Physics in Turkey Cooking: Revisit the Panofsky Formula

In 2008, Panofsky gave an empirical formula T = (1/1.5)W^2/3, for turkey baking time, T, in hours versus turkey weight, W, in pounds, the so-called Panofsky formula. Compared to the previously existing recipes based on the simple linear relationship between turkey weight and baking time, the Panofsky formula provides a more accurate estimate for the baking time. In this work, we conduct a comprehensive study of the turkey baking process, which leads to the mathematical derivation of the Panofsky formula under some approximations. We also generalize the Panofsky formula to define a general formula, T = (1/P)W^2/3, where P is defined as the Panofsky Constant. Under the 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. The dependency of the new Panofsky constant on the turkeys' thermal properties and other initial baking parameters was carefully mapped out.