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Private Pilot License Written Exam – Navigation

Navigation is the third section of my study notes for the private pilot license written exam. There are 5 sections in the Sharper Edge Exam Guide, with some sections divided into various subsections:

  • Charts and Projections
    • Basic Definitions
    • Chart Properties
  • Useful Concepts
  • Weight and Balance
  • Radio Aids to Navigation
    • NDBs and ADFs
    • The VOR
    • Distance Measuring Equipment(DME)
    • GPS
    • Determining position using data from radio nav aids
    • Intercepting tracks in and outbound
  • Use of Performance Tables and Charts

Basic Definitions
(Sharper Edge questions 3,4,17,35,56,64,66,68 and 71)
Longitude and latitude are divided into degrees, minutes and seconds. North/south coordinates (latitude) come before east/west coordinates (longitude).

A meridian is a line running from pole to pole; it is half a great circle.

A rhumb line is a line that cuts lines of longitude at a constant angle. It is a line that crosses the earth at on a constant direction.

A great circle is the shortest way across the Earth, but it cuts each line of longitude at a different angle. A great circle has the same diameter and center as the Earth.

Variation is the difference between true north and magnetic north. True north stays in the same place. Magnetic north (and south) shift. Isogonals are lines of constant magnetic variation. Agonic lines are lines of zero magnetic variation.

Deviation is the difference between what your magnetic compass reads and what it should read. In other words, if you want to steer 180 degrees magnetic (south) you may have to steer 176 degrees on your particular compass. Compasses have deviation cards on them. Sometimes this is worded as the difference between magnetic heading and compass heading.

Basic Navigation Definitions Pop Quiz

Chart Properties
(Sharper Edge Questions 18,19,58,64 and 66)

The earth is a sphere, so its round and in three dimensions. Charts are flat and in two dimensions. That means that 2 dimensional maps distort reality. As From the Ground Up points out, there are four properties or elements to a chart (areas, shapes, bearings and distances), and keeping any one of them as correct and representative of reality as possible means distortion in another.

There are two types of projection used for aeronautical charts: Lambert’s Conformal Conic (based on placing a cone of paper over the earth) and the Transverse Mercator (based on putting the earth inside a roll of paper, and called transverse because the roll runs parallel with the equator.

Transverse Mercator is used for VTA charts. These are the small charts covering terminal areas. Transverse Mercator can represent distance quite accurately over a small scale. These are 1:250,000 scale.

Lamberts Conformal Conic are used for VNC charts and WAC charts. VNC charts are charts that cover larger areas of land. They have one area on the front and another on the back. They are 1:500,000 scale (1 inch = about 8 miles). WAC charts are World Aeronautical Charts, and cover even larger areas. They are 1:1,000,000.

The “conformal” part means that the angles between meridians (lines running from pole to pole) and the parallels on the chart conform with what they would be on the actual ground. The scale of distance on a Lamberts Conformal Conic chart distorts very little, which is why a Great Circle track, the shortest distance between two points on the earth, appears as a straight line. (See From The Ground Up Air Navigation section for a good explanation of this).

For differences between projections look back at basic definitions. A Great Circle track curves, in reality, along the curve of the earth and is the shortest distance between two points. It cuts each line of longitude at a different angle. On a Mercator chart the lines of longitude and latitude are parallel, but this is achieved at the cost of distorting distance. On a regular Mercator projection the distortion is largest near the poles – we know that the lines of longitude are actually closer together at the poles than at the Equator, but the Mercator projection makes them look the same distance apart. A Transverse Mercator projection turns the map 90 degrees. This reduces the distance distortion as the chart displays areas closer to the poles.

The point being that on Transverse Mercator projections lines of latitude and longitude are parallel. On smaller scale maps the distortion is minimal and the Transverse Mercator projection is quite accurate at depicting scale on relatively small geographic areas. That’s why it’s used for VTA charts. But, parallel lines also means that a Great Circle track, which cuts lines of longitude at a different angle, appears curved: keep cutting parallel lines of longitude at a different angle and you can’t have a straight line.

On a Lambert’s Conformal Conic Great Circle tracks look like straight lines (lines on longitude on Lambert’s Conformal Conic get closer to each other as they get closer to the poles while on a Transverse Mercator the lines of longitude run parallel).

Another way to put it is that a straight line on a Transverse Mercator chart is close to a rhumb line track.

On a VNC (which is Lambert’s Conformal Conic) a straight line most closely represents a Great Circle track.

Rhumb lines, which cut lines of longitude at a constant angle look straight on Transverse Mercator and curved on Lamberts Conformal Conic.

Always measure your intended track and magnetic variation at the middle of your route.

Chart Properties – Navigation Pop Quiz

Useful Concepts
(Sharper Edge questions 5,6,7,26,27,28,29,30,31,37,38,48,49,55,65,67,73,74,75,76,77,78,83 and 87)

Dead reckoning is navigation based on a known position together with wind, air and ground vectors to estimate a new position. You start from the known position, determine your ground speed and then use your heading and time at that ground speed to estimate where you are.

