Treadmill Grade to Angle Conversion

Gym machines like treadmills and even some roads express the slop as "grade" in percentage. For example, most gym treadmills allow up to 15% grade. I've left going to gym since last few months and instead I'm doing this Snoqualmie Falls hike almost every other day (which is 0.5 miles one way and 300ft elevation). But occasionally I have to go to gym because of early sunsets. I usually put max grade (15%) and speed walk for one mile burning 350 cal. So naturally the question is how many feet I climbed?

For this I need to convert grade in % to angle. But what is "grade%"? Turns out it's ration of rise/run or in other words,

grade=\frac{tan(\theta)}{100}

So your vertical climb in feet is given by, \sin(\tan^{-1}(grade*100))*5280 miles

So by that calculation, at maximum grade on gym treadmill I climb 783.2 feet for each mile I walk. Not too bad.

 

Via conversation here.

Phun With Physics Simulations

This addictive program can easily keep you busy for rest of the weekend so be careful :). Phun is a physics simulator that even kids can use and its absolutely a delight. I watched the video and had to immediately download to give it a try. At first the interface might seem not as easy but after reading tutorial in main page and forums, you might be able to accomplish everything shown in video in less than 15 min of learning curve! Simply the easiest, powerful and most fun physics program I’ve come across.

Enjoy!

Hurricane Formations

Since yesterday night the question how Hurricane comes in to existence was eating me away. I resisted googling it and try to find the answer just for the fun. My instinct was that it must all come down to 2nd law of Thermodynamics (as always!). That means if there is high pressure somewhere, the inherent consequence would be to nullify the excess and have an equal average pressure everywhere. So I was mulling over kind of pressure patterns that would be required to ultimately cause slow rotations that we see on a hurricane. I planned out a little computer simulation of this with the guess that a ring of low pressure would probably produce hurricane-like whirlpool.

But, aha! I was dead wrong. It turns out that the 2nd law actually prevents cyclones from happening! My wife intuitively pointed out that hurricane would occur due to warm air that goes up where the cold air is but while it does so, the Coriolis effect kicks in which would produce whirlpool (similar to the whirlpool produced when flushing the toilet). Her intuition is awesomely right. All hurricanes in northern hemisphere go in anti-clockwise and southern hemisphere in clockwise. The huge power that a hurricane demonstrate is supplied by rotation of the Earth which itself is so massive.

I was also intrigued by how hurricanes are named. It turns out some international committee has preset list of names starting with letter A,B, C.. for each year. The list repeats every 6 years (i.e. names for 2005 hurricanes would be same as 2011). While now many names used are male’s names, previously only female names were used to name hurricanes!