Morphometric input parameter values used to simulate energy expenditures of two captive Whooping Cranes (one adult male, one adult female) in outdoor and in metabolic-chamber-like conditions.

Abbreviations: d = dorsal, v = ventral.
aDensity of fur or feathers has little effect on animal heat loss over a wide range of values [51].
bMeasurements on study animals were made while the animals were in hand for doubly-labeled water injections (prior to injections) using tape measures and rulers.
cDue to incorrect reading of ruler, the female’s feather depth was used for both animals.
dPhotographs were obtained by taking stills from time budget videos during the doubly-labeled water measurement period. The known height of the cranes’ leg bands were used to scale measurements of the lengths of the cranes’ unfeathered upper leg (tibiotarsal joint to bottom of feather line). Because bands were not visible in all photographs, the lengths of unfeathered upper legs were used to scale all other measurements. Measurements shown are an average of measurements from at least three photographs of each bird. To minimize effects of foreshortening, stills were in which the crane’s upper leg was in a vertical position and the crane’s front/back or side was perpendicular to the camera.
eThe torso was modeled as an ellipsoid incorporating the volume of the wings and the feathered (top) portion of the legs. The wings were included because cranes’ wings are almost always folded against the body (except when flying, which is rare for captive cranes). The feathered part of the upper legs was included because feathers have a significant impact on heat balance, making this part of the leg more similar to the torso than the unfeathered portion of the legs. The following steps were taken to calculate the estimate the appropriate ellipsoid size. (1) For each crane, the length and circumference of the torso, including the wings, was measured with a tape measure. The ratio of horizontal to vertical diameter for the torso plus wings was obtained from photographs (0.98 for the male and 1.07 for the female). The ratio and circumference were used to calculate the horizontal and vertical diameter of the torso, according to the formula

C≈π
[3(
a+b
)-(
3a+b
)(a+3b
)
]

, where C is the circumference of an ellipse, a is the semi-major radius, and b is the semi-minor radius. To obtain radii of a “flesh only” (i.e. unfeathered) ellipsoid, the dorsal and ventral feather depths were subtracted from the vertical diameter, and 4x the average of the dorsal and ventral feather depth were subtracted from the horizontal diameter. 4x feather depth was subtracted to account for the feathers on the outside of the ellipsoid and feathers between the wings and torso, which we assumed would be compressed by about 50%. 2x the average of dorsal and ventral feather depth was removed from the measured torso length. The volume of the “flesh only” ellipsoid was calculated using the formula
V=

4
3

πabc

where V is volume, and a, b, and c are the radii. (2) The “flesh only” volume of the feathered portion of the legs was estimated using the formula for the volume of a truncated cone with constant semi-major to semi minor axis ratio:
V=π

A
B

{

B
2

H
t
3

3

[
-B

H
t

/(
b
t

-B)
]
2

-

B
2

H
t
2

[
-B

H
t

/(
b
t

-B)
]

+B
2

H
t

}

where A and B are the semi-major and semi-minor axes of the large (proximal) end of the truncated cone and Ht is the height of the truncated cone. The length of the feathered portion of the leg, diameter at the proximal end, and diameter at the distal ends were measured from pictures. The average of side-to-side and front-to-back diameters were used. Feather depth was assumed to be the average of torso dorsal and ventral depths and was subtracted from diameters to obtain A and B. (3) The volume of the “flesh only” feathered leg was added to the volume of the “flesh only” torso-plus-wings ellipsoid to obtain the “flesh only” volume for final ellipsoid. The “flesh only” diameters of the new ellipsoid were calculated from the formula for the volume of an ellipsoid (above), maintaining the same a:b and b:c ratios as the torso-plus-wings “flesh only” ellipsoid. Torso feather depths were then added to diameters of the torso-plus-wings-plus-feathered-leg “flesh only” ellipsoid. 2x the average of the dorsal and ventral feather depths were added to the horizontal diameter, and the sum of the dorsal and ventral feather depths was added to the vertical diameter.
Morphometric input parameter values used to simulate energy expenditures of two captive Whooping Cranes (one adult male, one adult female) in outdoor and in metabolic-chamber-like conditions.