Towertalk
[Top] [All Lists]

## [TowerTalk] K-factor Revisited

 To: [TowerTalk] K-factor Revisited alsopb@gloryroad.net (alsopb) Mon, 01 Mar 1999 12:16:47 +0000
 ```Guys, My original query about just what the K-factor for rotors means and what it is supposed to protect against received no technical responses. I dug back into my college physics textbooks to see what I could determine. Beware, I may be in over my head here. Here are my conclusions. Torque limits can come from two places: 1) Starting torque imposed by trying to start the antenna turning in windy and non-windy conditions 2) Mechanical limits on stopping the antenna when it is turning or being tossed about in the wind. The origin of the K-factor has little to do with 1 or 2 but might instead be due to some limit on the mechanical ability of the rotor housing to withstand vertical twisting. First. The normal formula for torque is: Torque = moment arm x applied force. However, for torque about the mast axis, the force is not weight but rather only the forces of the wind. Think of it this way. Take a wrench and turn a nut that is positioned in the horizontal plane with the bolt upwards. No matter how hard you push down on the wrench the nut won't turn. You have to apply the force horizontally. Same way with the rotor. The only force (besides friction) is the wind force on the elements resisting the turning. Friction does have a weight term in it but let's assume that rotors are relatively friction free (at least in the lower 48 states and above freezing) . This wind force is proportional to antenna area and velocity of the wind raised to some power. The K factor has no stated wind speed associated with it. It does have the form of the moment arm times something. The torque required to start or stop a rotating object has the formula Torque = I x rotational acceleration I is the rotational moment of inertia and rotational acceleration is proportional to rpm. The I factor can be computed for complex objects with odd weight distributions from calculus I = integral of moment arm squared * dm Where dm is the incremental mass at the location of each moment arm Note that there is an r squared in the formula -- not r like the K factor has. The moment of intertia has been tabulated for various objects like dumbell and pipes. A 2 element antenna is like a combination of a dumbell and a pipe. I for the dumbell is the half the boom length * mass of the two elements I for the boom is the mass of the boom times the length of the boom divided by 12. For most beams the dumbell component predominates. For antennas of many elements (some close to the mast), the outer elements contribute the most to the value of I. Note: The the full weight of the antenna appears nowhere (at least not with a multiplier of 1.0) and that the moment arm is not the turning radius but rather half the boom length. Note there is the square of the boom length not the boom length to the first power. IMHO the bottom line. I have't got the faintest idea what the K factor is and what it is supposed to protect against. It's form suggests that it is related to wind forces but weight is used instead of wind force. It appears that it simply might be the force required to break loose from the housing in up and down drafts. In that case, the housing should fail and not the guts. Anybody else got ideas on just what K really is? Brian/K3KO -- FAQ on WWW: http://www.contesting.com/towertalkfaq.html Submissions: towertalk@contesting.com Administrative requests: towertalk-REQUEST@contesting.com Problems: owner-towertalk@contesting.com Search: http://www.contesting.com/km9p/search.htm ```
 Current Thread [TowerTalk] K-factor Revisited, alsopb <= [TowerTalk] K-factor Revisited, Tom Rauch [TowerTalk] K-factor Revisited, Pete Smith [TowerTalk] K-factor Revisited, froemke@ibm.net [TowerTalk] K-factor Revisited, Tom Rauch [TowerTalk] K-factor Revisited, Pete Smith [TowerTalk] K-factor Revisited, K7LXC@aol.com [TowerTalk] K-factor Revisited, Guy Olinger, K2AV Message not available[TowerTalk] K-factor Revisited, Guy Olinger, K2AV [TowerTalk] K-factor Revisited, Pete Smith