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The Wolfram|Alpha Team

Talking Turkey

November 25, 2013 —
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The holiday season is upon us again, and that means one thing: more turkey, please. Last year we introduced a tool for calculating how long you should cook a turkey. This year we’ve expanded our selection of useful tools to help you plan your turkey-related needs for the holidays. Now Wolfram|Alpha can help determine how much turkey you need to feed your guests, how long to defrost it, and if so inclined, how long to deep-fry it.

The first task in preparing a Thanksgiving Day turkey is to figure out how big of a turkey you really need. Now Wolfram|Alpha provides answers to questions like the turkey size needed for 6 adults and 2 children.

the turkey size needed for 6 adults and 2 children

We include adjustments to the portion size depending on whether your guests are heavy or light eaters. For those interested in their waistlines, we also include nutrition information based on serving size chosen, so that you can budget properly.

From the queries people already send us, we know a good deal about the distribution of dinner party sizes, at least when there is a question about how much turkey you really need. The frequency of queries asking for the amount of turkey for a set number of people shows a number of interesting spikes:

Frequency of queries asking for the amount of turkey for a set number of people

Most of these spikes occur at even numbers of people, suggesting that most people are inviting couples to their big dinners (such as siblings and their significant others). It also suggests that most people can guess the size of the turkey they need for groups less than 10. Wolfram|Alpha tells us that for 10 people, we need a 10- to 15-pound turkey (depending on people’s appetites). For a crowd of 15, however, we need something closer to 15- to 23-pounds.

Once you have your turkey, you need to get ready to cook it. For many people this first means defrosting it. If it is a large bird, then this process may begin days before the actual event. Wolfram|Alpha provides a simple formula for calculating the time it takes to defrost a turkey or other large amount of meat.

We provide two different calculations depending on the method used for defrosting: a cold water bath or in a refrigerator. In both cases you want the medium, whether it be water or air, to be less than 40 degrees Fahrenheit or 4.5 degrees Celsius, so that dangerous bacterial growth is limited.

There is a vast difference in the time it takes between the methods. For example, defrosting a 10-pound turkey can take 2 days:

meat defrosting time

Switching to a cold water bath speeds this up to 5 hours. This is because of water’s greater ability to transfer heat to the turkey. While it takes more space and effort, you are able to turn days of waiting into hours with this method.

Finally we get to the big day and the cooking of the turkey. Our turkey-cooking formula uses the standard cooking guidelines fitted to the heat equation for a spherical turkey. While this is obviously an approximation, with modern farm turkeys, this isn’t far from the truth.

Turkey curve

Wolfram|Alpha tells us that an 8-pound turkey takes 2 hours, 26 minutes to cook (or 3  hours with stuffing). But a 16-pound turkey takes 3 hours, 50 minutes to cook, not the nearly 5 hours you would expect by doubling the time. This is because of the geometry of the turkey. The mass of a turkey is proportional to the cube of its width. But the important element for heating is the surface area that scales by square of the width of the turkey. So a turkey twice as massive is only 1.26 times wider. It also has 1.59 times larger surface area. Multiplying 1.59 times the original time of 2 hours, 26 minutes gives us 3 hours, 51 minutes. This is almost exactly what Wolfram|Alpha returns.

For those of you who live in places like Denver, Colorado, locations at high altitude, the cooking time will vary slightly. This is because the boiling point of water is lower at high altitude, due to the thinner air. So to get the same heating effect, you need to cook food longer. In Denver, for example, water boils at 94.9°C or 202.8°F. We’ve included a simple adjustment to the times to account for that change. So if you want to know the time to cook a turkey in Denver, you’ll get a good answer.

Returning to some of the queries we receive, we can get a sense of the size of turkeys people are looking to cook. As you might expect, these are going to be tilted toward larger turkeys with longer and less certain cooking times.

Turkey histogram

The spike at 20 pounds is interesting, but might be just a nice round number people like to use. The peak around 13 or 15 pounds probably means they are the most commonly queried weights that relate to a real turkey. A 13-pound turkey takes 3 hours, 22 minutes to cook and 2.6 days to defrost in a refrigerator (use a cold water bath to speed that up to under 7 hours). The highest weight we’ve seen queried is 55 pounds, which would take almost 9 hours to cook. Wild turkeys rarely achieve that high a weight, topping out around 24 pounds. But farm-bred turkeys have reached weights of 80 pounds or more.

Recently, frying turkeys has become fashionable, and we’ve included a tool to figure out how long it takes to deep-fry a turkey. Deep-frying is faster than cooking a turkey in an oven because the medium of exchange, oil, can transfer heat much more readily than air. Also, many oils can be heated to much higher temperatures due to higher boiling points. A 13-pound turkey can be deep-fried in 45 minutes. Be careful though: those higher temperatures and the better rate of heat transfer can be dangerous should the oil splash.

Of course Wolfram|Alpha has more to say about turkeys than how to cook them. We can also look at the consumption rate of turkey. For example, there are 3.23 million living turkeys in Turkey, and 1.137 million short tons of poultry (including turkeys) are consumed each year there. The population of Turkey is 75.4 million people, which means that each Turkish person on average eats 32.48 pounds or 14.733 kilograms of poultry per year.

If we compare this to turkeys in the United States, we find a whopping 250 million turkeys being raised. This exceeds the numbers for all other livestock in the United States except chickens. Poultry consumption in the United States is 17.25 million short tons per year, which is roughly half a ton a second. The average consumption per person is 114.1 pounds or 51.755 kilograms per year, which is over three times as high as Turkey. If this meat was broken up into heavy portions, that would mean people were eating poultry (including turkey) 190 times a year, or at least every other day.

With that food for thought, we wish you a Happy Thanksgiving.

cooked turkey curve

Enjoy your turkey.

1 Comment

Wow, this turkey stuff is actually pretty cool!!!

Posted by Anthony Meanors December 8, 2013 at 3:50 am