Module 2: Physics

Module 2: Physics — Overview

Module 2 of the EASA Part-66 basic knowledge syllabus provides the fundamental physical principles that underpin all aircraft systems and structures. It is not merely an academic exercise; it is the essential theoretical foundation for the certifying staff's understanding of how and why aircraft components behave as they do. This module covers matter, mechanics, thermodynamics, optics, and wave motion, and it is a prerequisite for understanding more advanced modules on aerodynamics, electrical systems, and structures.

The syllabus is structured into sub-modules, each addressing a core area of physics. The knowledge levels (1, 2, or 3) dictate the depth of understanding required. For a B1.1 licence, a detailed understanding (Level 3) is expected for most topics, meaning you must be able to apply the principles to solve problems and explain system behaviour.

This study material synthesises the key concepts from the syllabus, focusing on the areas most frequently examined. It is structured to build your understanding from fundamental definitions to complex applications.

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2.1 Matter and Units

The International System of Units (SI)

Aviation is an international industry, and the SI system is the standard for all engineering calculations, technical publications, and maintenance data. While legacy imperial units (psi, inches, pounds) may still appear in some older documentation, all modern aircraft manuals and certification data use SI units. The certifying staff must be fluent in converting between these systems.

The seven base SI units are:

All other units are derived from these. For example, the unit of force, the newton (N), is derived as kg·m/s².

Key Derived Units in Aviation

• Force: The newton (N) is the force required to accelerate a mass of 1 kg at a rate of 1 m/s². This is a fundamental definition.
• Pressure: The pascal (Pa) is defined as one newton per square metre (N/m²). Because the pascal is a small unit, pressures in aviation are often expressed in kilopascals (kPa), megapascals (MPa), or bar (1 bar = 100,000 Pa).
• Energy/Work: The joule (J) is the work done when a force of 1 newton moves an object 1 metre in the direction of the force.
• Power: The watt (W) is the rate of doing work, equal to one joule per second (J/s).
• Electric Charge: The coulomb (C) is the quantity of charge transported by a constant current of one ampere in one second.
• Frequency: The hertz (Hz) is one cycle per second.

Unit Conversion

The ability to convert between imperial and SI units is a practical skill for maintenance. The most critical conversions for Module 2 are:

• Pressure: 1 psi = 6.89476 kPa. Therefore, a common hydraulic system pressure of 3000 psi is equivalent to 20.68 MPa.
• Length: 1 inch = 25.4 mm; 1 metre = 1000 millimetres.
• Mass: 1 kg = 2.20462 lb.
• Force: 1 N = 0.2248 lbf.

Exam Focus: You will be expected to perform these conversions accurately. A common error is misplacing the decimal point when converting between mm² and m² (e.g., 1 mm² = 1 × 10⁻⁶ m²).

Scalar and Vector Quantities

A fundamental distinction in physics is between scalars and vectors.

• Scalar quantities have only a magnitude (a numerical value). Examples include mass, temperature, time, speed, and energy.
• Vector quantities have both a magnitude and a direction. Examples include force, velocity, displacement, and acceleration.

This distinction is critical in mechanics. For example, when analysing forces on an aircraft, you must consider both the magnitude and the direction of each force.

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2.2 Mechanics: Statics, Dynamics, and Strength of Materials

Statics: Forces and Equilibrium

Statics is the study of bodies at rest or moving at constant velocity. The fundamental principle is that for a body to be in equilibrium, the vector sum of all forces acting on it must be zero (ΣF = 0), and the sum of all moments (torques) must also be zero (ΣM = 0).

Weight and Mass: The weight of an object is the force exerted on it by gravity. It is calculated as:

\[

W = m \times g

\]

Where:

• \( W \) = weight (N)
• \( m \) = mass (kg)
• \( g \) = acceleration due to gravity (9.81 m/s² on Earth)

A 10 kg mass therefore has a weight of 98.1 N. This distinction is crucial: mass is a property of the matter, while weight is a force that depends on the local gravitational field.

