Key Formulas & Equations
Lift Equation: L = ½ ρ v² S CL
L = lift (N), ρ = air density (kg/m³), v = velocity (m/s), S = wing area (m²), CL = lift coefficient
L = lift (N), ρ = air density (kg/m³), v = velocity (m/s), S = wing area (m²), CL = lift coefficient
Drag Equation: D = ½ ρ v² S CD
CD = CD0 + k CL² (parasitic + induced drag)
CD = CD0 + k CL² (parasitic + induced drag)
Bernoulli's Principle: P + ½ ρ v² + ρgh = constant
Where airflow speed increases over the wing, pressure decreases, creating lift.
Where airflow speed increases over the wing, pressure decreases, creating lift.
Ground Speed: GS = TAS + Wc (tailwind) or GS = TAS − Wc (headwind)
Time = Distance / Speed
Time = Distance / Speed
Fuel Required: Fuel = (Distance / Fuel Flow) × Safety Factor
Endurance: Time = Fuel / Fuel Flow Rate
Endurance: Time = Fuel / Fuel Flow Rate
Core Concepts
1. Four Forces of Flight
Lift (upward, opposes weight), Weight (downward, gravity), Thrust (forward, opposes drag), Drag (backward, air resistance). Flight occurs when lift ≥ weight and thrust ≥ drag.
Lift (upward, opposes weight), Weight (downward, gravity), Thrust (forward, opposes drag), Drag (backward, air resistance). Flight occurs when lift ≥ weight and thrust ≥ drag.
2. Principles of Aerodynamics
Airflow over and under the wing creates a pressure differential. The angle of attack (AoA) determines lift generation until the critical AoA is reached, causing a stall.
Airflow over and under the wing creates a pressure differential. The angle of attack (AoA) determines lift generation until the critical AoA is reached, causing a stall.
3. Navigation Systems
VOR (VHF Omnidirectional Range), GPS, INS (Inertial Navigation), and ADF (Automatic Direction Finder) enable pilots to determine position, heading, and course.
VOR (VHF Omnidirectional Range), GPS, INS (Inertial Navigation), and ADF (Automatic Direction Finder) enable pilots to determine position, heading, and course.
4. Meteorology for Aviators
Understanding METARs, TAFs, wind shear, icing conditions, turbulence, and pressure systems is essential for flight planning and safety.
Understanding METARs, TAFs, wind shear, icing conditions, turbulence, and pressure systems is essential for flight planning and safety.
5. Air Traffic Control (ATC)
Ground, tower, approach/departure, and center controllers manage aircraft separation using radar, radio communication, and standardized phraseology.
Ground, tower, approach/departure, and center controllers manage aircraft separation using radar, radio communication, and standardized phraseology.
Core Definitions
Angle of Attack (AoA): The angle between the wing chord line and the relative airflow. Critical for lift generation; exceeding the critical AoA causes a stall.
Stall: A condition where the angle of attack exceeds the critical value, causing airflow separation over the wing and sudden loss of lift. Not related to engine failure.
True Airspeed (TAS): The actual speed of the aircraft relative to the air mass. Differs from Indicated Airspeed (IAS) due to altitude and temperature.
Ceiling: The maximum altitude an aircraft can maintain level flight. Service ceiling: altitude where rate of climb drops to 100 ft/min.
Instrument Flight Rules (IFR): Regulations for flying solely by reference to instruments when visibility is below VFR minimums. Requires specialized pilot certification.
Worked Examples
Example 1: Lift Calculation
An aircraft wing (S = 30 m², CL = 1.2) flies at 100 m/s at sea level (ρ = 1.225 kg/m³):
L = 0.5 × 1.225 × 100² × 30 × 1.2 = 220,500 N (22.5 tonnes-force)
An aircraft wing (S = 30 m², CL = 1.2) flies at 100 m/s at sea level (ρ = 1.225 kg/m³):
L = 0.5 × 1.225 × 100² × 30 × 1.2 = 220,500 N (22.5 tonnes-force)
Example 2: Ground Speed with Wind
TAS = 250 knots, headwind = 30 knots: GS = 250 − 30 = 220 knots. Time for 440 nm: 440/220 = 2.0 hours
TAS = 250 knots, headwind = 30 knots: GS = 250 − 30 = 220 knots. Time for 440 nm: 440/220 = 2.0 hours
Example 3: Fuel Planning
Fuel flow = 250 kg/hr, distance = 1,000 nm, endurance speed = 200 knots. Time = 5 hours. Fuel needed = 5 × 250 = 1,250 kg + 45-min reserve (187.5 kg) = 1,437.5 kg
Fuel flow = 250 kg/hr, distance = 1,000 nm, endurance speed = 200 knots. Time = 5 hours. Fuel needed = 5 × 250 = 1,250 kg + 45-min reserve (187.5 kg) = 1,437.5 kg
Practice Problems
Problem 1: Calculate lift for an aircraft at 5,000 ft (ρ = 1.056 kg/m³), velocity 120 m/s, wing area 25 m², CL = 0.8.
Answer: L = 0.5 × 1.056 × 14,400 × 25 × 0.8 = 152,064 N
Answer: L = 0.5 × 1.056 × 14,400 × 25 × 0.8 = 152,064 N
Problem 2: A pilot needs to fly 600 nm with a fuel endurance of 4.5 hours. What minimum ground speed is needed?
Answer: GS = 600 / 4.5 = 133.3 knots
Answer: GS = 600 / 4.5 = 133.3 knots
Problem 3: What causes an aircraft stall and how is it recovered?
Answer: Exceeding the critical angle of attack causes airflow separation. Recovery: reduce AoA (push nose down), add power, level wings.
Answer: Exceeding the critical angle of attack causes airflow separation. Recovery: reduce AoA (push nose down), add power, level wings.
Problem 4: If TAS = 180 knots with a 25-knot tailwind, what is the ground speed and time for 360 nm?
Answer: GS = 205 knots. Time = 360/205 = 1.76 hours (1 hr 45 min)
Answer: GS = 205 knots. Time = 360/205 = 1.76 hours (1 hr 45 min)
Problem 5: Explain the difference between IAS and TAS.
Answer: IAS is read directly from the airspeed indicator (dynamic pressure). TAS is IAS corrected for altitude and temperature — the true speed through the air mass.
Answer: IAS is read directly from the airspeed indicator (dynamic pressure). TAS is IAS corrected for altitude and temperature — the true speed through the air mass.