# 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!

For a spherical turkey of constant density and thermal conductivity, 33 min/lb^{2/3} 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/lb^{2/3} 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!

Scale and dimension - From animals to quarks.

*Los Alamos Science**11*. Geoffrey B. West (1984). ↩︎Physics in turkey cooking: Revisit the Panofsky formula.

*AIP Advances*11(11). Yifei “Jenny” Jin, Lisa R Wang, and Jian Jim Wang (2021). ↩︎*Mathematical modelling: a case studies approach*. Reinhard Illner, C Sean Bohun, Samantha McCollum, and Thea van Roode (2005). ↩︎