Hot Spot U.S.A.

Tuesday, August 1st, 2006

With tomorrow’s temperatures forecasted to be above 100 degrees, Chapel Hill is going to be one very hot spot.

As if centrally scripted, local news folks, punching up the drama of the weather story, have been issuing dire warnings not of the “real” heat but of the “felt” heat. “Think it’s going to be hot tomorrow? With the heat index, that 100 degrees will feel like a thousand!” Etc. Ad nauseum.

For the last 35 years, I’ve always assumed the “heat index” was a bit of a bugaboo – a pseudo-science calculation surfing the collective American conscience with little or no factual underpinnings.

Well, turns out there is a calculation:

HI = -42.379 + 2.04901523T + 10.1433127R – 0.22475541TR – 6.83783×10 -3 T 2 – 5.481717×10 -2 R 2 + 1.22874×10 -3 T 2R + 8.5282×10 -4 TR 2 – 1.99×10 -6 T 2 R 2


T = ambient dry bulb temperature degrees Fahrenheit
R = relative humidity
The equation is only useful for temperatures 80 degrees or higher, and relative humidities 40% or greater.
NOAA National Weather Service chart of Heat Index
That looks rather ad-hoc to this curious science guy, so I delved a bit deeper and found this commonly cited article [PDF] explaining the genesis of the equation.

Now that summer has spread its oppressive ridge over most of the Southern Region, NWS phones are ringing off their hooks with questions about the Heat Index. Many questions regard the actual equationused in calculating the Heat Index. Some callers are satisfied with the response that it is extremely complicated. Some are satisfied with the nomogram (see Attachment 1). But there are a few who will settle for nothing less than the equation itself. No true equation for the Heat Index exists. Heat Index values are derived from a collection of equations that comprise a model. This Technical Attachment presents an equation that approximates the Heat Index and, thus, should satisfy the latter group of callers.

The Heat Index (or apparent temperature) is the result of extensive biometeorological studies. The parameters involved in its calculation are shown below (from Steadman, 1979). Each of these parameters can be described by an equation but they are given assumed magnitudes (in parentheses) in order to simplify the model.

  • Vapor pressure. Ambient vapor pressure of the atmosphere. (1.6 kPa)
  • Dimensions of a human. Determines the skin’s surface area. (5′ 7″ tall, 147 pounds
  • Effective radiation area of skin. A ratio that depends upon skin surface area. (0.80)
  • Significant diameter of a human. Based on the body’s volume and density. (15.3 cm)
  • Clothing cover. Long trousers and short-sleeved shirt is assumed. (84% coverage)
  • Core temperature. Internal body temperature. (98.6°F)
  • Core vapor pressure. Depends upon body’s core temperature and salinity. (5.65 kPa)
  • Surface temperatures and vapor pressures of skin and clothing. Affects heat transfer from the skin’s surface either by radiation or convection. These values are determined by an iterative process.
  • Activity. Determines metabolic output. (180 W m-2 of skin area for the model person walking outdoors at a speed of 3.1 mph)
  • Effective wind speed. Vector sum of the body’s movement and an average wind speed. Angle between vectors influences convection from skin surface (below). (5 kts)
  • Clothing resistance to heat transfer. The magnitude of this value is based on the assumption that the clothing is 20% fiber and 80% air.
  • Clothing resistance to moisture transfer. Since clothing is mostly air, pure vapor diffusion is used here.
  • Radiation from the surface of the skin. Actually, a radiative heat-transfer coefficient determined from previous studies.
  • Convection from the surface of the skin. A convection coefficient also determined from previous studies. Influenced by kinematic viscosity of air and angle of wind.
  • Sweating rate. Assumes that sweat is uniform and not dripping from the body.

From Rothfusz, L. P., 1990:The heat index equation (or, more than you ever wanted to know about heat index). NWS Southern Region Technical Attachment, SR/SSD 90-23, Fort Worth, TX.

So, to be as accurate as possible, tomorrow, if you’re 5’7″ 147 pounds, wearing long trousers and a short-sleeved shirt made of %80 air, have an average human diameter (unlike my 46″ waist), plan only to walk 3.1 MPH and sweat uniformally, it’ll feel like a bazillion degrees.



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