The time it takes to properly roast a whole turkey is proportional to its weight to the ⅔ power. My old mathematical modelling textbook specifically recommends 45 minutes per lb2/3 when cooked at 350℉.
For a spherical turkey of uniform thermal conductivity α and density ρ, a precise formula has been derived:
t = \ln\left(\frac{2(T_h - T_0)}{T_h - T_f}\right) \frac{1}{\pi^2\alpha} \left(\frac{3}{4\pi\rho}\right)^{2/3} m^{2/3}where the oven is set at Th and the center of the turkey needs to reach a temperature of Tf from T0.
The more general ⅔ power law does not depend on unrealistic assumptions about the turkey’s shape or thermodynamic properties; it can be derived from pure dimensional analysis and applied to turkey-shaped meat-based objects by fitting a curve to specific cook times used by chefs.