AVIATION MATHEMATICS

Training and Testing Training Resources and Guides Pilot Training Download: Pilot’s Handbook of Aeronautical Knowledge Airplane Flying Handbook

Requirements for Private Pilot Certificate 14 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 multiple choice questions Must be completed in 2.5 hrs A score of 70% required to pass

Training and Testing Under Testing, select: Sample Airman Knowledge Test Questions Under Pilot, select Private Download: 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: ESTAdd 5 hours CSTAdd 6 hours MSTAdd 7 hours PSTAdd 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

#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.

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 Mile Historical 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= km

Modern definition of Nautical Mile 1nm = 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

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

#256PLT 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 KLGA13/31 and 4/22 KDCA 1/19, 15/33, and 4/22 KIAD1L/19R, 1R/19L, and 12/30 KCLT 18R/36L, 18L/36R, and 5/23 KLEX4/22 and 8/26

#201PLT 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 8/26 RUNWAY 8RUNWAY 26 Runway heading: 085 magnetic, 081 true 265 magnetic, 261 true RUNWAY 4RUNWAY 22 Runway heading: 046 magnetic, 042 true 226 magnetic, 222 true Runway 4/22

KLEX (Blue Grass Airport) 265 magnetic 226 magnetic

Runway Numbers …one of the odd things about Americans is that they leave the initial zero off of runway designations. The above (runway “seven”) would be runway "zero seven" in Canada. I always think single digit runway numbers look very rural and hicktown.

Standard Weights ITEMWEIGHT General Aviation Crew and Passenger 170 lbs each Gasoline6 lbs/U.S. gallon Oil7.5 lbs/U.S. gallon Water8.35 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 V HP = Minimum dynamic hydroplaning spd Once hydroplaning starts, it can continue at speeds well below the minimum initial hydroplaning speed

Hydroplaning Speed V HP = 9√(tire pressure) Tire pressure usually ranges from 80 psi to 200 psi √(tire pressure) ranges from 9 to 14 V HP usually ranges from 81 knots to 126

Crosswind Components Wind Angle to Runway Calculate Crosswind Component 0 or %None 030 or %Half 045 or %Two-thirds 060 or %Almost all %All

Headwind and Tailwind Components Wind Angle to Runway Calculate Headwind or Tailwind Component 0 or %All 030 or %Almost all 045 or %Two-thirds 060 or %Half %None

WIND COMPONENTS Wind AngleCrosswindHeadwind 15° 1/419/20 30° 1/29/10 45° 2/3 60° 9/101/2 75° 19/201/4

METAR Aviation Routine Weather Report KLGA Z 26011KT 10SM SCT045 SCT190 M01/M10 A2988 RMK AO2 SLP119 4/003 T KLGA Z 31018G24KT 10SM SCT050 BKN190 04/M11 A2993 RMK AO2 PK WND 30027/1718 SLP133 4/ T

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 Conversion C = (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) × 11/20 11/20 = 0.55 but 5/9 =.55…