One of the most common foods prepared at this time of the year, and arguably the most common kitchen disaster, is turkey.
There are several employees here at Maplesoft (myself included) who are full-fledged foodies: not only do we enjoy eating good food, but we enjoy preparing it with all our cool kitchen gadgets. Just as mathies may compare calculators, we compare chef’s knives. So being a foodie and a mathie, I was quite intrigued when a co-worker sent me an article that found the optimal cooking temperature for a turkey.
For those of you who have had to take on the task of preparing a turkey, you’re probably familiar with this basic rule of thumb (thousands of burnt turkeys must have contributed to this rule): preheat the oven to 400°F, and then cook it for 20 min/lb at 350 °F. Essentially what this rule means is that the time required to cook a turkey is directly proportional to the mass of the turkey. We know that this cannot be true because some people who adhere to this rule will have a turkey that is moist and tender, and others will have a turkey that is dry and tough. If we take more variables into account, like the size of the turkey (l), oven temperature (T), average density (ρ) and thermal conductivity (κ) we can create a function with respect to time . We can now do a bit of dimensional analysis on this to evaluate the accuracy of the traditional rule of thumb. By using dimensional analysis, we can formulate a relation between a set of known variables, even though we are not sure of the relationship between these variables. The immediate advantage of this procedure is that less experimentation is required to establish a relationship between the variables, allowing us to take given data and see how it will fit with the equations that are created in the analysis. I won’t go into full detail here, but I’ve created a Maple worksheet that shows the calculations used in the analysis. The important part comes from the graphs that are generated:
The black dots represent various cooking times of various sizes of birds. The red line is the old rule of thumb, which you can clearly see is not very reliable. The green line represents the new rule of thumb which falls in line much better. So, what is the magical formula that you should use? Based on the analysis: where x is in lbs and the resulting time is in minutes. Now I will be honest, I haven’t put this to the test yet, but I’ll be sure to try it out this Christmas.