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## Resources

Modeling Scenario

## 9-014-TurkeyCook-ModelingScenario

Author(s): Michael Karls

Ball State University, Muncie IN USA

Keywords: sphere heat equation turkey Panofsky radial symmetry

## Abstract

The goal of this project is to investigate several models for the cooking time for a turkey based on weight, test these models with data obtained from heating curves for turkeys of various weights, and develop a new model to fit this data.

## Citation

Researchers should cite this work as follows:

## Description

A dilemma facing many cooks during the holiday season is determining the time needed to safely cook a turkey. Guidance that can be found in sources such as cookbooks, newspaper articles, and cooking websites is often based on USDA approximate cooking times for a whole turkey by weight.  Oven temperature is 325 F (163 C) and a turkey is considered safely cooked when it reaches an internal temperature of at least 165 F (73.9 C).  Suppose we wish to find a more accurate means to determine cooking time for a turkey based on weight.  In particular, is there a formula one can use to determine cooking time as a function of weight?

In this project, students collect data from heating curves for turkeys of various weights, estimate cooking times with three models (Panofsky, modified Panofsky, and a Cookbook algorithm) and compare to actual times.

Next, they learn about a model for radial heat flow in a sphere, which involves the one dimensional heat equation and a series solution, use this model to show how to obtain the modified Panofsky model, and create a new model that can be used to describe the temperature at any time for a turkey of a given weight.  This model is checked with heating curve data for the turkeys of various weights, used to estimate the cooking time for the turkeys of known weights, and compared to the first three models.

## Authors

Author(s): Michael Karls

Ball State University, Muncie IN USA