fDfPfunctions {afpt} R Documentation

## Coefficient for thrust dependency of drag and power factors

### 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

```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.

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 HedenstrĂ¶m, 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

`computeFlappingPower`

### Examples

```## 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

```

[Package afpt version 1.1.0.1 Index]