The original purpose of grid navigation was to ease the difficulties facing the navigator during high latitude flights. But grid can be used at all latitudes, particularly on long routes because grid uses a great circle course for a heading reference. Grid is simply a reorientation of the heading reference and does not alter standard fixing techniques.
Problems Encountered in Polar Navigation
Two factors peculiar to polar areas that make steering more difficult than usual are magnetic compass unreliability and geographic meridians converging at acute angles. The combined effect of these two factors makes steering by conventional methods difficult if not impossible. Each factor is examined below.
Unreliability of Magnetic Compass
Maintaining an accurate heading in high latitudes is difficult when a magnetic compass is used as the heading indicator. Built to align itself with the horizontal component of the earth’s magnetic field, the compass instead must react to the strong vertical component that predominates near the magnetic poles. Here, the horizontal component is too weak to provide a reliable indication of direction. As a result, compass performance becomes sluggish and inaccurate. The situation is further aggravated by the frequent magnetic storms in the polar regions that shift the magnetic lines of force.
But even if these conditions did not exist, the mere proximity to the magnetic pole would sharply reduce compass usefulness. While the aircraft may fly a straight course, the compass indicator would swing rapidly, faithfully pointing at a magnetic pole passing off to the left or right. To cope with the unreliable magnetic compass, we use gyro information for our heading inputs.
Problem of Converging Meridians
The nature of the conventional geographic coordinate system is such that all meridians converge to the pole. Each meridian represents a degree of longitude; each is aligned with true north (TN) and true south. On polar charts, the navigator encounters 1 degree of change in true course for each meridian crossed; thus, the more closely the aircraft approaches a pole, the more rapidly it crosses meridians. Even in straight-and-level flight along a great circle course, true course can change several degrees over a short period of time. You are placed in the peculiar position of constantly altering the aircraft’s magnetic heading in order to maintain a straight course. For precision navigation, such a procedure is clearly out of the question. Notice in Figure 14-1 that the course changes 60° between A and B and much nearer the pole, between C and D, it changes 120°.
Figure 14-1. Converging meridians.
The three polar projections most commonly used in polar areas for grid navigation are the transverse Mercator, the polar stereographic, and the polar gnomonic. The transverse Mercator and polar stereographic projections are used inflight, the polar gnomonic is used only for planning. The Lambert conformal projection is the one most commonly used for grid flight in subpolar areas. The division between polar and subpolar projections varies among the aeronautical chart series. For example, the division is at 70° of latitude for the JN series, and at 80° of latitude for the Operational Navigation Chart (ONC) series charts
Grid Overlay
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.
Figure 14-2. Grid overlay.Figure 14-3. Great circle true direction changes.Figure 14-4. Great circle true direction is constant.
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.
Figure 14-5. Correction for the moon’s parallax.
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.
Figure 14-6. Grid overlay superimposed on Lambert conformal (convergence factor 0.785).
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.
Chart Transition
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°).
| Computed: | Applied: | ||
| 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)
Figure 14-7. Crossing 180th meridian on subpolar chart.
Example:
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.
Grivation
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.
Figure 14-8. Grivation. [click image to enlarge]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.
Gyro Precession
To eliminate the difficulties imposed by magnetic compass unreliability in polar areas, you disregard the magnetic compass in favor of a free-running gyro. Gyro steering is used because it is stable and independent of magnetic influence. When used as a steering instrument, the gyro is restricted so its spin axis always remains horizontal to the surface of the earth and is free to turn only in this horizontal plane. Any movement of a gyro spin axis from its initial horizontal alignment is called precession. The two types of precession are real and apparent, with apparent broken into earth rate, transport, and grid transport precession. Total precession is the cumulative effect of real and apparent precession.
Real Precession
Real precession is the actual movement of a gyro spin axis from its initial alignment in space. [Figure 14-9] It is caused by such imperfections as power fluctuation, imbalance of the gyro, friction in gyro gimbal bearings, and acceleration forces. As a result of the improved quality of equipment now being used, real precession is considered to be negligible. Some compass systems have a real precession rate of less than 1° per hour. Electrical or mechanical forces are intentionally applied by erection or compensation devices to align the gyro spin axis in relation to the earth’s surface. In this manner, the effects of apparent precession are eliminated and the gyro can then be used as a reliable reference.
Figure 14-9. Real precession.
Apparent Precession
The spin axis of a gyro remains aligned with a fixed point in space, while your plane of reference changes, making it appear that the spin axis has moved. Apparent precession is this apparent movement of the gyro spin axis from its initial alignment.
Earth Rate Precession
Earth rate precession is caused by the rotation of the earth while the spin axis of the gyro remains aligned with a fixed point in space. Earth rate precession is divided into two components. The tendency of the spin axis to tilt up or down from the horizontal plane of the observer is called the vertical component. The tendency of the spin axis to drift around laterally; that is, to change in azimuth, is called the horizontal component. Generally, when earth rate is mentioned, it is the horizontal component that is referred to, since the vertical component is of little concern.
