It’s important to do your due diligence and understand the thermodynamics equations behind cooking a turkey so that you can cook it just right. After all, what kind of cook would you be if you couldn’t explain the thermal resistance of turkey to your in-laws? Or, for that matter, calculate how long your mom’s turkey will take to cook given its thermal conductivity and heat capacity. Let’s walk through the equations and engineer our way through holiday dinner!
First, we need to break down what exactly a turkey is in the nature of thermodynamics equations. Believe it or not, there have been many scientific studies covering the thermodynamics of cooking a Turkey, and most researchers simplify the shape into a spherical form. Now, this spherical bird body is heated through radiation, conduction, and convection in the cooking process – we’ll take all of these into account. Radiation can be controlled by covering the turkey in aluminum foil, conduction can be controlled by using different pan materials, and convection is ultimately controlled by oven temperature. Our main cooking heat source in turkey cooking is going to be convection, which will cause a temperature gradient moving from the surface of the turkey inward. Now, to start adding some numbers and theory.
In one scientific paper, Physicist Peter Barnham notes:
“Solving the thermal diffusion equations for the ideal spherical turkey shows that the cooking time depends linearly on the temperature difference between the oven and the uncooked turkey and also on the square of the radius of the bird.”
For the purpose of calculations, let’s assume the following thermal properties of the turkey:
Thermal Conductivity: .4 BTU/ft-˚F-h
Density: 60 lbm/ft^3
Heat Capacity: 1 BTU/lbm/ft^3
h = 20 BTU/ft^2˚F-h
Weight: 20 lbs
So, there are our turkey properties, now time to set up a differential equation and solve for how long it would take to cook this turkey. You can find the calculations for the thermal analysis of this turkey below, with the final cooking time coming to 5.0397 hrs.
Now we have walked through how to solve for the cooking time of a turkey of a given weight, let’s examine the effect other properties would have on our holiday bird. Say, for example, if we stuffed the bird with stuffing. Travis Mikjaniec examined this by creating an engineering simulation of a semi-realistic turkey. You can read his full analysis here, but he essentially modeled the turkey with a cavity in the middle and analyzed air flow in convection heating. Comparing normal convection airflow of a turkey in an oven with and without stuffing, he found that the difference in airflow was negligible. Resultingly, the negligible airflow change meant that the cooking time between a stuffed turkey and a non-stuffed turkey was essentially the same.
Thus far, we have concluded that cooking a bird with stuffing doesn’t cause any difference to cooking time, and we have calculated how to find cooking time the technical way. But wait, doesn’t everyone know the “20 minutes per pound” rule on most turkey packaging? Why go through all of this analysis when you can just follow the instructions. I hate following instructions and doing things the easy way – it’s just a fact of my life. Also, the instructions are wrong. Gasp. That’s right, weight has absolutely nothing to do with how a turkey cooks, it’s more about thickness, so if you happen to have a rather bulbous and heavy turkey, you might not cook your turkey well enough. Or if you had a turkey that was a little flat, you might burn your glorious roast. Holiday dinners just got a lot more complex through the eyes of engineering.
Here’s what you can do, take some time to solve that differential equation above to find an approximate time to cook your turkey. However, that differential equation is based on a spherical model of a turkey, and unless you have an oddly shaped bird, turkeys aren’t spheres. There will be some inherent problems with this model, and if you don’t want to trust this model to a “T”, it’s time to pull out your computer and start making a spreadsheet as you cook your turkey.
The spreadsheet is going to serve two purposes.
- To track the temperature of the turkey as it cooks allowing you to do a trendline analysis and predict when it will be perfectly cooked.
- To serve as a measure of your technical prowess that you can show off to your coworkers.
As it turns out, the temperature change in a turkey is a fairly linear process with the beginning and end exponentially diverging to the temperature of the turkey initially and the oven temperature, respectively. Here’s the graph that mechanical engineer Mike Swanson made, with the blue line being the actual measurements and the dotted line being a predicted trend line.
What I am suggesting that you do is combine the differential equation analysis from the beginning of this article and work to develop a predictive model of how the turkey will cook based on initial temperature measurements. Given that the cooking time of a given turkey will likely extend beyond two hours, you should be able to develop an accurate model of when your turkey will be done.
The “perfect turkey” means that the muscle fibers in the meat are perfectly degraded and the meat, both white and dark, is cooked thoroughly without being too dry or tough. You will want to closely monitor your bird to make sure it is cooked to the right temperatures throughout. Just because you are a good at math doesn’t automatically mean that your turkey will be cooked perfectly.
Now, we mainly focused on cooking a turkey using a convection oven here, but you can also deep fry your turkey to provide for a much faster heat transfer coefficient, and thus a quicker cooking time. To give a brief overview of deep frying, most of the cooking is going to occur through conduction with the hot oil. The advantage to deep frying is that because of the faster conduction heat transfer, your turkey will cook through much faster, thus keeping the skin from becoming too burnt. This method also allows you to lock in moisture to the meat – but deep frying a turkey is also very dangerous.
To close out this analysis, we will end with a discussion on white and dark meat. Dark meat needs to be cooked to a higher temperature so the muscle fibers can be broken down. To accomplish this without cooking the meats separately, simply place an ice pack on the breast of the turkey when thawing. This will allow the legs to warm faster, so when the bird is put in the oven, the dark meat and white meat will be cooked perfectly, simultaneously.
I would suggest not spending your holidays ignoring your family and doing thermal analysis on your turkey, but this can certainly be a conversation starter to have around the holiday table.