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Five Mile Final | An Aviation Sandbox

Pilot's Handbook of Aeronautical Knowledge

Chapter 16: Navigation

Air navigation is the process of piloting an aircraft from one geographic position to another while monitoring one's position as the flight progresses.

Flight planning includes plotting the course on an aeronautical chart, selecting checkpoints, measuring distances, obtaining pertinent weather information, and computing flight time, headings, and fuel requirements.

Methods include pilotage (navigating by reference to visible landmarks), dead reckoning (computations of direction and distance from a known position), and technology (radio navigation, GPS). While any one of these three methods may lead a flight's successful outcome, all three methods should be used during flight planning and relied upon throughout the flight.

Aeronautical Charts

The three aeronautical charts used by VFR pilots are.

Sectional charts are the most common charts. By referring to the chart legend, a pilot can interpret most of the information on the chart. Sectional charts are revised every 56 days, except for some areas outside the conterminous United States, where they are revised annually.

VFR terminal area charts (TAC) are helpful when flying in or near Class B airspace. They have a more detailed display of topographical information and are revised semiannually, except for several Alaskan and Caribbean charts.

World aeronautical charts (WAC) are designed at a size and scale convenient for navigation by moderate speed aircraft. Symbols are the same as sectional charts, except that there is less detail due to the smaller scale. WACs are revised annually except several Alaskan charts and the Mexican/Caribbean charts, which are revised every 2 years

Sectional chart and legend.

Latitude and Longitude

Any specific geographical point can be located by reference to its longitude and latitude. Circles parallel to the equator (lines running east and west) are parallels of latitude. Meridians of longitude are drawn from the North Pole to the South Pole and are at right angles to the Equator. The Prime Meridian — in Greenwich, England — is used as the zero-line for measurements to the east and west.

The Earth revolves at the rate of 15 degrees an hour, which covers 360 degrees in 24 hours. The standard practice is to establish a time zone for each 15 degrees of longitude, but the lines are irregular due to the specific needs of communities and regions.

In most aviation operations, time is expressed in terms of the 24-hour clock (e.g., 1500 hours refers to 3:00 pm). Universal Coordinated Time (UTC), often referred to as Zulu time, is the standard time system in aviation. It is the local time at the Prime Meridian.

Meridians and parallels: the basis of measuring time, distance, and direction.
Compass rose.

A course is the intended path of an aircraft over the ground. As measured on the chart, the course is known as the true course (TC). This is the direction measured by reference to a meridian or true north (TN).

The heading is the direction in which the nose of the aircraft points during flight. Usually, it is necessary to head the aircraft in a direction slightly different from the TC to offset the effect of wind. The true heading (TH) is the direction in which the nose of the aircraft points during a flight when corrected for wind. In no-wind conditions, true course and true heading are identical.

The Earth is not uniformly magnetized, and the magnetic north pole is about 1,300 miles from the geographic/true north pole. The amount and direction of variation changes slightly from time to time. Variation is the angle between true north and magnetic north (MN), expressed as east variation or west variation depending upon whether MN is to the east or west of TN.

On aeronautical charts, isogonic lines are depicted as broken magenta lines that connect points of equal magnetic variation. Each isogonic line includes the direction and amount of variation. The agonic line has no variation between true and magnetic north. It the United States, it can be seen on aviation charts from Lake Superior to the east coast of Florida.

Magnetic meridians are in red, while the lines of latitude and longitude are in blue.
Magnetic meridians are in red while the lines of longitude and latitude are in blue.

Variation for the geographical location of the flight must be calculated, which results in a magnetic course.

Each aircraft has its own internal effect upon the onboard compass. Some adjustment of the compass, referred to as compensation, can be made by a technician to reduce this error, but the remaining correction must be applied by the pilot. Deviation is established on the aircraft's compass card (also called a deviation card) and applied by the pilot to the magnetic course, which results in the compass course. The compass course can be used to fly the aircraft from point to point.

The following method is used by many pilots to determine compass heading/compass course:

Effect of variation on the compass.

Wind

Wind is a mass of air moving over the surface of the Earth in a definite direction. An aircraft flying within a moving mass of air will be affected by it. The aircraft moves through the air. Meanwhile, the air is moving over the ground. At the end of each flight, the location of the aircraft is a result of the forward movement of the aircraft through the air mass, as well as the movement of the air mass in reference to the ground. These two motions are independent.

Airspeed is the rate of the aircraft's progress through the air. Groundspeed (GS) is determined by combining the movement of the aircraft with that of the air mass, and thus is the rate of the aircraft's inflight progress over the ground.

The direction in which the aircraft is pointing as it flies is called heading. Its actual path over the ground — a result of the motion of the aircraft and the motion of the air — is called track. The angle between the heading and the track is called the wind correction angle (WCA), also referred to as the drift angle.

The wind correction angle is expressed in terms of degrees right or left of the true course. Pilots use wind correction angles to counteract drift and make the track of the aircraft coincide with the desired course. For example, if the wind is from the left, the desired track is maintained by changing the aircraft's heading to point toward the wind to a calculated degree.

Establishing a wind correction angle that counteracts wind drift and maintains the desired course.

Fuel Consumption

Fuel consumption in gasoline-fueled aircraft is measured in gallons per hour, while jet fuel is generally quantified by its density and volume, due to the large quantities typically used and the variations in volume caused by changes in temperature.

For simple aircraft with reciprocating engines, the operating handbook provides gallons-per-hour values to assist with preflight planning. The fuel requirement for each flight is determined by calculating the distance the aircraft can travel at a known rate of fuel consumption for the expected groundspeed (which factors for wind). A reserve amount of fuel also is required by regulation and should be included in flight planning.

Flight Planning

When conducting flight planning, pilots often will use an E6B or electronic flight calculator, which can compute numerous solutions for common flight-planning equations. A plotter is a combination protractor and ruler that used to determine course and distance.

Pilotage is navigation by reference to landmarks or checkpoints. Checkpoints selected should be prominent features, and several should be selected for the route, so that too much reliance is not placed on a single checkpoint. Some features on sectional charts, such as radio antennas and grass airfields, can be difficult to see from the air. Medium and large airports, rivers and lakes, well-traveled highways, and powerlines can be prominent checkpoints.

Some visual checkpoints, such as rivers, highways, and powerlines, can be used as brackets, which the pilot may use to determine that the flight is still on course — for example, if the entire course is south of a specific river.

