
of course, you have to measure from the base to the outer guy tie off
point.

**Leg C (the hypothenuse)
is the unknown guy wire length that we are looking for.**

The "right
triangle" is formed by the angle at the base of the tower or mast forming
a 90 degree angle to the earth AND the guy point away from the
installation.

**Here is the
formula:**

Said another way... C squared = A
squared plus B squared

**We will be using the
first formula above in this example to figure out how long our guy wire
"C" needs to be in the drawing above since "C" is the unknown in our
situation. We already know what "A" and "B" are in
length.**

**So.....**

**Using the
formula:**

**C squared = A squared
plus B squared so we insert our known numbers, 50 and
70.**

**C squared = 50 squared
plus 70 squared. (in case you have forgotten, "squared" means multiplying
by itself)**

**So.... C squared = 50
times 50 equals 2500 + 70 times 70 equals 4900...adding together 2500 +
4900 we get 7400.**

**So.....C squared =
7400**

**Now since C is squared,
we need to take the square root of 7400. Here is where your handheld
calculator comes in handy unless you are Einstein. Plug in the 7400 in the
calculator and get the square root......**

**Our answer is the square
root of 7400.......86.02 feet!**

**So....."C" in the drawing
above, which represents our unknown guy wire length, is now known to
us as 86.02 feet! Don't forget to add a few inches or so for the
wrapping of the guy wire points, tying off, etc on each end.**

Now
you say to yourself, either I have to buy a 100 foot role of guy
wire for that length and cut what I need rather than splice
lengths from 2 50 foot roles which is not a very good idea especially for
tower guying...Murphey just cost me some more money!
Rats!

**Now for the other
guys required for your installation use the same formula
above making sure you know how high the
guy attachment point is for each set
of guys and the distance out from the
tower or mast to tie off the guy wire...then
just plug in the numbers into the formula like in the example above.
This method works for any tower, mast, etc as long as it forms a "right
triangle" with the earth below it. We are simply using math to
represent the installation in this example.**

**Another
example:**

**Your mast is 30 feet
tall. The mast will be guyed at it's top and then extend outward to the
ground. The distance from the base of the mast to the guy point is 35
feet...how long will this unknown guy wire be?**

**Using the first formula
given above:**

**C squared = A squared + B
squared.**

**C squard = 30 squared +
35 squared.**

**C squared = 900 +
1225**

**C squared =
2125**

**Taking the square
root of 2125 =46.09 feet!**

**Warnings and Notes:**

**This method only works for towers
and masts on flat ground installations when the angle between
the mast or tower and the guy point out from it is 90 degrees.
For angles other than 90 degrees....just let Murphey rule...buy more guy
wire than you think you will need plus some and a little more! Charge it
to Murphey's law on his bank account! If you really wanted to get into
some more complicated math, then do a search on Google for more
on the Pythagorean theorem. The "math" gets more complicated when the
angle is not 90 degrees! Good luck.**

Using this method explained above, you will know exactly how
much guy wire to use per guy.

**Always use the recommended tower or mast mfg's guying
specifications for your height, wind load, etc for your particular
installation. Be safe, not sorry. Never install
a tower or mast near power lines. Murphey says
that one or the other will fall.**

**More good reading on tower and mast
installations and the Pythagorean theorem:**

**Rohn Tower Brochure with guying
suggestions.**

**Rohn Telescoping Mast Brochure with guying
suggestions.**

**Pythagorean theorem calculators:
(off site)**

**http://www.analyzemath.com/Geometry_calculators/pythagorean.html**

**http://www.algebra.com/calculators/geometry/pythagorean.mpl**

**If you know of another method
of determining the unknown guy wire length that is simple to use, please
give us your input! n4ujw AT
hamuniverse.com...thanks!**