we recorded a flock of 18 trained racing pigeons ( columba livia , mean mass 0.461 kg , standard deviation ( sd ) 0.045 kg ; mean span 0.691 m , sd 0.039 m ) during voluntary flights with synchronised back - mounted 10 hz raw doppler and pseudorange gps and 300hz 12 bit precision tri - axial accelerometers ( + / 12 g ) and tri - axial gyroscopes ( + / 2000dps ) .
sensor , logger and mounting mass ( 35 g ) constituted < 8% body mass  while this is larger than usually accepted on wild - bird studies , and would also have imposed a slight increase in body drag , the fact that extended , voluntary flights were performed , including circling at 2 g , demonstrates that this load was not prohibitive .
experiment protocols were approved by the rvc local ethics and welfare committee . a gps base station ( novatel flexpak g2l and gps-702-gg antenna ) and ultrasonic anemometer ( 1hz , windmaster ( gill instruments ltd . , uk ) ) on a nearby rooftop provided synchronised measurements .
we found best fit ( least squares ) partial regression coefficients k for third order polynomials of airspeed , induced power factor , climbing power factor , acceleration power factor ( figure 2 ) and flock factors ffahead and ffbehind using the following expressions : 
 frequency ( hz ) or dorsal amplitude ( m ) = airspeed componentk1vair+k2vair2+k3vair3induced powercomponent+k4adorsal2vair+k5(adorsal2vair)2+k6(adorsal2vair)3climbing powercomponent+k7vz+k8vz2+k9vz3acceleration powercomponent+k10arostralvgps+k11(arostralvgps)2+k12(arostralvgps)3forward flock factorcomponent+k13ffahead+k14ffahead2+k15ffahead3rear flock factorcomponent+k16ffbehind+k17ffbehind2+k18ffbehind3constant+constant each power component takes account of the kinematic contribution towards power  for instance , induced power is proportional to the square of body weight ( hence dorsal acceleration to take account of turns ) and inversely proportional to airspeed .
individual pigeon was included as a categorical variable , thus taking some account of the morphological variability between pigeons .
the dataset was first bounded to remove extreme values ( frequencies 5 to 10hz ; air speed 11 - 18 m/s ; dorsal acceleration 8.81 to 20.81 ms ; vz=4 to 4 m/s ; flock factors<0.1 ; acceleration power within + / 39.2 w / kg , equivalent to the vz bounding ) , leaving 171,209 flaps .
the overall model fitted the data with r=0.48 ( frequency ) or r=0.37 ( dorsal amplitude ) ( statistical tables in supplementary information ) .
we recorded a flock of 18 trained racing pigeons ( columba livia , mean mass 0.461 kg , standard deviation ( sd ) 0.045 kg ; mean span 0.691 m , sd 0.039 m ) during voluntary flights with synchronised back - mounted 10 hz raw doppler and pseudorange gps and 300hz 12 bit precision tri - axial accelerometers ( + / 12 g ) and tri - axial gyroscopes ( + / 2000dps ) .
sensor , logger and mounting mass ( 35 g ) constituted < 8% body mass  while this is larger than usually accepted on wild - bird studies , and would also have imposed a slight increase in body drag , the fact that extended , voluntary flights were performed , including circling at 2 g , demonstrates that this load was not prohibitive .
experiment protocols were approved by the rvc local ethics and welfare committee . a gps base station ( novatel flexpak g2l and gps-702-gg antenna ) and ultrasonic anemometer ( 1hz , windmaster ( gill instruments ltd . , uk ) ) on a nearby rooftop provided synchronised measurements .
we found best fit ( least squares ) partial regression coefficients k for third order polynomials of airspeed , induced power factor , climbing power factor , acceleration power factor ( figure 2 ) and flock factors ffahead and ffbehind using the following expressions : 
 frequency ( hz ) or dorsal amplitude ( m ) = airspeed componentk1vair+k2vair2+k3vair3induced powercomponent+k4adorsal2vair+k5(adorsal2vair)2+k6(adorsal2vair)3climbing powercomponent+k7vz+k8vz2+k9vz3acceleration powercomponent+k10arostralvgps+k11(arostralvgps)2+k12(arostralvgps)3forward flock factorcomponent+k13ffahead+k14ffahead2+k15ffahead3rear flock factorcomponent+k16ffbehind+k17ffbehind2+k18ffbehind3constant+constant each power component takes account of the kinematic contribution towards power  for instance , induced power is proportional to the square of body weight ( hence dorsal acceleration to take account of turns ) and inversely proportional to airspeed .
individual pigeon was included as a categorical variable , thus taking some account of the morphological variability between pigeons .
the dataset was first bounded to remove extreme values ( frequencies 5 to 10hz ; air speed 11 - 18 m/s ; dorsal acceleration 8.81 to 20.81 ms ; vz=4 to 4 m/s ; flock factors<0.1 ; acceleration power within + / 39.2 w / kg , equivalent to the vz bounding ) , leaving 171,209 flaps .
the overall model fitted the data with r=0.48 ( frequency ) or r=0.37 ( dorsal amplitude ) ( statistical tables in supplementary information ) .
 flying birds often form flocks , with social1 , navigational2 and anti - predator3 implications . further , flying in a flock can result in aerodynamic benefits , thus reducing power requirements4 , as demonstrated by a reduction in heart rate and wingbeat frequency in pelicans flying in a v - formation5 . but 
 how general is an aerodynamic power reduction due to group - flight ? 
 v - formation flocks are limited to moderately steady flight in relatively large birds , and may represent a special case . what are the aerodynamic consequences of flying in the more usual  
 cluster 6,7 flock ? here , we use data from innovative back - mounted gps and 6 degree of freedom inertial sensors to show that pigeons 1 ) maintain powered , banked turns like aircraft , imposing dorsal accelerations of up to 2 g , effectively doubling body weight and quadrupling induced power requirements ; 2 ) increase flap frequency with increases in all conventional aerodynamic power requirements ; and 3 ) increase flap frequency when flying near , particularly behind , other birds . therefore , 
 unlike v - formation pelicans , pigeons do not gain an aerodynamic advantage from flying in a flock ; indeed , the increased flap frequency  whether due to direct aerodynamic interactions or requirements for increased stability or control  suggests a considerable energetic cost to flight in a tight cluster flock . 
Methods summary
Measurements
Power models
Supplementary Material