Study guide
15.3 Variation, Deviation, Wind Triangle, and E6B
FAA Private Pilot — Airplane PAR
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1 Introduction & Exam Overview
1.1 Current Exam Facts 1.2 ACS Codes, the AKTR, and How to Use This Guide
2 Pilot Qualifications & Medicals
2.1 Eligibility, Training, and Knowledge-Test Authorization 2.2 Private Pilot Privileges and Limitations 2.3 Medical Certificates, Duration, and Disqualification 2.4 BasicMed (14 CFR 61.113(i) and Part 68)
3 Airworthiness, Documents & Currency
3.1 Required Pilot and Aircraft Documents 3.2 Inspections, Airworthiness Directives, and Preventive Maintenance 3.3 Inoperative Equipment and 91.213 3.4 Recent Flight Experience and the Flight Review
4 14 CFR Part 91 Operating Rules
4.1 Right-of-Way, Minimum Safe Altitudes, and Speed Limits 4.2 VFR Cruising Altitudes, Altimeter Settings, and Oxygen 4.3 Fuel Requirements, Transponder, ADS-B, and ELT 4.4 NOTAMs, TFRs, and Accident/Incident Duties
5 National Airspace System
5.1 Class A, B, and C Airspace 5.2 Class D, E, and G Airspace and VFR Weather Minimums 5.3 Special Use Airspace 5.4 Other Airspace, TFRs, TRSA, ADIZ, and SFRA
6 Aviation Weather Theory
6.1 Atmosphere, Pressure, Temperature, and Density 6.2 Stability, Clouds, and Moisture 6.3 Air Masses and Fronts 6.4 Wind, Jet Stream, and Local Wind Systems
7 Weather Hazards
7.1 Thunderstorms and Convective Weather 7.2 Structural Icing, Frost, and Carburetor Ice 7.3 Fog, Low Ceilings, and Visibility 7.4 Wind Shear, Microbursts, Turbulence, and Mountain Waves
8 Weather Products & Briefings
8.1 METAR Decoding 8.2 TAF and Graphical Forecast Products 8.3 PIREPs, AIRMET, SIGMET, Convective SIGMET, and Winds Aloft 8.4 Briefings and Go/No-Go Decisions
9 Principles of Flight
9.1 Four Forces and Lift Production 9.2 Angle of Attack, Critical AoA, and Stalls 9.3 Drag, L/D, and Ground Effect 9.4 Axes, Stability, and Flight Controls
10 Maneuvering Flight, Stalls & Spins
10.1 Load Factor, Bank Angle, and Stall Speed 10.2 Left-Turning Tendencies 10.3 Slow Flight, Power-On/Off Stalls, and Spin Awareness 10.4 Steep Turns and Ground-Reference Maneuvers
11 Powerplant, Fuel & Electrical Systems
11.1 Reciprocating Engines, Mixture, Detonation, and Preignition 11.2 Ignition, Magnetos, Carburetor vs Fuel Injection 11.3 Fuel Grades, Contamination, and Fuel-System Management 11.4 Electrical System and Alternator Failure
12 Flight Instruments & Avionics
12.1 Pitot-Static Instruments and Blockage Errors 12.2 Gyroscopic Instruments, Vacuum Failure, and Magnetic Compass Errors 12.3 Engine Instruments, Transponder Modes, and Basic Avionics
13 Aircraft Performance
13.1 Pressure Altitude, Density Altitude, and Performance Effects 13.2 Takeoff and Climb Performance 13.3 Cruise, Descent, and Landing Performance 13.4 Wind, Gradient, Surface, and Crosswind Component
14 Weight and Balance
14.1 Weight-and-Balance Principles 14.2 Moment, CG, and Sample Computations 14.3 Forward and Aft CG Effects 14.4 V-Speeds, Markings, and Limitation Placards
15 Charts, Pilotage & Dead Reckoning
15.1 Sectional Chart Symbology and Airspace Depiction 15.2 Pilotage and Dead Reckoning 15.3 Variation, Deviation, Wind Triangle, and E6B 15.4 VFR Cross-Country and Fuel Planning
16 Radio Navigation, Lost Procedures & Airport Operations
16.1 VOR Navigation 16.2 GPS, RAIM, and Radar Services 16.3 Lost Procedures and Diversion 16.4 Communications, Light-Gun Signals, Lighting, and Traffic Patterns
17 Aeromedical Factors
17.1 Hypoxia, Hyperventilation, and Carbon Monoxide 17.2 Spatial Disorientation, Illusions, and Vision 17.3 Scuba-to-Flight, Alcohol/Drugs, and IMSAFE