Dead reckoning is navigation solely by means of computations based on time, airspeed, distance, and direction. The result of dead reckoning computations is heading and groundspeed.

The wind triangle is a graphic explanation of the effect of wind upon flight. The result of a wind triangle computation is groundspeed, heading, and time enroute. While flight computers and aviation apps can instantly deliver navigation parameters, new aviation students benefit from constructing wind triangle diagrams as an aid to the complete understanding of wind effect. See the wind triangle section below for more details.

Per regulations, the pilot in command (PIC) of an aircraft shall become familiar with all available information concerning that flight before the start of the flight. This would include (but not be limited to) weather observations and forecasts, fuel requirements, alternate/emergency airports, and known traffic delays.

The Chart Supplement handbook (formerly the Airport/Facility Directory) includes recent information on airport location, elevation, runway and lighting facilities, services, fuel available, radio frequencies, traffic information, remarks, and other pertinent information.

Notices to Airmen (NOTAMs) are issued every 28 days and should be checked for additional information on hazardous conditions or changes that have been made since issuance of the Chart Supplement.

The Pilot's Operating Handbook (POH) or Airplane Flight Manual (AFM) should be consulted for weight-and-balance information, performance charts, and fuel consumption charts.

When charting a course, an aviation chart (such as Sectional or TAC) should be used to determine the route and total distance between the points of departure and arrival.

VFR Flight Plans

A VFR flight plan is not legally required, but instead is used for purposes of search and rescue.

The flight plan should be filed with a Flight Service Station (FSS) just prior takeoff. It should be opened from the air via radio communications with Flight Service, just after departure. A flight plan is held by the FSS until one hour after the proposed departure time and then canceled if the actual departure time is not received.

FSS frequencies can be found on aviation charts, either as remote communications outlets (RCO) or associated with VOR information blocks. The expected salutation when contacting Flight Service over the air is "Radio" (e.g. "Seattle Radio") and the aircraft's tail number is proceded by the national registration letter, rather than the aircraft type (e.g. "November 172SP").

Do not forget to close the flight plan upon arrival. The FAA recommends this is done via telephone to avoid radio congestion.

Ground-Based Navigation

There are three radio navigation systems available for use for VFR navigation: the VHF Omnidirectional Range (VOR) system, Nondirectional Radio Beacons (NDB), and the Global Positioning System (GPS).

An omnidirectional range is a VHF radio transmitting ground station that projects straight line courses ("radials") from the station in all directions. The Very High Frequency (VHF) Omnidirectional Range (VOR) system is present in three slightly different navigation aids, although the VOR functions are identical among all three:

Radials (or "courses") projected from the station are aligned to magnetic north. Because the equipment is VHF, the signals transmitted are subject to line-of-sight restrictions. Generally, the reception range of the signals at an altitude of 1,000 feet above ground level (AGL) is about 40 to 45 miles, with better range at higher altitudes.

VHF transmissions follow a line-of-sight course.
VOR indicator.

VORs and VORTACs are classed according to operational use:

VOR Tests & Identification

VOR signals are normally accurate within 1°, but aging equipment can diminish accuracy, particularly at greater distances from stations. VOR accuracy checks are not a regulatory requirement for VFR flight, but they should be done periodically.

Pilots can complete VOR checks at a VOR test facility (VOT), at certified airborne checkpoints, and at ground checkpoints located on airport surfaces. A list of the airborne and ground checkpoints is published in the Chart Supplement. These can be performed by the pilot.

If an aircraft has two VOR receivers installed, a dual VOR receiver check can be made by tuning both VOR receivers to the same VOR ground facility. While VFR flight does not require VORs to be checked to specific tolerances, instrument flight tolerances are recommended. For IFR operations, a dual VOR ground check cannot have a variance greater than 4°, while an airborne check cannot have a variance greater than 6°.

VOR stations can be identified by Morse code tones or a recorded voice. If a VOR is out of service for maintenance, the coded identification is removed and not transmitted. Any station not transmitting an identifier should not be used for navigation. VOR receivers will present an alarm flag (or "unreliable signal flag") to indicate when signal strength is inadequate, either due to distance or altitude limitations.

Pilots should always positively identify the station by its code or voice identification before using a VOR for navigation.

VOR Operation

The VOR navigation instrument may feature a Course Deviation Indicator (CDI), Horizontal Situation Indicator (HSI), or a Radio Magnetic Indicator (RMI).

A Course Deviation Indicator (CDI) includes an Omnibearing Selector (OBS), a CDI needle, and an ambiguity indicator, typically referred to as the "TO/FROM" indicator.

The OBS is an azimuth dial that can be rotated to select a desired radial. It also can be rotated to center the CDI, which then indicates the VOR radial on which the aircraft is flying. The ambiguity indicator will present either "TO" or "FROM".

As the OBS is rotated, the CDI indicates the position of the radial relative to the aircraft. The CDI moves to the right or left if the aircraft is flown or drifting away from the radial which is set in the course selector.

When the CDI is centered, the OBS indicates either the course "FROM" the station or the course "TO" the station.

The Horizontal Situation Indicator (HSI) combines the magnetic compass with navigation signals and a glideslope. The desired course is selected by rotating the course select pointer, in relation to the compass card. The course deviation bar displays the aircraft's position relative to the selected course.

The Radio Magnetic Indicator (RMI) consists of a compass card, a heading index, two bearing pointers, and pointer function switches. The two pointers are driven by any two combinations of a GPS, an ADF, and/or a VOR, as selected by the pilot.

See the Pilot's Handbook of Aeronautical Knowledge, Chapter 16, for procedures on tracking with a VOR.

Distance Measuring Equipment

Distance Measuring Equipment (DME) measures and displays the slant-range distance of an aircraft from a VOR/DME or VORTAC. Slant-range distance is the direct distance between the aircraft and the station, and thus is affected by aircraft altitude. For example, passage directly over a station at an altitude of 6,076 feet (AGL) would show 1 NM on the DME.

Most DME receivers also provide groundspeed and time-to-station modes of operation.

VOR/DME RNAV is not a separate ground-based NAVAID, but a method of navigation using VOR/DME and VORTAC signals specially processed by the aircraft's RNAV computer. See the Pilot's Handbook of Aeronautical Knowledge, Chapter 16, for more information.

