Module 2: Physics

Module 2: Physics – B3 Licence Category

1. Module Overview

Module 2 of the EASA Part-66 basic knowledge syllabus provides the foundational physical principles required for the safe maintenance, inspection, and certification of aircraft. For the B3 (light aeroplane) category, this module covers the core areas of matter, mechanics, thermodynamics, optics, and basic electrical theory. A certifying engineer must apply these principles daily—from calculating centre of gravity for weight and balance, to understanding hydraulic system pressures, thermal expansion of components, and the behaviour of pitot-static instruments.

The syllabus is divided into the following key areas, each with defined knowledge levels (1 = overview, 2 = general knowledge, 3 = detailed theory):

• 2.1 Matter (Level 1–2): States of matter, density, and material properties.
• 2.2 Mechanics (Level 2–3): Statics, dynamics, kinematics, and kinetics.
• 2.3 Thermodynamics (Level 2): Temperature, heat, expansion, and gas laws.
• 2.4 Optics (Light) (Level 1): Basic principles.
• 2.5 Wave Motion and Sound (Level 1–2): Basic principles.
• 2.6 Fluid Mechanics (Level 2–3): Pressure, hydraulics, and aerodynamics.

This study material synthesises the knowledge required to answer typical exam questions and, more importantly, to apply these principles in a maintenance environment.

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2. Key Concepts Explained in Detail

2.1 Units of Measurement and Conversions

The International System of Units (SI) is the standard for all aviation maintenance documentation and calculations. However, legacy tooling, American-manufactured aircraft, and certain maintenance manuals still use Imperial units. A certifying engineer must be fluent in converting between systems.

Example – Torque Conversion: A torque specification of 25 N·m is equivalent to 25 × 0.7376 = 18.44 lb-ft. This is critical when using Imperial-calibrated torque wrenches on components specified in SI units.

Example – Volume Conversion: A fuel tank of 200 litres has a volume of 200 × 0.001 = 0.2 m³. This conversion is used in fuel mass calculations (mass = density × volume).

2.2 Matter and Material Properties

Matter exists in three primary states relevant to aviation: solid, liquid, and gas. Each state has distinct physical properties that influence aircraft design and maintenance.

• Solids: Have a definite shape and volume. They exhibit elasticity (return to original shape after deformation) and plasticity (permanent deformation). Key mechanical properties include:
• Strength: Ability to withstand load without failure (tensile, compressive, shear).
• Hardness: Resistance to indentation or scratching.
• Toughness: Ability to absorb energy without fracturing.
• Brittleness: Tendency to fracture without significant plastic deformation.
• Ductility: Ability to be drawn into wire (e.g., copper).
• Malleability: Ability to be hammered or rolled into sheets (e.g., aluminium).
• Liquids: Have a definite volume but take the shape of their container. They are incompressible for practical purposes, a principle exploited in hydraulic systems. Liquids exhibit viscosity (internal resistance to flow), which changes with temperature.
• Gases: Have no definite shape or volume and are compressible. Their behaviour is governed by the gas laws (Boyle's, Charles's, and the General Gas Law).

Material Properties in Maintenance: Understanding material properties is essential for selecting correct repair techniques. For example, ice is a crystalline solid with high compressive strength but low shear strength. Therefore, mechanical de-icing (scraping) applies a shear force to break the ice layer, rather than attempting to crush it.

2.3 Statics: Forces, Moments, and Equilibrium

Statics is the study of bodies at rest or moving at constant velocity. A body is in equilibrium when the vector sum of all forces and moments acting upon it is zero.

• Force (F): A vector quantity measured in Newtons (N). It has magnitude, direction, and point of application.
• Moment (or Torque, M): The turning effect of a force about a pivot point. M = F × d, where d is the perpendicular distance from the line of action of the force to the pivot. The SI unit is the Newton-metre (N·m).

Example – Torque Application: A force of 100 N applied perpendicular to a torque wrench handle of 0.3 m length produces a torque of 100 N × 0.3 m = 30 N·m.

Centre of Gravity (CG): The point where the entire weight of an object is considered to act. For an aeroplane, the CG position is critical for stability and control.

Weight and Balance Calculation: The CG is calculated using the principle of moments:

• Moment = Mass × Distance from datum (kg·m).
• Total Moment = Sum of all individual moments.
• CG Position = Total Moment / Total Mass.

Example – CG Shift: An aeroplane with a mass of 1,150 kg and a CG at 2.40 m aft of the datum has a moment of 1,150 × 2.40 = 2,760 kg·m. Loading 50 kg of cargo at a station 3.10 m aft of the datum adds a moment of 50 × 3.10 = 155 kg·m. The new total moment is 2,915 kg·m, and the new total mass is 1,200 kg. The new CG is 2,915 / 1,200 = 2.43 m aft of the datum. This must be checked against the CG envelope (forward and aft limits) to ensure the aeroplane remains within its certified limits.

Newton's Laws of Motion:

1. First Law (Inertia): A body at rest stays at rest, and a body in motion stays in motion at constant velocity, unless acted upon by a net external force.
2. Second Law (Acceleration): The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass. F = ma. Also expressed as impulse: Force = change in momentum / time.
3. Third Law (Action-Reaction): For every action, there is an equal and opposite reaction.

