HOW STRONG is the wind? The question is readily answered with an anemometer. In most of these instruments the flow of air around an obstruction develops a force that varies with wind speed. The force determines the position of a pointer on a scale that is calibrated in units of speed. One popular anemometer consists of a small windmill that spins an electric generator. The output of the generator varies with the velocity of the windmill and measured by a calibrated meter.

Many anemometers of this type have been built by amateurs. The instruments are easy to make and convenience to use but difficult to calibrate. The problem of calibration has now been solved with a portable anemometer that can also be used as a secondary standard. The instrument was developed a few months ago by P. L. Clemens while he was serving as visiting professor at the Von Karman Institute for Fluid Dynamics at Rhode-Saint-Genesè in Belgium. Clemens discusses the calibration of anemometers and the construction of his new instrument as follows:

"The techniques of calibrating anemometers tend toward two extremes: accurate but expensive and simple but inaccurate. Wind-tunnel calibrations fall in the first category. Good wind tunnels are not readily available, and the cost of their operation is beyond the resource of most experimenters. For this reason many amateurs have resorted to a calibration procedure of the second kind. In that procedure the instrument to be calibrated is supported outside a moving automobile. The scale is graduated by reading the speedometer as the vehicle accelerates through a series of test velocities.

"It is difficult to imagine a more hazardous and unreliable method of calibration. The details of the procedure tend to distract the driver even though others make the observations and record the data. Moreover, the data are likely to be in error. Automobile speedometers are rarely accurate at low velocities, which are of most interest in the anemometry of sports. Attempts to average out the movement of the local air mass by such expedients as heading into the wind while making one set of observations and then reversing course for another set usually fail because of variations with time in the direction and speed of the local air. In addition the anemometer under calibration is immersed in a field of aerodynamic flow disturbed by the automobile. The velocity of the air in this field usually differs substantially from the gross velocity of the automobile. Experimenters who rely on this method of calibrating are lucky to emerge from the experience with a scale error of less than 30 percent.

"It was in response to the need for a simple and reasonably accurate method of calibrating anemometers that I undertook the design of the instrument I shall describe. It is a pendulum anemometer, consisting of a pendulum bob suspended at the center of a protractor. When the pendulum swings in the plane that contains the velocity vector of the wind, the resulting force deflects the pendulum from the vertical at an angle that varies with wind velocity. The angle is a measure of the speed of the wind.

"The basic principle of the device dates back at least to the 15th century. My contribution consists in making a pendulum anemometer that can be duplicated exactly with inexpensive materials. The device was calibrated in a high-precision wind tunnel. The calibration can be transferred directly to all exact copies of the instrument. The copies can be used either as secondary standards for calibrating anemometers of other types or as primary instruments for measuring air speed.

"The force that deflects the pendulum from the vertical arises primarily from the flow of air around the bob. If a spherical bob is tethered by a suspension of negligible area, the deflecting force is independent of the angle the pendulum makes with respect to the vertical, and the sensitivity is a function of the ballistic coefficient of the bob. The first consideration in the design of such an anemometer is the selection of a sphere capable of generating reasonable deflection angles through the anticipated range of wind velocity.

"The central problem with my instrument was finding a readily available and inexpensive sphere manufactured to close tolerances. Table-tennis balls proved to be ideal. Manufacturers are obliged to meet rigid specifications of diameter and weight that have been established by the International Table Tennis Federation. The median diameter (37.7 millimeters) may vary by no more than 1.3 percent and the weight (2.465 grams) by no more than 2.56 percent.

"In choosing the suspension cord that supports the pendulum bob one must pay attention to the properties of the cord that might influence the performance of the anemometer. The cord should have a smooth surface, negligible weight and a small diameter. My first experiments were made with monofilament nylon cord having a diameter of .08 millimeter and weighing .011 gram per meter. This cord is available in sporting-goods shops and is commonly used to tie fishing flies. The breaking strength is about 400 grams. Monofilament nylon thread is also available in shops that sell sewing supplies. After my initial experiments I used cord of .2-millimeter diameter with no observable difference in performance.

"The cord must be firmly attached to the ball. The attachment should add minimum weight to the assembly and should introduce minimum aerodynamic interference. To make the attachment I pierced the ball with a sewing needle at two diametrically opposite points. (The perforations also create two shallow indentations.) A needle threaded with the monofilament cord is passed through the ball. The free end of the cord is fastened to the ball with a dab of plastic cement. After the cement has hardened, surplus cord is trimmed as close as possible to the surface. Use a cement that does not attack the ball chemically. Test weighings indicate that the cementing operation, when performed with reasonable care, adds less than a milligram to the mass of the ball.

