Thursday, October 06, 2011

The Ugg point

In case you didn't know, barometric pressure, or the pressure at which air density changes with altitude, can be determined either of two ways.

Equation 1

${P}=P_b \cdot \left[\frac{T_b}{T_b + L_b\cdot(h-h_b)}\right]^{\textstyle \frac{g_0 \cdot M}{R^* \cdot L_b}}$

Equation 2

${P}=P_b \cdot \exp \left[\frac{-g_0 \cdot M \cdot (h-h_b)}{R^* \cdot T_b}\right]$

Simple enough, right? Good.

The dew point, or the temperature at which a parcel of air must reach before vapor turns into water, is calculated like this . . .

A well-known approximation used to calculate the dew point Td given the relative humidity RH and the actual temperature T of air is:

$T_d = \frac {b\ \gamma(T,RH)} {a - \gamma(T,RH)}$

where

$\gamma(T,RH) = \frac {a\ T} {b+T} + \ln (RH/100)$

Knowing how we derive both barometric pressure and the dew point is essential to calculate accurately the "Ugg point," or the point at which the occasionally worn and seen Ugg boot suddenly becomes the essential footwear statement for the female fashionista between the ages of 13 and 34 and, sadly, the teen-wannabe Cougar Moms between the ages of 37 and 53. You know how in mid-March, at least in the Washington, D.C.-area, those few days in the middle of the month when, after two or three consecutive days in the high 60s, you notice a couple of crocuses here and there, and the bulbs you forgot you planted in the fall yield a couple of tulips? And then just as quickly as temperatures rose and the ground teased us with glorious color, winter comes back, and we have to endure two or three more weeks of dark and gray before the pastels of spring emerge again? So it is with the Ugg boot, perhaps the shoe industry's most unsightly contribution to popular culture since whatever those strange objects are called that resemble a hybrid of a ballet flat and a child's corrective shoe. Once the temperature drops below 60 degrees in Washington, sending the nation's elite scrambling for their L.L. Bean catalogues so they can begin layering themselves to death in enough clothing to guarantee population management for at least the next seven months, you're likely to see a few Uggs here and there. But the real onslaught comes once the average temperature drops to:

UP = U(x) - % [NFF + BSL]
_______________
[L,W + OMG!! (xx)]

whereas

UP= Ugg Point
NFF = North Face Fleece
BSL = Black Stretch Leggings
LW = Like, Whatever
OMG = Oh, My God!!

so
AVGT = B(1) RHy + HUH? (x) FIH
______________________________

SHOEUNCOOLNESS

whereas

AVGT = Average Temperature
B = Barometric Pressure
RH = Relative Humidity
HUH= Clueless
FIH = Four Inch Heels

then

The Ugg point, or that point at which this inexplicable cultural phenomenon, moves from occasional nuisance to c