fDfPfunctions: Coefficient for thrust dependency of drag and power factors

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

Computes the thrust requirement dependency factor for drag and power factors in flapping flight based on reduced frequency (kf) and strokeplane angle (phi).

Usage

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fD.ind(kf, phi)
fD.pro0(kf, phi)
fD.pro2(kf, phi)
fP.ind(kf, phi)
fP.pro0(kf, phi)
fP.pro2(kf, phi)

Arguments

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)

Details

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 non-flapping flight as D = kD * Dnf . The factor kD depends on reduced frequency kf, strokeplane angle phi and the thrust-to-lift 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.

Value

Numeric value

Note

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.

Author(s)

Marco Klein Heerenbrink

References

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

See Also

computeFlappingPower

Examples

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## 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

afpt documentation built on Sept. 2, 2017, 1:06 a.m.