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.
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 semiannually 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
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.
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.
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. 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.
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.
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:
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.
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.
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 a 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.
Since sectional charts may be up to six months old, Aeronautical Chart Bulletins should be checked for major changes that have occurred since the last publication date of each sectional chart being used. These can be found as a subsection in the Chart Supplement.
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.
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.
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.
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.
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° of radials (crossing at a 90° angle), you are 6 minutes from the station. Memorize the formula as depicted below (which is not even remotely to scale). You can recall it as "60 V 360." You can write this depiction down on paper the moment the knowledge test starts.
This formula accepts variables:
To determine the distance to the station, determine how far you can travel at your current groundspeed, using the time-to-station 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:
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.
Time to NDB station
This is one just "T ÷ D." The bearing change value requires a unit of time expressed in seconds.
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."
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.
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.
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.
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
You can write this formula down on paper the moment the knowledge test starts (a sample problem is included here):
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.
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.
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:
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.
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.
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.
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)
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.
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.
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.
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. 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 at the top of 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.
Next, create a graphic representation that includes all of the provided variables. This typically will include a course line, a wind line, departure and terminal altitudes, airspeed, temperature, etc.
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 X-values above the diagram will fill in.
In many cases, test questions can require locating as many as three variables — i.e., determine a groundspeed, which is used to determine a leg time, which is used to determine the amount of fuel used. However, while flight-data story problems are complex at first glance, they are straightforward "find X" tasks with the use of an electronic E6B.
Departure path: Straight out
Takeoff time: 1030 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.
— This is a good question to practice a sketched diagram. The stated X-factors are distance and time to 8,500. Two additional X-factors, not stated, are groundspeed and altitude increase. 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.
Altitude increase can be determined by subtracting 1,500 from 8,500 (7,000), which cancels out the MSL variables. Use the HDG/GS function on an electronic E6B to determine a groundspeed of 96.4, which cancels out the heading, wind, and airspeed values. Time to altitude can be determined by dividing 7,000 by 500 (14 minutes), which cancels out the FPM variable. Use the "Distance Flown" function to determine 22.5 miles, which cancels out the groundspeed and time to altitude values.
These questions seem like a lot to process, but identifying all known and unknown factors, and then replacing the known factors with the unknown, is a reliable process.
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.
— Another good one for a sketched diagram. Draw a course line with three segments. Note 140 kts. above the course line, and both 36 gal. 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 an electronic E6B's 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 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 Distance Flown function to factor 140 kts for 1:21 to determine a distance of 189.7 miles.
While cruising at 135 knots and on a constant heading, the ADF needle decreases from a relative bearing of 315° to 270° in 7 minutes. The approximate time and distance to the station being used is 7 minutes and 16 miles.
While maintaining a constant heading, a relative bearing of 10° doubles in 5 minutes. If the true airspeed is 105 knots, the time and distance to the station being used is approximately 5 minutes and 8.7 miles.
— This appears to be an ADF question.
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°.
— Effect of Wind, PHAK
Given a true course of 345°, a true heading of 355°, a true airspeed of 85 kts, and a groundspeed of 95 kts, wind direction and speed are 113° and 19 knots.
— Effect of Wind, PHAK
How far will an aircraft travel in 2-1/2 minutes with a groundspeed of 98 knots? 4.08 NM.
How far will an aircraft travel in 3-1/2 minutes if its groundspeed is 55 knots? 3.2 miles.
— Determine that 55 knots is 0.91 of 60 knots/one mile, and thus 3.5 x 0.91 = 3.208. Use Or use "Distance Flown" on an electronic E6B. This requires "short time" on a manual E6B.
If a true heading of 230° results in a ground track of 250° and a true airspeed of 160 knots results in a groundspeed of 175 knots, the wind would be from 135° at 59 knots..
— Place the groundspeed under the grommet (175 kt.). Place the ground track (250°) under the true index. Locate the true airspeed on the true airspeed arc (160 kt.). Mark a 20° left deviation (230° - 250° = Ð20°). Move the mark under the true index. Wind is from 135° (under the true index). The mark is now at 234 kt. — or +59 kt.from the grommet.
If fuel consumption is 15.3 gallons per hour and groundspeed is 167 knots, how much fuel is required for an aircraft to travel 620 NM? 57 gallons.
— With a flight calculator, find leg time, then fuel required. The result is 56.8 gallons.
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 246° and 13 knots.
— This can be deduced with the "HDG/GS" function on an electronic E6B by testing all three answers, but note that the scenario provides a ground track, while the E6B will provide a wind-correction angle. The WCA must be deducted from the heading to confirm the uncorrected drift.
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, it will take 4.4 gallons of fuel to fly to the station.
— First, determine that the time to the station is 24 minutes (4*60/10=24). Then, divide 11 by roughly one-third (20 min. = 1/3 hour) to arrive at 3.63. Interpolate to arrive at 4.4 gallons over 24 minutes.
Determine the wind direction and speed. 113° and 19 knots.
On a cross-country flight, point X is crossed at 1015 local. What is your expected arrival time at point Y? Use the following information to determine your ETA.
Distance between X and Y = 32 NM
Forecast wind = 240° at 25 kts
Pressure altitude = 5,500 ft
Ambient temperature = +05°C
True course = 100°
The indicated airspeed is 110 knots.
Answer: 1029 local.
— With a flight calculator, find true airspeed, then groundspeed, then leg time.
Pressure altitude 12,000 ft
True air temperature +50 °F
From the conditions given, the approximate density altitude is 14,130 feet.
True course: 345°
True heading: 355°
True airspeed: 85 kts
Groundspeed: 95 kts
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.
True course: 238°
Indicated airspeed: 160 kts
Ambient temperature: 15°C
Pressure altitude: 8,500 ft
Forecast wind: 160° at 25 kts
Under these conditions, the magnetic heading and groundspeed would be approximately 233° and 171 knots.
On a cross-country flight, point A is crossed at 1500 hours and the plan is to reach point B at 1530 hours. Use the following information to determine the indicated airspeed required to reach point B on schedule.
Distance between A and B: 70 NM
Forecast wind: 310° at 15 kts
Pressure altitude: 8,000 ft
Ambient temperature: –10°C
True course: 270°
The required indicated airspeed would be approximately xxxxxx knots.
— A tough question. Groundspeed to reach point B is 140 kt (obvious). With the wind, this requires a 152 kt true airspeed. Corrected for pressure and altitude, the indicated airspeed is 137 kt. This is a difficult problem to solve with an electronic E6B, since it works backwards. It is easier to solve with a manual E6B.