Saturday, August 7, 2010

Burning calories running uphill

The other day I ran up a really big hill - Mount Carmel in Israel, in fact - wearing my Garmin Forerunner 305.
It keeps track of your speed and heart rate and is supposed to tell you how many calories your burned (it knows my weight, age and gender). It's pretty good on the flats, but completely wrong in the climb!

Here are the pertinent numbers (just the first few from a longer climb):

mile...av speed....climb...calories
1........5.7 mph......55 ft....162
2........4.4 mph....325 ft....128
3........3.8 mph....450 ft....115
4........4.3 mph....337 ft....133

The actual effort expended in miles 2 - 4 was very high: with a 10-15% grade you're really working (and it was a hot July day) yet the calories were very low (especially for a 200 pound guy).

I'm a physicist and I decided to do a bit of "back of the envelope math".

You recall from high school that an object with mass m being raised by a distance h increases its potential energy by m x g x h

Using round numbers (g=10 m/s^2), a 100 kg person climbing 100 meters increases his potential energy by 100 kJ.

The body is roughly 25% efficient in converting calories to "work done", which conveniently means that 1 kJ of "net work" costs about 1 kcal of "food work". (1 cal is approx 4.2 J).

This suggests a simple modification to the conventional "calorie calculators" you find online. To get a more accurate estimate of your work done you can add the following term:

Calories due to climbing = (body mass in kg) x (height climbed in meters) / 100

You add this correction to whatever your conventional "running on the flat" calculator comes up with.

After I had come up with this equation I found a blog

which talked about the same problem and which included a reference to a scientific paper from the Journal of Applied Physiology
which describes measurements done on athletes to come up with accurate estimates of the calories burned as they run on a treadmill. They found pretty much the same relationship (although you have to wade through the descriptions and the graphs to get to the essence) - that when you climb, you expend about 40 J / kg / m (see figure 3), with only a weak dependence on the slope (once it's a "real" slope - more than a few % grade).

I look forward to hearing people's thoughts on this - and perhaps one day Garmin will include a better equation in their running GPS.

Saturday, April 4, 2009

Fixing a Wacom Bamboo pen

My daughter's Bamboo graphics pad stopped working. Oddly enough the eraser side of the pen was still OK - but the stylus side was dead. This suggested it was the pen - not the pad or the connection - that was at fault.
I found a brilliant blog at
which described my symptoms, and had pictures for a similar pen. But the Bamboo pen has a slightly different design so I thought I would document the disassembly (including what went wrong for me...).

The tip of the pen contains a coil with a ferromagnetic core. This core breaks when you drop the pen - this means it doesn't make as strong of a magnetic field and that means the pad can't sense the pen (or vice versa). To get to the core, you have to take the pen apart (carefully - there is a lot of sensitive electronics inside!)

First step: remove the plastic tab next to the buttons:

Note where I put the screwdriver. Gently ease it under the tab and nudge until you get something like this:

This is where I went wrong and forced the tab off. With a snap something broke, and when I looked closely I saw I should probably have slid the tab (moved in in the direction of my fingers in this picture) rather than pull up and away from the pen - see this picture:

Even better - I could have just left it alone. I later found that the top and bottom half of the stylus are only held together at one point - and so just lifting the tab at one end is enough to free the two halves. With the tab off, careful jiggling allowed me to separate the top and bottom of the pen (it takes quite a bit of force: be careful not to bend it as the two parts separate, or you will break the circuit board inside):

As the two parts separated I could see the little blue tab that I had broken off:

Next, I needed to liberate the electronics board which was still being held by the buttons. I was a bit apprehensive now, but it turns out that this time you can just use a small screwdriver and nudge the buttons straight up and off:

After carefully easing the circuit board out of the barrel I could see the broken coil (it didn't look broken, but when I pulled very gently on the end it came apart, showing a crack):

I pulled out the plastic tip (I needed to turn it to free it - not sure if I could have pulled but with the coil looking quite fragile I decided to play it safe - you don't want to break the little wires that hold it in place). Now, using some Loctite superglue gel (the kind that doesn't go everywhere but still sticks like crazy), and with my daughter's help to hold the crack open as I applied the glue, I was able to put a couple of small dabs in the crack and push it tightly shut - in the process pushing most of the glue out of the crack:

Two more cautions before putting it all back together.
First, make sure there is no glue on the inside - or you won't be able to put the plastic tip back in. Holding the assembly vertical, I moved the tip in and out a few times - it did come out sticky so I kept wiping it clean, until it went in and out without getting sticky.
Second - you want to make sure the glue has time to dry properly, and with the smallest possible gap in the ferrite core. To so this, I held the assembly vertically and let it sit for about an hour - long enough for the superglue to really set. A shot glass and some tissue paper did the trick:

When everything was dry, I put it all back together again. But for the little blue tab that had broken off and the white mark on the blue tab where I had bent it when I should have slid it, it was "good as new". And more importantly, it worked again!

A Great Big ThankYou to Abiyasa - the blogger who inspired me to do this. Let me know if it worked for you!