VOR Time and Distance Checks

To do a time and distance check using a CDI:

If calculating time to the station, if a bearing change of 10° requires two minutes (120 seconds), divide the change in bearing by the time in seconds. 120 divided by 10 = 12. The station is 12 minutes away.

Time-distance check example.
Time-distance check formula using a CDI.

The angle of intercept is the angle between the heading of the aircraft (intercept heading) and the desired course. Each degree, or radial, is one (1) nautical mile wide at a distance of 60 nautical miles from the station. Angle of intercept can be steep at further distances from a station (no greater than 90°), but should be moderate or shallow when close to a station, so that the pilot does not fly through the intended radial.

The Visual Formula

If it takes 60 seconds to traverse 10° across radials (crossing at a 90° angle), it will take 360 seconds to reach the station after turning inbound.

You can recall this rule as "60 V 360," per the (not-to-scale) diagram below.

Stated simply, the time to the station is greater by a factor of 6 than the time it takes to traverse 10° across radials — 6(x) = y, when x is the time to traverse 10° of radials and y is time to the station.

You can write this depiction down on paper the moment the knowledge test starts.

Time to Station.

This formula accepts variables:

  • If it takes 30 seconds to traverse 10° of radials, you are 3 minutes from the station.
  • If it takes three minutes to traverse 10° of radials, you are 18 minutes from the station.
  • If it takes four minutes to traverse 20° of radials, you are 12 minutes from the station (since it takes two minutes to traverse 10°).

To determine the distance to the station, rather than the time to the station, determine how far you can travel at your current groundspeed, using the time-to-station product as the duration of flight. This can be done with a manual E6B. For an electronic E6B, use the "distance flown" function.

Calculating VOR Time & Distance with the E6B

Time and distance to a VOR station is fairly straightforward when using a manual E6B.

For any 10° radial change, the time on the B and C rings of the E6B correspond to traverse-time (C-ring) and time to station (B-ring). For example, if it takes 120 seconds (2:00 minutes) to traverse 10° of radials, the time to the station is 12 minutes. Those two values are paired around the B/C rings — the B-ring represents time in seconds (absent the final '0'), while the C-Ring is the same time in 00:00 format. In this case, the 12 isn't 120 seconds, but instead 12 minutes. Most time-to-station problems can be worked out by using a 10° traversal as the basis:

  • If it takes one minute to traverse 10 ° of radials, you are 6 minutes from the station.
  • If it takes two minutes to traverse 10 ° of radials, you are 12 minutes from the station.
  • If it takes two minutes to traverse 20 ° of radials, you are 6 minutes from the station.

For a calculated approach, spin the C-ring (time) so that it aligns with the degrees of radial to traverse on the A-ring. The value on the B-ring that's under the "10" is the time to the station. Thus, if it takes five (5) minutes to traverse 20 degrees of radial, you are 15 minutes from the station.

Once the time to the station is known, the E6B can be used to determine the distance to the station For example, if you are flying at a groundspeed of 90 kts. and are 12 minutes from the station, then you are 18 miles from the station. Place the speed index on 90, use the B-ring for time, and refer to the A-ring for distance. The time/distance formula is printed on the face of the E6B, so there is no need to memorize it.

Automatic Direction Finder (ADF)

The Nondirectional Radio Beacon (NDB) system, which is accessed via an Automatic Direction Finder (ADF), is gradually being phased out in the United States. See the Pilot's Handbook of Aeronautical Knowledge, Chapter 16, for more information.

Pilot knowledge tests may include time and distance problems using the NDB system.

The NDB Formulas

Distance to NDB station

Distance-to-station questions will provide airspeed, time of bearing change, and degrees of traverse. The formula to remember for these questions is "A x T ÷ D." The bearing change value requires a unit of time expressed in minutes.

  • When flying at 160 kts
  • if it takes 2 minutes to change
  • 10 deg.
  • then the distance to the station is 32 miles
  • (160 x 2 ÷ 10 = 32)

Time to NDB station

This is one just "T ÷ D." The bearing change value requires a unit of time expressed in seconds.

  • A bearing change of 5 deg.
  • over 1.5 minutes
  • means the airplane is 18 miles from the station
  • (90 ÷ 5 = 18)

Imagining these values in relation to an aircraft planform makes them more memorable. You can write this depiction down on paper the moment the knowledge test starts. Don't forget that distance problems require a bearing change in minutes, while time problems require a bearing change in seconds. "Use the ticker for time."

Time to Station: NDB.

Global Positioning System (GPS)

The Global Positioning System (GPS) broadcasts a signal from a constellation of satellites, which is then used by receivers to determine precise positions anywhere in the world. It differs significantly from conventional, ground-based electronic navigation. It is expected that GPS will become aviation's primary means of electronic navigation.

VFR pilots should never rely solely on one system of navigation. GPS should not be used to solve all VFR navigational problems. GPS navigation must be integrated with other forms of electronic navigation, as well as pilotage and dead reckoning. VFR pilots should always check to see if a GPS unit has RAIM capability. If not, GPS may be considered unreliable if disagreement exists with other radio navigation, pilotage, or dead reckoning.

VFR waypoints provide VFR pilots with a supplementary tool to assist with position awareness while navigating visually in aircraft equipped with area navigation receivers. VFR waypoints should be used as a tool to supplement current navigation procedures. VFR waypoint names consist of five letters beginning with the letters "VP" and are retrievable from navigation databases. VFR waypoint names are not intended to be pronounceable, and they are not used in ATC communications.

The baseline GPS satellite constellation consists of 24 satellites positioned in six earth-centered orbital planes with four operation satellites and a spare satellite slot in each orbital plane. Users with a clear view of the sky have four to eight satellites in view.

Receiver Autonomous Integrity Monitoring (RAIM) allows the GPS unit to verify the integrity (usability) of signals received from the GPS constellation. GPS-derived altitude should not be relied upon to determine aircraft altitude, since the vertical error can be quite large and no integrity is provided.

A RAIM error may indicate that there are not enough satellites available to provide RAIM integrity monitoring. Another type of error may indicate that the RAIM integrity monitor has detected a potential error that exceeds the limit for the current phase of flight.

Selective Availability (SA) is a method by which the accuracy of GPS is intentionally degraded, so as to deny hostile use of precise GPS positioning data. Selective Availability was discontinued on May 1, 2000, but many GPS receivers are designed to assume that it is still active.

