Now that we have T+D as one way to quantify our misery during a run, I think we need another way to quantify another source of unpleasantness: bugs. I'm sure many, if not all of you, have experienced runs where you discover upon finishing numerous bugs plastered to your body and perhaps swallowed.
Clearly more bugs means a more unpleasant run, but one can't just compare the number of bugs on one's body to another person, since there are significant factors that vary with the individual that would cause encounters with more or fewer bugs. Specifically: how fast one runs, the duration of the run, and the individual's cross-section area. Other factors, such as the tilt of the body and presence/absence of hat are considered to be second-order effects.
Bug Impact Index
In order to quantify this for no useful purpose, I introduce the BII: Bug Impact Index. Here is the precise mathematical formula: BII = A * N/(S*T*H).
N: the number of bugs you ran into, as evidenced by them being stuck to your body. Swallowed/inhaled bugs also count - this number is taken on your honor.
S: the average speed of your run in mph
T: the duration of your run in hours
H: your height in feet - a proxy for your cross-section area
A: I call this
@avondale's scaling factor, which is equal to 10 mph*h*ft/bug, and conveniently cancels out units appropriately and makes the result be a reasonable-sized, unitless number.
The BII allows two runners who have done runs of different durations, for example, compare the relative nastiness of the bug population for each run in an objective way.
Example
Tonight I ran for 48 minutes (0.8 h) at an average speed of 5.0 mph. My height is 5 ft 3 in, so 5.25 ft. I had 8 bugs on my body and swallowed 1, for N = 9. Hence my BII = (10)(9)/0.8/5.0/5.25 = 4.3.
Future Work
Future research pertaining to the BII will involve the investigation of the BFP (bug-free path), which is the average distance in any direction between bugs. The establishment of a BFP for different regions of the country will enable a more rigorous comparison of the BII between runners of different areas of the country.
(Hope you enjoy! My semester is almost over! Hooray!)