How can I estimate the cooking time of a roast?

I never remember what worked before, or to write it down someplace. In any case the size and starting temperature will vary. The instructions I learned from refuse to give a time at all, and the first time my guests were waiting hours past the expected dinner time; another time it was ready so early that I had to call everyone to come right away.

For dinner every Jan 1 I make a rib roast:

which I cook very slowly, as taught by “Good Eats”. I no longer use the flower pot, though, as the oven is good enough to use a open roasting pan.

To summarize, this is the slow method of putting in an oven (or bury a crock in the coals) at (a mere) 200°F

The main variable for me would be the starting temperature. From the ’fridge, it might be a chilly 40° in the center, or might be 52, or anything really depending on how it was aged and when it was taken out. The size is 10 pounds, which is 4 bones. The cross section is the same as the generic picture, but mine is about twice as tall (tall in the photo; but that's width in the oven, if it matters).

So we start out with a thermal gradient, and end that step with a thermal gradient too, as the heat still moves toward the center even after it's removed from the oven. I expect about 10 degrees of “carry over”, which should tell you something about the thermal properties of the material.

Can someone help me with a quick thermodynamic formula that will tell me the expected time until the external heat should be removed, based on the starting temperature of the center? Then, what should I be expecting for equilibrium if the outside is insulated, and how long would that take?

(actually I don't really need to to reach equilibrium because I return to a very hot oven to char the outside; but that's fast enough that the center doesn't know what's happening and intermediate locations are still working on the wave of temp. difference from the original 200° bake).

• Using a meat thermometer is much simpler than estimating shapes, and using formulas. whatscookingamerica.net/Information/MeatTemperatureChart.htm Jan 1, 2015 at 5:29
• Yes, the thermometer will tell me when it's reached the temperature. I use two. I know what temperature I'm aiming for, as noted in the question. I just don't want to be aimless as knowing when it will be dinner time (as explained in the post). Jan 1, 2015 at 5:41
• here is a recipe similar to your . timing is 4 to 6 hours, the delta(t) is large . chow.com/recipes/30234-slow-roasted-prime-rib-au-jus?page=all Jan 1, 2015 at 7:48
• So, the real appeal of hotdogs is revealed: homogeneous emulsified material of uniform dimension can always be cooked to perfection and with exact timing. Jan 1, 2015 at 9:32
• Would Seasoned Advice be a better home for this question? Feb 14, 2015 at 19:36

Typically meat at the usual oven temperature of 350 F takes about 20 minutes per pound. The objective is to get the interior of the roast cooked which means getting it up to between 160 F and 170 F.

In Short, you are using an convection oven at 350 degrees to raise the temperature of the meat from around 70 F to 170 F, a rise of 100 F in N minutes.

If the oven is only at 200 F, does it make sense that it will take a lot longer to raise the temperature of the meat to 160 F to 170 F.

350 - 70 = 280 200 - 70 = 130

280 / 100 = 2.8 130 / 100 = 1.3

2.8/1.3 = 2.154 Times as long. so 43 minutes per pound.

I would use less than this number though, as it is impossible to fix when it is overcooked.

• 160°F ? what kind of meat are you familiar with? Alton Brown notes, “Toast: 146° and up”, and “narrow range of joy in between 127 and about 132”. Jan 1, 2015 at 19:25
• 160°F ? What kind of Physicist are you? Either use Kelvins or Rankines!
– Aron
Jul 8, 2015 at 1:46
• Fahrenheits are priceless. Aug 7, 2015 at 22:26