Flying in a flock comes at a cost in pigeons

. Author manuscript; available in PMC: 2011 Dec 23.

Published in final edited form as: Nature. 2011 Jun 22;474(7352):494–497. doi: 10.1038/nature10164

	Frequency (Hz) or dorsal amplitude (m) =
Airspeed component	$K_{1} V_{air} + K_{2} V_{air}^{2} + K_{3} V_{air}^{3}$
Induced power component	$+ K_{4} \frac{{\overset{‒}{a_{dorsal}}}^{2}}{V_{air}} + K_{5} {(\frac{{\overset{‒}{a_{dorsal}}}^{2}}{V_{air}})}^{2} + K_{6} {(\frac{{\overset{‒}{a_{dorsal}}}^{2}}{V_{air}})}^{3}$
Climbing power component	$+ K_{7} V_{z} + K_{8} V_{z}^{2} + K_{9} V_{z}^{3}$
Acceleration power component	$+ K_{10} \overset{‒}{a_{rostral}} V_{GPS} + K_{11} {(\overset{‒}{a_{rostral}} V_{GPS})}^{2} + K_{12} {(\overset{‒}{a_{rostral}} V_{GPS})}^{3}$
Forward Flock Factor component	$+ K_{13} F F_{ahead} + K_{14} F F_{ahead}^{2} + K_{15} F F_{ahead}^{3}$
Rear Flock Factor component	$+ K_{16} F F_{behind} + K_{17} F F_{behind}^{2} + K_{18} F F_{behind}^{3}$
Constant	+Constant