At 02:59 PM 2003-09-03, Bob Gates wrote:
> If you have a tower rated to hold 30sf of antenna at 70 mph, and 10sf at
>90mph, what correlation, if any, can you draw about the load handling ability
>at
>80mph. Is there a linear relationship, or does it require a whole new set of
>calcs?
The relationship is NOT linear, although in Bob's particular example, a more
accurate answer isn't very far from the number he would get if he did assume it
was linear.
The charts in the Rohn catalogs for decades showed the pressure on a tower and
beam to be related to the SQUARE of the wind velocity. Thus, the ratio of
allowable antenna square footage at 90 mph to that at 70 mph would be 4900 /
8100, or 60%, if the tower itself had no surface area. So if you ignored the
wind load on the tower, you would conclude that the allowable antenna surface
area at 90 mph was 60% of that at 70 mph, or 18 square feet. Clearly, the
tower has surface area, and it's pretty likely the manufacturer has included it
in the 90 mph calculation, which came out at 10 square feet for allowable
antenna area, not 18.
A VERY ROUGH APPROXIMATION for finding the allowable antenna area at other wind
speeds is to assume that the entire tower can be represented by an effective
wind loading of "T" square feet applied at the top. (We know that's a gross
over-simplification, but since we don't know anything about the tower at this
point, it's the best we can do.) Then we surmise from the manufacturer's 70
mph and 90 mph ratings the following equality:
(30 + T) x 70 x 70 x K = (10 + T) x 90 x 90 x K.
The equality is based on the assumption that the tower manufacturer uses the
SAME total force from the wind loading on the tower plus antenna in his
calculations at various different wind speeds. K is an "arbitrary" constant
that goes away, so we're not going to worry about its dimensions or meaning.
Dividing both sides by K and collecting all terms with T in them on the right
hand side, we get
(147,000 - 81,000) = (8100 - 4900) x T
or: T = 20.63 square feet (effective tower wind loading applied at the top).
Thus, at 70 mph, the total force on the tower and antenna is K x (30 + 20.63) x
70 x 70, or K x 248,000. Similarly, at 90 mph, we get K x (10 + 20.63) x 90 x
90, or K x 248,000.
Now we can calculate the allowable antenna square footage (call it "F") at 80
mph:
(F + 20.63) x 80 x 80 x K = 248,000 x K
or: F = 18 square feet of allowable antenna area for 80 mph winds, versus the
20 square feet Bob would calculate by assuming it was a linear curve between
the figures for 70 and 90 mph.
Bud, K2KIR
_______________________________________________
See: http://www.mscomputer.com for "Self Supporting Towers", "Wireless Weather
Stations", and lot's more. Call Toll Free, 1-800-333-9041 with any questions
and ask for Sherman, W2FLA.
_______________________________________________
TowerTalk mailing list
TowerTalk@contesting.com
http://lists.contesting.com/mailman/listinfo/towertalk
|