Double track error is a correction method to re-gain the correct track when you are less than halfway through the journey. Calculate the angle that you have drifted off track, then double that and correct your heading by that many degrees. If you’re flying a heading of 180 degrees and you’re 4 degrees off track, alter your heading by 8 degrees until you’re back on track.

If you’re more than halfway through the journey and you use this method you won’t regain your track until you’re past your destination.

Opening and closing angle method requires that you find the angle you’re off track from your starting point (the opening angle) as well as the angle between where you are and your destination (the closing angle). Use this if you’re more than halfway through the journey. Add the degrees of the opening and closing angle together and adjust your heading by that much.

Visual correction requires that you pick a landmark over your route. When you’re off route you fly to the landmark. If you can do all of this visually (i.e., you can see the landmark out the window because you’re not far off course) its very straightforward. If you can’t see the landmark but you know that a) you’re off course and b) you know where you are on the chart you can determine the heading required to fly to the landmark, and also determine how much you’ve drifted and correct for it.

For example, if you are unaware of a southerly wind that is making you drift north, but you determine that you’ve drifted north you can calculate the heading required to get to the landmark from the chart. If it requires you to steer 100 degrees on the chart you might determine that you’ve been blown north by a southerly wind which is going to continue to blow, requiring you to compensate for the drift and fly a heading of 106 degrees.

Distance, Speed and Time Calculations:

Distance = Groundspeed x Time
Groundspeed = Distance/Time
Time = Distance/Groundspeed
The two things you’ll get most easily are time and distance, which then gives you an accurate groundspeed. You need a watch and a chart with landmarks.

Fuel Burn and Endurance Calculations

Fuel used = GPH x Time
GPH = Fuel used/Time
Endurance = distance/fuel flow

For example:
2 hour flying uses 10 gallons of fuel (10/2=5 GPH)
5 GPH = 10 gallons used in 2 hours (2×5=10)
Distance/hour equals 200 nm/2 hours = 100 nm/hour
Endurance = fuel/gph (15 gallons/5GPH=3)

One in 60 Rule
If you drift 1 degree over 60 nm you will be 1 nautical mile off track.
5 degrees over 60 nm means 5 nms off track. Or, 5 degrees over 30 nm means 2.5 nm off track.

Or, 2.5 nm off track over 30 nm means 5 degrees off track.

Climb and Descent Calculations

Average rate of climb tells you how long it takes to get to altitude. 600 fpm to 3,000 feet = 3000/600 = 5 minutes. GPH while climbing = 5 gph = .5 gallons per minute. 5 minutes x .5 = 2.5 gallons.

True Airspeed From Indicated Airspeed
True airspeed increases about 1.5% over indicated airspeed each 1,0000′ below 20,000′ and by about 2% for every thousand feet over 20,0000′.

IAS is what the gauge reads.
CAS is airspeed calibrated for position and instrument error.
TAS is CAS corrected for density.

Weight and Balance

Moment = arm x weight.
Arm comes from the manual for the airplane.
Weight comes from whatever is going in the plane.
Whether the moment and weight are within the envelope is plotted from the w/b envelope chart in the manual.

The further the weight is from the CoG the more the weight effects the airplane. The relationship is not straightforward enough to have a simple rule about arm, therefore arm must come from the airplane manual.

Once you have the arm and the weight you can calculate moment, and moment can be plotted graphically on the airplane envelope (also from the manual) to see if you are within limits.

Obviously, you can change moment by changing arm, but arm comes from the manual. How can you change it? Change the position of the weight. A position closer to the CoG has a smaller arm. A position forward of the CoG increases nose down weight; one behind the CoG decreases nose down weight. You can move weight around somewhat.

Standard empty weight is the airplane with standard equipment and oil plus unusable fuel.

Basic empty weight is the weight of the airplane plus optional equipment, oil and other fluids.

Useful load is maximum weight minus basic empty weight.

Payload is useful load minus fuel weight.

Useful Concepts & Weight and Balance- Navigation Pop Quiz

Radio Aids to Navigation

My name is Rob Chipman and I’m a realtor and pilot based in Vancouver, BC. I AM NOT A FLIGHT INSTRUCTOR AND I AM NOT OFFERING FLIGHT INSTRUCTION! I am sharing my study notes and other things I’ve learned while getting my education as a pilot. You’re welcome to make use of this information, but do not treat it as expert advice.

I really enjoy flying, real estate and the Chilcotin.  My company is Coronet Realty Ltd., located at 3582 East Hastings Street, Vancouver, BC, V5K 2A7. I have a C-150L that I own with two other pilots, based out of Pitt Meadows. Do not hesitate to contact me by email if I can help you do anything, especially if its likely to be interesting or concerns selling remote property in British Columbia.

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