Sunday, October 25, 2009

Two Pie Are...

I ran today... first time I've done so since I hurt my foot.  Like a good patient, I've stayed off of it since my last run on September 30.

I ran 9.01 miles just under an hour and 20 minutes.  If'n you're interested in the run, you can find the yada yada about it here: http://connect.garmin.com/activity/17084336.

I don't usually run the loop at Memorial Park, but I decided I would today... in case my foot started acting up, I'd be no more than a mile and a half away from the car.  The loop is three miles.  At least that's what everyone says, but in reality, it's about 2.9 miles (according to my Garmin 305, that is).

I ran one loop clockwise... one counterclockwise... and the final one clockwise.  (Of course I had to run a little more than three loops to get my nine miles).

Anyway, during my run, I noticed a sign that said, "Stay to the right."  Well, if you're running clockwise, that puts you on the inside of the loop, and obviously running counterclockwise puts you on the outside of the loop.

Since I had all of this random information in my head, I wondered how much further you ran if you ran counterclockwise (on the outside of the loop) as opposed to running clockwise (on the inside of the loop).  I said to myself, "Self, you should calculate that when you get home."  Followed by, "You really are a dork!"

Well, dork or not, I calculated it...




The following are some assumptions and some constants:
  • the width of the trail is 12 feet
  • the loop is a circle
  • you run clockwise on the inside of the path for the entire loop
  • you run counterclockwise on the outside of the path for the entire loop
  • π = 3.14159
  • the formula for the circumference (C) of a circle is C = 2πr, where r = radius
  • there are 5,280 feet in a mile
(I sure hope you appreciate the accuracy of these calculations!!!)

We know the circumference of the inner circle--3 miles.
3 = 2πr
so r = 3/2π
Plug in the numbers...
r = 0.477464829821269 miles, or if we convert it to feet we get r = 2521.0143014563 feet.

Since we assumed the trail is 12 feet wide, that makes the radius of the outer trail 2521.0143014563 + 12 feet, or 2533.0143014563 feet.

Well, now it's simple to solve for the circumference of the outer circle...
As before...
C = 2πr; therefore,
C = 2π(2533.0143014563)
C = 15915.3982236 feet
And since we know there are 5,280 feet in a mile, the outer circumference is 3.01427996659091 miles.

That's a difference of 0.01427996659091 miles... or 75.3982235999985 feet. if we think about it in football terms, that's equivalent to 25.1327411999995 yards.

And let's say you run 9 minute miles... running counterclockwise will take you 0.128519699318179 minutes... or an additional 7.71118195909075 seconds!  The following table lists some pace times and the additional time it'll take you to make it around:

Pace
(mins/mile)
Extra time
(seconds)
7
6.0
8
6.9
9
7.7
10
8.6
11
9.4
12
10.3
20
17.1

So if you want to save 7 or 8 seconds, run clockwise on the inside of the path!

DORK!!!