Turkey times

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 lb^2/3 when cooked at 350℉.

For a spherical turkey of uniform thermal conductivity $α$ and density $ρ$ , a precise formula has been derived:

t = ln (\frac{2 (T_{h} - T_{0})}{T_{h} - T_{f}}) \frac{1}{π^{2} α} {(\frac{3}{4 π ρ})}^{2 / 3} m^{2 / 3}

where the oven is set at $T_{h}$ and the center of the turkey needs to reach a temperature of $T_{f}$ from $T_{0}$ .

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.