One of the greatest of all cooking challenges is knowing when food is "done". Sometimes a thermometer is your best friend especially for cuts like steaks or white meat chicken breasts. Or pork tenderloin. In these cases, a mere 5 degrees F separates tender from tough. No amount of pressing on the surface and watching it rebound, or divining juices for color is as accurate as a good digital thermometer.
Alternatively, for baked goods weighing food is often the best strategy.
However, even if you learn to reliably separate "done" from "oops", predicting cooking time is equally valuable. Otherwise, the green beans are ready an hour before the rib roast has rested, and no one wants to eat soggy limp green beans.
Perhaps a "rule of thumb" exists, one that is accurate and predictable under all conditions. Like "30 minutes a pound" or "5 minutes an inch for medium rare".
And these rules do exist. Equations to accurately predict^{1} how fast a slab of aluminum will heat in an oven are easy to derive and well known something along the lines of:
(where L is the distance to the center of the slab, T_{raw} is the unheated starting temp, and D is the thermal diffusivity)
The problem is, food cooks very differently than a lump of inert aluminum. Food not only heats up in an oven, it also evaporatively cools. While the above equation correctly predicts aluminum will eventually reach the oven's temperature setting, food never rises above the boiling point of water, 212F. In fact, moist food can stall and plateau at 150F for hours when cooked low and slow! Plus, food oozes delicious juices and fat, shrinks as collagen hydrolyzes and turns into gelatin, and is surrounded by a bubble of moist, insulating air whose size depends on airflow and oven proportions.
Can you predict cooking times in the face of these realworld complexities? Absolutely, though it takes considerable computing power, a mix of rigorous and heuristic modeling, and lots of accurate data. Unfortunately, few rules of thumb emerge from this more detailed analysis.
Alternatively, tables or graphs basedoff actual cooking times are sometimes the most practical solution. For example, here I've cooked pork tenderloins at three different oven temperatures (each tenderloin about 2.5" thick weighing 1 lb) :
In the first 10 minutes of cooking, heat is diffusing from the oven to the center of the tenderloin. Thus the delay in temperature rise. This delay is almost independent of oven temperature.
The curves are similar and roughly exponential after the first few minutes of baking. But even exponentials are problematical as rules of thumbs. For example, there is a larger gap between the 250F/350F curves than the 350F/450F curves, and the relative gap grows at higher temperatures. So any simple rule of thumb is suspect.
Another way to view the same data is to flip the chart around, and ask, for a given desired internal temperature, how long will it take to cook in different ovens? In other words, how long until it is "done"?
For example, pork tenderloin is perfect around 140F (yes, it is pink, but will coast to 145F before serving and that satisfies the USDA for safety). The blue dotted line indicates it takes:
Time to reach 140F: 
40 minutes @ 450F 
55 minutes @ 350F 
90 minutes @ 250F 
To cook dark meat chicken of the same thickness (say a rollatini), 180F190F is best:
Time to reach 180F: 
65 minutes @ 450F 
90 minutes @ 350F 
3 hours @ 250F 
Note the huge time penalty cooking at 250F almost 175% slower^{2} than at 450F. Why would anyone accept this time penalty to cook a simple hunk of meat?
The reason is uniformity. The hotter and faster a thick piece of food cooks, the greater the difference in temperature between the surface and center. When 5F matters for tenderness, a low slow cook followed by quick sear to brown and flavor the crust, is often the best strategy. Otherwise the outside is tough, while only the center remains tender.
What about the dependence of cook time on thickness? Well, again realworld data trumps simple rules of thumb. Although a " diffusion equation" inspired rule predicts the time grows in proportion to the thickness of the food "squared", in reality that rule breaks down below an inch or so in thickness. Not bad above, except in low and slow cooks when the meat loses 30% of its initial weight....
So what is to be done? Well, I'm accumulating a compendium of data taken over multiple cooks and in multiple ovens, and using this data as the basis for a cooktime prediction tool based on a little theory, and a lot of interpolation.
Stay tuned for more details. And we will be looking for volunteers to help validate the predictions there is only so much meat I can eat in the interest of kitchen science.