Lost Procedures

If a pilot becomes lost, the first thing to do is climb, which increases radio and navigation reception range, as well as radar coverage. It's possible to determine position by plotting an azimuth from two or more navigational facilities. GPS can be used to determine the position and the location of the nearest airport.

Communicate with any available facility using frequencies shown on the sectional chart. A controller may offer radar vectors or Direction Finding (DF) assistance. For this, the controller requests the pilot to hold down the transmit button for a few seconds and then release it. This may be repeated, with requested heading changes.

If the flight condition becomes dangerous, transmit on 121.5 and set the transponder to 7700. Flight facilities and many airliners monitor the emergency frequency.

Flight Diversion

A flight may not reach its intended destination due to weather, a system malfunction, or poor preflight planning. Before any cross-country flight, check the charts for airports or suitable landing areas along or near the route of flight. Also consider the use of navigational aids that can be used during a diversion.

In an emergency, divert promptly toward your alternate destination. Attempting to complete all plotting, measuring, and computations involved before diverting to the alternate destination may only aggravate an actual emergency. Give priority to flying the aircraft while dividing attention between navigation and planning.

Off-Course Correction

Off-Course Triangles.

This type of question may come up in FAA tests, but it is not covered in the current Pilot's Handbook of Aeronautical Knowledge. It is covered in manual E6B instructions. It may not be a feature of your electronic E6B.

The basic math

  1. Divide the distance off course by the distance covered (which will be 0.x);
  2. Multiply the quotient by 60;
  3. Divide the distance off course by the distance remaining (which will be 0.x);
  4. Multiply the quotient by 60;
  5. Add both factors to determine the required wind-correction angle.

You can write this formula down on paper the moment the knowledge test starts (a sample problem is included here):

Off-Course Correction.

The detailed version…

If wind has caused you to drift off your intended course during a flight, you can calculate a new wind-correction angle that will set you on a course to your destination.

The problem requires calculating two unknown angles of two right triangles. The squares of both triangles are perpendicular from your location, at the intended course. Your drift off course, and your new course, are the hypotenuses of the triangles.

The angles located at your departure point and your destination must be determined. In trigonometry, these unknown angles are referred to as Theta (Θ). After the Θ values are calculated, they are combined, which provides a correction to your current heading — and thus, a new heading.

Mathematical formula

In order to determine correction angle after drifting off course, divide the distance off course by the distance covered, and then multiply the result by 60. (This will be the sides of the right triangle that are not the hypotenuse.) Since it's unlikely that you would drift several miles off course after traveling relatively few miles, the quotient will be less than one (1).

This step will be done twice, for both the distance traveled and the distance not yet traveled. Add both results for the total course correction.

Thus:

  • If you have flown 95 miles and and are 12 miles off course;
  • And you have another 80 miles to your destination:
  • 12 ÷ 95 = 0.1263
  • 0.1263 x 60 = 7.578°
  • 12 ÷ 80 = 0.15
  • 0.15 x 60 = 9.0°
  • 7.578 + 9.0 = 16.578°

The new heading requires a 17° turn into the wind.

Using the E6B

The course-correction problem can be solved quickly with a manual E6B:

  • Locate the distance you are from your intended course on the A-ring.
  • Locate the distance you have traveled from your destination on the B-ring.
  • Rotate both factors so that they align.
  • The correction angle can be found at the speed index.

Repeat these steps to find the Θ of the right triangle that lies between your current location and your destination.

Add both correction angles to determine your change in heading.

Trigonometry

Stated in trigonometric terms, the angle to calculate, at the departure and arrival ends, is Theta (Θ). The intended course is the adjacent side from Θ, while the distance drifted from the course is the opposite side from Θ. The course caused by drift is the hypotenuse. The acute angles of a right triangle are complementary, which is to say the sum of both angles equals 90.

The Wind Triangle

Groundspeed, heading, and time en route for any flight can be determined by using the wind triangle, which is a graphic explanation of the effect of wind upon flight. Students are encouraged to learn this method, which only requires a calculator and simple math.

Steps in drawing the wind triangle.

  • Setting paper lengthwise, draw a horizontal line. The left end of this line will have a fulcrum, which can be designated with a small dot.
  • The horizontal line is the true course line. The true course of the flight can be appended to the line.
  • Determine the reported winds aloft on the route or leg of the flight.
  • Place a protractor, plotter, or E6B wheel over the fulcrum.
  • Draw a wind line by drawing a line from the fulcrum. The angle of the line will be the difference between the true course and the reported wind.
  • This line must be angled on the side of the true course line where the wind is from. It may help to draw a small arrow at the far end of the true course line representing the wind.
  • If the reported wind is a headwind, the wind line will extend away from the true course line. If the reported wind is a tailwind, the wind line will extend in the same direction as the true course line.
  • Mark the wind velocity with a point on the wind line, using units equivalent to the wind velocity (e.g., 10 miles on a plotter to represent 10 knots of wind).
  • Determine the airplane's true airspeed. For a practice problem, 90 knots is a common TAS for small airplanes.
  • From the velocity point on the wind line, draw a line that connects to the true course line in units that correspond to the airplane's true airspeed. This is the airspeed/WCA line.
  • The difference in angle between the true course line and the airspeed/WCA line is the drift angle, also called the wind-correction angle.
  • Measure the true course line from the fulcrum to where it intersects with the airspeed/WCA line. The units correspond to the groundspeed.
  • Place a protractor, plotter, or E6B wheel over the true course line, aligning the compass with the true course.
  • Determine the heading by applying the wind-correction angle into the wind (i.e., if the wind is from the left, subtract the WCA from the true course. If the wind is from the right, add the WCA to the true course.)
  • An E6B or flight calculator can be used to apply the groundspeed to the course distance, resulting in time en route.

Flight Calculations

These categories are easily solved with an electronic E6B.

Time = Distance/Groundspeed (T=D/G)
To find time in flight, divide distance by groundspeed.

Distance = Groundspeed x Time (D=GSxT)
To find a distance covered, multiply groundspeed (miles per minute) by time (minutes).

Groundspeed = Distance / Time
To determine groundspeed, divide the distance flown by the duration of flight.

Creating a Navigation Log

Jeppesen Navigation Log.