"The upper end of the suspension cord is passed through the index hole of an ordinary plastic protractor. The protractor serves as the scale for measuring the angular deflection of the pendulum with respect to the horizontal. (This may seem to conflict with the previous statement that the angle is measured with respect to the vertical. Mathematically the angles are complementary. Measuring with respect to the horizontal is a convenience in that it conforms to the usual scale markings on commercially made protractors.)

"Adjust the length of cord between the upper surface of the ball and the index hole of the protractor to 30 centimeters (12 inches) and attach the free end of the cord to the rear surface of the protractor with cement. Similarly, cement an ordinary spirit level parallel to and near the base line of the protractor [see illustration at right]. A baton about 40 centimeters long should be attached to the assembly. The baton can be made of wood dowel stock about half an inch in diameter. The baton enables the observer to support the instrument beyond the zone of disturbed air that surrounds his body. Wind-tunnel measurements indicate that the presence of the observer has a negligible effect on the measurements if he remains at least three body diameters toward one side of the instrument and does not move upstream.

"The aerodynamic characteristics of the instrument were determined by a series of measurements made in a wind tunnel. From these data I derived an equation that expresses the calibration at standard conditions of atmospheric pressure and temperature. Air speed is equal to a constant multiplied by the square root of the cotangent of the pendulum angle indicated by the protractor: , in which u is the air speed m miles per hour and a is the angle. The resulting calibration is listed in the accompanying table [below left]. The data are also plotted as a graph [see illustration below right].

"Significant error may be introduced as atmospheric pressure and temperature depart from standard conditions. For maximum accuracy such departures must be taken into account. The equation, as modified to include these corrections, is , where T is the temperature in degrees Celsius and P is atmospheric pressure in millimeters of mercury.

"In using the instrument one stands with the right shoulder facing into the wind. Grasp the baton in the right hand and hold the instrument at arm's length. Level the protractor and read the deflection of the pendulum directly from the scale. The contrast between the cord and the scale can be increased by applying a dab of colored enamel to the cord in the zone where it crosses the scale.

"As with any anemometer, the observer should select an open area, free of obstructions to windward. Velocity gradients and turbulent eddies can be expected downwind from buildings, trees, shrubbery, fences and the observer himself. By the same token do not expect to make accurate measurements near the edge of a boat. Rain or spray that wets the ball increases its weight and decreases accuracy. The bob responds quickly to gusts and lulls, causing the pendulum to oscillate. The knack of reading maximum and minimum indications of the oscillating pendulum to find the average value of the angle comes with practice. Under most conditions the accuracy of the measurements is better than 6 percent."

V G. BLANCHETTE, an engineer of Pass Christian, Miss., has stirred up a tempest in a baking pan, thereby enabling experimenters to probe the mechanism of violent whirlwinds without leaving the kitchen. The required materials include only a table, an electric fan a vacuum cleaner and a shallow vessel holding water. Blanchette writes: "It is possible to set up in the laboratory or at home a small-scale demonstration that characterizes the extremely vigorous and dynamic conditions associated with tornadoes. The equipment utilizes low air velocities to develop an aerodynamic funnel of such vigorously circulating winds that materials at the surface are drawn into the vortex. Theoretical considerations of the convergent airflow forces in the model lead to possible explanations of how and why tornadoes develop and may explain other unusual tornado-like phenomena.

"The model tornado is created by mounting the suction tube of a vacuum cleaner horizontally about 4-1/2 inches above the top of a flat table and directing the breeze of an electric fan at right angles across the suction tube [see illustration at left]. Face the outlet of the vacuum cleaner away from the table to prevent the high-velocity exhaust from disturbing the air in the vicinity of the model. Put the fan 10 to 15 feet from the model and adjust it to create a mild breeze, not a stiff wind.

"Turn on the fan and the vacuum cleaner. Tornado-like winds will form between the top of the table and the inlet hose after some experimental adjusting of the velocity of the cross breeze. To detect the vortex put a shallow pan of water on the table directly under the hose. A shallow baking pan holding about an eighth of an inch of water works well.

"At the point where the tip of the vortex darts to the surface the water is pulled up into a hump that marks the lower end of the 'static line,' around which the winds rotate. The hump can be seen easily (by the refraction of light) as an image at the bottom of the pan. The hump disappears when the fan is turned off.

"At certain adjustments of the crosswind the funnel of the miniature tornado wanders randomly, striking here and there on the surface of the water as the terminal point of the static line swings in response to local air movement. At other adjustments it remains almost stationary for relatively long intervals. The height of the hump can be observed by sighting horizontally across the surface of the water. Usually it stands from a quarter of an inch to half an inch high.

