# Time to Cook A Turkey

1. Apr 4, 2014

### bluecheez

According to this website, there is an equation obtained empirically to obtain the amount of time it takes to cook a Turkey:

t = W(2/3)/1.5

Is there any theory to support such a relation? Yes, the internal structure of a turkey is complicated so I'm sure the proper way to do it is to numerically model a PDE of the heat equation.
But are there any approximates we can use in real life to get a good idea of how long it'll take to cook something?

2. Apr 4, 2014

### Staff: Mentor

The W2/3 seems to suggest that the heat transfer is dominated by conduction. Approximate the turkey by a sphere, and look up the solution to the transient heat conduction problem for a sphere, assuming that the temperature is T0 at time zero and that the oven temperature is at T. The solution to this heat conduction problem is in the literature, expressed as the average temperature change as a function of the Fourier number. Decide what temperature the center of the sphere has to reach for the turkey to be considered cooked. This will correspond to a specific value of the Fourier number. The Fourier number has an r2 in the denominator, which is proportional to W2/3.

3. Apr 7, 2014

### marcusl

The diffusion of heat into many objects, including a sphere and a semi-infinite slab, results in the relationship t~x^2 to reach a given temperature where x is a linear distance. For a sphere, the appropriate distance measure is r, so t~r^2. Since weight is proportional to r^3, you have that t~W^(2/3). It is only the numerical factor of 1.5 that needs to be empirically determined.

4. Apr 8, 2014

### gmax137

Interesting. For "normal" range of turkey weights, the Panofsky formula is nearly linear and is close to "90 minutes plus 11 minutes per pound." For turkeys from 8 to 24 pounds, the maximum deviation between the formula and this linear approximation is less than 8 minutes, which is negligible. It is important to get the bird close to room temperature before putting it in the oven, otherwise these "rules" won't work well.

5. Dec 24, 2016

### pickycat

What units are the weight and the time? SI or Imperial?

6. Dec 24, 2016

Staff Emeritus
w^2/3 is proportional to surface area. That's not crazy - I'd expect the true answer to be between 2/3 and 1. The 1.5 is just a constant from using conventional units. In Natural Turkey Units, this would be 1.

7. Dec 25, 2016

### vanhees71

The weight in SI are Newton in imperial units it's pound. I strongly recommend to stay within one system of units. There are tragic and expensive examples for technical failures only because two systems of units where at use. I think one mars probe launched by the NASA only failed because one person thought in feet and the other in metres. I guess it was NASA's fault using SI units .

8. Dec 25, 2016

### pickycat

Ha, Ha! Very true! YET, I was asking about the time and the weight in the particular turkey cooking time function of the turkey's weight. In the meantime, I did search some more and I found that in this particular relationship the time has to be in hours, while the weight is in pounds. (Had I assumed SI units, like MOST physicists would use, I would have the same tragic outcome as NASA did!!)

9. Dec 25, 2016

### vanhees71

Well, use a thermometer, and you get your turkey right to the point!