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List of symbols and abbreviations

The dimensions are given in terms of mass, M, length, L and time, T.

{u,v,wL/T disturbance velocities in {x,y,z
{x,y,zstreamwise, spanwise and vertical directions 
A tip-to-tip wingbeat amplitude 
AR  wing aspect ratio (=2b/c
b wing semispan 
c mean chord length in flightwise direction 
Cd  section drag coefficient 
CD  wing drag coefficient 
CL  wing lift coefficient 
Cp  section lift coefficient 
f 1/T wingbeat frequency 
g L/T2 acceleration due to gravity 
l characteristic length 
L M.L.T.–2 lift 
m body/aircraft mass 
q M/LT2 dynamic pressure 
r position along wingspan 
Re  Reynolds number (=Uc/v
Reloc  local Re 
S L2 wing planform area 
St  Strouhal number (=fA/U
t time 
T wingbeat period 
U L/T flight speed 
uloc L/T local incident velocity on a wing section 
Ump L/T estimated flight speed for minimum power 
u′ L/T root mean square of velocity fluctuations 
W M.L.T–2 bird/aircraft weight (=mg
wtip L/T vertical component of wingtip speed 
α deg. aerodynamic angle of attack 
α0 deg. local twist from stroke plane 
αw deg. local α due to vector sum of U and wtip 
δt small time interval (DPIV effective exposure time) 
Γ L2/T circulation/strength of a vortex patch, or on a lifting wing 
λ  wavelength 
μ M/LT viscosity 
ν L2/T kinematic viscosity (=μ/ρ) 
ρ M/L3 air density 
ωi 1/T vorticity component in the ith direction {i=x,y,z
{u,v,wL/T disturbance velocities in {x,y,z
{x,y,zstreamwise, spanwise and vertical directions 
A tip-to-tip wingbeat amplitude 
AR  wing aspect ratio (=2b/c
b wing semispan 
c mean chord length in flightwise direction 
Cd  section drag coefficient 
CD  wing drag coefficient 
CL  wing lift coefficient 
Cp  section lift coefficient 
f 1/T wingbeat frequency 
g L/T2 acceleration due to gravity 
l characteristic length 
L M.L.T.–2 lift 
m body/aircraft mass 
q M/LT2 dynamic pressure 
r position along wingspan 
Re  Reynolds number (=Uc/v
Reloc  local Re 
S L2 wing planform area 
St  Strouhal number (=fA/U
t time 
T wingbeat period 
U L/T flight speed 
uloc L/T local incident velocity on a wing section 
Ump L/T estimated flight speed for minimum power 
u′ L/T root mean square of velocity fluctuations 
W M.L.T–2 bird/aircraft weight (=mg
wtip L/T vertical component of wingtip speed 
α deg. aerodynamic angle of attack 
α0 deg. local twist from stroke plane 
αw deg. local α due to vector sum of U and wtip 
δt small time interval (DPIV effective exposure time) 
Γ L2/T circulation/strength of a vortex patch, or on a lifting wing 
λ  wavelength 
μ M/LT viscosity 
ν L2/T kinematic viscosity (=μ/ρ) 
ρ M/L3 air density 
ωi 1/T vorticity component in the ith direction {i=x,y,z
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