[TowerTalk] Help with calculations...

[Grant Saviers]

It's not too difficult since you don't need to calculate the stress in 
the tower and assume it is strong enough to handle the lifting force.

1. Calculate the moment arms for the tower only. Either assume a uniform 
weight/ft x the length x halfway up = x ft-lbs.  Or more accurately for 
a non uniform tower, sum the moments of each sections weight at each 
sections midpoint height, i.e.  w1 x h1 + w2 x h2 + ... etc. = x 
ft-lbs.  principle: Uniform weight/ft can be assumed to be point loads 
at their center.
2. Add the moments for the rotator + mast + antenna, using the same 
process.  wt mast x distance from tower base to its midpoint, etc.
3. Now you know the total moment (torque) needed at the base of the 
tower to rotate it from the horizontal.  e.g. 6000 ft-lbs
4. To calculate the lift force, the angle of the pull up rope needs to 
be known.  Simple trig can figure it out.
5. Principle: for a hinged base, force along the length of the tower 
does nothing to raise it, only force perpendicular to the rope attach 
point.  So the base lifting moment needs to be translated to the place 
the rope attaches.  i.e 6000 ft-lbs/15ft up or a 400lbs upward force 
will start moving the tower upward.
6. The initial force in the lift rope is the perpendicular lift 
force/sine(lift rope angle to ground).  i.e. a straight up lift is 400# 
and a lift along the tower takes infinite force.  The lift rope force 
goes down as the tower elevates, but since the angles are changing that 
is a more complex calculation and not necessary for sizing things.
7.  You can use the same trig to calculate the downward and horizontal 
forces you will apply to your roof.  A safer choice is to run another 
rope over the rooftop and back to a fixed point, so the load on the roof 
is only downward.  Then a turning block can bring the lift rope back to 
the tower location.  I don't think most stick pitched roof construction 
can handle heavy side loads at the peak (all nails from rafters into 
ridge rafter and usually wimpy ties between opposing rafters).
8. The lifting rope can be as many part block/tackle as needed.  I 
particularly like sailboat ball bearing blocks and low stretch rope for 
these lifts. Suitable (2000# swl) blocks are about $50 each 2/3 part and 
good low stretch 7/16 rope is about $1/ft.

the cautions are:

1. Is the tower strong enough to stand the point load lift force?  A 
rule of thumb for tower crane lifts is at 2/3 the height so as the tower 
raises the base rests on the ground and takes some weight until the 
crane supports the entire weight with the tower nearly vertical (what it 
is designed to do).  Using a sling around the tower can move the load to 
two legs but it can't slip.
2. Attachment of the lifting rope to the house and the rope needs to be 
strong enough, e.g. 20% of breaking strength is the norm max load.

I've used this approach for many mast/tower lifts using guyed fixed 
derricks.

Grant KZ1W  not a structural eng, YMMV, caveat emptor

On 9/17/2013 8:20 AM, Ray, W4BYG wrote:
> I have a 64' aluminum 14"/18" tower with a steel hinged base.  I have
> previously raised and lowered it several times with 16' ground mounted, back
> guyed gin pole and HD block and tackle, pulled by my car.  This was done
> successfully by intuitive estimation of the loads, plus a large safety
> margin factor.
>
> However, I am in a different qth and installation scenario (now 75 years
> young) .  I would like to be able to raise the tower with beam/feedline
> installed while on the ground with a tilt hinge mount, and then temporarily
> anchored to my roof line (with appropriate inside bracing), for raising.  I
> can calculate the tower alone loads, but I'm not sure about the added load
> of the beam at the end or top.  Thus, I would like to more accurately
> calculate the estimated loads on the tackle/hardware to the roof.
>
> My question:  Is there a formula(s) in which I can enter the linear tower
> weight as well as well as the beam weight at the top, then the attachment
> location, to estimate or determine what the rigging loads would be at the 13
> ' level of the tower and the 13' height at the roof line?  This would assist
> me in determining the needed attachments and bracing for the  hardware  to
> the roof rafters.  I am estimating it will be about 1200 lbs or so, but I
> would like to be more sure.
>
> I was not able to find anything online that I could decipher and apply.
>
> Any assistance will be appreciated.
>
> Ray, W4BYG
>
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