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Determining Wind Chill: When the Sensor is Not the Issue

If you are deciding what to wear before going outside, it’s not enough to know the temperature: it’s often important to also know wind-chill temperature. Wind chill is an apparently simple situation where the motion of the air cools the heated source. It’s somewhat analogous to using forced air to cool a hot component, heat sink, circuit card, or system. Weather reports often give both the air ambient temperature as well as the wind-chill temperature, especially n colder areas where wind chill can accelerate frostbite times.

The physics principle is simple: moving air carries heat away, and does so much better than still air (natural conduction); the amount of heat that the air carries is a function of its velocity and volume, Further, when surface moisture is involved, as in the case of people and skin, there are also evaporative-cooling considerations as well.

[BTW, here are two quick ways you can assess someone’s understanding of thermal concepts:

— first, ask “does a rock ‘feel’ wind chill?” The answer is no, of course. But if they argue that it is “yes” for a rock which is being warmed by the sunlight, well, that shows real understanding

–second, ask “why do they spray orange groves with water to delay freezes as the temperature drops, letting ice form on the fruit; it seems counterintuitive?” The answer is that as the cold air causes a phase transition of the water from liquid to solid, the water gives up heat (ice has less heat energy than water, of course) and that heat is transferred to the surface on which the ice forms – in this case, the oranges.]

It would seem that since measuring wind speed accurately is fairly easy, determining the wind-chill factor would be easy as well. But that is not the case. There are many ways to measure air speed; two of them are:

— the classic spinning-cup anemometer. This works well (but can ice up), is easy to calibrate, and it consumes little or no power (in fact, there are all-mechanical versions which use a spinning cable and then a readout, in an arrangement which is similar to an old-style mechanical speedometer). It is also visually impressive and somewhat dramatic.

–the hot-wire anemometer, an all-electronic analog approach with no moving parts. The principle is obviously more complicated than the spinning-cup design: a wire element is heated by an applied current, and the temperature of this hot wire is kept constant via a regulated current source. The applied current that is needed to maintain that constant temperature is proportional to the air velocity.

Hot wire designs are not only used for weather; they are used in air ducts and even for liquid flow in pipes. These front-end circuits are also popular entries in the “Design Ideas” section of EDN; one such circuit “Transistor linearly digitizes airflow” and they are also covered by many patents offering variations and improvements on the basic design.

So what’s the problem? It’s simple: the correlation between wind speed — however accurately it is measured — and the perceived wind-chill temperature is not unambiguous. Instead, it depends on many hard-to assess factors, and many of them are literally “human” factors.

A recent article in The Wall Street Journal , “Developing Wind-Chill Factor Required Cold Calculation ” provided a good overview of the quandary. The National Weather Service in the United States has a useful standard chart (updated November 1, 2001) in the Table below and online calculator (link here), but reality may not always agree:

This table from the National Weather Service shows their fully researched relationship among variables of air temperature, wind speed, and associated wind-chill temperature.

This table from the National Weather Service shows their fully researched relationship among variables of air temperature, wind speed, and associated wind-chill temperature.

Their formula has coefficients to four significant digits and is highly non-linear, implying a challenging thermal model and curve-fitting exercise:

where T is the air temperature (o F) and V is the wind speed (mph).

(It would have been nice if they also had the equation in metric format using o C and km/hr, but that’s a petty complaint—but working out the metric equivalent would be good math exercise for algebra students!)

The NWS also adds some caveats: “Wind Chill Temperature is only defined for temperatures at or below 50o C F and wind speeds above 3 mph. Bright sunshine may increase the wind chill temperature by 10o C F to 18o C F.”

What we have is an analog-sensor and analysis situation which is counter to our usual scenario. Here, we can measure the unknown variable (air speed) with high accuracy and precision using one of several approaches and circuits. However, transforming the reading into a conclusion with high confidence is difficult, because there are many situation-dependent factors and even some subjective judgment issues.

Are there any other practical ways you have used to measure air speed? Have you ever had a similar dilemma between the high accuracy of the data versus any resultant ambiguity or uncertainty in the analysis?

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Transistor linearly digitizes airflow

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