Moment (Torque): A moment is the turning effect of a force. It is calculated as the product of the force and the perpendicular distance from the pivot point to the line of action of the force.

\[

M = F \times d

\]

Where:

• \( M \) = moment (N·m)
• \( F \) = force (N)
• \( d \) = perpendicular distance (m)

This principle is applied when torquing fasteners. A force of 500 N applied perpendicular to a torque wrench handle at a distance of 0.3 m produces a torque of 150 N·m.

Pascal's Principle: This principle is the basis of all hydraulic systems. It states that pressure applied to a confined fluid is transmitted equally and undiminished to every part of the fluid and the walls of the containing vessel. This allows force multiplication:

\[

\frac{F_1}{A_1} = \frac{F_2}{A_2}

\]

If a force of 200 N is applied to a small input piston with an area of 0.005 m², the pressure is 40,000 Pa. This pressure acts on a larger output piston with an area of 0.02 m², producing a force of 800 N. The pressure is the same throughout the system, but the force is proportional to the area.

Dynamics: Motion and Energy

Dynamics is the study of bodies in motion and the forces that cause that motion.

Newton's Laws of Motion:

1. 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. The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass: \( F = ma \).
3. For every action, there is an equal and opposite reaction.

Work, Energy, and Power:

• Work is done when a force moves an object over a distance. \( W = F \times d \). The SI unit is the joule (J). A force of 50 N moving an object 3 m does 150 J of work.
• Kinetic Energy is the energy a body possesses due to its motion. \( KE = \frac{1}{2}mv^2 \). A 2 kg mass moving at 5 m/s has a kinetic energy of 25 J.
• Potential Energy is the energy a body possesses due to its position. \( PE = mgh \).
• Power is the rate of doing work. \( P = \frac{W}{t} \). The SI unit is the watt (W), which is one joule per second.

Rotational Motion:

• Angular Velocity (ω) is the rate of change of angular displacement, measured in radians per second (rad/s). To convert from rpm: \( \omega = \frac{2\pi \times rpm}{60} \).
• Moment of Inertia (I) is the rotational equivalent of mass. It depends on the mass and its distribution about the axis of rotation.
• Rotational Kinetic Energy is given by \( KE = \frac{1}{2}I\omega^2 \). A turbine disc with a moment of inertia of 0.5 kg·m² rotating at 10,000 rpm (ω = 1047.2 rad/s) stores approximately 274 kJ of energy. This stored energy is a significant safety consideration during maintenance.

Strength of Materials

This is a critical area for certifying staff, as it deals with the behaviour of materials under load.

Stress is the internal resistance of a material to an applied force, defined as force per unit area:

\[

\sigma = \frac{F}{A}

\]

The SI unit is the pascal (Pa). A steel tie rod with a cross-sectional area of 120 mm² (120 × 10⁻⁶ m²) carrying a tensile load of 18 kN experiences a stress of 150 MPa.

Strain is the deformation of a material relative to its original length:

\[

\epsilon = \frac{\Delta L}{L_0}

\]

Strain is dimensionless. A rod that stretches from 1.200 m to 1.204 m has a strain of 0.00333.

Hooke's Law and Young's Modulus: Within the elastic limit, stress is directly proportional to strain. The constant of proportionality is Young's Modulus (E):

\[

E = \frac{\sigma}{\epsilon}

\]

This allows calculation of elongation. A steel tie rod (E = 200 GPa) with a cross-sectional area of 200 mm² carrying a 40 kN load will experience a stress of 200 MPa, a strain of 0.001, and an elongation of 0.5 mm over a 500 mm length.

