Antennas and open-frame structures

Wind loading and structural response

Lecture 23 Dr. J.D. Holmes

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

Antennas and open-frame structures

• Radio telescope

• Paraboloid dish

f

Focus

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

Antennas and open-frame structures

• Radio telescope

• Paraboloid dish

Wind

FX

FY

e

b

d

Fy force generates significant moments about dish supports

Antennas and open-frame structures

• Radio telescope

• Paraboloid dish

Total moment

Azimuth angle, 135o

Altitude moment

Azimuth moment

Effect of boundarylayer profile

0 20 40 60 80 90Zenith angle, degrees

0.10

0.08

0.06

0.04

0.02

0

CM

Zenith angle

Focus

Azimuth

angle

Wind

Alti

tude

ax

is

PLAN VIEW

AbUρ

MC 2

ha21M

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)

bA2

a21D Uρ

)D()(C

A = (b2/4) (projected area)

Antennas and open-frame structures

• Microwave dish antenna

• Interference factor WIND

WIND

Da

WINDDt

De

aDtDeD

iK

a.DiKtDeD

Antennas and open-frame structures

• Microwave dish antenna

• Interference factor

0

0.5

1

1.5

0 45 90 135 180Wind direction (degrees)

Inte

rfe

renc

e fa

ctor

Experimental dataEquation with t=0.5

Ki = exp [-k(CD)2]. [(1+t) + t cos 2( - d - 90)]

Antennas and open-frame structures

• Cell-phone antenna

• isolated panels

b

Cd 1.1

120O

Cd (ref.b) 0.8

Antennas and open-frame structures

• Cell-phone antenna

• grouped panels

~2b

combinedCd (ref.b) 1.1

combinedCd (ref.b) 0.9

grouping gives large reduction in total drag

Antennas and open-frame structures

• Cell-phone antenna

• grouped panels

total drag of group : about 30% less than sum of individual elements

0o

60o

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 1.00

Solidity ratio,

CD

solidity = ‘solid’ area of frame/total enclosed area

drag coefficient relatively independent of details of member arrangement

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 1.00

Solidity ratio,

CD

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,

0.45δ0.45

2 b

sδ1ψ

sb

For circular members, equivalent solidity to calculate 2 , e 1.2 1.75

0 < < 0.5

Antennas and open-frame structures

• Open frames

• 3 frames in series. Solidity = 0.1

X() = force normal to frame

AUρ

)X()(C

2a2

1

NX

αα

angle of attack,

spacing/width = 1.0

spacing/width = 0.1

15 75

A = projected area of one frame at 0o angle of attack

Antennas and open-frame structures

• Open frames

• 3 frames in series. Solidity = 0.5

A = projected area of one frame at 0o angle of attack

Maximum CXN at 30o to 45o

angle of attack,

spacing/width = 1.0

spacing/width = 0.1

15 75

AUρ

)X()(C

2a2

1

NX

αα

Antennas and open-frame structures

• Open frames

• 10 frames in series. Solidity = 0.1

A = projected area of one frame at 0o angle of attack

angle of attack,

spacing/width = 1.0

spacing/width = 0.1

15 75

AUρ

)X()(C

2a2

1

NX

αα

• 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

angle of attack,

spacing/width = 1.0

spacing/width = 0.1

15 75

AUρ

)X()(C

2a2

1

NX

αα

Antennas and open-frame structures

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.

• Drag coefficients for lattice tower (Lecture 21)

= solidity of one face = area of members total enclosed area

Australian Standards

0.0 0.2 0.4 0.6 0.8 1.0

Solidity Ratio

4.0

3.5

3.0

2.5

2.0

1.5

Dra

g co

effic

ient

C

D (

=0O

)

Square cross section with flat-sided members (wind normal to face)

(ASCE-7 : CD = 4.02 – 5.9 +4.0 )

includes interference and shielding effects between members

Antennas and open-frame structures

CD = 4.2 - 7 (for 0.1< < 0.2)

CD = 3.5 - 3.5 (for 0.2< < 0.5)

• Drag coefficients for lattice tower

CD = 3.5 - 4 (for 0.1< < 0.3)

CD = 2.9 – 2 (for 0.3< < 0.5)

Triangular cross section with flat-sided members

(ASCE-7 : CD = 3.42 – 4.7 +3.4 )

Antennas and open-frame structures

• 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

End of Lecture 23

John Holmes225-405-3789 JHolmes@lsu.edu