Physics in turkey cooking: Revisit the Panofsky formula

Back in 2008, Panofsky gave an empirical formula, T=11.5W2/3, for turkey baking time, T, in hours vs turkey weight, W, in pounds, the so-called Panofsky formula or Panofsky constant. Compared to the previously existed recipes that are based on the simple linear relationship between turkey weight and baking time, the Panofsky formula provides a more accurate estimate for the baking time. For instance, a general guideline of 13–20 min/lb was widely recommended in all previous turkey baking recipes. In this work, we conduct a comprehensive study of the turkey baking process that leads to a mathematical derivation of the Panofsky formula under some approximations. We also generalize the Panofsky formula to define a general Panofsky formula, T=1PW2/3, where P is defined as the Panofsky constant. Under spherical approximations, we then apply an accurate physical solution of the heat transfer equation and use the rigorous solution with numerical methods to study the generalized Panofsky formula and the Panofsky constant. We found that the generalized Panofsky formula can be perfectly applied to all turkey baking scenarios for baking time calculations. Furthermore, we did a careful analysis of the Panofsky constant, which equals 1.5 in the original Panofsky formula. The dependency of the new Panofsky constant on thermal properties of the turkeys and other initial parameters of baking, e.g., initial and final center temperature of the turkeys, oven temperature, thermal conductivity, specific heat, and turkey’s density, was carefully analyzed and mapped out. The Panofsky constant, P, could vary from 1.1 to 1.9 depending on these thermal parameters.