Pressure Pattern Navigation

This category discusses pressure differential techniques and how they affect pressure pattern navigation. Topics, such as constant pressure surface, geostophic wind, pressure computations and plotting, D readings, effective true airspeed, K factor, pressure line of position, Bellamy drift, and the MB-4 solution of Bellamy drift are all discussed. Also explained are the limitations of pressure differential techniques and how they are affected my meteorological conditions.

Pressure Differential Techniques (Part One)

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.

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.

Figure 15-1. Constant pressure surface.Figure 15-2. Contours. [click image to enlarge]

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.

Figure 15-3. Changing contours of constant pressure surface. [click image to enlarge]Figure 15-4. Pressure gradient.Figure 15-5. Buys-Ballots Law.

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 D₁. Take the second reading (D₂) 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, D₂ – D₁, is an expression of the slope or pressure gradient experienced by the aircraft. Subtracting D₁ from D₂ 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 D₂ – D₁ 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.

Figure 15-6. Pastagram. [click image to enlarge]

Pressure Differential Techniques (Part Two)

Effective True Airspeed (ETAS)

To determine a PLOP, you must compute the ETAS from the last D reading. The ETAS is the TAS that the aircraft flew from the last fix to the next fix air position. [Figure 15-7] If the aircraft has maintained a constant true heading (TH) between D readings, the ETAS equals the average TAS. But, if the aircraft has altered heading substantially between the D readings, the effective TAS is derived by drawing a straight line from the fix at the first D reading to the final air position. This line is called the effective airpath (EAP). ETAS is computed by measuring the effective air distance (EAD) and dividing it by the elapsed time. In Figure 15-7, an aircraft flew at 400 knots TAS from the 0820 fix to the 1020 air position via a dogleg route. The EAD is 516 nautical miles (NM); consequently, the ETAS is 258 knots.

K Factor

The constant K takes into account Coriolis and the gravity constant for particular latitudes.

Midlatitude is the average latitude between D1 and D2. It is in tabular form in Figure 15-8. In the table, this constant is plotted against latitude since Coriolis force varies with latitude. In using the ZN formula, enter the table with midlatitude and extract the corresponding K factor.

Figure 15-8. Pressure pattern worksheet/K factors table.

On MB-4 computers, a subscale of latitude appears opposite the values for K factors on the minutes scale. K is computed so that with slope expressed in feet and distance in NM, the geostrophic windspeed is in knots. For training purposes only, the K factors for 20° N or S to 14° N or S are listed in Figure 15-9.

Figure 15-9. K factors table below 20°.

Crosswind Displacement

ZN is the displacement from the straight-line airpath between the readings. Therefore, a PLOP must be drawn parallel to the effective airpath. With all the necessary values available, the ZN formula can be rearranged for convenient solution on the DR computer as follows:

Printed instructions on the face of MB-4 computers specify that to compute crosswind component, set EAD on the minutes scale opposite D₂ – D₁ on the miles scale. The crosswind component (V) is not to be confused with ZN. The V is crosswind velocity in knots. V must then be multiplied by the elapsed time between D₂ and D₁ in order to compute the ZN. Substitute ETAS for EAD on the MB-4 computer, and read the ZN over the K factor (or latitude on the subscale).

Pressure Line of Position (PLOP)

After you determine ZN, you need to figure out whether to plot it left or right of the EAP. Recall that wind circulation is clockwise around a high and counterclockwise around a low in the Northern Hemisphere; the opposite is true in the Southern Hemisphere. In the Northern Hemisphere, when the value of D increases (a positive D₂ – D₁), the aircraft is flying into an area of higher pressure and the drift is left. [Figure 15-10A] When the value of D decreases (a negative D₂ – D₁), the aircraft is flying into an area of lower pressure and the drift is right. [Figure 15-10B] Use the memory device PLOP to remember Plot Left On Positive (in the Northern hemisphere) Always plot the PLOP parallel to the EAP, as shown in Figure 15-11. Cross the PLOP with another LOP to form a fix, or use it with a DR position to construct an MPP.

Figure 15-10. Pressure pattern displacement.Figure 15-11. Plotting the PLOP.

Bellamy Drift

Bellamy drift is a mean drift angle calculated for a past period of time. It is named for Dr. John Bellamy who first demonstrated that drift could be obtained from the use of pressure differential information. Bellamy drift is used in the same way as any other drift reading.

An advantage of Bellamy drift is its independence from external sources. It can serve as a backup if the primary drift source fails, but will not give groundspeed. Bellamy drift is less accurate than Doppler or INS derived sources, but is better than using forecast drift or having none at all.

Figure 15-12. Solution of Bellamy drift by using PLOP. [click image to enlarge]In Figure 15-12, a PLOP has been plotted from the following information:

D₁ at a fix at 1000 hrs
D₂ at an air position at 1045 hrs
Zn = –20 NM
Constant TH of 90°

Next, construct an MPP on the PLOP. This is done by swinging the arc, with a radius equal to the ground distance traveled, from the fix at the first D reading to intersect the PLOP. The ground distance traveled can be found by multiplying the best known groundspeed (groundspeed by timing, metro groundspeed, etc.) by the time interval between readings. The mean track is shown by the line joining D₁ and the MPP. The mean drift is the angle between true heading and the mean track (8°R). Thus, the Bellamy drift is 8° right.

MB-4 Solution of Bellamy Drift

Compute Bellamy drift on the slide rule side of the DR computer by placing the ZN over the ground distance and reading the Bellamy drift angle opposite 57.3. [Figures 15-13 and 15-14] This can be set up in a formula as follows:

Figure 15-13. Computer solution of Bellamy drift.

Figure 15-14. Mathematical solution of Bellamy drift. [click image to enlarge]

Limitations of Pressure Differential Techniques

Pressure navigation is limited by a few meteorological considerations. The basic accuracy of the LOP in average conditions is about 5 to 10 miles. It will rapidly become worse under the following conditions: tightly circulating pressure systems of highs and lows, flying through a front, or carelessness in reading or computing the information. Bellamy drift has another limitation. To determine drift you must stay on one heading long enough to take two readings about 20 minutes apart.

ZN is a displacement in NM perpendicular to the EAP. Compute ZN on the MB-4 using the equation:

Determine ETAS by using the EAD and time. Measure EAD along a straight line between the two points in question. In the Northern and Southern Hemispheres, the sign of the ZN is the sign of the drift correction. Use airplot in conjunction with a fix position to plot the PLOP, and plot it parallel to the EAP. If the absolute altimeter fails, use pressure by temperature as a backup. With this method, use temperature and pressure altitude to find equivalent D readings. If you change altitudes, restart pressure at the new altitude, or correct the last D reading prior to the altitude change with a pastagram. Another expression of the PLOP is Bellamy drift, used as a backup source of drift angle. Figure 15-15 shows a fix determined by a PLOP and a celestial LOP.

Figure 15-15. Fix using PLOP and celestial line of position. [click image to enlarge]