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AVIATION MATHEMATICS
www.faa.gov
Training and Testing
Training Resources and Guides
Pilot Training
Download:
• Pilot’s Handbook of Aeronautical Knowledge
• Airplane Flying Handbook
www.faa.gov
www.faa.gov
Requirements for Private Pilot Certificate14 CFR Part 61
• Minimum age 17
• Read, speak, write, understand English
• Current third-class medical certificate
• Score at least 70% on the Knowledge Test
• Total of 40 hrs of instruction & solo flight time
• Pass an oral exam and flight check
FAA Knowledge Test: Private Pilot – Airplane
• Minimum age 15
• 60 multiple choice questions
• Must be completed in 2.5 hrs
• A score of 70% required to pass
www.faa.gov
Training and Testing
Under Testing, select:
Sample Airman Knowledge Test Questions
Under Pilot, select Private
Download:
Airman Knowledge Test Question Bank
Airman Knowledge Test Question Bank
• Contains over 300 questions for Private Pilot
• Does NOT provide answers
• Each sample question has a code number, corresponding to a Learning Statement Code
Learning Statement Reference Guide
• Contains over 500 Learning Statements
• First 100 involve: “Calculate” (some quantity)
“Interpret” (a graph, chart, etc)
• The rest are mostly “Recall”
Mathematical Concepts• Rounding off• Converting units• Estimating• Interpolation• Subscripted variables• Square Roots• Ratio and Proportion• Formulas (e.g., for Weight and Balance)• Variation (direct and inverse)• Vectors and Trig (e.g., for crosswind components)
#62 PLT 012
An aircraft departs an airport in the central standard time zone at 0845 CST for a 2-hr flight to an airport located in the mountain standard time zone. The landing should be at what coordinated universal time?
A) 1345Z
B) 1445Z
C) 1645Z
Learning Statement PLT 012:
Calculate aircraft performance: time/speed/distance/course/fuel/wind
UTC = Coordinated Universal Time
• The time at the 0° line of longitude which passes through Greenwich England
Often called Zulu time
Prime Meridian
Time zones change every 15° of longitude
360° / 24 = 15°The Earth revolves at 15° per hour
To Convert to UTC:
EST Add 5 hours
CST Add 6 hours
MST Add 7 hours
PST Add 8 hours
(For daylight saving time, subtract 1 hour from the calculated times).
An aircraft departs an airport in the central standard time zone at 0845 CST for a 2-hr flight to an airport located in the mountain standard time zone. The landing should be at what coordinated universal time?
A) 1345Z
B) 1445Z
C) 1645Z
#1PLT309
If an airplane weighs 2,300 pounds, what approximate weight would the airplane structure be required to support during a 60° banked turn while maintaining altitude?
A) 2,300 pounds.
B) 3,400 pounds.
C) 4,600 pounds.
Learning Statement PLT309:
Recall load factor - angle of bank
In straight and level, unaccelerated flight
LIFT = WEIGHT and THRUST = DRAG
Level Turn
Straight and level flight
Wings support a load equal to the sum of the weight of the airplane plus its contents
Load Factor = Total Lift /Weight
Load factor = 1G in straight and level flight
Load Factor = Total Lift /Weight
Ratio of the load supported by wings to the actual weight of the aircraft and its contents.
Turns Increase the Load Factor
Wings must support a load equal to the weight of the airplane plus the load imposed by centrifugal force.
Load Factor vs. Bank Angle
#1 PLT309
If an airplane weighs 2,300 pounds, what approximate weight would the airplane structure be required to support during a 60° banked turn while maintaining altitude?
A) 2,300 pounds.
B) 3,400 pounds.
C) 4,600 pounds.
If an airplane weighs 3,300 pounds, what approximate weight would the airplane structure be required to support during a 30° banked turn while maintaining altitude?
A) 1,200 pounds.
B) 3,100 pounds.
C) 3,960 pounds.
If an airplane weighs 4,500 pounds, what approximate weight would the airplane structure be required to support during a 45° banked turn while maintaining altitude?
A) 4,500 pounds.
B) 6,750 pounds.
C) 7,200 pounds.
How far will an aircraft travel in 2-1/2 minutes with a groundspeed of 98 knots?
A) 2.45 NM
B) 3.35 NM
C) 4.08 NM
Nautical MileHistorical Definition
1 nm = length of 1 minute of arc of latitude along any meridian
10,000,000 m from Equator to North Pole along the Meridian of Paris
Historical Definition of Meter
• 10,000,000 m from Equator to North Pole along the Meridian of Paris
• 40,000,000 m = Circumference of Earth = 40,000 km
Historical Definition of Nautical Mile
• 360 degrees * 60 minutes/degree = 21,600 minutes in a circle of longitude
• 1 nautical mile = the length of 1 minute of arc on a meridian
• 1nm = 40,000 km /21,600=1.85185 km
Modern definition of Nautical Mile
1nm = 1852.0 m
1 nm ≈ 1.15 statute miles
1 KNOT = 1 nautical mile / hr
How far will an aircraft travel in 2-1/2 minutes with a groundspeed of 98 knots?
