The roast turkey formula
I don't often roast a whole turkey, so when I do I always forget how long it's going to take. Fortunately, dimensional analysis shows that the time it takes to properly roast a whole turkey is proportional to its weight to the ⅔ power.Scale and dimension - From animals to quarks. Los Alamos Science 11. Geoffrey B. West (1984). A literature review recommends 45 min/lb⅔ at 350℉.Mathematical modelling: a case studies approach. Reinhard Illner, C Sean Bohun, Samantha McCollum, and Thea van Roode (2005) A first course in mathematical modeling. Frank R. Giordano (1985)
For a spherical turkey of uniform thermal conductivity and density , a more precise formula has been derived:Physics in turkey cooking: Revisit the Panofsky formula. AIP Advances 11(11). Yifei “Jenny” Jin, Lisa R Wang, and Jian Jim Wang (2021).
where the oven is set at and the center of the turkey needs to reach a temperature of from .