A gyro located at the North Pole, with its spin axis initially aligned with a meridian, appears to turn 15.04° per hour in the horizontal plane because the earth turns 15.04° per hour. [Figure 14-10] As shown in Figure 14-10A, the apparent relationship between the Greenwich meridian and the gyro spin axis changes by 90° in 6 hours, though the spin axis is still oriented to the same point in space. Thus, apparent precession at the pole equals the rate of earth rotation. At the equator, as shown in Figure 14-10B, no earth rate precession occurs in the horizontal plane if the gyro spin axis is still aligned with a meridian and is parallel to the earth’s spin axis.
Figure 14-10. Initial location of gyro affects earth rate precession. [click image to enlarge]
Vertical Component
When the gyro spin axis is turned perpendicular to the meridian, maximum earth rate precession occurs in the vertical component. [Figure 14-11] But the directional gyro does not precess vertically because of the internal restriction of the gyro movement in any but the horizontal plane. For practical purposes, earth rate precession is only that precession that occurs in the horizontal plane. Figure 14-11 illustrates earth rate precession at the equator for 6 hours of time.
Figure 14-11. Direction of spin axis affects earth rate precession. [click image to enlarge]
Precession Variation
Earth rate precession varies between 15.04°/hour at the poles and 0°/hour at the equator. It is computed for any latitude by multiplying 15.04° times the sine of the latitude. For example, at 30° N, the sine of latitude is 0.5. The horizontal component of earth rate is, therefore, 15°/hour right × 0.5 or 7.5°/hour right at 30° N. [Figure 14-12]
Figure 14-12. Earth precession varies according to latitude. [click image to enlarge]
Steering by Gyro
Obviously, if the gyro is precessing relative to the steering datum of GN or TN, an aircraft steered by the gyro is led off heading at the same rate. To compensate for this precession, an artificial real precession is induced in the gyro to counteract the earth rate. At 30° N latitude, earth rate precession is equal to 15° × sin lat = 15 × .5 or 7.5° per hour to the right.
Offsetting Each Rate Effect
Hence, if at 30° N latitude, a real precession of 7.5° left per hour is induced in the gyro, it balances exactly and offsets earth rate effect. In ordinary gyros, a weight is used to produce this effect but, since the rate is fixed for a given latitude, the correction is good for only one latitude. The latitude chosen is normally the mean latitude of the area in which the aircraft operates. The N-1 and AHRS compass systems have a latitude setting knob that you can use to adjust for the earth rate corrections.
Earth Transport Precession (Horizontal Plane)
Earth transport precession is a form of apparent precession that results from transporting a gyro from one point on the earth’s surface to another. The gyro spin axis appears to move because the aircraft, flying over the curved surface of the earth, changes its attitude in relation to the gyro’s fixed point in space. [Figure 14-13] Earth transport precession causes the gyro spin axis to move approximately 1° in the horizontal plane for each true meridian crossed. This effect is avoided by using GN as the steering reference.
Figure 14-13. Earth transport precession.
Grid Transport Precession
Grid transport precession exists because meridian convergence is not precisely portrayed on charts. The navigator wants to maintain a straight-line track, but the gyro follows a greatcircle track, which is a curved line on a chart. The rate at which the great-circle track curves away from a straight-line track is grid transport precession. This is proportional to the difference between convergence of the meridians as they appear on the earth and as they appear on the chart and the rate at which the aircraft crosses these meridians.
Summary of Precession
Real precession is caused by friction in the gyro gimbal bearings and dynamic unbalance. It is an unpredictable quantity and can be measured only by means of heading checks.
Earth rate precession is caused by the rotation of the earth. It can be computed in degrees per hour with the formula: 15.04 × sin lat. It is to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. All gyros are corrected to some degree for this precession, many by means of a latitude setting knob.
Earth transport precession (horizontal plane) is an effect caused by using TN as a steering reference. It can be computed by using the formula (change longitude/hour × sine mid latitude). The direction of the precession is a function of the TC of the aircraft. If the course is 0° – 180°, precession is to the right; if the course is 180° – 360°, precession is to the left. This precession effect is avoided by using GN as a steering reference.
Grid transport precession is caused by the fact that the great circles are not portrayed as straight lines on plotting charts.
The navigator tries to fly the straight pencil-line course, the gyro a great circle course. The formula for grid transport precession is change longitude/hour (sin lat – CF), where CF is the chart convergence factor. The direction of this precession is a function of the chart used the latitude and the TC. Direct substitution into the formula produces an answer valid for easterly courses, such as 0° – 180°. For westerly courses, the sign of the answer must be reversed.
Gyro Steering
Gyro steering is much the same as magnetic steering, except that GH is used in place of true heading (TH). GH has the same relation to GC as TH has to true course (TC). The primary steering gyro in most aircraft provides directional data to the autopilot and maintains the aircraft on a preset heading. When the aircraft alters heading, it turns about the primary gyro while the gyro spin axis remains fixed in azimuth. If the primary gyro precesses, it causes the aircraft to change its heading by an amount equal to the precession.