Foreflight and other flight planning applications can create navigation logs rapidly, and the FAA has updated the Airman Certification Standards (ACS) to permit private pilot applications to present a flight plan using an EFB app (such as Foreflight) rather than traditional methods. However, applicants are likely to have faster, smoother oral exams when the examiner's proposed cross-country flight is presented on an aviation sectional with a navigation log, since the larger form-factor of paper will make the problems and solutions highly visible.

The most common navigation log templates are from Jeppesen and ASA, with only minor variations.

The planning process should begin with departure and arrival airports.

The route of flight should then be examined for flight legs, which may bring the flight over diversion airports and landmarks, and away from hostile terrain, busy airspace, and special-use airspace. Route selection is not an exact science is is a matter of the pilot's best judgment.

Measure each leg using an aviation plotter. Enter the value in the "Dist." column for each leg, using the first box ("Leg"). All legs can then be totaled, with the flight's total distance entered in the box at the top of the column, and/or the box in the "Totals" row.

The flight's cruising altitude should be selected, based on the hemispheric rule, as well as the preferred glide range. (The aircraft's flight manual will have glide information, or use AGL altitude x 3 and convert the result to miles.)

After the cruising altitude is selected, Top of Climb and Top of Descent should be included as checkpoints.

The navigation log can then be filled in with all checkpoints.

Finding Compass Heading: Where the Nose Goes

The middle section of the Jeppesen navigation log is used to determine the aircraft's compass heading, which is done with the multi-step process previously outlined in this chapter.

Use the azimuth on an aviation plotter to determine the true course (TC) for each leg. This is the aircraft's intended track when referencing lines of latitude and longitude. Note that the TC is entered on the Jeppesen log in the "TC" column. (There is a prominent "Course" column, which could be used for the TC, but probably is better used for the compass heading.)

Use a weather source, such as AviationWeather.gov, to determine winds aloft. For training purposes, any wind value can be used, such as "360 at 10." (Winds are always reported in true, not magnetic.)

To find the x-value wind correction angle (WCA), use an E6B. Inputs are true course, wind direction, and wind velocity. This value (which is expressed as plus or minus/left or right) is then entered for each leg in the same column as TC, in the second box of that column.

To find the x-value true heading, use the inputs TC and WCA. Add or subtract WCA from TC and enter the result in the true heading box for each leg, which is the next column.

To determine the magnetic variation (Var) along the route, refer to isogonic lines on the aviation chart. This value (which is expressed as plus or minus/left or right) is then entered for each leg in the same column as TH, in the second box of that column.

To find the x-value magnetic heading (MH), use the inputs TH and Var. Add or subtract Var from TH and enter the result in the magnetic heading box for each leg, which is the next column. (Remember that "East is least and west is best.")

To determine the compass deviation (Dev) along the route, refer to the aircraft's compass deviation card. This value (which is expressed as plus or minus/left or right) is then entered for each leg in the same column as MH, in the second box of that column.

To find the x-value compass heading (CH), use the inputs MH and Dev. Add or subtract Dev from MH and enter the result in the compass heading box for each leg, which is the next column.

Time and Distance

In order to determine the time it will take to reach the destination, the airplane's true airspeed is required.

Typically, the aircraft's flight manual will offer indicated airspeeds (IAS) for various power settings. A power setting should be selected for the flight.

The flight manual should present calibrated airspeeds (CAS) for indicated airspeeds. The Jeppesen nav log only offers one "CAS" box.

True Airspeed (TAS) can be determined using the flight manual or an E6B. This is then entered in the "TAS" column or for each leg.

Airspeed used from departure to top-of-climb typically is the aircraft's Vy airspeed. The true airspeed will vary, depending on the difference between the departure airport's field elevation and the aircraft's cruising altitude. Consult the flight manual to determine if either a specific or average airspeed can be for the nav log's climb leg.

Top of Climb

Finding time and distance to top-of-climb can be done with an E6B. The inputs are groundspeed, climb-rate in feet per minute, and vertical distance between the departure airport and cruising altitude.

For example, if the aircraft will climb at an average of 500 feet per minute from sea level to 7,500 feet, then the time to top of climb is 15 minutes (7,500 ÷ 500).

If the aircraft will climb with a groundspeed of 80 knots, then the aircraft will travel 20 miles in 15 minutes, which is the distance to top of climb. This can be done with a manual E6B or the "leg time" function on an electronic E6B.

For straight-up math, convert the groundspeed from hours to minutes (80 knots ÷ 60 minutes = 1.3 miles per minute)…
multiply the velocity in minutes by the leg-length (1.3 miles per minute x 15 = 19.5 minutes)…
to determine that the time to TOC is 19:30, or about 20 minutes.

Descent planning

The navigation log's Top of Descent (TOD) checkpoint should include a visual reference on the sectional, if one is available.

To select Top of Descent, determine the vertical distance between the cruising altitude and the traffic pattern altitude. Multiply this value by three and convert to miles. Add two miles for the traffic pattern and pattern entry leg.

For example, if an aircraft will descent from 7,500 feet to a traffic pattern altitude of 1,000 feet, the vertical distance is 6,500. Multiply by 3 to get 19,500, or 19.5 miles. Add 2 to get 21.5 miles.

This can then be rounded up. The TOD should be 22 miles from the airport.

The pilot can use the cruise airspeed for descent or select a different airspeed, consulting the aircraft's flight manual. This should be factored to True Airspeed (TAS) and averaged for the descent. This average airspeed should be entered on all legs from TOD to the destination.

Time en Route

To find the x-value Groundspeed, use the inputs wind direction, wind velocity, and true airspeed (TAS). This is quickly accomplished with an electronic E6B. Enter the groundspeed for each leg in the "GS" column, using the first box for each leg, "Est." or estimated. Leave the second box in this column for each leg blank, , "Act." or actual. Each leg's actual groundspeed can be calculated and entered during the flight.

To find the x-value Leg Time, use the inputs groundspeed and distance. Enter the values for each leg in the first box of the "ETE" (estimated time en route) column. Leave the second box in this column for each leg blank, , "ATE." or actual time en route. Each leg's actual time can be entered during the flight.

When a "time off" value is known (or established for training purposes), this can be entered in the "Time Off" box and the "ETA" (estimated time of arrival) can be entered for each leg, while the "ATA" (actual time of arrival" can be entered during the flight.

