# 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/lb 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 $\alpha$ and density $\rho$, 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).

$t=\frac{\ln\left(\frac{2(T_h-T_0)}{T_h-T_f}\right)}{\pi^2 \alpha} \left(\frac{3}{4\pi\rho}\right)^{2/3} m^{2/3}$

where the oven is set at $T_h$ and the center of the turkey needs to reach a temperature of $T_f$ from $T_0$.