Example – Equilibrium: A helicopter hovering at constant altitude has zero net force acting on it. The upward lift (rotor thrust) exactly balances the downward weight. Similarly, a helicopter descending at a constant rate is in equilibrium; the upward forces (rotor thrust) equal the downward forces (weight).

Example – Resultant Force: An engine producing 2,000 N of thrust against a total drag of 1,500 N results in a net forward force of 500 N.

Example – Impact Force (Impulse-Momentum): A bird of mass 0.5 kg decelerated from 100 m/s to 0 m/s in 0.01 seconds experiences a force of F = (m × Δv) / t = (0.5 × 100) / 0.01 = 5,000 N. This principle is used to assess impact damage on components like compressor blades.

2.4 Kinematics: Linear and Rotational Motion

Kinematics describes motion without considering its causes.

• Linear Velocity (v): Rate of change of displacement, measured in metres per second (m/s).
• Angular Velocity (ω): Rate of change of angular displacement, measured in radians per second (rad/s).
• Relationship: For a point at radius r from the centre of rotation, the linear velocity is v = ω × r.

Example – Rotor Tip Speed: A helicopter rotor blade of 5 m length rotating at 300 rpm. First, convert rpm to rad/s: ω = 300 × (2π / 60) = 31.42 rad/s. Then, tip speed v = 31.42 × 5 = 157.1 m/s. This can also be calculated by finding the circumference (2πr = 31.4 m) and multiplying by revolutions per second (5 rev/s), giving 157 m/s. Tip speed is a critical parameter for rotor performance and noise.

Rotational Kinetic Energy: A rotating body stores kinetic energy given by E = ½ I ω², where I is the moment of inertia (kg·m²). This energy is proportional to the square of the angular velocity.

Example – Autorotation Energy: If rotor speed decays from 400 rpm to 350 rpm, the ratio of final to initial energy is (350/400)² = 0.766. This represents a 23.4% decrease in stored rotational kinetic energy. This is a crucial consideration during autorotation, where the pilot manages this stored energy to control the rate of descent and flare.

2.5 Fluid Mechanics: Pressure, Hydraulics, and Aerodynamics

Pressure (P) is defined as force per unit area: P = F / A, measured in Pascals (Pa) where 1 Pa = 1 N/m². In aviation, pressure is often expressed in bar (1 bar = 100,000 Pa) or psi.

Example – Hydraulic Pressure: A force of 5,000 N applied to a piston of area 20 cm² (0.002 m²) produces a pressure of 5,000 / 0.002 = 2,500,000 Pa = 25 bar.

Pascal's Law: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This is the principle of hydraulic multiplication.

Example – Hydraulic Multiplication: A force of 50 N on a small piston of area 0.002 m² creates a pressure of 25,000 Pa. This pressure acts on a larger piston of area 0.1 m², producing a force of 25,000 × 0.1 = 2,500 N. This allows a small input force to lift a heavy load.

Hydraulic Power: The power delivered by a hydraulic pump is the product of pressure and flow rate: P = p × Q, where p is pressure in Pascals and Q is flow rate in cubic metres per second (m³/s).

Example – Pump Power: A pump delivering 3,000 psi (20,685,000 Pa) at a flow rate of 5 gallons per minute (0.0003154 m³/s) delivers approximately 20,685,000 × 0.0003154 = 6,524 W ≈ 6.5 kW.

Atmospheric Pressure and Pitot-Static Systems: The pitot-static system measures dynamic pressure for airspeed indication. A pitot tube measures total (pitot) pressure, while static ports measure ambient (static) pressure. The airspeed indicator (ASI) displays the difference (dynamic pressure).

• Blocked Pitot Tube: If the pitot tube is blocked but the drain hole is clear, the trapped pressure acts as a reference. As the aeroplane climbs, static pressure decreases, but the trapped pitot pressure remains high, causing the ASI to over-read.
• Blocked Static Port: If the static port is blocked but the pitot tube is clear, the trapped static pressure remains at the value at the time of blockage. During a climb, the static pressure inside the instrument is too high, reducing the differential pressure and causing the ASI to under-read. During a descent, the opposite occurs, and the ASI over-reads.

Cabin Pressurisation: The pressure difference between the cabin and the outside atmosphere is critical for structural integrity. For example, a cabin pressure of 100 kPa at an outside pressure of 80 kPa results in a differential pressure of 20 kPa.

2.6 Thermodynamics: Temperature, Heat, and Expansion

Temperature is a measure of the average kinetic energy of the particles in a substance. It is measured in Kelvin (K), Celsius (°C), or Fahrenheit (°F). The Kelvin scale is an absolute scale, with 0 K being absolute zero.

Conversion: K = °C + 273.15.

Example: An ambient temperature of 15°C is equivalent to 15 + 273.15 = 288.15 K, which rounds to 288 K. This is essential for engine performance calculations, as gas turbine performance is referenced to International Standard Atmosphere (ISA) conditions.