"Occasionally a small drop of water is pulled from the top of the hump. The surface of the water also circulates around the small area adjacent to the static line. The circulation is relatively sluggish, however, and does not suggest the violent motion of the air at higher elevations along the static line.

"After the model has run for a time the end of the vacuum hose becomes damp. This condition indicates that moisture is being drawn into the hose. Caution: Do not lower the hose to the point where it would suck water into the vacuum cleaner.

"More dramatic effects can be created by replacing the pan of water with a surface of powdered material such a dry plaster of Paris. To make this experiment dry the hose and spread the powdered material on the table over a 12-inch area. Turn on the vacuum cleaner and adjust the fan to create a gentle cross breeze in front of the powdered area. Simultaneously sight horizontally across the table to see the material ejected from the surface. When the velocity of the crosswind is properly adjusted, a thin funnel will develop around the static line and suck powder into the swirling air above.

"The flow lines can be made visible with smoke. Put the source of smoke at the surface near the static line. At first the smoke may appear to move lazily, with little tendency to flow in any particular direction, but when the apparatus is in proper adjustment, a typical 'twister' will develop that is impressive to observe.

"Why does the whirlwind develop? When the vacuum hose is positioned at a substantial distance from other objects, air enters the opening in a uniform, symmetrical flow. Velocity increases as the flow approaches the hose [see at right]. When the hose is near the table, which represents the ground plane, the vertical flow becomes asymmetric. A static line forms from a point on the ground plane and curves upward, entering the hose at a point near the bottom [see illustration at lower left]. The static line represents the backbone of the model.

"Surrounding the static line is a pattern of continuous flow lines that curve upward and converge toward the static line. The air velocity increases as the flow lines converge. The flow into the hose will not by itself form a swirling wind, although it does meet two basic conditions associated with tornadoes: high-level horizontal flow, which is simulated by the flow of air into the low-pressure sink at the hose, and an unusual area of vertical flow surrounding the static line. The third basic condition, which is essential for the development of a tornado, is a horizontal flow near the ground plane. In the model the crosswind is provided by the fan.

"The velocity of the crosswind must not be high or it will warp the high level flow excessively. Even a gentle cross breeze significantly affects flow lines near the surface. The crosswind contributes an additional velocity vector that is perpendicular to the normal flow lines, as at point A in the illustration.

"The horizontal displacement thus induced evolves into a circulation around the static line and initiates the converging spiral [see illustration at right]. The velocity at any point A can be resolved into two vector components. One component represents upward movement that converges with adjacent flow lines. The second component represents circulation around the static line. By the principle of the conservation of momentum the velocity of the second component increases inversely with the radius of the circulation. In effect, both sets of forces combine to increase the velocity as air rushes up the spiral.

"The velocity can become impressive. For example, the velocity of a mass of air circulating at a radius of 2-1/2 inches increases from 15 feet per second to 150 feet per second when the radius is reduced to 1/4 inch. In theory the mass can approach sonic velocity as the radius is further reduced.

"The high-velocity rotation reduces the pressure on the static line below the entrance of the hose, with the result that flow lines converge farther down the static line. The process evidently continues until pressure at the surface in the swirling core is significantly lowered. The result resembles a miniature tornado [see illustration at left].

"The model demonstrates a number of features that are characteristic of full- scale tornadoes. As in nature's storm centrifugal force creates a partial vacuum at the center of the funnel. Rotation can occur in either sense, clockwise or counterclockwise, depending on the local winds. The tip of the downward projecting funnel may wander in the air or dip to the surface, where it reacts vigorously over a relatively small area.

"Although the motion appears to be random, it is governed by forces that displace the static line. Occasionally the tip of the funnel drifts as much as 18 inches from the vacuum hose, creating a track in the powdered surface that extends to the edge of the table. A larger model would demonstrate that two or more funnels can appear simultaneously, because the pattern of local airflow can generate more than one static line.

"For these reasons I am convinced that continued study of the model would result in data and measurements that would improve our understanding of tornado-like phenomena. Some of the experimental problems could be eased by scaling up the apparatus to a size sufficient for generating whirlwinds measured in feet instead of inches. Such models, apart from their possible value as demonstrations, would make fascinating playthings."

Bibliography

THE MEASUREMENT OF FLUID VELOCITY AND PRESSURE. J. R. Pannell. Edward Arnold & Co., 1924.

PHYSICS OF THE AIR. William J. Humphreys. McGraw-Hill Book Company, Inc., 1940.

PHYSICAL METEOROLOGY. John C. Johnson. John Wiley & Sons, Inc., 1954.

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