## June23th 2015 Calculating Calories

← June 22th 2015 Counting Calories | ● | June 23th 2015 Calculating Coefficients →

Given a particular track, how can we (approximately) calculate the spent calories from the track?

We basically only have time $t$ and velocity $v(t)$. So we define the calories spent as time integral of a function $W(v)$, where $W(v) is describing the actual power level for a particular velocity and activity.

Since the function $W(v)$ is not known, we first assume that it can be represented as a quadratic polynomial:

Then the spent calories are

Using discrete arithmetic the calories are

For each track the above three terms can be easily tabulated. So we create 3 tables, where each entry corresponds to the corresponding sum term of the above formula:

Now we write

So for a particular period of time from starting time $t_i$ to end time $t_j$ the spent calories during that time period are:

This is a general equation for the calories spent during a particular activity, where the coefficients $c_0$, $c_1$ and $c_2$ are specific for the particular activity and person.

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