# Using isobars to calculate wind speed

Those of us who look at weather charts know that close isobars (lines of equal pressure) mean strong winds. With sufficient experience, one can guess the wind speed in a familiar area with a quick glance at an MSL (mean sea level) weather chart.

However, for those of us who are inexperienced, or in an unfamiliar area, there is a tool we can use. Theory tells us that, under stable conditions, wind speed over the open ocean and in areas away from the equator is proportional to the pressure gradient divided by the sine of the latitude. Because of surface friction, the wind direction at sea level is about 15° away from the isobar lines toward lower pressure.

Look at the equation below. If G and Lat respectively denote the pressure gradient in millibars per degree of latitude (millibars per 60 nautical miles) and the latitude of the area of interest and if, in addition, the isobars are almost straight and parallel, then (approximately):

wind speed = 6.8 x G/sinLat

This formula is useful to within about 15° of the equator. As an example, suppose we want to estimate the wind speed and direction at the point X on the MSL weather chart above. We note that X (just east of New Caledonia) is at about 22° south and that the nearby isobar lines are approximately straight and parallel. To obtain the pressure gradient, G, we must take two measurements and then do some arithmetic. Recall that what we need is the number of millibars per degree of latitude. The principle we use is:

millibars per degree = (millibars per millimeter) x (millimeters per degree)

First, to get the distance between isobars, we measure the distance between points A and B and find it to be about 17 millimeters. Since the isobar lines are every four millibars, we have four millibars per 17 millimeters or four per 17 millibars per millimeter. Next, to get the scale of the chart, we measure the distance between points C and D and find that to be about 30 millimeters. Since points C and D are 10° apart on the chart, the scale of the chart is 30/10 or three millimeters perdegree of latitude. Thus the gradient:

G = (4/17) x (30/10) = 0.7 mb per degree (approximately)

Another way to view this arithmetic is to notice that there is 30/17 (or almost two) sets of four millibars per 10° (or nearly eight millibars per 10°) so that there is 4 x (30/17) = 7.06 mb per 10°. Divide by 10 to see that there is about 0.7 millibars per degree.The sine of 22° (remember that 22° is the latitude we’re interested in) is about 0.375. So we estimate the wind speed at X to be:

6.8 x(0.7/0.375) = 13 knots (approximately)

Because the isobar lines lie almost exactly east to west, the wind direction is about 105° true (90° + 15°). Recall that in the Southern Hemisphere the wind circulates counterclockwise around a high and clockwise around a low. The reverse is true in the Northern Hemisphere. This circulation is caused by the Coriolis force. The Coriolis force is at a maximum in the polar regions and is zero at the equator (that is why our equation only works away from the equator).

If the isobars are curved around a high or a low, then centrifugal force enters the equation. This force is approximately proportional to the square of the wind speed divided by the radius of curvature of the isobars and is directed outward. To allow for this, add up to 20% for circulation around a high and subtract between 20% and 40% for circulation around a low. This is also an approximation. Tight turns with high wind speeds require a larger correction and soft turns with low wind speeds require a lesser correction.

Thomas McCullough is a professor of mathematics at California State University, Long Beach. He and his wife Joan are currently sailing the Great Barrier reef aboard Malagueña, their Cal 48 sloop.