Starting a Grid Navigation Leg
Grid navigation is normally entered while airborne on a constant heading. A constant heading is necessary because grid entry is accomplished by resetting the compass from a magnetic to a grid reference while on the same heading. After obtaining a grid celestial or inertial navigation system (INS) heading check, reset the compass immediately to the correct grid heading to avoid heading errors, because the precomputed grid Zn is only good for shot time. Since the exact grid heading is set at the beginning of the navigation leg, precession is assumed to be zero until subsequent heading checks assess the accuracy of the gyro. The grid heading is normally obtained using a variant of the TH method or the INS TH. Using this method, set a grid Zn in the sextant azimuth counter before collimating on the body. Other heading shot methods can be used, but would delay resetting the gyro to accomplish math computations after the heading shot. Although any celestial body may be used, navigators commonly use the sun or Polaris, depending on the time of day. [Figure 14-14]
Figure 14-14. Grid precomp. [click image to enlarge]
Using a Zn Graph
In order to get an accurate grid Zn for daytime grid entry, the navigator must compute Zn of the sun for a time and geographic position where the grid navigation leg begins. If the geographic position for grid entry is known well in advance, you can prepare a Zn graph for a time window. A Zn graph makes grid entry easier, because it is usable for an extended period of time, therefore eliminating the need to precomp for a specific time. The graph can be constructed during flight planning, thus reducing workload in the air.
To construct the graph, precomp and plot Zn on one axis and time on the other. [Figure 14-15] Set up the time axis to cover the planned start time and several minutes earlier and later. Plot grid Zn on the other axis using normal precomp procedures and the start point coordinates. Because the time/ Zn slope is close to linear, precomping at 20–30 minute intervals and connecting the points gives acceptable accuracy. When the sun is near local noon, precomp Zn at closer intervals because the Zn changes rapidly. To use the graph when it is finished, enter on the time axis. Then extend a line perpendicular to the time axis until reaching the time/Zn line. Finally, read the appropriate Zn on the Zn axis.
Figure 14-15. Zn graph.
Figure 14-15 demonstrates using a graph to get a grid Zn for the time of 1700Z. Although preparing a Zn graph takes a while, it pays dividends as long as you actually fly over the planned geographic point within the time frame covered by the graph.
Applying Precession to the DR
The most accurate method for applying precession to the DR is the all behind/half ahead method. This method corrects for the banana effect most commonly associated with precession. Since the full effect of precession does not occur at one time, we have to account for the gradual increase of precession.
Step 1—Determine the Hourly Rate
In Figure 14-16, grid entry occurred at 1700. At 1720, the navigator obtained a heading shot or MPP. The heading shot determined precession correction to be –2 and the compass was reset to the GH. On the MB-4 computer, place the –2 correction on the outside scale and the time since grid entry (20 minutes) on the inside scale. The hourly rate now appears above the index (6.0R). To minimize error, the hourly rate has to be computed to the nearest tenth of a degree.
Figure 14-16. Inflight log. [click image to enlarge]Step 2—Compute All Behind/Half Ahead
Since precession begins at the last time the gyro was reset, for this example we need to start at grid entry 1700. At 1700, all behind would be determined to be 0 minutes and halfahead to the next dead reckoning (DR) (1706) would be 3 minutes. To determine the amount of precession correction to be used, leave the hourly rate (6.0) over the index and look above 3 minutes. The computed precession correction for the 1706 DR is –0.3° or 0 for use on the log. Next, we need to determine the precession correction for the 1720 DR. At 1706, all behind is 6 minutes and half ahead is 7 minutes. The total time used to compute the precession correction for this DR is 13 minutes. Again, using the hourly rate, precession correction for the 1720 DR is –1.3° or –1° for the log.
KC-135 Method
Since the all behind/half ahead method tends to keep you behind, the KC-135 method is used by some navigators to predict precession. This method basically uses half of the computed precession correction for future DRs/MPPs when the precession correction is determined between two positions. Though not as accurate as the all behind/half ahead method, the KC-135 method can be effective if used with short DRs. Using the KC-135 method, compensate for precession around the turn by getting a heading shot immediately before and after the turn, resetting the gyro after the heading shot restarts precession.
False Latitude
A second method of compensating for precession while inflight involves the use of false latitude inputs into the gyro compass. Most gyro compasses have a latitude control that allows the navigator to compensate for earth rate precession (ERP). Normally, the latitude control is set to the actual latitude of the aircraft. However, other values may be set. For example, if the aircraft is at 30° N and the latitude control knob is set to 70° N, the gyro overcorrects for ERP. Since ERP is right in the Northern Hemisphere, the correction is to the left. Thus, setting a higher than actual latitude corrects for right precession over and above that for ERP. Since ERP 1 5°/hour × sine latitude, a table such as in Figure 14-17 can be developed to use this procedure.
Figure 14-17. False latitude correction table.
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