A) 2.45 NM
B) 3.35 NM
C) 4.08 NM
nmhr
nm
hr
08.498min
60
min5.2
When operating below 18,000 feet MSL in VFR cruising flight more than 3,000 feet above the surface and on a magnetic course of 0° through 179°, any odd thousand-foot MSL altitude plus 500 feet (3,500, 5,500, etc.) is appropriate. On a course of 180° through 359°, even thousands plus 500 feet (4,500, 6,500, etc.) is appropriate. (B09) 14 CFR §91.159
Which VFR cruising altitude is appropriate when flying above 3,000 feet AGL on a magnetic course of 185°?
A) 4,000 feet
B) 4,500 feet
C) 5,000 feet
#256 PLT 467
Which cruising altitude is appropriate for a VFR flight on a magnetic course of 135°?
A) Even thousandths.
B) Even thousandths plus 500 feet.
C) Odd thousandths plus 500 feet.
Reciprocal Headings
If Initial Heading < 180°
Reciprocal Heading = Initial Heading + 200° – 20°
If Initial Heading > 180°
Reciprocal Heading = Initial Heading – 200° + 20°
Runway 9/27
Runway Numbers
• Runway numbers are in reference to magnetic north
• Determined from the approach direction
Runway Numbers
• Start with magnetic heading of runway
• Round to nearest 10°
• Drop the last digit
Runways
• KLGA 13/31 and 4/22
• KDCA 1/19, 15/33, and 4/22
• KIAD 1L/19R, 1R/19L, and 12/30
• KCLT 18R/36L, 18L/36R, and 5/23
• KLEX 4/22 and 8/26
#201 PLT 141
The numbers 8 and 26 on the approach ends of the runway indicate that the runway is orientated approximately
A) 008° and 026° true.
B) 080° and 260° true.
C) 080° and 260° magnetic.
KLEX (Blue Grass Airport)
Runway 8/26RUNWAY 8 RUNWAY 26
Runway heading:
085 magnetic, 081 true
265 magnetic, 261 true
RUNWAY 4 RUNWAY 22
Runway heading:
046 magnetic, 042 true
226 magnetic, 222 true
Runway 4/22
KLEX (Blue Grass Airport)
265 magnetic
226 magnetic
Standard Weights
ITEM WEIGHT
General Aviation Crew and Passenger
170 lbs each
Gasoline 6 lbs/U.S. gallon
Oil 7.5 lbs/U.S. gallon
Water 8.35 lbs/U.S. gallon
An aircraft is loaded 110 lbs over maximum certificated gross weight. If fuel (gasoline) is drained to bring the aircraft weight within limits, how much fuel should be drained?
A) 15.7 gallons
B) 16.2 gallons
C) 18.4 gallons
Dynamic Hydroplaning
• Airplane tires ride on a thin sheet of water
• Results in loss of braking and directional control
• VHP = Minimum dynamic hydroplaning spd
• Once hydroplaning starts, it can continue at speeds well below the minimum initial hydroplaning speed
Hydroplaning Speed
• VHP = 9√(tire pressure)
• Tire pressure usually ranges from 80 psi to 200 psi
• √(tire pressure) ranges from 9 to 14
• VHP usually ranges from 81 knots to 126
Crosswind Components
Wind Angle to Runway
Calculate Crosswind
Component
0 or 180 0.0 0% None
030 or 150 0.5 50% Half
045 or 135 0.7 70% Two-thirds
060 or 120 0.9 90% Almost all
090 1.0 100% All
Headwind and Tailwind Components
Wind Angle to Runway
Calculate Headwind or Tailwind
Component
0 or 180 1.0 100% All
030 or 150 0.9 90% Almost all
045 or 135 0.7 70% Two-thirds
060 or 120 0.5 50% Half
090 0.0 0% None
WIND COMPONENTS
Wind Angle Crosswind Headwind
15° 1/4 19/20
30° 1/2 9/10
45° 2/3 2/3
60° 9/10 1/2
75° 19/20 1/4
METARAviation Routine Weather Report
• KLGA 181151Z 26011KT 10SM SCT045 SCT190 M01/M10 A2988 RMK AO2 SLP119 4/003 T10111100 11006 21017 53018
• KLGA 181751Z 31018G24KT 10SM SCT050 BKN190 04/M11 A2993 RMK AO2 PK WND 30027/1718 SLP133 4/003 933022 T00391106 10039 21011 51002
Dewpoint
• The temperature to which air must be cooled to become saturated
• Temperature at which the air can hold no more moisture
• dewpoint ≤ temperature
Dewpoint
• If Temp = Dewpoint, the air is saturated and Relative Humidity (RH) = 100%
• When air is saturated, moisture begins to condense out as fog, dew, frost, clouds, rain, hail, or snow
Temperature-dewpoint spread
• TDS = Temperature-dewpoint spread = difference between the air temperature and the dewpoint
• TDS = T – DP
Temperature-dewpoint spread
• With a small TDS, the air is close to saturation. This usually results in fog or low clouds.
• Anticipate fog when the TDS is 5°F or less and decreasing.
Temperature Conversion F = (9/5 * C) + 32
• To calculate °F, double the °C, subtract 10%, then add 32°.
• F = 2C – (10% of 2C) + 32°
• Very accurate since 9/5 = 1.8 and 2C - 0.2C = 1.8C
Temperature ConversionC = (F - 32) × 5/9
• To calculate C, subtract 32 from deg F, add 10%, then divide the result by 2
• C = [(F - 32) + 10%] ÷ 2
• Not as accurate as F to C shortcut since 1.1(F-32)/2 = (F-32) × 11/2011/20 = 0.55 but 5/9 = .55…
