Civil Engineering Reference
In-Depth Information
Appendix C
AERODYNAMIC DERIVATIVES FROM
SECTION MODEL DECAYS
From wind tunnel section model tests the aerodynamic derivatives were first quantified
by the interpretation of in-wind simple decay recordings as described by Scanlan &
Tomko [17]. From such testing six aerodynamic derivatives may be extracted, as shown
in the following.
The section model contains two intentional modes, one in the across wind vertical
direction and one with respect to torsion, i.e.:
0
φ
ª
º
()
[
]
z
ƷǗǗ
x
=
=
«
(C.1)
»
1
2
0
φ
¬
¼
θ
Internal unintentional flexibilities beyond those associated with these modes are most
often insignificant, in which case
1
φ≈≈
. It is in the following taken for granted
z
θ
that their still-air properties
(
)
(
)
V
V
0
0
V
V
0
0
ω
==
==
ω
ζ
==
==
ζ
½
¾
¿
1
z
1
z
and
(C.2)
(
)
(
)
ω
ω
ζ
ζ
2
θ
2
θ
are known, and that any additional response contributions from other modes are
insignificant or have effectively been filtered off. The testing strategy is to set the section
model into decaying free motion at a suitable choice of mean wind velocity settings.
Idealised recordings from such a test are illustrated in Fig. C.1. The velocity dependent
response curves may mathematically be fitted to
r
ªº
(
)
( ) ( )
r
Vxt
,,
ƷLj
(C.3)
x Vt
,
=
=
⋅
«
¬¼
r
θ
c
ªº
η
ª
º
z
( )
1
( )
Lj
Vt
,
exp
t
where:
=
=
λ
⋅ ⋅
«
(C.4)
«»
»
r
(
)
c
⋅
exp
− ⋅
i
ψ
η
¬¼
¬
¼
r
2
θ
