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!