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Tying Roasts Together to Cook

I have 3 bottom rounds of beef that weight an average of 13 pounds each. I want to tie them together to cook. My recipe, which is for a steamship roast, is 5 minutes per pound at 500 degrees, then turn oven off for two hours then turn oven on again at 300 degrees for 45 minutes for medium to well done.

My question is do I cook them for the combined weight time or do I cook them for the time of the largest roast. If the combine weight is used, do I need to adjust this time?

I am tying the roast together for the purpose of making them fit into the oven.

I have already posted the answer to cooking two roasts at once if they are not tied together (see Cooking Two Roasts at Once), but when they are being tied the question is a lot harder to answer.

The common guideline for how much time that it takes to cook a roast is minutes per pound.  According to McGee (On Food and Cooking: The Science and Lore of the Kitchen), however, the time is more accurately proportional to the square of the thickness, or the weight raised to the 23 power.

What do these numbers mean?  Start with thickness.  If a roast of some given thickness takes, say, 1 hour to cook, then if you double the thickness, it should take 22 = 4 times as long or four hours to cook, and if you triple the thickness, it will take 32 = 9 hours. 

Now if you go by weight, what the formula tells you is that smaller roasts take more time per pound than do larger ones.  You have likely seen this if you have looked at suggested times to cook a turkey.  An unstuffed eight pound (3.61 Kg) turkey will take about 2 34 hours, or about 20 minutes per pound (0.454 kg).  An unstuffed 24 pound (10.9 Kg) one will only take about 5 hours or 12 1/2 minutes per pound.

Obviously there is something wrong with these two estimates, given that in one case the time is rising wildly, while with the other it is decreasing in minutes per pound.  The reason is in part because the estimate based on thickness uses the mechanics of heat transfer and only looks at one dimension, so it ignores the heat coming in from the other sides of the roast, and also because you seldom get a roast that is twice as thick as another but measures the same in the other two dimensions.  In other words, the weight increases as something like the cube of the thickness, so on a per unit weight basis that roast that is three times as thick will weight something close to 27 times as much (33 = 27) and the cooking time per unit weight is 9/27 or 1/3 as long.

Estimated cooking time depends, of course, on a large number of other factors.  These might include how accurate the oven thermostat is, what material the roasting pan is made from and what color it is, the internal temperature of the meat when you start roasting it, and so on.

To make matters even more complicated, your recipe isn't at constant heat.  The two hours rest in the oven with the heat off is completely unpredictable in terms of how much the oven will cool down during that time.  There is simply no way to predict accurately how long it will take, since the amount of time depends on the shape of the roasts and how you end up tying them together.  I would suggest using the recipe as stated as if you were cooking a 40 pound roast, but use a meat thermometer to see how well done the tied together roast is getting, and be prepared to eat a lot earlier or later than you planned.

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