Manual for calculating optimal flight speed in birds


The optimum flight speed of a bird may depend on what is the aim of the flight. If the aim is migration (maximum range), the bird has to move as long as possible per unit energy. If, however, the distance covered is less important, as in food search, the speed that requires the minimum energy consumption (minimum power) should be the optimum (Alerstam 1982). For more information about the theory of flight speed in birds, see Pennycuick (2008), Hedenström, (2002) and references therein.

Getting started

You need to do two things to prepare yourself for calculating optimal flight speed in birds:

  • On your computer, start a program for statistical computation and graphics called R (, and
  • Load a function made for this purpose into the memory of R.

    The latter is done by running this command within R:

    You have now loaded a function called powercurve and are ready to use it for calculating a bird's optimal velocity for:

  • Minimum power (Vmp), and
  • Maximum range (Vmr).

    Performing the calculations

    The following command is an example of how to use the powercurve-function:
    powercurve(m=0.4, wingspan=0.6675581, altitude=50, temp=12, minvel=2.5, maxvel=30)

    The result of this command is a graphical output that looks as follows:

    The parameters used in the above function fits to the size of a pigeon (Columba livia). The general meaning of each parameter in the powercurve-function is explained in the table below:
    m wingspan altitude temp minvel maxvel
    Body mass of the bird (kg) Wingspan of the bird (m) Flight altitude of the bird (m) Approximate temperature at the given altitude (Celcius) Minimum velocity of the bird in question (m/sec) Maximum velocity of the bird in question (m/sec)2
    The two latter parameters (minvel and maxvel) are just approximate values to get the "correct" scale on the x-axis.


  • Alerstam, Thomas (1982), Fågelflyttning, Signum, ISBN: 91-85330-45-0.

  • Hedenström, Anders (2002), Aerodynamics, evolution and ecology of avian flight, Trends in Ecology & Evolution 17(9): 415-422.

  • Pennycuick, Colin J. (2008). Modelling the Flying Bird. pp 496, Elsevier inc., Theoretical Ecology Series, Volume 5., ISBN: 0080557813, 9780080557816

    This page was last updated on: Friday 27 September 2013 by Knut Helge Jensen