# Using a Barometer to Determine Altitudes

By Ed Perley

Do you ever wonder how deep that ravine behind you house is? Or how high that hill above your town is? Or how tall is the that big building on main street? You can easily estimate the height of an object with a barometer.

## How to Do It

Because a mercury column barometer is very cumbersome (and expensive) you would probably want to use an aneroid barometer, the kind you commonly see with a circular dial. Wait for a day when the weather is relatively stable. Changes in both atmospheric pressure and temperature can influence accuracy. The best time probably would be when the area to be tested is under a large stable high pressure area with little or no wind. You measure the difference in barometric pressure between two sites at different elevations.

Go to the first site and record the barametric pressure to the nearest .01 of an inch of mercury. Go to the second site as quickly as possible, being careful to not jar the barometer, and record the barametric pressure. Then return to the first site and record the pressure again. Repeat this process as many times as is practical. The more data you obtain, the more accurate the results.

Calculate the mean (average) pressures for the two sites, and calculate the difference between the two means. Multiply this number by 1000 to get the approximate height difference. For instance, if a site at the base of a hill gives a reading of 30.30 and the top of the hill gives a reading of 30.10, the difference in presure is .20. Multiplying by 1000 gives the height of the hill, 200 feet. If your altitude is more than a few thousand feet above sea level, or you wish your results to be as accurate as possible, use the equations described below. Also, if you prefer to use the metric system, those equations are also shown below.

PLEASE NOTE: An aneroid barometer has a rather limited range of pressures to which it can be set. Be careful that you do not take it to an altitude so high that the pressure will be outside the range of the instrument. Permanent damage to it might result. A barometer with a range of 28.00 to 32.00 inches of mercury, would have an altitude range of about 4000 feet.

## Scientific Basis

The Barometric Formula of Babinet can be used to calculate the relationship between altitude, temperature and atmospheric pressure. It is shown below:

Z = C x ( Bo - B ) / ( Bo + B )
C = 52494 x ( 1 + To + T - 64 ) / 900

Z = The difference in altitude in feet.
Bo and B = Barometric pressures in inches of mercury at two altitudes.
To and T = Farenheit temperatures at the two altitudes.

The equation can be simplified if you assume that the temperatures at the two altitudes are the same. Then, if both altitudes are within a few thousand feet above sea level, the equation can be simplified further to:

Z = 952 ( Bo - B )

The formula can also be expressed in metric units, as shown below:

Z = C ( Bo - B ) / ( Bo + B )
C = 16000 ( 1 + 2 ( To + T ) ) / 1000

Z = The difference in altitude in meters.
Bo and B = Barometric pressures in mm of mercury at two altitudes.
To and T = Centigrade temperatures at the two altitudes.

There is a problem with using an aneroid barometer to determine altitudes. Because they are used to monitor weather changes rather than absolute pressure, all aneroid barometers are set to sea level. If you are working with altitudes much over sea level, you should make some corrections for maximum accuracy.

An aneroid barometer at an altitude of 1000 feet above sea level shows a pressure of about 30 inches of mercury when the atmospheric pressure is really 29. Similarly, at 5000 feet, the pressure is about 26 inches, and at 9000 feet it is 22 inches, even though the barometer will be set to about 30 inches.

Because of this, at higher altitudes, the numerical constant that you multiply by the pressure difference becomes larger than that given above. For instance, if both altitudes are close to 1000 feet above sea level, it is 985. At 5000 feet, it is 1100, and at 9000 feet it is 1430.

From Handbook of Chemistry by Norbert Adolph Lange, McGraw Hill Book Co., 1961 page 1680.
For other editions, look under "Barometers" in index.

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