We recently purchased a Nordictrack elliptical trainer. The machine is pretty nice, but both my wife and I immediately noticed a major annoyance: there wasn’t any documentation about how many “miles” the elliptical travels over the course of a workout. We’re both accustomed to that form of measurement; the number of revolutions per workout was essentially meaningless.

So I put on my 10th grade geometry hat and figured it out. Here’s what I did.

Goal:

**Use simple geometry to determine how many Nordictrack revolutions equal one mile.**

First, measure the radius (r) of the encased wheel (this is the distance from the center to the outer edge). For improved accuracy, I measured from the center to the middle of the axle that attaches to the foot platforms. On my machine, the radius was 10 inches. But we really need the diameter, which is 2(r), or 20.

So, we have the first part of equation, diameter (d): 20 ”

In order to determine the distance that the wheel would travel if it rolled freely, I need to measure to know the circumference of the wheel. This is the total length as measured all the way around the wheel, like you would get if you wrapped a tape measure around it.

Here’s where the geometry comes into play: since I cannot wrap a tape measure around the wheel, I use this formula to calculate the circumference (C):

* C = d(PI)*

PI is that weird number that you remember from school. I won’t even bother with any details; for this explanation we’ll just agree that it is an important number and we’ll say it is 3.14159265.

So, the equation starts to take specific form:

* C = 20(3.14159265) or C = 62.831853″*

Now that we have the C, we can calculate the miles per revolution. To do this, first convert C, which is in inches, to feet:

* 62.831853″ = 5.236′*

Now we know that every time the wheel revolves one complete turn (a revolution), we theoretically have traveled 5.236 feet. How many equal a mile? One more calculation:

* 5280 feet / 5.236 feet = 1008.4 revolutions*

So, to travel one mile on the Nordictrack you have to pedal 1008 (or so) revolutions.

Tags: nordictrack, elliptical, workout, conversion, mileage