I am going to try to do this and keep the math simple. Maximum loads are different in a 3 guy and a 4 guy system. In a 4 guy system the worst case is when the wind is straight down the guywire. Then one guy wire takes the full load of the wind on the tower. In this case the guy tension is proportional to the wind load,and the Horizontal Component of the Guy Tension is Horizontal Component of the Guy Tension = 1 * Wind Load If the wind is coming exactly between two guy wires in a 4 guy system, each guy wire must support 1/2 the load, but the guy wire is not pulling inline with the load, it is 45 degrees off, so the guy tension is proportional to 1/2 the wind load divided by the cosine of the angle between the wind load vector and the guy tension vector: The horizontal component of the guy tension is: Horizontal Component of the Guy Tension = Wind load / (2 * cos (45 degrees)) which is Horizontal Component of the Guy Tension = 0.707 * Wind Load For a 4 guy system, the worst loading on the guys is when the wind is exactly inline with one up wind guy anchor. In a three guy system, the worst case for the guy is not when the wind is in line with the guy. The worst case is when the wind is exactly 30 degrees off one side of the guy like this: Top View of Tower \ \____ / / ^ Wind blowing to the top of the page from the bottom. The guy at the top of the sketch isn't doing anything. The guy going to the right is not pulling into the wind, it is only balancing the offset tension from the guy running down and to the left. It is the only one doing anything to resist the wind force, but it is pulling off at a 30 degree angle. But there is only one, so the horizontal component of the guy tension is: Horizontal Component of the Guy Tension = Wind Load /(1* Cos (30 degrees)) which is Horizontal Component of the Guy Tension = 1.154 * Wind Load Now if we look at a wind coming from the left in the little sketch, we see that we have two guys working for us, but they are pulling 60 degrees off. Using the equation above we get: Horizontal Component of the Guy Tension = Wind Load /(2* Cos (60 degrees)) or Horizontal Component of the Guy Tension = 1 * Wind Load Thus a 4 guy system places a smaller worst case load on the guy wires and guy anchors than does a 3 guy system. Now to go a little further into Tower Engineering 101: There are two basic considerations in a guyed tower: The guy wires have to resist the wind, and the tower has to resist the guy wire loads so it doesn't buckle. The tower buckling is caused by the fact the guy wires run down hill so any pull on them pushes down on the tower. So what is the down load on the tower in different wind conditions for 3 guy system and a 4 guy system? Glad you asked - I'll try to explain. ;-) The simplest case to understand is the wind coming right inline with the guy anchor. The wind is trying to push the tower over and (if we have a pined tower base) the only thing holding it is the pull on the guy wire. If the anchor is at 80% of the tower height, the guy is running up from the anchor (assuming no sag) at an angle defined as: Horizontal Guy Angle = arc Cotan (.80) = 90 degrees - arctan (.80) = 51.3 degrees. if you go out to 100% then Horizontal Guy Angle = 90 degrees - arctan (1) = 45 degrees. Now the Horizontal Component of the Guy Tension required to resist the wind load is related to the Guy Tension and the Horizontal Guy Angle in the following way: Horizontal Component of the Guy Tension = Guy Tension * cosine ( Horizontal Guy Angle ) or another way to say it is: Horizontal Component of the Guy Tension Guy Tension = ---------------------------------------------------------------- cosine ( Horizontal Guy Angle ) And the Guy Tension is what pulls down on the tower. The Down Force on the Tower is: Down Force on the Tower = Guy Tension * sine ( Horizontal Guy Angle ) Bear with me we are going to do a little high school algebra and combine the equations. ( And the equations are going to get very wide so watch out for word wrapping!!!) Horizontal Component of the Guy Tension Down Force on the Tower = ---------------------------------------------------------------- * sine ( Horizontal Guy Angle ) cosine ( Horizontal Guy Angle ) or sine ( Horizontal Guy Angle ) Down Force on the Tower = Horizontal Component of the Guy Tension * ------------------------------------------------ cosine ( Horizontal Guy Angle ) Now a Sine / Cosine is the Tangent function so Down Force on the Tower = Horizontal Component of the Guy Tension * tangent ( Horizontal Guy Angle ) But Horizontal Component of the Guy Tension is dependant on the wind force and the angle between the wind and the guy wire from above. In the 4 guy system case the wind is straight down the guy line. So we only have one guy "working" for us and the Down Force on the Tower is Down Force on the Tower = (1 * Wind Load) * tangent ( Horizontal Guy Angle ) In the 4 guy system if we have the wind coming between the guys then we have two guys working for us, as above, and each one contributes to the download on the tower: Down Force on the Tower = 2 * ( 0.707 * Wind Load) * tangent ( Horizontal Guy Angle ) or Down Force on the Tower = 1.414 * Wind Load * tangent ( Horizontal Guy Angle ) So the worst case tower compressive load in 4 guy system is when the wind is right between two guy anchors. In a 3 guy system we have to look at the problem for winds in 30 degree increments. Obviously the inline case is the same as the 4 guy system. The 30 degree off case has two guys that have tension because of the wind load. The guy running down and to the left in the sketch above has: Horizontal Component of the Guy Tension = 1.154 * Wind Load so for this one guy: Down Force on the Tower = 1.154 * Wind Load * tangent ( Horizontal Guy Angle ) Now the Horizontal Component of the Guy Tension in the guy running off to the right is related to the tension on the guy taking the wind load as Horizontal Component of the Second Guy Tension = Horizontal Component of the First Guy Tension * Sin ( 30 degrees ) = 0.5 * Horizontal Component of the First Guy Tension >From this we know that the second guy adds an additional load to the tower of: Down Force on the Tower = 0.5 * 1.154 * Wind Load * tangent ( Horizontal Guy Angle ) So adding the two together we get Total Down Force on the Tower = ( 1+ 0.5 ) * 1.154 * Wind Load * tangent ( Horizontal Guy Angle ) or Total Down Force on the Tower = 1.731 * Wind Load * tangent ( Horizontal Guy Angle ) Now if we swing the wind around so it comes from the left, then we have two guys "working" for us, but they are pulling at a 60 degree offset. >From our work above we know that EACH guy has a Horizontal Component of the Guy Tension of: Horizontal Component of the Guy Tension = Wind Load /(2* Cos (60 degrees)) or Horizontal Component of the Guy Tension = 1 * Wind Load Again we know that the Down Force on the Tower for each guy is: Down Force on the Tower = Horizontal Component of the Guy Tension * tangent ( Horizontal Guy Angle ) or Down Force on the Tower = 1 * Wind Load * tangent ( Horizontal Guy Angle ) So for our two guys, the Total Down Force on the Tower is Total Down Force on the Tower = 2 * Wind Load * tangent ( Horizontal Guy Angle ) So a 4 guy system will place a lower maximum load on the guy wires and a lower maximum download load on the tower than a 3 guy system. Now I know the sharper of you are thinking that I am ignoring the weight of the guy wires the wind load on the guy wires. You are correct. However, I have calculated in these factors many times and I find that they amount to less than 3% of the total loads in a typical 100' amateur installation. For shorter installations they make even less difference. I hope this had been somewhat informative and gives a little insight into the technical issues of tower design. You can have a lot of fun when you start to take into consideration guy wire sag, guy wire wind load, lateral deflection of the tower, and ice loading. It gets real complicated, real fast. Then for the tower over 500' you get to look at dynamic response and oscillations of the whole tower system in varying wind profiles. For that you need a computer and specialized software. Those I leave to the real professionals. Steven H. Sawyers PE ARRL Volunteer Consulting Engineer