[TowerTalk] Re:An Engineering Question

[John D. Peters]

Daniel H. Arney Jr. wrote:
> 
> Stan Griffiths wrote:
> >
> > >Hi,
> > >
> > >Just reflecting on the problem of placing guy anchors
> > >closer to the base of the tower...
> > >
> > >Interesting how yachting designers plan their rigging to
> > >keep 100+ foot masts upright, when they are limited
> > >by the beam of the yacht.  And how many square feet
> > >of sail area?
> > >
> > >Martin ZL1ANJ
> >
> > For what it's worth, I notice that a yacht's mast is not vertical with
> > respect to the earth's surface when under sail.  It rolls the boat over
> > pretty good.  Again, I suspect the mechanics of this are quite different
> > than antenna towers.
> >
> > Stan  w7ni@teleport.com
> >
> 
> You have to remember that a boat under sail power is flying a wing, it
> is an AIRFOIL that flys just like a wing of an airplane, just happens to
> be in the vertical plane. This is without going into all of the detail.
> Please do not find the thread and try to thread the needle. Not radio
> related. just a point.
> Hank KN6DI
> 
> --
>It is NOT possible to train every reader to become a mechanical engineer 
nor a yacht designer on this forum.

However, if you passed high school algebra, and trig, and plane geometry 
you probably know enough for a good start.

The mast (any of them) must be supported by the guys, forestay, backstay, 
and however many stays close to the beam, and the bearing the mast passes 
through into the cabin, and the socket into which it is seated. The mast 
is twisted, and subject to bending force perpendicular to the mast, which 
is distributed along the length of the mast (or at least the length with 
sail attached if you reef).  The amount of force is a function of the 
wind velocity, the sail area, the sail shape, and the angle that the sail 
is set relative to the wind.  However, in any case the force is trying to 
bend the mast in some direction and the bending moment is the 
perpendicular force times the length of the mast from the socket. The 
force is balanced by the combination of stays, some to the top of the 
mast, some attached by horizonal strength members at several points along 
the mast. A 170 ft mast may have 3 or 4 sets of stay attachments. This 
force is countered by the many tons of lead in the keel, under the force 
of gravity, times the distance from the pivot point to the center of mass 
in the keel. The force may be resolved into a righting moment, but that 
righting moment will equal the torque on the mast acting as the upseting 
moment. In any direction.  The horizontal component of the force is 
driving the boat, forward and sideways.  The only function of the stays 
is to transmit the force from the mast to the hull.  The force is usually 
simplified to a total force times the distance from the center of gravity 
to the center of buoyance. The more you tip, the greater the distance in 
the lever. Try 870 sq ft on each jib and 1300 or 1800 sq ft on the main. 
Double that if you want to run up the genoa or a spinnaker.  Makes your 
10 sq ft TA33 a pretty tame sail. 

Your guyed tower is exactly the same problem.  The sail area is the area 
of your tower, all antennas, masts, rotors, and wires.  You can pick a 
wind, determine the horizontal pressure at any place on the tower. Or 
make an approximation by calculating the pressure on each 10 ft piece. 
The pivot point is the base of the tower, AND any point on the tower. The 
vertical load is the weight of the tower and everything on it plus the 
vertical component of all the guy force.  The twisting moment is the 
unbalanced wind load applied to the antenna system trying to rotate the 
mast.  The twist will either be balanced by your guys on the torque 
suppressor, or the structure of the tower, or the tower will fall.  The 
horizontal force on the system will either be balanced by the horizontal 
component of the force from each set of guys or the guys will pull out, 
snap, or the tower will bend.  If you have 40 sq ft of sail above the 
tower, and above the top set of guys, you should work out the horizontal 
force at the attachment point for every antenna and see what the bending 
force on the mast is at the top of the tower. The force times the mast 
length above the tower top is one lever, and it must be balanced by an 
equal moment of the distance from the top of the tower to the bearing 
inside the tower times the side thrust force applied at the lower end of 
your mast.  Your guys may hold while your mast bends, the tower top 
section bends, or the bearings fail.  If the system holds, then the 
bending load is being transmitted to the tower, and you need to calculate 
the bending moment being applied to each section in the tower. If your 
guys are too far apart the tower may bend between the guys.

If you leave up too much sail the mast WILL break, or the stays will pull 
out, or the boat WILL roll over.  A knockdown really screws up your 
storage in the cabin!

Overload your tower and it will really screw up your backyard. 

I think the ANSWER to "An Engineering Question" is to hire a PE to look 
at your planned system if YOU don't want to follow the tower mfr specs 
and recommendations.  

73 John K1ER

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