Date: Wed, 20 Jul 2016 19:58:01 -0700
From: Grant Saviers <grants2@pacbell.net>
To: "Roger (K8RI) on TT" <K8RI-on-TowerTalk@tm.net>,
towertalk@contesting.com
Subject: Re: [TowerTalk] Biggest rotor that will fit in a Rohn 25G
The assertion is often made that a longer mast inside the tower
strengthens the tower. I think not.
So perhaps those with civil/structural engineering skills greater than
my novice level could help me to understand why lowering the rotator
lowers the tower stresses. My analysis follows.
For a perpendicular wind load to the tower and antenna, and a given
antenna height above the tower, the lateral force exerted on the tower
is the same whether there is 1' or 100' of mast inside the tower.
Given that a large antenna should be close to the top of R25, the added
moment from the mast applied to the tower top is essentially independent
of the mast below the top, when the top section has a mast sleeve such
as tapered R25 or big UST crank ups. Thus the amount of side load on
the rotator is also minimal on towers with those tubular mast tops since
the mast can only move a fraction of a degree inside that tube.
Some posters claim that a mast "strengthens" the tower, but the ratio
of the bending moment of inertia is large from 2" x 0.25wall mast to a
10' stick of R25. The moment of inertia for R25 per factory spec sheet
is 15.3 in^4 and for 2"od x 0.25 wall is 0.54 in^4. In other words the
R25 tower is almost 30 times stiffer in resisting bending than the 2"
mast. Hence the mast makes an insignificant contribution to the
strength of the tower. (see Leeson's analysis of sleeved elements in
Physical Design of Yagi Antennas)
A stock "thrust bearing" (Yaesu, Rohn) may have enough slop to allow the
mast to pivot at the top plate quite a bit, at least the Rohn one I used
(never again!) could let the mast achieve scary angles when the rotator
was removed. So in this case there is some moment transferred to the
rotator bearings and mounting plate, but the tower resists those
bending loads 30x better than the mast.
A lattice tower is engineered to have high stiffness due to the large
"diameter" (distance to the neutral axis) and low weight by using small
tube legs and welded bracing to distribute the loads among the legs.
While it is beyond my skills to compute the stress distribution for 10'
of R25 loaded as a cantilever, IMO it will withstand a lot more force
before it fails than a 10' length of 2" diameter mast.
Grant KZ1W
## the mast wont strengthen any tower. If you look in leesons book,
He sez the bending moment on the tower is normal bending moment you
would have at the bottom of the mast, as it enters the top bearing.
But he then converts the bending moment in ft lbs...to inch lbs, by multiplying
x 12. Then he take the bending moment in inch lbs.... and simply divides by
the
distance, in inches, between the top bearing..and what ever is below it,
like a 2nd
bearing...or a rotor.
## IE: 2500 ft lbs X 12 = 30,000 inch lbs. Say the rotor is down 4 ft
below top of tower.
Its then 30,000 / 48 inchs = 625 ft lbs. ( you can also just use 2500 / 4
= 625 ft lbs)
Assume the wind is from the north. The side force experienced at the south
side of the top bearing
is now 625 lbs. The side force experienced at the north side of the rotor is
also 625 lbs.
## If you now instead insert the mast 10 ft into the tower, its now becomes
2500 /10 = 250
lbs on the side of the top bearing..and also the rotor. So yes, putting the
mast lower into the tower
will help a lot.
## heres where that concept wont work. Put the mast 10 feet into the tower,
but now use a 2nd thrust
bearing, say 4 ft below tower top. IE: top bearing, then 2nd bearing down 4
ft, then the rotor down 10 ft.
## all the forces are between the 2 x bearings..... = 625 lbs The portion
of the mast below the 2nd bearing.... between
2nd bearing and rotor, plays no part in the results. That portion of the mast
could be made of way lesser strength
since all it has to handle is the torque of the array.
## If any of you have leesons book, its explained at the top of page 7-14
Jim VE7RF
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