Electronic Supplementary Material
The Mechanical Power Requirements of Avian Flight
1. Flights in wind tunnel
Zebra finches and budgerigars (body mass zebra finch 12.7 ± 0.9 g, budgerigar 45.0 ±
2.1g) were trained daily until they could sustain at least 15 minutes of continuous, steady flight at 10 (zebra finch) or 12 (budgerigars) m s
-1
. Birds were housed in cages with ad libitum access to a commercial seed mix and water. Supplemental vitamin enriched, high protein egg food was also provided daily.
The wind tunnel at the University of Leeds is an open circuit Eiffel-type wind tunnel with a closed working section with dimensions 0.52 m

0.52 m

0.95 m (width

height
 length) and square in cross-section. Meshes constructed from nylon line were placed upstream (15 mm spacing) and downstream (7.5 mm spacing) of the working section to ensure that the birds remained within the working section. The wind tunnel was calibrated across a range of speeds from 2 m s
-1
to 20 m s
-1
using a hot wire anemometer
(Dantec). A removable perch could be placed at the front of the working section. Birds were trained to initiate flight when the perch was removed and to land again when the perch was presented to them.
2. Sonomicrometry and electromyography
Two sonomicrometry transducers were implanted into the superficial facia of the pars sternobrachialis region of the pectoralis muscle running between the central intramuscular tendon and the keel of the sternum under isoflurane induced anaesthesia.
The sonomicrometry transducers were approximately 25% of the muscle fascicle length

apart in the resting muscle (equivalent to distances of approximately 4 mm in zebra finch and 7 mm apart in budgerigar).
The average EMG intensity of muscle activity during flight was calculated by rectifying and integrating the EMG bursts, and dividing by the burst duration. Relative intensity of muscle activation was calculated by dividing EMG intensity at each flight speed by the maximum recorded intensity for each bird.
3. Kinematics and aerodynamic model to calculate flight power
Position, velocity and acceleration of the centre of mass
The position of the centre of mass of the bird (estimated as the centre of the body) relative to a fixed origin in the wind tunnel was digitized from high-speed video recordings. Positional data ( x , horizontal and z , vertical) were smoothed using fourthdifference smoothing (Lanczos, 1957; Rayner and Aldridge, 1985). The x and z coordinates of the centre of mass of the birds were differentiated (equations 11 and 12 a-d in Rayner and Aldridge, 1985) to obtain bird velocities ( x  and z  ) and the same methods were used to obtain accelerations from the velocities (  x  and  z  ). The overall velocity (

) of the bird’s centre of mass was calculated as follows:
  x  2  z  2
The elevation of the velocity vector (

) was calculated as:
  tan

1 z 
(1)
(2)

Body forces
The horizontal ( F x
) and vertical ( F z
) forces acting upon the bird were calculated as follows:
F x

M b
 x  
1
2

S b
C
D , par x  2
F z

M b
(  z   g )
(3)
(4) where, M b
is body mass, g is gravity, S b
is body frontal area, C
D,par
parasite drag coefficient. Note that in calculating the forces on the bird in this way, any contribution from body lift is ignored.
Induced velocity and power
During the flapping phases of flight, thrust was calculated as the vector sum of the weight support, parasite drag and acceleration of the centre of mass (Wakeling and Ellington,
1997):
T

F x
2 
F z
2
(5)
During non-flapping periods, thrust is zero.
The induced velocity was calculated using classical actuator disc theory from the momentum flux of air needed to balance the thrust. The actuator disc represents the swept area ( D ) over which the wings interact with the air and was calculated from wing kinematics. Induced velocity ( w ) at the level of the actuator disc for forward flight is given by Wakeling and Ellington (1997):

w
4 
2
 w
3 sin

'
 
2 w
2 


T
2

D


2

0 (6) where -
 ΄ is the angle at which the velocity vector is inclined to the actuator disc and ρ
is air density.

'
 
(
  
) where

is the stroke plane angle with respect to the horizontal.
(7)
The area of the actuator disc ( D ) was estimated as:
D
  l w
2 where

is the stroke amplitude, l w
is wing length during the downstroke
During the flapping phase ( i ), induced power was calculated as:
P
 ind , i kw i
T i
(8)
(9)
Profile power
The mean profile power needed to overcome the pressure and friction drag acting on the wing during the downstroke was calculated as:
P pro
, i

2 (
1
2

V
R
3
S w
C
D , pro
) (10) where S w
is wing area, C
D,pro
is the profile drag coefficient, V
R
is the resultant velocity calculated at the estimated position of the centre of lift (taken as 2/3 l w
based on the estimated position of the centre of lift in a hovering pigeon; Pennycuick, 1967):

V
R

( w
 z  
4
3
 l w n sin

)
2 
(

4
3
 l w n cos

)
2 where n is wingbeat frequency.
Parasite power
The parasite power required to overcome drag on the body was calculated as:
(11)
P
 par
1
2

