afpt (version 1.1.0.4)

amplitude: Flapping flight optimal amplitude

Description

This function returns the angular peak amplitude of the flapping motion, optimized for minimum induced power for prescribed reduced frequency (kf), strokeplane angle (phi), and thrust-to-lift ratio (TL).

Usage

amplitude(kf, phi, TL)

Value

Angular peak amplitude of the flapping motion in degrees.

Arguments

Using \(f\) for wingbeat frequency, \(b\) for wingspan, and \(U\) for air speed:

kf

reduced frequency (\(k_f = \frac{2 \pi f b}{U}\)); valid range between 1 and 6

phi

strokeplane angle in radians; valid range between 0 and 0.87 rad (50 deg)

TL

thrust requirement or the trust-to-lift ratio; valid range between 0 and 0.3

Author

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 tools:::Rd_expr_doi("10.1098/rspa.2014.0952")

See Also

computeFlappingPower

Examples

## reduced frequency
kf <- 2*pi*4/10 # 4 Hz at 10 m/s for 1m wing span
## strokeplane angle
phi <- 20*pi/180 # 20 degrees
## thrust ratio
TL <- 0.2
## wingbeat amplitude
theta <- amplitude(kf,phi,TL)
print(theta)
#   [1] 49.17679