Pressure differential flying is based on a mathematically derived formula. The formula predicts windflow based on the fact that air moves from a high pressure system to a low pressure system. This predicted windflow, the geostrophic wind, is the basis for pressure navigation. The formula for the geostrophic wind (modified for a constant pressure surface), combined with inflight information makes available two aids to navigation: Bellamy drift and the pressure line of position (PLOP). Bellamy drift gives information about aircraft track by supplying net drift over a set period of time. Using the same basic information, the PLOP provides a line of position (LOP) as valid as any other type.

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## Constant Pressure Surface

To understand pressure differential navigation, you should know something about the constant pressure surface. The constant pressure surface is one on which the pressure is the same everywhere, even though its height above sea level will vary from point to point as shown in Figure 15-1. The pressure altimeter will show a constant reading. A constant pressure surface is shown on a constant pressure chart (CPC) as lines that connect points of equal height above sea level. These lines are referred to as contours and are analogous to contour lines on land maps. [Figure 15-2] The intersection of altitude mean sea level (MSL) and constant pressure surfaces form isobars. A comparison of isobars and contours is shown in Figure 15-2. The geostrophic wind will blow along and parallel to the contours of a CPC just as it blows along and parallel to the isobars of a constant level chart.

## Geostrophic Wind

The shape and configuration of the constant pressure surface determine the velocity and direction of the geostrophic wind. Flying with 29.92 set in the pressure altimeter will cause the aircraft to follow a constant pressure surface and change its true height as the contours change. [Figure 15-3] The slope of the pressure surface, also known as the pressure gradient, is the difference in pressure per unit of distance as shown in Figure 15-4. The pressure gradient force (PGF), or slope of the pressure surface, and Coriolis combine to produce the geostrophic wind. The speed of the geostrophic wind is proportional to the spacing of the contours or isobars. Closely spaced contours form a steep slope and produce a stronger wind, while widely spaced contours produce relatively weak winds. According to Buys-Ballots Law, if you stand in the Northern Hemisphere with your back to the wind, the lower pressure is to your left. [Figure 15-5] The opposite is true in the Southern Hemisphere where Coriolis deflection is to the left. Further study of Figure 15-5 shows that as you enter a low or a high system, your drift will be right or left, respectively. The opposite is true as you exit the system. Since the geostrophic wind is based on a constant pressure surface, you must fly a constant pressure altitude. A minimum of 2,000 to 3,000 feet above the surface will usually eliminate distortion introduced through surface friction. Near the equator (20° N to 20° S), Coriolis force approaches zero, and pressure navigation is unreliable, pressure differential navigation is reliable in midlatitudes.

## Pressure Computations and Plotting

In determining a PLOP or Bellamy drift by pressure differential techniques, use the crosswind component of the geostrophic wind over a given period of time. To determine your pressure pattern displacement (ZN), use the following equation:

This formula gives the direction and crosswind displacement effect of the pressure system you’ve flown through. To solve for ZN, you must understand how to obtain and apply such special factors as D readings, effective true airspeed (ETAS), effective airpath (EAP), effective air distance (EAD), and K values.

## D Readings

The symbol D stands for the difference between the true altitude (TA) of the aircraft and the pressure altitude (PA) of the aircraft. There are two methods for obtaining D values. The first uses an absolute altimeter to measure TA on overwater flights and the pressure altimeter to measure PA. The second method uses outside air temperature (OAT) readings to determine equivalent D values if the absolute altimeter fails. For both methods, the D value is expressed in feet as a plus (+) or minus (–) value. To determine the correct D reading using the altimeter method, assign a plus (+) to TA, a minus (–) to PA, and algebraically add the two. Remember the city in Florida (TAMPA) to keep the signs right. Take the first D reading in conjunction with the initial fix for the pressure navigation leg. This is D_{1}. Take the second reading (D_{2}) at the next fix. Always take the readings at the same time relative to the fix, usually about 4 minutes before fix time. The value, D_{2} – D_{1}, is an expression of the slope or pressure gradient experienced by the aircraft. Subtracting D_{1} from D_{2} determines the change in aircraft TA between readings. When this altitude change is compared with the distance flown, the resulting value becomes an expression of the slope. The value of D_{2} – D_{1} indicates whether the aircraft has been flying upslope (+) or downslope (–).

Take readings carefully, because an erroneous reading of either altimeter will produce an incorrect D reading and a bad LOP. Gently tap the pressure altimeter before reading it to reduce hysteresis error.

Maintain a constant PA to ensure consistent D readings. If you change altitudes, start with a new D at the new altitude, or correct the previous reading by use of a pastagram. The pastagram will allow you to continue accurately, even though you have changed altitude. The pastagram uses average altitude and average temperature change to determine a correction to the D reading taken before the altitude change. Figure 15-6 shows a pastagram with instructions for its use and a sample problem.