S b
C
D , par

3
(12) where C
D,par
is the parasite drag coefficient. The power required to overcome the drag on the data cable was added on to the body parasite power. Drag on the data cable was measured in the wind tunnel at speeds ranging from 4 to 16 m s
-1
at 2 m s
-1
intervals. The data cable was attached to a force transducer (FORT100, WPI) and held in a position that simulated its attachment to the bird during flight. Power was calculated by multiplying drag by air velocity.
Total, mean aerodynamic power during intermittent flight
The thrust generated during flapping imparts energy to the centre of mass of the bird that must balance any loss of height or speed during the non-flapping phase. The induced, parasite and profile power requirements calculated during flapping, therefore account for the entire power requirements over the whole flight period. The mean aerodynamic power ( P aero
) is given by:
P aero
  n
1
 t i
( P ind , i

P pro , i
 t f

P par , i
)
(13)

for flapping period i =1 to n , where
 t is flapping duration for phase i and
 t f
is total flight duration (flapping and non-flapping phases).
Coefficients used in the aerodynamic flight power calculations
We used the minimum and a typical range of values for the coefficients previously reported in the literature. Minimum values: C
D,par
0.05 (Tucker, 2000); C
D,pro
0.01
(Tobalske et al., 2003); k 1.0; S b
=0.00813
M b
0.666
(Pennycuick et al., 1988); Typical values: C
D,par
0.13 (Rayner, 1999); C
D,pro
0.02 (Rayner, 1979); k 1.2 (Pennycuick, 1975);
S b
=0.00813
M b
0.666
(Pennycuick et al., 1988).
4. Assessment of muscle performance in vitro
There is little physiological data on muscles that operate at in vivo cycle frequencies that are comparable to budgerigar and zebra finch pectoralis muscle. In order to assess the performance and viability of our muscle preparations, we have used scaling relationships for a number of physiological measurements taken from other power generating muscles.
Mean stress difference (  ) is a measure of muscle performance that directly relates to locomotion and is the difference between the mean power generated during shortening and that generated during lengthening (Casey and Ellington, 1989). In a wide range of aerobic muscles during maximal performance in vivo or under in vitro conditions,  is dependent on cycle shortening duration (Fig. S1). During maximal in vivo power output in budgerigar and zebra finch muscle preparations,

falls within the 95% confidence limits of this relationship (Fig. S1). The similarity between the data we have collected

here and the scaling relationships for physiological measurements derived from previous studies, gives us confidence in the reliability of our measurements.
Maximum isometric tetanic stresses ( P
0
; mean±S.E.M) were: budgerigar 223±16 kNm -2
,
N=9; zebra finch 167±10 kNm -2
, N=7. For comparison, P
0 was 131-200 kNm
-2
in quail pectoralis muscle (Askew and Marsh, 2001; Johnston, 1985), 122 kNm
-2
in starling pectoralis muscle (Biewener et al., 1992) and 92-104 kNm -2 in hylid frogs (Girgenrath and Marsh, 1999).
Our recording of muscle strain and activity pattern in a single region of the pectoralis muscle precludes us from taking into account regional differences in fascicle performance as has been suggested in some other birds (Soman et al., 2005). How regional differences in muscle strain affect work output is uncertain since regional differences in force production are unknown. In the absence of regional force measurements it is unclear what effect these regional strain patterns will have on power production. However, this may represent a source of error in our estimation of whole muscle performance.

k l w
M b n
P ind,i
P pro,i
P
0
S b
S w
T v
V
R w x , z
 , z 
 x  ,  z  induced velocity correction factor wing length body mass wingbeat frequency induced power during flapping profile power during flapping maximum isometric stress body frontal area wing area thrust overall velocity of the centre of mass resultant velocity on the wing induced velocity co-ordinates describing the horizontal and vertical position of the bird velocity of the centre of mass in the x and z directions, respectively acceleration of the centre of mass in the x and z directions

-
 ΄ the angle at which the forward velocity of the bird is inclined to the actuator disc
β
Δt
Δt f
 angle of the stroke plane with respect to the horizontal plane flapping duration total flight time stroke amplitude
ρ

χ air density mean stress difference elevation of the velocity vector

Figure S1
Figure S1. The effects of cycle shortening duration on mean stress difference for a range of aerobic power generating muscles. Data are from zebra finch ( Taenopygia guttata ) pectoralis muscle (this study) and budgerigar ( Melopsittacus undulatus ) pectoralis muscle
(this study); “birds in vivo
” are European starling (
Sturnus vulgaris ) pectoralis muscle
(Biewener et al., 1992), mallard ( Anas platyrhynchos ) pectoralis muscle (Williamson et al.
, 2001), cockatiel ( Nymphicus hollandicus ) pectoralis muscle (Hedrick et al., 2003) and pigeon ( Columba livia ) pectoralis muscle (Biewener et al., 1998); “flight muscles in vitro
” are tettigonid (
Neoconocephalus triops ) wing muscles (Josephson, 1985) and hawkmoth dorsoventral muscle (Stevenson and Josephson, 1990); “other muscles in vitro” are Hyla versicolor and H. chrysoscelis external oblique muscles (Girgenrath and
Marsh, 1999), mouse ( Mus ) and rat ( Rattus ) diaphragm muscle (Altringham and Young,
1991), mouse soleus muscle (Askew and Marsh, 1997) and rat soleus muscle (Swoap et

al., 1997). Scaling relationships for data excluding the data from this study, are indicated by solid lines and the upper and lower 95% confidence limits by broken lines.

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