1. Antennas and open-frame structures
Wind loading and structural response
Lecture 23 Dr. J.D. Holmes
Antennas and open-frame structures

2. Antennas and open-frame structures
Antennas - isolated structures - radio telescopes and microwave antennas
Antennas - attached to towers - aerodynamic interference
Single frames
Multiple frames
Lattice towers
Common feature : aerodynamic interference between various elements - e.g. antennas and supporting tower or other antennas, members of a frame

3. Antennas and open-frame structures
Radio telescope
Paraboloid dish f
Focus

4. Antennas and open-frame structures
Radio telescope 2f
Paraboloid dish
Normal to dish surface intersects axis at 2  focal length
Approximate center of aerodynamic forces e d C

5. Antennas and open-frame structures
Radio telescope
Paraboloid dish
Wind FX FY e b  d
Fy force generates significant moments about dish supports

6. Antennas and open-frame structures
Radio telescope
Paraboloid dish
Total moment
Azimuth angle, 135o
Altitude moment
Azimuth moment
Effect of boundary
layer profile
Zenith angle, degrees
0.10
0.08
0.06
0.04
0.02 CM
Zenith angle b
Focus a
Azimuth angle
Wind
Altitude axis
PLAN VIEW

7. Antennas and open-frame structures
Microwave dish antenna
Impermeable dish
0.0
0.5
1.0
1.5
2.0 20 40 60 80
100
120
140
160
180
1% turbulence
10% turbulence
 (degrees) b 
A = (b2/4) (projected area)
Small effect of turbulence

8. Antennas and open-frame structures
Microwave dish antenna
WIND Da Dt De
Interference factor

9. Antennas and open-frame structures
Microwave dish antenna
Interference factor
0.5 1
1.5 45 90
135
180
Wind direction (degrees)
Interference factor
Experimental data
Equation with t=0.5 
Ki = exp [-k(CD  )2]. [(1+t) + t cos 2( - d - 90)]

10. Antennas and open-frame structures
Cell-phone antenna
isolated panels
120O
Cd (ref.b)  0.8 b
Cd 1.1

11. Antennas and open-frame structures
Cell-phone antenna
grouped panels
~2b
combined
Cd (ref.b)  1.1
combined
Cd (ref.b)  0.9
grouping gives large reduction in total drag

12. Antennas and open-frame structures
Cell-phone antenna
grouped panels 0o
60o
total drag of group : about 30% less than sum of individual elements

13. Antennas and open-frame structures
Single frame. Two-dimensional. Normal wind
sharp-edged members
2.0
1.0
0.5
Solidity ratio,  CD
solidity = ‘solid’ area of frame/total enclosed area
reference area for drag coefficient = ‘solid’ area of frame
drag coefficient relatively independent of details of member arrangement

14. Antennas and open-frame structures
Single frame. Two-dimensional. Normal wind
2.0
1.0
0.5
Solidity ratio,  CD
at low solidity, members act as individual elements
at high solidity, frame acts as a solid plate (Lecture 8)
intermediate solidity : aerodynamic interference between members CD  1.6

15. Antennas and open-frame structures
Pairs of frames. Two-dimensional. Normal wind s b
CD(2) = CD(1) [ 1 + 2]
1 CD(1) is drag coefficient of upstream frame (downstream frame influences upstream frame)
2 CD(1) is drag coefficient of downstream frame
approximately, 1  1,
0 <  < 0.5
For circular members, equivalent solidity to calculate 2 , e  1.2 1.75

16. Antennas and open-frame structures
angle of attack, 
spacing/width = 1.0
spacing/width = 0.1 15 75
3 frames in series. Solidity = 0.1
X() = force normal to frame
A = projected area of one frame at 0o angle of attack

17. Antennas and open-frame structures
angle of attack, 
spacing/width = 1.0
spacing/width = 0.1 15 75
3 frames in series. Solidity = 0.5
A = projected area of one frame at 0o angle of attack
Maximum CXN at 30o to 45o

18. Antennas and open-frame structures
angle of attack, 
spacing/width = 1.0
spacing/width = 0.1 15 75
10 frames in series. Solidity = 0.1
A = projected area of one frame at 0o angle of attack

19. Antennas and open-frame structures
angle of attack, 
spacing/width = 1.0
spacing/width = 0.1 15 75
Open frames
10 frames in series. Solidity = 0.5
A = projected area of one frame at 0o angle of attack
Maximum CXN at 30o to 45o

20. Antennas and open-frame structures
Design method :
‘Wind loads and anchor bolt design for petrochemical facilities’ (ASCE)
Needs more wind tunnel studies for pipe racks etc.

21. Antennas and open-frame structures
Drag coefficients for lattice tower (Lecture 21)
Square cross section with flat-sided members (wind normal to face)
Australian Standards
Solidity Ratio d
4.0
3.5
3.0
2.5
2.0
1.5
Drag coefficient CD (q=0O)
CD =  (for 0.1< < 0.2)
CD =  (for 0.2< < 0.5)
(ASCE-7 : CD = 4.02 – 5.9 +4.0 )
 = solidity of one face = area of members  total enclosed area
includes interference and shielding effects between members

22. Antennas and open-frame structures
Drag coefficients for lattice tower
Triangular cross section with flat-sided members
CD =  (for 0.1< < 0.3)
CD = 2.9 – 2 (for 0.3<  < 0.5)
(ASCE-7 : CD = 3.42 – 4.7 +3.4 )

23. Antennas and open-frame structures
Drag coefficients for lattice tower
Cross section with circular members
depends on Reynolds Number
for super-critical flow - Cd for cross section ~ 0.5 times that for equivalent sharp-edged tower with same solidity
some members may be in super-critical flow - others in sub-critical flow

24. End of Lecture 23 John Holmes 225-405-3789 JHolmes@lsu.edu