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Antennas and open-frame
structures
Wind loading and structural response
Lecture 23 Dr. J.D. Holmes
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Antennas and open-frame structures
Single frames
Multiple frames
Antennas - isolated structures - radio telescopes and microwave
antennas
Lattice towers
Antennas - attached to towers - aerodynamic interference
Common feature : aerodynamic interference between various elements - e.g.
antennas and supporting tower or other antennas, members of a frame
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Antennas and open-frame structures
Radio telescope
Paraboloid dish
f
Focus
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Antennas and open-frame structures
Radio telescope
Paraboloid dish
Normal to dish surface intersects axis at 2 focal length
2f
Approximate center of aerodynamic forces2
2fed
e
d
C
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Antennas and open-frame structures
Radio telescope
Paraboloid dish
Wind
FX
FY
e
b
d
Fy force generates significant moments about dish supports
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Antennas and open-frame structures
Radio telescope
Paraboloid dish
Total
moment
Azimuth
angle,
135o
Altitude
moment
Azimuth
moment
Effect of
boundary
layer
profile
0 20 40 60 80 90
Zenith angle, degrees
0.10
0.08
0.06
0.04
0.02
0
CM
Zenith
angle b
Focus
aAzimuth
angle
WindAltitude
axis
PLAN VIEW
AbU
MC
2
ha21M
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Antennas and open-frame structures
Microwave dish antenna
Impermeable dish
Small effect of turbulence
0.0
0.5
1.0
1.5
2.0
0 20 40 60 80 100 120 140 160 180
1% turbulence
10% turbulence
(degrees)
b
A2
a2
1D
U
)D()(C
A = (b2/4)
(projected area)
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Antennas and open-frame structures
Microwave dish antenna
Interference factor WIND
WIND
Da
WINDDt
De
aD
tD
eD
iK
a.Di
Kt
De
D
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Antennas and open-frame structures
Microwave dish antenna
Interference factor
0
0.5
1
1.5
0 45 90 135 180Wind direction (degrees)
Interference
factor
Experimental data
Equation with t=0.5
Ki = exp [-k(CD )2]. [(1+t) + t cos 2( - d - 90)]
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Antennas and open-frame structures
Cell-phone antenna
isolated panels
b
Cd1.1
120O
Cd (ref.b) 0.8
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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
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Antennas and open-frame structures
Cell-phone antenna
grouped panels
total drag of group : about 30% less than sum of individual elements
0o
60o
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Antennas and open-frame structures
Open frames Single frame. Two-dimensional. Normal wind sharp-edged members
reference area for drag coefficient = solid area of frame
2.0
1.0
0.5 1.00Solidity ratio,
CD
solidity = solid area of frame/total enclosed area
drag coefficient relatively independent of details of member arrangement
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Antennas and open-frame structures
Open frames Single frame. Two-dimensional. Normal wind
at high solidity, frame acts as a solid plate (Lecture 8)
at low solidity, members act as individual elements
intermediate solidity : aerodynamic interference between members CD 1.6
2.0
1.0
0.5 1.00Solidity ratio,
CD
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Antennas and open-frame structures
Open frames Pairs of frames. Two-dimensional. Normal wind
1 CD(1) is drag coefficient of upstream frame
(downstream frame influences upstream frame)
CD(2) = CD
(1) [ 1 + 2]
2 CD(1) is drag coefficient of downstream frame
approximately, 1 1,
0.45
0.45
2b
s1
sb
For circular members, equivalent solidity to calculate 2,
e 1.2 1.75
0 < < 0.5
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Antennas and open-frame structures
Open frames
3 frames in series. Solidity = 0.1
X(a) = force normal to frame
AU
)X()(C
2a2
1
N
X
angle of attack, a
spacing/width = 1.0
spacing/width = 0.1
15 75
A = projected area of one frame at
0o angle of attack
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Antennas and open-frame structures
Open frames
3 frames in series. Solidity = 0.5
A = projected area of one frame at0o angle of attack
Maximum CXN at 30o to 45o
angle of attack, a
spacing/width = 1.0
spacing/width = 0.1
15 75
AU
)X()(C2
a21
N
X
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Antennas and open-frame structures
Open frames
10 frames in series. Solidity = 0.1
A = projected area of one frame at0o angle of attack
angle of attack, a
spacing/width = 1.0
spacing/width = 0.1
15 75
AU)X()(C2
a21
NX
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Open frames
10 frames in series. Solidity = 0.5
A = projected area of one frame at0o angle of attack
Maximum CXN at 30o to 45o
angle of attack, a
spacing/width = 1.0
spacing/width = 0.1
15 75
AU)X()(C2
a21
NX
Antennas and open-frame structures
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Antennas and open-frame structures
Open frames
Design method :
Wind loads and anchor bolt design for petrochemical facilities (ASCE)
Needs more wind tunnel studies for pipe racks etc.
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Drag coefficients for lattice tower (Lecture 21)
= solidity of one face = area of members total enclosed area
AustralianStandards
0.0 0.2 0.4 0.6 0.8 1.0Solidity Ratio
4.0
3.5
3.0
2.5
2.0
1.5
Drag
coefficient
CD (=0O)
Square cross section with flat-sided members (wind normal to face)
(ASCE-7 : CD = 4.025.9 +4.0 )
includes interference and shielding effects between members
Antennas and open-frame structures
CD = 4.2 - 7 (for 0.1
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Drag coefficients for lattice tower
CD = 3.5 - 4 (for 0.1
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Drag coefficients for lattice tower
depends on Reynolds Number
for super-critical flow - Cd for cross section ~ 0.5 times that for
equivalent sharp-edged tower with same solidity
Cross section with circular members
Antennas and open-frame structures
some members may be in super-critical flow - others in sub-critical flow
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End of Lecture 23
John Holmes225-405-3789 [email protected]
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