afpt (version 1.1.0.4)

findMinimumTimeSpeed: Find speed for migration time minimization

Description

This function performs a numerical optimization to find the airspeed for which \(\frac{P+P_\mathrm{dep}}{U}\) is minimum..

Usage

findMinimumTimeSpeed(bird,
  EnergyDepositionRate=1.5*bird$basalMetabolicRate,
  lower=NULL,upper=NULL,
  windSpeed=0,windDir=0,...)

Value

Returns data.frame (power.chemical) of flight performance at maximum range speed for bird.

Arguments

bird

bird description object (see Bird)

EnergyDepositionRate

The rate at which the bird accumulates energy at stopover sites

lower

lower speed limit (optional)

upper

upper speed limit (optional)

windSpeed

wind magnitude (in m/s; optional)

windDir

wind direction (in degrees; optional)

...

optional arguments: climbAngle (in degrees), and optional arguments for computeFlappingPower.

Author

Marco Klein Heerenbrink

Details

This function performs a numerical optimization to find the airspeed that minimizes the combination of flight time and time required to (re)gain the energy reserves to cover the flight cost. If the bird would fly faster, it would need to spend more time refueling. If it flew slower, the reduced refueling time that comes with the lower cost of transport does not offset the longer flight time. Mathematically this problem works out as minimizing \(\frac{P+P_\mathrm{dep}}{U}\) Hedenström 1998, which is technically the same optimization as for the maximum range speed (see details findMaximumRangeSpeed). The default energy deposition rate, the rate at which a bird accumulates energy during a stopover, is set to 1.5 times the basal metabolic rate (Lindström 1991).

References

Lindström, Å. (1991) Maximum fat deposition rates in migrating birds. Ornis Scand. 22, 12-19 (doi:10.2307/3676616)

Hedenström, A. & Alerstam, T. (1997) Optimum fuel loads in migratory birds: distinguishing between time and energy minimization. J. Theor. Biol. 189, 227–34. (doi:10.1006/jtbi.1997.0505)

Hedenström, A. & Alerstam, T. (1998) How fast can birds migrate? J. Avian Biol. 29, 424-432. (doi:10.2307/3677161)

See Also

computeChemicalPower, computeFlappingPower

Examples

## Define a bird:
myBird = Bird(
  massTotal = 0.215, #  (kg) total body mass
  wingSpan = 0.67, #  (m) maximum wing span
  wingArea = 0.0652, #  (m2) maximum wing area
  type = "passerine"
)

minimumTimeSpeed <- findMinimumTimeSpeed(myBird,1.5*myBird$basalMetabolicRate)
minimumTimeSpeed[c('speed','speed.migration',
    'power','power.chem','power.dep',
    'strokeplane','amplitude','frequency')]
#     speed speed.migration   power power.chem power.dep strokeplane amplitude frequency
#  11.74944        1.962213 2.74058   15.36634  3.080752    16.49244  38.03366  5.948083