AVIATION MATHEMATICS

1. AVIATION MATHEMATICS

2. www.faa.gov Training and Testing Training Resources and Guides Pilot Training Download: • Pilot’s Handbook of Aeronautical Knowledge • Airplane Flying Handbook

3. www.faa.gov

4. www.faa.gov

5. 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

6. 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

7. www.faa.gov Training and Testing Under Testing, select: Sample Airman Knowledge Test Questions Under Pilot, select Private Download: Airman Knowledge Test Question Bank

8. 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

9. 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”

10. 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)

11. #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

13. UTC = Coordinated Universal Time • The time at the 0° line of longitude which passes through Greenwich England Often called Zulu time

14. Prime Meridian

15. Time zones change every 15° of longitude 360° / 24 = 15° The Earth revolves at 15° per hour

16. 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).

17. 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

18. #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. Learning Statement PLT309: Recall load factor - angle of bank

19. In straight and level, unaccelerated flight LIFT = WEIGHT and THRUST = DRAG

20. Level Turn

21. Straight and level flight Wings support a load equal to the sum of the weight of the airplane plus its contents

22. Load Factor = Total Lift /Weight Load factor = 1G in straight and level flight

23. Load Factor = Total Lift /Weight Ratio of the load supported by wings to the actual weight of the aircraft and its contents.

24. Turns Increase the Load Factor Wings must support a load equal to the weight of the airplane plus the load imposed by centrifugal force.

25. Load Factor vs. Bank Angle

29. #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.

30. 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.

31. 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.

32. 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

33. Nautical Mile Historical Definition 1 nm = length of 1 minute of arc of latitude along any meridian

34. 10,000,000 m from Equator to North Pole along the Meridian of Paris

35. 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

36. 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

37. Modern definition of Nautical Mile 1nm = 1852.0 m 1 nm ≈ 1.15statute miles

38. 1 KNOT = 1 nautical mile / hr

39. 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

43. 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

45. 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

46. #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.

48. Reciprocal Headings

49. Runway 9/27

50. Runway Numbers • Runway numbers are in reference to magnetic north • Determined from the approach direction