think metric about weather

Think metric about weatherAuthor(s): WILLIAM W. K. FREEMANSource: The Arithmetic Teacher, Vol. 22, No. 5 (MAY 1975), pp. 378-381Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41188787 .

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Think metric about weather

WILLIAM W. K. FREEMAN

Teaching is the third career of William Freeman, a graduate of Yale

(history) and Massachusetts Institute of Technology (civil engineering). Immediately on retirement from a career as the statistician of an

insurance company, he began to teach Latin and mathematics, and is now head of the mathematics department of the Tower School in Marblehead, Massachusetts, specializing in metrics, on which he

writes a column for the Salem Gazette.

use a language with facility, a person must think in that language. An English-speaking person can use

French with facility only if he thinks in French; he is less fluent if he thinks in English and has to translate. In the same way, to use metric easily one must think metric.

When Great Britain decided to go metric, a tourist in London found as early as 1969 that sidewalk displays of temperature by banks were in degrees Celsius (named in honor of the astronomer who invented the centigrade scale). Anticipat- ing the same development in the United States, the mathematics department at the Tower School in Marblehead began in the fall of 1972 to post daily the 8 a.m. Celsius temperature, rounded to the nearest 5 °C, together with a word giving a name to the temperature in the unfamiliar units; e.g., 15 °C mild.

For consistency, a table was developed for descriptive designations, ranging from "scorching hot" to "bitter cold." In the process of fitting numbers to the descriptions, it became clear that "mild" in summer is not the same as "mild" in winter, so a seasonal table resulted (table 1). Al- though the National Weather Service has concluded that one cannot use terms such as "mild" to describe accurately what all individuals are actually feeling, we believe

there is sufficient consensus in a given locality on the approximate feel of the temperature to justify this scheme as a means of teaching children to think in Celsius degrees rather than Fahrenheit. Because people in Montreal, Marblehead, and Mi- ami differ in what they consider a "cold" day, for example, the descriptions in table 1 are specifically for Marblehead. The scheme of these designations is illustrated by "mild," the median name, which drops 5 °C for each season: it is 20 °C in summer, 15 °C in fall, and 10 °C in winter.

In addition to breaking the bonds of unnecessary exactness, rounding to the nearest 5 °C has another purpose. Until teachers have had enough experience with Celsius thermometers to think metric, they may take a surreptitious peek at the easily remembered pairs of Celsius and Fahrenheit temperatures:

40 °C 104 °F 35 °C 95 °F 10 °C 50 °F 0°C 32 °F

-15 °C 5 °F -40 °C -40 °F

Remembering that a change of 5 °C ■= 9 °F, to find the equivalent of 20 °C, for example, they may start at 10 °C (50 °F) and go up two jumps of 9 °F to reach a

378 The Arithmetic Teacher



Table 1 Seasonal temperatures in Marblehead, Massachusetts

Spring Summer & Fall Winter

45°C| 45 °C ' Scorching hot

40 j 40

35 Very Hot > Very hot 35 Very warm «

30 Hot J 30

25 Warm Hot I 25

20 Mild Warm f 20 Warm ' 15 Cool Mild I 15

10 Ì Cool Mild 10 } Cold '

5 j N Cool 5

0 /Cold J ( 0

S Cold J - 5 1-5 > Very cold -10 I Very cold f -10 -15 Very cold -j _15

-20 Í -20 -25 -25

~30 Bitter cold- ~~30

-35 -35

-40 -40

comfortable 68 °F as the equivalent of 20 °C.

Any one adapting the scheme shown in table 1 to his own locality would need to use the consensus of the inhabitants. A winter day considered "cold" in Marble- head, for example, is -5 to -10 °C, while a "cold" day in Montreal is lower by 15 °C; i. e., a temperature of, -20 to -25 °C is "cold" in Montreal. Because Marblehead has a somewhat moist climate moderated by the Atlantic Ocean, the temperatures in tables for other localities might show not only a shift up or down from table 1, but also a greater range of temperatures. The development of a table for a particular town, however, would help pupils to think

metric even if the actual values in the table were only approximate.

Thinking of the varying seasonal designation of a particular temperature led to consideration of the effect of humidity in summer and wind chill in winter, and resulted in the development of charts of effective temperature. (Figs. 1 and 2) Curves of equal feeling by the human body are only an approximation due to sunshine, clothing, physical condition, and so on, and interaction of humidity and wind chill. If 30% relative humidity is considered normal for a "mild" summer day (20 °C, table 1) in Marblehead, 80% humidity makes it feel almost like 25 °C, which is "warm." Similarly, if the humidity is 30%

May 1975 379



Fig. 1. Effective temperature depending on humidity (Reprinted with permission of the American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., ASHRAE Transactions, Vol. 65, 1959, p. 130.)

Fig. 2. Effective temperature depending on wind chill (Wind chill effects from Don Kent Instru- ments. )



and the dry bulb reads 35 °C, the day is "very hot," but if the humidity is above 50%, the day is called a "scorcher."

In winter (see fig. 2), a "cool" day (0 °C) with a wind of 40 km/h, feels not just "cold" but "very cold" (-15 °C) ; and a "very cold" day (-10 °C) with wind of even 40 km/h brings a person down to the frostbite danger line, -30 °C. Notice that the lower the dry bulb temperature is, the faster the drop to and below the frostbite danger line. This is the time to warn your kids to cover up and to keep moving.

Wind speed in kilometers per hour (fig. 2) is about 1.6 times the speed in miles per hour. Kilometers per hour can there- fore be taken as about double miles per hour.

Since there are very few anemometers

readily available from which to get wind speed readings for the wind chill effect in figure 1, excerpts from the Beaufort scale are included in table 2. From these, wind speed can be estimated.

Although there is an interaction of the effect of humidity and of wind chill, this is ignored as being too complicated. The dry bulb temperature in figures 1 and 2 is adjusted for only humidity for 15 °C and above, and for only wind chill below 15 °C.

Everybody talks about weather, and at Tower School talk about the weather has proved to be an interesting way to intro- duce students to the expected metrication of the United States. Pupils at the Tower School, from grade 9 down to grade 3, post daily the effective temperature with its designation, with a warning of frostbite danger when appropriate.

Table 2 Beaufort scale of wind speed*

Terms used Statute Kilo- by Nati miles meters Weather

Force Specification for use on land per hour Knots per hour Service

2 Wind felt on face; leaves rustle, ordinary 4-6 6-11 Light vane moved by wind Av. 5 8

3 Leaves and small twigs in constant motion; 7-10 12-19 Gentle wind extends light flag

4 Raises dust and loose paper ; small 11-16 20-29 Moderate branches are moved

5 Small trees in leaf begin to sway, crested 17-21 30-39 Fresh wavelets form on inland waters

6 Large branches in motion; whistling heard 25-31 22-27 40-50 "Ì in telegraph wires; umbrellas used with difficulty > Stronß

7 Whole trees in motion; inconvenience felt 28-33 51-61 in walking against wind J

8 Breaks twigs off trees; generally impedes 34-40 62-74 1 progress I Gale

9 Slight structural damage occurs (chimney 41-47 75-87 pots and slate removed) J

* Adapted from A Course in Piloting, Seamanship and Small Boat Handling Charles F. Chapman 1941 p. 165.

May 1975 381



think metric about weather

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