Shear Stress and Torsion: Shear stress occurs when forces are applied parallel to a surface. In a shaft under torsion, the maximum shear stress is given by:

\[

\tau = \frac{T \times r}{J}

\]

Where:

• \( T \) = torque (N·m)
• \( r \) = radius of the shaft (m)
• \( J \) = polar second moment of area (m⁴), which for a solid circular shaft is \( J = \frac{\pi d^4}{32} \)

Fatigue: A material subjected to cyclic loading below its yield strength can fail suddenly after many cycles. This phenomenon is known as fatigue. It is a progressive, localized structural damage mechanism and is a primary concern in aircraft structural integrity. The failure occurs without significant plastic deformation, making it particularly dangerous.

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2.3 Thermodynamics

Thermodynamics is the study of heat, work, and energy transfer. It is fundamental to understanding engines, air conditioning, and hydraulic systems.

Temperature and Heat

• Temperature is a measure of the average kinetic energy of the particles in a substance. It is measured in kelvin (K) or degrees Celsius (°C). The Kelvin scale is an absolute scale, with 0 K being absolute zero. \( T(K) = T(°C) + 273.15 \).
• Heat is the transfer of thermal energy between substances at different temperatures. It is measured in joules (J).

Specific Heat Capacity (c) is the amount of heat energy required to raise the temperature of 1 kg of a substance by 1 K. The heat energy required to change the temperature of a mass is:

\[

Q = mc\Delta T

\]

Where:

• \( Q \) = heat energy (J)
• \( m \) = mass (kg)
• \( c \) = specific heat capacity (J/(kg·K))
• \( \Delta T \) = change in temperature (K)

For example, to raise a 0.5 kg turbine blade (c = 450 J/(kg·K)) from 20°C to 620°C requires 135 kJ of energy.

Sensible Heat is the heat that causes a change in temperature without a change of state. The rate of heat removal in an air conditioning pack, for example, is calculated as:

\[

\dot{Q} = \dot{m} \times c_p \times \Delta T

\]

Where \( \dot{m} \) is the mass flow rate (kg/s) and \( c_p \) is the specific heat capacity at constant pressure. For air, \( c_p \) ≈ 1005 J/(kg·K).

Gas Laws

The behaviour of gases is described by a set of laws that are essential for understanding pneumatic systems, accumulators, and engine cycles.

• Boyle's Law: At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume. \( P_1V_1 = P_2V_2 \). If the volume is halved, the pressure doubles.
• Gay-Lussac's Law: At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature. \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \). This is critical for hydraulic accumulators, where a temperature increase will cause a pressure increase.
• Charles's Law: At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature.
• The Ideal Gas Law: This combines the above: \( PV = nRT \), where \( n \) is the number of moles and \( R \) is the universal gas constant.

Important: When using these laws, temperatures must be in kelvin and pressures must be absolute (gauge pressure + atmospheric pressure).

Heat Transfer Mechanisms

Heat is transferred by three mechanisms:

1. Conduction: Transfer of heat through a solid material by molecular collision. Metals are good conductors.
2. Convection: Transfer of heat by the bulk movement of a fluid (liquid or gas). This is the dominant mode of heat transfer within a moving fluid, such as hydraulic fluid in a line.
3. Radiation: Transfer of heat by electromagnetic waves. This does not require a medium and is negligible at typical hydraulic system temperatures.

Thermodynamic Processes

• Isothermal Process: Occurs at constant temperature (Boyle's Law applies).
• Adiabatic Process: Occurs with no heat transfer (Q = 0). In an adiabatic compression, work is done on the gas, increasing its internal energy and thus its temperature.
• Isentropic Process: An adiabatic and reversible process, meaning entropy remains constant. For an ideal gas, \( \frac{T_2}{T_1} = \left(\frac{P_2}{P_1}\right)^{(\gamma-1)/\gamma} \), where \( \gamma \) is the specific heat ratio (1.4 for air).

The Second Law of Thermodynamics states that all real processes are irreversible and result in an increase in entropy. This is why the actual temperature ratio across a fan is higher than the ideal isentropic ratio, indicating inefficiencies.

