The graticule of the grid overlay eliminates the problem of converging meridians. [Figure 14-2] It is a square grid and, though its meridians are aligned with grid north (GN) along the Greenwich meridian, they do not converge at GN. While the grid overlay can be superimposed on any projection, it is most commonly used with the polar stereographic (for flights in polar areas) and the Lambert conformal (for flights in subpolar areas). This is because a straight line on these projections approximates a great circle. As the great circle course crosses the true meridians, its true direction changes but its grid direction remains constant. [Figures 14-3 and 14-4] All grid meridians are parallel to the Greenwich meridian and TN along the Greenwich meridian is the direction of GN over the entire chart.
Relationship of Grid North to True North
Because grid meridians are parallel to the Greenwich meridian, the aircraft longitude and the convergence factor (CF) of the chart govern the angle between GN and TN.
CF of 1.0
Figure 14-5 shows that charts having CFs of 1.0 display GN to TN relationship as a direct function of longitude. In the Northern Hemisphere at 30° W, GN is 30° W of TN; at 60° W, GN is 60° W of TN. Similarly, at 130° E longitude, GN is 130° E of TN. In the Southern Hemisphere, the direction of GN with respect to TN is exactly opposite.
CF of Less than 1.0
Figure 14-6 shows a chart with a CF of less than 1.0 with a grid overlay superimposed on it. The relationship between GN and TN on this chart is determined in the same manner as on charts with a CF of 1.0. On charts with a CF of less than 1.0, the value of the convergence angle at a given longitude is always smaller than the value of longitude and is equal to the CF times the aircraft longitude.
Relationship of Grid Direction to True Direction
Use the following formulas to determine grid direction.
In the Northern Hemisphere:
Grid direction = true direction + west longitude × CF
Grid direction = true direction – east longitude × CF
In the Southern Hemisphere:
Grid direction = true direction – west longitude × CF
Grid direction = true direction + east longitude × CF
Polar angle is used to relate true direction to grid direction. Polar angle is measured clockwise through 360° from GN to TN. It is simple to convert from one directional reference to the other by use of the formula:
Grid direction = true direction + polar angle
To determine polar angle from convergence angle (CA), apply the following formulas:
In the northwest and southeast quadrants, polar angle = CA
In the northeast and southwest quadrants, polar angle = 360° – CA.
Since the relationship of the true meridians and the grid overlay on subpolar charts differs from that on polar charts because of different CFs, the overlays do not match when a transition is made from one chart to the other. Therefore, the grid course (GC) of a route on a subpolar chart is different than the GC of the same route on a polar chart. The chart transition problem is best solved during flight planning:
- Select a transition point common to both charts.
- Measure the subpolar GC and the polar GC.
- Compute the difference between the GCs obtained in step two. This is the amount the compass pointer must be changed at the transition point. NOTE: If the GC on the first chart is smaller than the GC on the second chart, add the GC difference to the directional gyro (DG) reading and reposition the DG pointer; if the GC on the first chart is larger, subtract the GC difference.
Example: Chart transition from a subpolar to a polar chart. GC on subpolar chart is 316°. GC on polar chart is 308°. GC difference is 8°. Gyro reading (grid heading (GH)) is 320°. The transition is from a larger GC to a smaller GC; therefore, the GC difference (8°) is subtracted from the GH value read from the DG (320°). The DG pointer is then repositioned to the new GH (312°).
|From (subpolar) GC||316°||Old (subpolar) GH||320°|
|GC difference||–8°||GC difference||–8°|
|To (polar) GC||308°||New (polar) GH||312°|
Caution: Do not alter the aircraft heading; instead, simply reposition the DG pointer to the new GH.
Crossing 180th Meridian on Subpolar Chart
When a flight crosses the 180th meridian on a subpolar grid chart, the GH changes because of the convergence of grid meridians along this true meridian. This is very similar to the chart transition procedure described above. When using a subpolar chart that crosses the 180th meridian on an easterly heading [Figure 14-7A to B], the apical angle must be subtracted from the GH. Conversely, the apical angle must be added to the GH when on a westerly heading. [Figure 14-7B to A] The apical angle can be measured on the chart at the 180th meridian between the converging GN references. The angle can also usually be found on the chart border, or computed by use of the following formula:
Apical angle = 360° – (360° × CF)
Given: Chart CF 0.785
Find: Apical angle
Apical angle = 360° – (360° × 0.785)
Apical angle = 360°– 283°
Apical angle = 77°
Caution: Do not alter the aircraft heading when crossing the l80th meridian; instead, simply reset the DG pointer to the new GH.
The difference between the directions of the magnetic lines of force and GN is called grivation (GV). GV is similar to variation and used to convert MH to GH and vice versa. Figure 14-8 shows the relationship between GN, TN, and MN. Lines of equal GV (isogrivs) are plotted on grid charts.
The formulas for computing GV in the Northern Hemisphere are:
GV = (–W convergence angle) + W variation
GV = (–W convergence angle) – E variation
GV = (+E convergence angle) + W variation
GV = (+E convergence angle) – E variation
If GV is positive, it is W grivation; if grivation is negative, it is E grivation. For example, if variation is 17° E and convergence angle is 76° W, using the formula:
GV = (–West convergence angle) + (–E variation)
GV = (–76) + (–17) = –93
GV = 93° E
To compute MH from GH, use the formula:
MH = GH + W grivation
MH = GH – E grivation
In the Southern Hemisphere, reverse the signs of west and east convergence angle in the formula above.