18 ADM, Night Operations & Emergencies
18.1 ADM, Hazardous Attitudes, PAVE, and DECIDE 18.2 Night Operations and Night Illusions 18.3 Emergency Descent, Engine Failure, and System Malfunctions 18.4 Survival Gear, ELT, and Forced-Landing Considerations
19 Preflight Procedures & Airport Ground Operations
19.1 Preflight Assessment, Airworthiness Determination, and the Preflight Inspection 19.2 Flight Deck Management, Passenger Briefings, and Engine Starting 19.3 Taxi Operations: Signs, Markings, Lighting, and Runway Incursion Avoidance 19.4 Before-Takeoff Check, After-Landing, and Securing the Airplane
20 Class-Specific Knowledge: Seaplane & Multiengine
20.1 Seaplane and Water Operations Knowledge 20.2 Multiengine Knowledge: VMC, VYSE, and Engine-Out Fundamentals
15.3 Variation, Deviation, Wind Triangle, and E6B
Key Takeaways Explain This Topic AI
True course is measured on the chart from true north. True heading is true course plus or minus wind correction. Magnetic heading is true heading plus or minus variation. Compass heading is magnetic heading plus or minus deviation (TVMDC).
East is least, west is best: when converting from true toward compass, subtract easterly variation or deviation and add westerly. Variation comes from the charted isogonic line; deviation comes from that airplane’s compass card.
A 90° wind of 20 knots on a 090° true course at 120 knots TAS requires about a 10° crab into the wind (true heading ≈ 100°) and a groundspeed of √(120² − 20²) ≈ 118 knots.
Time (hours) = distance ÷ groundspeed; fuel gallons = hours × gallons per hour. The E6B (manual or electronic) is only as good as the TAS, wind, and fuel-flow numbers you give it.
Last updated: August 2026
ACS PA.VI.A.K5 wants heading, speed, course, wind correction angle, time, and true airspeed. PA.I.D.K3a is the same math on the planning task. Compass turning and acceleration errors (ANDS / UNOS) were Chapter 12; this section is the preflight conversion from a true line on paper to a number you can fly.
True, magnetic, compass — TVMDC
The sectional is drawn to true north . The magnetic compass points at magnetic north , then the airplane’s own iron and radios tug it a few more degrees ( deviation ). The memory stack is TVMDC :
True → Variation → Magnetic → Deviation → Compass.
Going down the stack (true toward the compass you actually steer), east is least (subtract) and west is best (add) . Going back up the stack, reverse the signs.
Variation is the angle between true north and magnetic north. It is a location error. You read it from the isogonic line nearest the route (or interpolate between two lines). It is the same for every airplane over that spot.
Deviation is the angle between magnetic north and what this compass reads. It is an airplane error. You read it from the compass correction card in that cockpit, usually tabulated every 30°. It changes with heading and with which radios are on. There is no isogonic line for deviation.
Worked conversion. True heading 100° . Nearest isogonic line 7°E . Compass card on a 090° heading says 2°W (use the nearest tabulated heading).
Magnetic heading = 100 − 7 = 093° (east is least).
Compass heading = 093 + 2 = 095° (west is best).
If the variation had been 7°W, magnetic heading would have been 100 + 7 = 107°, then 107 + 2 = 109° compass. Students who apply variation to the course and then forget to apply it again after wind, or who apply the compass card to true heading, invent a 10-degree miss that the checkpoint will reveal 15 minutes later.
