8. Cooking Temperature: Inverse Square Law

This is the first in the following series of blogs on the ideal cooking temperature for grilling a steak over live coals:

1. Cooking Temperature: Ideal Temperature
2. Cooking Temperature: 1600 Degrees?
3. Cooking Temperature: Need to Modify Grill Height
4. Cooking Temperature: Measure Temperature
5. Cooking Temperature: Measure Grill Height
6. Cooking Temperature: Calculate Ideal Grill Height
7. Cooking Temperature: Modify Grill Height
8. Cooking Temperature: Inverse Square Law

Previous blogs describe (1) how to measure the temperature of a grill at the grill level and (2) how to measure the distance from the grill level to the live coals.

With these two measurements, the ideal distance from the grill level to the live coals can be calculated. As described in a blog on how to calculate this ideal distance, the calculation is complex. This blog describes the complex formula, for those who are comfortable with math.

One of the fundamental laws of thermodynamics, as applied to a backyard grill, states that temperature varies in inverse proportion to the square of the distance between the grill and the coals. This is called the inverse square law.

The formula of the inverse square law is as follows, where:

d1 = original distance

t1 = temperature at d1

d2 = new distance

t2 = temperature at d2

Using these variables, then the basic formula of the inverse square law is:

t1 / t2 = d2^2 / d1^2

Since d1, t1 and t2 are known, the formula for solving for d2 is:

d2 = ((t1 / t2) * d1^2)^0.5

In a previous blog, we show that the ideal cooking temperature at the grill level is exactly 750°. Applying this temperature to the formula assumptions, t2 (the new temperature) always equals 750°, so the formula may be resolved as follows:

d2 = ((t1 / 750°) * d1^2)^0.5

As an example, if the original distance of the grill above the coals is 5” (d1), and if the temperature at this distance is 370° (t1), then, in order to increase the temperature to 750° (t2), the formula may be applied, and the result shows that the distance of the gill above the coals must be changed to 3.5” (d2).

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