Fuel Burn

Consult the aircraft's flight manual to determine the gallons per hour (GPH) required for each leg. Typically, the leg to Top of Climb will require more fuel than the cruise and descent legs.

To estimated the x-value fuel required for each leg, use a manual or electronic E6B. The inputs are GPH and leg time.

The aircraft's total usable fuel capacity can be used to determine how much fuel is estimated to remain at the end of each leg, which can be entered in the "REM" box in the fuel column.

Don't forget that VFR operations require a 30-minute fuel reserve during daylight operations and a 45-minute reserve at night.

Commercial Pilot & Flight Instructor Test Questions

Which statement about longitude and latitude is true? Lines of longitude cross the equator at right angles..

The angular difference between true north and magnetic north is magnetic variation.

When converting from true course to magnetic heading, a pilot should subtract easterly variation and right wind correction angle.
— When converting a true course to a true heading, subtract a left wind correction angle or add a right wind correction angle (compass headings increase when read to the right). When converting from a true heading to a magnetic heading, "east is least, west is best."

When converting from a magnetic course to a true course, a pilot should add easterly variation regardless of heading.
— When converting from a magnetic course to a true course, add easterly variation or subtract westerly variation. "East is least, west is best" in reverse.

When converting from a true heading to a true course, a pilot should subtract right wind correction angle.
— This is in reverse of the typical flight planning steps, since true course becomes true heading when wind is applied. The formula for determining a compass course is written on the manual E6B.

When planning a distance flight, true course measurements on a Sectional Aeronautical Chart should be made at a meridian near the midpoint of the course because the angles formed by lines of longitude and the course line vary from point to point..
— Meridians of longitude are straight, non-parallel lines that meet at the north pole. Along a long route, their angles will curve, and thus vary. "Isogonic lines" are distractors.

When operating under VFR at more than 3,000 feet AGL, cruising altitudes to be maintained are based upon the magnetic course being flown.
— "True course" and "magnetic heading" are the distractors.

According to 14 CFR Part 91, what is the appropriate VFR cruising altitude, when above 3,000 ft. AGL, for a flight on a magnetic course of 090°? 5,500 ft. (91.159)

Course measurements on a Sectional Aeronautical Chart should be made at a meridian near the midpoint of the course because the angles formed by lines of longitude and the course line vary from point to point. (Dead Reckoning, PHAK)

Transponder

When making routine transponder code changes, pilots should avoid inadvertent selection of which codes? 7500, 7600, 7700.

Which transponder code should the pilot of a civilian aircraft never use? 7777.

VOR Navigation

When checking the course sensitivity of a VOR receiver, how many degrees should the OBS be rotated to move the CDI from the center to the last dot on either side? 10° to 12°.

Which statement is true concerning the operation of DME? DME coded identification is transmitted once for each three or four times that the VOR coded identification is transmitted.

When using VOT to make a VOR receiver check, the CDI should be centered and the OBS should indicate that the aircraft is on the 360 radial.

When using a VOT to check the accuracy of a VOR receiver, with the CDI centered, what should the OBS indicate if no error exists? 180° TO, 360° FROM.

The three individual navigation services provided by a VORTAC facility are VHF VOR azimuth, UHF TACAN azimuth, and UHF TACAN distance information.
— TACAN operates in the UHF band.

When navigating using only VOR/DME based RNAV, selection of a VOR NAVAID that does not have DME service will result in loss of RNAV capability.

Misc.

What equipment code would you enter in item 10 of an ICAO flight plan for an aircraft with a standard IFR package including a VHF radio, VOR, and ILS receiver; an IFR-approved GPS; and a mode C transponder? SG/C.
— S = standard IFR package (VHF radio, VOR, ILS receiver). G = IFR-approved GPS. C = mode C transponder.

How long will a Flight Service Station hold a VFR flight plan past the proposed departure time? One (1) hour.

How much time do you have to close a VFR flight plan before search and rescue procedures are initiated? One-half hour after your ETA.

ATC advises traffic 12 o'clock. This advisory is relative to your ground track.

Which button/feature provides information on the closest airport at any given time? Nearest.

Flight Calculations

A note on story problems: These are among the most intimidating questions on FAA knowledge tests, and a good strategy is to skip over them during a first pass. Answer the easiest questions first and then complete these more complex questions at the end.

Each question asks that you locate one or more 'X' values. Note these on your scratch-paper. There may be additional 'X' values that you will need to identify along the way to solve the variables required by the question.

If the answer requires an airspeed value, note that airspeed will be calculated as indicated airspeed to true airspeed to groundspeed. It's a good idea to write "IAS > TS > GS" at the top of each diagram to recall this process. (Questions that ask for an indicated airspeed will work in the opposite direction.)

If the answer requires a heading or track, recall that flight planning goes from true course to true heading (correcting for wind) to magnetic heading (correcting for variation) and then compass heading (correcting for deviation). A few story problems will provide magnetic variation, while very few (or none) provide compass deviation. Most of the problems ask the test-taker to solve for heading and groundspeed.

Next, create a graphic representation that includes all of the provided variables. This typically will include a course line and a wind line. Other provided values should be added to the diagram, such as altitude, airspeed, temperature, distance, etc. While the wind may be from the left or right, it doesn't matter on which side of the course-line the wind line is placed.

Using an electronic E6B, search for the calculations that will identify the missing variables using the known data. When known data has been used to find a missing variable, the known variable can be crossed off the diagram, which reduces complexity. Data on the diagram will start to disappear, while the X-values will fill in, including the X-values required to answer the question correctly.

(I recommend the latest model of Sporty's electronic E6B, which can be used during proctored tests. I am not selling any, and this is not a paid endorsement. Also, it has a nice backlight and auto-shutoff.)

Find magnetic heading and groundspeed.

GIVEN:
True course: 193°
Variation: 8°E
Indicated airspeed: 120 knots
Ambient temperature: 10°C
Pressure altitude: 6,500 feet
Forecast wind: 160° at 20 knots

Under these conditions, the magnetic heading and groundspeed would be approximately 180° and 117 knots.

This question covers VFR flight planning at the Private Pilot level. It should present no difficulty for anyone taking a Commercial Pilot, Ground Instructor, or Flight Instructor exam.

A true course and indicated airspeed are provided. The X-factors are true airspeed, groundspeed, true heading, and magnetic heading.

