Description Usage Arguments Details Value Note Author(s) References See Also Examples
Computes the thrust requirement dependency factor for drag and power factors in flapping flight based on reduced frequency (kf
) and strokeplane angle (phi
).
1 2 3 4 5 6 

Using f for wingbeat frequency, b for wingspan, and U for air speed: 
kf 
reduced frequency (kf = 2 * π * f *b / U); valid range between 1 and 6 
phi 
strokeplane angle in radians; valid range between 0 and 0.87 rad (50 deg) 
Flapping of the wings alters the drag components on the wing. A drag component in flapping flight can be related to the drag component in nonflapping flight as D = kD * Dnf . The factor kD depends on reduced frequency kf, strokeplane angle phi and the thrusttolift ratio T/L: kD = 1 + fD(kf,phi) * T/L . Functions fD.ind
,fD.pro0
and fD.pro2
compute fD(kf,phi) for induced drag, zero lift profile drag and lift dependent profile drag, respectively.
Similarly, the flapping power components can be computed as: P = k_P * Dnf * U, again with kP = 1 + fP(kf,phi) * T/L . Functions fP.ind
,fP.pro0
and fP.pro2
compute fP(kf,phi) for induced power, zero lift profile power and lift dependent profile power, respectively.
Numeric value
Thrust requirement is the sum of all drag components in flapping flight divided by the lift. This means the thrust requirement itself is a function of the values of fD.
Marco Klein Heerenbrink
Klein Heerenbrink, M., Johansson, L. C. and Hedenström, A. 2015 Power of the wingbeat: modelling the effects of flapping wings in vertebrate flight. Proc. R. Soc. A 471, 2177 doi: 10.1098/rspa.2014.0952
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44  ## reduced frequency
kf < 2*pi*4/10 # 4 Hz at 10 m/s
## strokeplane angle
phi < 20*pi/180 # 20 degrees
## thrust ratio
TL < 0.2
## induced drag factor:
fDind < fD.ind(kf,phi)
kDind < 1 + fDind*TL
print(kDind)
# [1] 1.623659
## zero lift drag factor:
fDpro0 < fD.pro0(kf,phi)
kDpro0 < 1 + fDpro0*TL
print(kDpro0)
# [1] 1.014899
## lift dependent profile drag factor:
fDpro2 < fD.pro2(kf,phi)
kDpro2 < 1 + fDpro2*TL
print(kDpro2)
# [1] 1.511107
## induced power factor:
fPind < fP.ind(kf,phi)
kPind < 1 + fPind*TL
print(kPind)
# [1] 1.996891
## zero lift power factor:
fPpro0 < fP.pro0(kf,phi)
kPpro0 < 1 + fPpro0*TL
print(kPpro0)
# [1] 1.076046
## lift dependent profile power factor:
fPpro2 < fP.pro2(kf,phi)
kPpro2 < 1 + fPpro2*TL
print(kPpro2)
# [1] 1.811983

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