Thermal Expansion: Most materials expand when heated and contract when cooled. The change in length (ΔL) of a solid is given by:

ΔL = α × L₀ × ΔT

Where:

• α = coefficient of linear expansion (per Kelvin or per °C).
• L₀ = original length (m).
• ΔT = change in temperature (K or °C).

Example – Aluminium Tail Boom: An aluminium tail boom (α = 23 × 10⁻⁶ /°C) of length 4.5 m, experiencing a temperature rise from 15°C to 45°C (ΔT = 30°C), will expand by ΔL = 23 × 10⁻⁶ × 4.5 × 30 = 0.003105 m = 3.1 mm. This expansion must be accommodated in control cable tensions and structural joints.

Example – Percentage Change: A rotor blade experiencing a temperature drop of 40 K will contract by a fractional amount ΔL/L = α × ΔT = 23 × 10⁻⁶ × 40 = 0.00092, or 0.092%.

Expansion of Liquids: Liquids also expand when heated. Hydraulic fluid reservoirs must have sufficient expansion space to accommodate the increased volume when the system is hot. A completely full cold reservoir can lead to excessive pressure and system failure when the fluid heats up.

Combustion and Gas Turbine Operation: In a gas turbine engine, the exhaust gas temperature (EGT) is a key performance indicator. A lean fuel/air mixture (excess air) burns hotter, leading to higher EGT. A rich mixture (excess fuel) has a cooling effect due to the latent heat of vaporisation of the excess fuel, resulting in lower EGT. A higher-than-normal EGT for a given power setting is a classic symptom of a lean condition.

2.7 Electrical Fundamentals

Basic electrical theory is part of Module 2. Key relationships are defined by Ohm's Law and the power equation.

• Ohm's Law: V = I × R, where V is voltage (volts), I is current (amperes), and R is resistance (ohms).
• Electrical Power: P = V × I = I² × R = V² / R, measured in watts (W).

Example – Navigation Light: A 28 V DC navigation light with a resistance of 4 ohms dissipates power P = V² / R = (28)² / 4 = 784 / 4 = 196 W. Alternatively, the current is I = V / R = 7 A, and power is P = V × I = 28 × 7 = 196 W.

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3. Important Formulas and Procedures

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4. Common Relationships Between Concepts

• Pressure, Force, and Area: The same pressure can produce different forces depending on the area it acts upon. This is the basis of hydraulic force multiplication.
• Torque, Force, and Distance: The same torque can be achieved with a small force at a long distance or a large force at a short distance. This is why torque wrench length matters.
• Thermal Expansion and Material Properties: The coefficient of linear expansion (α) is a material property. Different materials (aluminium, steel, composites) expand at different rates, which is why dissimilar metal joints require special attention to thermal stress.
• Kinematics and Kinetics: Kinematics describes motion (velocity, acceleration), while kinetics relates motion to its causes (force, torque). For example, rotor tip speed (kinematics) determines the centrifugal force on the blade (kinetics).
• Gas Laws and Engine Performance: Temperature, pressure, and volume of gases are interrelated. Changes in ambient temperature and pressure affect engine performance and airspeed indications.
• Newton's Laws and Flight: Newton's first law explains equilibrium (hover, constant descent), the second law explains acceleration (take-off, climb), and the third law explains thrust generation (action-reaction).

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5. Typical Exam Focus Points

For the EASA Part-66 Module 2 exam (B3 category), candidates should focus on the following areas, which are frequently tested:

1. Unit Conversions: Be fluent in converting between SI and Imperial units, especially for torque (N·m ↔ lb-ft), pressure (Pa ↔ bar ↔ psi), and volume (litres ↔ m³).
2. Centre of Gravity Calculations: Be able to calculate the new CG after adding, removing, or shifting mass. Understand the concept of the CG envelope and its limits.
3. Torque and Moments: Understand the calculation of torque (M = F × d) and its application in weight and balance and torque wrench usage.
4. Pressure and Pascal's Law: Be able to calculate pressure from force and area, and understand hydraulic force multiplication.
5. Rotational Motion: Be able to convert rpm to rad/s and calculate linear velocity at a given radius (e.g., rotor tip speed).
6. Thermal Expansion: Be able to calculate linear expansion (ΔL = α × L₀ × ΔT) and understand its practical implications for clearances and system design (e.g., hydraulic reservoir expansion space).
7. Newton's Laws: Understand the concept of equilibrium (net force = zero) for constant velocity motion, and be able to calculate resultant forces.
8. Pitot-Static System Errors: Understand the effects of blocked pitot tubes and static ports on airspeed indications during climbs and descents.
9. Rotational Kinetic Energy: Understand the square relationship between angular velocity and stored energy (E = ½ I ω²), particularly for autorotation.
10. Electrical Power: Be able to calculate power using Ohm's Law and the power equation.
11. Thermodynamics (EGT): Understand the relationship between fuel/air mixture and exhaust gas temperature in gas turbine engines.
12. Material Properties: Understand the difference between tensile, compressive, and shear strength, and how this relates to maintenance practices (e.g., de-icing).