The problem first requires a known true airspeed. Using the Sporty's electronic E6B, select "Speed > Plan TAS." Enter a pressure altitude of 6,500 and a temperature of 10° C. For calibrated airspeed, use the indicated airspeed 120 knots. The true airspeed is 134.1 knots.

To determine the true heading, use the E6B's "Heading/Groundspeed" function, entering a wind direction of 160°, a wind speed of 20 knots, and a course of 193°. The calculator will automatically enter 134.1 knots for the true airspeed. The groundspeed is 116.9 knots, and the true heading is 188°.

To determine the magnetic heading, subtract magnetic variation ("east is least") from the true heading: 188° – 8° = 180°.

GIVEN:
Departure path: Straight out
Takeoff time: 10:30 DST
Winds during climb: 180° at 30 kts
True course during climb: 160°
Airport elevation: 1,500 ft
True airspeed: 125 kts
Rate of climb: 500 ft/min

What would be the distance and time upon reaching 8,500 feet MSL? 23 NM and 1044 DST.

The stated X-factors are distance and time to 8,500. Two additional X-factors, not stated, are groundspeed and the vertical distance to top-of-climb.

Draw a course line with 160° and a wind line of 180° at 30 kts. At the departure end, note 1030 DST and 1,500 MSL. At the terminal end, note 8,500 MSL. On the course line, note 125 kts. and 500 FPM.

The vertical distance to top-of-climb can be determined by subtracting 1,500 from 8,500 (7,000), which crosses out the MSL variables. That one's easy.

Use the Sporty's electronic E6B's "Heading/Groundspeed" function to determine a groundspeed of 96.4 knots, which crosses out the heading, wind, and airspeed values.

Time to top-of-climb can be determined by dividing 7,000 by 500. It's 14 minutes, which crosses out the FPM variable.

Add the 14 minutes required to reach top-of-climb to the 10:30 departure time. Arrival time at top-of-climb is 10:44.

Use the "Distance Flown" function to determine 22.5 miles, which crosses out the groundspeed and time to top-of-climb values.

GIVEN:
Usable fuel at takeoff: 36 gal
Fuel consumption rate: 12.4 gal/hr
Constant groundspeed: 140 kts
Flight time since takeoff: 48 min

According to 14 CFR Part 91, how much farther can an airplane be flown under night VFR? 189 miles.

Draw a course line with three segments. Note 140 knots above the course line, and both 36 gallons and 12.4 GPH at the start of the course line.

The left and right segments have known time values: 0:48 and 0:45 (the legal fuel minimum for night operations). The center segment's time and fuel available are X-factors.

The fuel used during the known legs can be determined with the Sporty's E6B's "Required > Fuel" function. In this case, segment one requires 9.9 gal. while segment three requires 9.3 gallons. Thus, the known fuel is 19.2 gallons, which means the unknown fuel (36 − 19.2) is 16.8 gallons, which fills one of the two X-factors in segment two.

To determine the time the airplane will spend in segment two, use the "Flight > Endurance" function to factor 16.8 gallons used at a rate of 12.4 GPH, which returns 1:21.

Finally, the question requires to solve how far the airplane can travel in segment two. Use the "Flight > Distance Flown" function to factor 140 knots for 1:21 to determine a distance of 189.7 miles.

On a cross-country flight, point A is crossed at 1015 local. Using the information below, what is your expected arrival time at point B? 1029 local.

Distance between A and B: 32 NM
Forecast wind: 240° at 25 kts
Pressure altitude: 5,500 ft
Ambient temperature: 5° C
True course: 100°
Indicated airspeed: 110 knots.

The various "Point A / Point B" questions ask users to work through a series of airspeeds. An initial airspeed is provided, and the answer to the question will require a missing airspeed.

In this case, the process is indicated airspeed > true airspeed > groundspeed. This is straightforward enough, since cross-country flight planning works in this direction to determine when the aircraft will arrive at a destination.

The X-factor is the arrival time at point B. However, we can see that the question actually is asking how long it will take the airplane to fly 32 miles. Or, it's actually asking how fast the airplane is flying over the ground given the indicated airspeed and winds aloft.

Using Sporty's electronic E6B, select "Speed > Plan TAS." Enter pressure altitude 5,500 and temperature 5° C. For calibrated airspeed, enter the indicated airspeed of 110 knots. The result is a true airspeed of 119.6 knots.

Next, select "Heading/Groundspeed." Enter wind direction, wind speed 25, course 100°. The calculator will automatically add 119.6 knots of true airspeed. The result is a groundspeed of 137.7 knots (with a heading of 108°).

Finally, we need to know how long it will take to cover 32 miles with a groundspeed of 137.7 knots. Select "Flight > Leg Time." Enter 32 miles. The calculator will automatically enter a groundspeed of 137.7 knots. The answer is 13:57, or about 14 minutes. (This last step can be done quickly with a manual E6B's time & distance function.)

All that's left is the arrival time at Point B. We left point A at 10:15, so we will arrive at point B at 10:29.

On a cross-country flight, location A is crossed at 1015 and arrival at location B is expected at 1030. What indicated airspeed is required to reach point B on schedule? 103 knots.

Distance between A and B: 30 NM
Forecast wind: 220° at 20 kts
Pressure altitude: 6,500 ft
Ambient temperature: 10°C
True course: 110°

This task works in the other direction from the previous problem. It requires groundspeed > true airspeed > indicated airspeed. This is the inverse of cross-country flight planning, where indicated airspeed is corrected for altitude and temperature to determine true airspeed, and then corrected for wind to determine groundspeed.

Note that the question uses the word "required." All of the speed problems are "required" problems, and two E6B functions will be "required" functions on the Sporty's calculator.

As always, identify the X-factor and all given variables. In this case, X is indicated airspeed.

By drawing a course line on a piece of paper with locations A and B, we can note that they are 15 minutes apart, and that the distance between the two is 30 NM. Therefore, in order to travel 30 NM over the ground in 15 minutes, we will need to determine a required groundspeed. This can be done by pairing 15 minutes and 30 miles on a manual E6B and checking the velocity at the speed index. Sporty's electronic E6B has a "Speed > GS" function that does the same thing. The required groundspeed is 120 knots.

