Statistical Analysis of Turkey Cooking

Step 3 Background and Methodology

Cooking time is dependent on cooking temperature, food starting temperature, food volume, food shape (spherical), food surface area, and food density.

Lets assume spherical turkey and that all turkeys have the same (or very similar) density. The volume of a given turkey will be (4/3)*pi*r³ where r is dependent on food density. So for a given r, we can find the surface area as 4*pi*r² (FYI: Volume of a sphere is the Integral of Surface Area).

The following was calculated assuming a 10lb turkey has a radius of 10 units.
So a 10lb (and a radius of 10) turkey has a volume of : 1333 * pi
and a surface area of: 400 * pi
and a radius: 10

Now let us double our mass and go for 20lb. Remember that the density is the same (and our only mathematical constant).

The following is based of the 10lb turkey calculations (keep in mind, these are quick estimate calculations).
Volume: 2666 * pi
Surface Area: 634 * pi
Radius: ~12.59

What we find is that if we double the mass, the volume is increased by a factor of 2. However, the surface area is only increased 1.59 times. So we have twice the amount of mass to heat, but only a 1.59 times the surface area to move said heat. On the bright side, our heat does not have to travel twice the distance :)

So it can clearly be seen that cooking time estimates is some sort of voodoo best described by thermodynamisits (? :P) OR by those with meat probes.

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Before collecting data, the instruments were calibrated (if applicable) and then cleaned. The probe was placed in the thigh in what is usually considered the "normal" location to get an accurate temperature reading for dark meat (which takes longest to cook).

The data was then recorded at regular intervals. When the correct "doneness" was reached, a final reading was taken before removing and cleaning the probe. Using the collected data, a basic analysis was completed although time constraints due to final examination schedule made this a bit hasty.