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.
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.
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.
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.
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.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:
|ZN = +12.1||Ground distance = 95 NM|
|Time = 0:30||Drift = 7° left|
|GS = 190 knots|