My GPS is ripping me off

In May 2014 on May 16, 2014 at 1:03 pm


Sarah: Today’s Google doodle is of 18th century mathematician and philosopher Maria Gaetana Agnesi.

Quite a coincidence really, as this morning I’ve had maths on my mind.

“No, please no! Not maths!”

I hear some of you scream (through the magic of the internet).

But wait…wait! I shall explain.

I’m recovering from an ankle injury, and so went for a gentle run this morning and included 10 ‘grandstands’ in my workout. Grandstands are quite simply trips up and down a staircase for the purpose of getting one’s heart-rate elevated and adding a bit of extra challenge for the big muscles in the back of the legs (ie arse and hamstrings). Luckily there is a beautiful old grandstand adjacent to an oval in my suburb, and so off I went.

Because I like to keep track of my progress, I use an App called Runkeeper to record my runs. It uses the GPS in my phone to monitor where I go, and reports on time and pace as well.

This all works swimmingly when I run on a flat surface.

However I was less than happy to see that when I started heading upstairs for the grandstands, I was being ripped off. The distance I was travelling per grandstand was not appearing in my running record. And it’s because of maths.

Here’s where I need to refer to my diagram shown above. Imagine these are the stairs I use to exercise; I have overlaid a triangle to make my point.

True for all triangles, there are 3 sides and 3 angles. In this particular example, it is a right angled triangle (shown at bottom right). Now, if you recall your high school maths you’ll know that the side of the triangle opposite the right angle (known as the hypotenuse) is the longest side of the triangle – shown here as a yellow line. This is the distance I travel when I go up and down the stairs.

But Runkeeper – or more specifically my GPS – can’t see the hypotenuse. Because the satellite floating above Earth that monitors the position of my phone is looking straight down, it can only see the bottom side of the triangle, the red line. Which is shorter than the hypotenuse! Which is why I am being ripped off in my records!

Could someone who cares about my self-esteem and bragging rights please rectify that?

(image thanks to Eric Sanchez on flickr)


  1. Your phone GPS is actually tracking you in 3D space, it’s probably just not that accurate. Even purpose built GPS receivers such as the handheld devices used for bushwalking are only accurate to about 10 metres. Plenty of room for error when you’re dealing with 3 or 4 stoerys, say about 15-20m in the vertical. Does your phone app give you an elevation plot of any type? You may see a jumble of lines from the grandstand sections of your run.

  2. Thanks Michael for the comment.

    The elevation barely shows it at all! Must just be poor accuracy.

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