Roasting a turkey takes time proportional to the ⅔ power of its weight

I don't often roast a whole turkey, so when I do I always forget how long it's going to take. Fortunately, I know where to find a recipe: mathematical modelling textbooks!

Many (inferior) cookbooks simply say something like "20 minutes per pound," implying a linear relationship with weight. However, there exist superior cookbooks… that recognize the nonlinear nature of this relationship… [For] geometrically similar birds [with] the same physical characteristics,

t=constant×w2/3.t = \text{constant} \times w^{2/3}.

Scale and Dimension [1]

For a spherical turkey of constant density and thermal conductivity, 33 min/lb2/3 at 350℉ would theoretically suffice [2], but based on a fit to actual recipes, the textbook I used in undergrad suggests it would take 45 min/lb2/3 at 350℉ [3].

Of course, all such equations are only approximations given the many uncontrolled factors in a real-life kitchen, so make sure you monitor the actual temperature as you're cooking!

  1. Scale and dimension - From animals to quarks. Los Alamos Science 11. Geoffrey B. West (1984). ↩︎

  2. Physics in turkey cooking: Revisit the Panofsky formula. AIP Advances 11(11). Yifei “Jenny” Jin, Lisa R Wang, and Jian Jim Wang (2021). ↩︎

  3. Mathematical modelling: a case studies approach. Reinhard Illner, C Sean Bohun, Samantha McCollum, and Thea van Roode (2005). ↩︎