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. As Geoffrey West explains:

Many (inferior) cookbooks simply say something like "20 minutes per pound," implying a linear relationship with weight. However, there exist superior cookbooks, such as the Better Homes and Gardens Cookbook, that recognize the nonlinear nature of this relationship... [For] geometrically similar birds [with] the same physical characteristics, t = constant × w2/3.

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

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!

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