The groundspeed must be maintained regardless of wind conditions, so we need to know how fast the airplane must travel through the air, compensating for wind, in order to maintain the required rate over the ground. Thus, our next step is to determine the airplane's required true airspeed. Sporty's electronic E6B has a "Required > TAS" function where we can enter wind direction, wind speed, course, and groundspeed. This results in a true airspeed of 114.7 (and a heading of 119°). Using a manual E6B will be a longer process for most people.

But we're still looking for an indicated airspeed, not a true airspeed. The "Required > CAS" function on Sporty's electronic E6B will work, even though it's determining calibrated airspeed and not indicated airspeed (typically there's only a small differential between the two). If we enter a pressure altitude of 6,500, a temperature of 10° C, and a true airspeed of 114.7 knots, our calibrated airspeed will be 102.7 knots, which will be very close to one of the three possible answers on the test.

GIVEN:
Distance 200 NM
True course 320°
Wind 215° at 25 kts
True airspeed 116 kts
Rate of fuel consumption 19 gal/hr

What would be the approximate groundspeed and amount of fuel consumed? 120 knots; 31.7 gallons.

The X-factors are groundspeed and fuel burned.

We don't need to convert indicated/calibrated airspeed to true airspeed, since that's already been provided. We can use the true airspeed, course, and wind information to get a groundspeed with our electronic E6B's "Heading/Groundspeed" function. With a wind direction of 215 and a wind speed of 25, a course of 320, and a true airspeed of 116, our groundspeed is 119.9 knots (with a heading of 308°). That's about 120 knots, and it's one of our X-factors.

Now that we know how fast we are going over the ground, we can determine how long it will take to travel 200 NM using the "Flight > Leg Time" function. Enter a distance of 200. The calculator will automatically enter a groundspeed of 119.9 knots. The leg time is 1:40:05 — another X-factor.

Now we need our final X-factor, fuel burn. Select "Required > Fuel." The calculator will automatically enter a leg time of 1:40:05. Enter 19 gallons per hour (FPH). We will burn 31.7 gallons of fuel on the leg.

Given a distance off course of 9 miles, a distance flown of 95 miles, and a distance to fly of 125 miles, the total correction angle to converge at the destination would be 10°.

This is determined using two quotients, each multiplied by 60, and then combined. It's best to have this formula memorized just before the test and make it one of the things to write down on scratch paper before looking at questions.

The provided variables are distance flown, distance remaining, and distance off course. The X-factor is the correction angle that will provide a new course.

The miles off course needs to be divided by both the distances flown and remaining, which will provide quotients smaller than one (1):

  • 9 ÷ 95 = 0.094
  • 9 ÷ 125 = 0.072

Multiply the results by 60, so that we have factors greater than one (1):

  • 9 ÷ 95 = 0.094 x 60 = 5.64
  • 9 ÷ 125 = 0.072 x 60 = 4.35

Add the results to determine the total wind correction angle required to reach the destination: 9.99, or 10° into the wind.

How far will an aircraft travel in 2.5 minutes with a groundspeed of 98 knots? 4.08 NM.

How far will an aircraft travel in 3.5 minutes if its groundspeed is 55 knots? 3.2 miles.

Solving these problems with a manual E6B requires a method called "short time." With the Sporty's electronic E6B, "Flight > Distance Flown" is a two-step function. Enter the groundspeed and time to return the X-factor of distance.

Don't forget that time variables must be entered starting with hours, then minutes, then seconds, separated by colons. Thus on the calculator's screen it will appear as "00:03:30".

Given a true course of 325°, a true heading of 345°, a true airspeed of 90 kts, and a groundspeed of 100 kts, wind direction and speed are 082° and 34 knots.

This question expects that you will be able to use your airplane as a weather-sensing device, with full knowledge of your true course, true heading, true airspeed, and groundspeed from the instrumentation on the flight deck. It's not a practical question, but it does challenge pilots to run an equation in the right direction.

The apparent purpose of the question is to get test-takers to use the wind-side of the manual E6B. However, the "Wind > Wind" function on Sporty's electronic E6B will provide the solution quickly: 081.6° and 34.4 knots.

If a true heading of 135° results in a ground track of 130° and a true airspeed of 135 knots results in a groundspeed of 140 knots, the wind would be from 245° and 13 knots.

Same type of question, easily solved. Note that this question uses the term "ground track," whereas the previous question used "true course." Sporty's electronic E6B's "Wind > Wind" function uses "CRS" for either one of these terms. Both questions use the term "true heading," which is "HDG" in the function.

If fuel consumption is 16.2 gallons per hour and groundspeed is 155 knots, how much fuel is required for an aircraft to travel 530 NM? 56 gallons.

The X-factors are time-en-route and fuel required.

Start with the "Flight > Leg Time" function on the Sporty's electronic E6B. Enter the distance (530 NM) and the groundspeed (167 knots) to determine that the aircraft will cover the route in 3:25:10.

Select "Required > Fuel." The calculator will automatically enter 3:25:10 for the time-factor. Enter 16.2 gallons per hour (FPH). The airplane will require 55.4 gallons of fuel.

If a wingtip bearing change is 10°, the time between bearing change is four minutes, and the rate of fuel consumption is 11 gallons per hour, how many gallons of fuel will be required to fly to the station? 4.4 gallons.

The X-factors are the time to the station and the fuel required.

Recall that the time to a station is greater than the time it takes to traverse 10° of radials by a factor of six (6).

Therefore, if it takes four minutes to traverse 10° of radials, it will take 24 minutes to reach the station — 6(4) = 24.

Select "Required > Fuel" on the Sporty's electronic E6B. Enter a time of 00:24:00 and gallons per hour (FPH) of 11. The required fuel is 4.4 gallons.

If a wingtip bearing change is 10°, the time between bearing change is five minutes, and your groundspeed is 110 knots, what is your distance from the station? 70 miles.

The X-factors are the time and the distance to the station. The groundspeed variable is provided.

Again, the time to a station is greater than the time it takes to traverse 10° of radials by a factor of six (6).

Therefore, if it takes five minutes to traverse 10° of radials, it will take 30 minutes to reach the station — 6(5) = 30.

Using the "Flight > Distance Flown" function on the Sporty's electronic E6B, enter a groundspeed of 110 and a time of 00:30:00. The aircraft is 70 miles from the station.

Robert Wederquist   CP-ASEL - AGI - IGI
Commercial Pilot • Instrument Pilot
Advanced Ground Instructor • Instrument Ground Instructor

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