- Quantity Where it comes from Typical PAR trap
- True course (TC) Plotter on the sectional, true north Measuring from a VOR rose (magnetic) and calling it true
- Wind correction angle (WCA) Wind triangle / E6B Applying WCA to magnetic course before variation
- True heading (TH) = TC ± WCA Crab into the wind Crabbing with the wind because “the tail is blowing me left”
- Magnetic heading (MH) = TH ± variation Isogonic line Using last year’s remembered variation
Compass heading (CH) = MH ± deviation Compass card in this airplane Using a generic “2°E everywhere” or ignoring the card
The heading indicator is slaved to nothing in a typical trainer. Set it to the compass in straight, unaccelerated flight (the only time Chapter 12 says the compass is honest), then fly the heading indicator, and reset it about every 15 minutes.
Wind triangle — a full numeric example
If there is no wind, true heading equals true course and groundspeed equals TAS. There is almost always wind. PHAK’s wind triangle is three vectors: the airplane through the air (TAS along the heading), the air over the ground (wind), and the airplane over the ground (GS along the course).
Given: true course 090° , wind 180° / 20 knots (from the south at 20), TAS 120 knots .
The wind is 90° to the course — a pure right crosswind if you fly east. You crab into the wind, to the right (south).
Crosswind component = 20 × sin(90°) = 20 knots .
sin(WCA) = 20 / 120 = 1/6 ≈ 0.1667 .
WCA = arcsin(0.1667) ≈ 9.6° , which an E6B reads as 10° .
True heading = 090 + 10 = 100° .
Because the wind is exactly abeam the course, none of it is a headwind along the course, but the crab reduces the along-track component of TAS:
GS = √(TAS² − wind²) = √(120² − 20²) = √(14,400 − 400) = √14,000 ≈ 118.3 knots , which the E6B calls 118 knots .
Check: 120 × cos(9.6°) ≈ 118.3. Same number. A student who subtracts the entire 20 knots as a headwind (GS 100) or who adds it as a tailwind (GS 140) has not drawn the triangle. A student who crabs left to 080° will be blown north of course.
Apply the TVMDC numbers from above and the thing you actually steer is about 095° compass on this example, not 090, and not 100.
On the wind face of a mechanical E6B you place the wind dot upwind of the grommet by 20 knots, rotate the true course under the true index, and slide the card until the TAS 120 arc sits under the grommet. The dot’s left/right offset is the WCA; the number under the grommet is GS. An electronic E6B is the same triangle. If you enter magnetic wind into a true-course problem, or true wind into a magnetic-course problem, the box will still print a confident wrong heading. Winds aloft are true ; METARs are magnetic . Know which one you typed.
Time, speed, distance, and fuel flow
Once GS exists, the rest is the 60-to-1 arithmetic the E6B was built for:
- Time (hours) = distance (NM) ÷ GS (knots)
- Distance = GS × time
- GS = distance ÷ time
177 NM at 118 knots is 177 / 118 = 1.50 hours = 1 hour 30 minutes . At 8.0 gallons per hour that cruise burns 12.0 gallons before reserve. Section 15.4 adds 91.151 and climb fuel; do not stop at 12.0 and call the airplane legal.
TAS itself is not the airspeed indicator. Calibrated airspeed plus pressure altitude and temperature (the E6B true-airspeed window, or the POH cruise chart) produce TAS. Density altitude that raises TAS also raises true fuel flow on a normally aspirated engine for the same indicated power setting — PA.VI.A.K5d and PA.VI.A.K6 are why you open the POH instead of inventing “we always burn 8 gallons.”
PAR scenario: TC 090°, wind 180/20, TAS 120, variation 7°E, deviation 2°W. You should be able to write, without a personality, WCA 10° right, TH 100°, GS 118, MH 093°, CH 095°, and 177 NM in 1+30. If any one of those numbers is a guess, the checkpoint in 15.2 will be in the wrong place, and the 91.151 fuel number in 15.4 will be a guess too.