Heat Exchangers

Heat exchangers are used in air conditioning and engine oil cooling systems. The Log Mean Temperature Difference (LMTD) is used to calculate the driving force for heat transfer in a heat exchanger. For a counter-flow heat exchanger:

\[

LMTD = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}

\]

Where \( \Delta T_1 \) and \( \Delta T_2 \) are the temperature differences between the hot and cold fluids at each end of the exchanger.

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2.4 Fluid Mechanics (Statics and Dynamics)

Fluid mechanics is the study of liquids and gases in motion and at rest. It is fundamental to hydraulics, pneumatics, and aerodynamics.

Fluid Statics: Hydrostatic Pressure

Pressure in a fluid at rest increases with depth due to the weight of the fluid above. The increase in pressure due to a height of fluid is:

\[

\Delta P = \rho g h

\]

Where:

• \( \rho \) = fluid density (kg/m³)
• \( g \) = acceleration due to gravity (9.81 m/s²)
• \( h \) = height of the fluid column (m)

The pressure at the surface of the fluid is added to this to find the absolute pressure at depth.

Gauge vs. Absolute Pressure

• Gauge pressure is the pressure measured relative to atmospheric pressure.
• Absolute pressure is the pressure measured relative to a perfect vacuum.

The relationship is: Absolute Pressure = Gauge Pressure + Atmospheric Pressure.

A hydraulic system operating at 3000 psi gauge has an absolute pressure of 3000 psi + 14.7 psi = 3014.7 psi, which is approximately 2.08 × 10⁷ Pa.

Fluid Dynamics: Bernoulli's Principle

Bernoulli's principle states that for an incompressible, frictionless fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. For horizontal flow:

\[

P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2

\]

The term \( \frac{1}{2}\rho v^2 \) is the dynamic pressure, and \( P \) is the static pressure. The sum of the two is the total pressure.

This principle is the basis for:

• Venturi tubes used in fuel flow measurement. As fluid velocity increases at the throat, static pressure decreases.
• Pitot-static systems used to measure airspeed. The pitot tube measures total pressure, and the static port measures static pressure. The difference is dynamic pressure, which is proportional to the square of the airspeed: \( q = \frac{1}{2}\rho v^2 \).

Hydraulic Actuators

The force exerted by a hydraulic actuator is calculated as:

\[

F = P \times A \]

Where \( A \) is the effective area of the piston. For extension, the effective area is the full piston area. For retraction, it is the piston area minus the rod area.

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2.5 Electricity and DC Circuits

This section covers the fundamental principles of electricity, which are essential for understanding aircraft electrical systems.

Basic Quantities

• Electric Current (I): The rate of flow of electric charge, measured in amperes (A).
• Voltage (V) or Electromotive Force (EMF): The electrical potential difference, measured in volts (V).
• Resistance (R): The opposition to the flow of current, measured in ohms (Ω).
• Charge (Q): The quantity of electricity, measured in coulombs (C). \( Q = I \times t \). A battery supplying 20 A for 30 minutes delivers 36,000 C.
• Capacitance (C): The ability of a component to store charge, measured in farads (F). \( C = \frac{Q}{V} \). A capacitor storing 0.02 C at 100 V has a capacitance of 200 µF.

Ohm's Law

Ohm's Law is the fundamental relationship in DC circuits:

\[

V = I \times R

\]

A resistor with 12 V across it and 3 A flowing through it has a resistance of 4 Ω.

Series Circuits

In a series circuit, the current is the same through all components, and the total resistance is the sum of the individual resistances:

\[

R_{total} = R_1 + R_2 + R_3 + \dots

\]

Internal Resistance

A real battery has an internal resistance (r). When it supplies current to a load (R), the terminal voltage is less than the EMF due to the voltage drop across the internal resistance:

\[

V_{terminal} = EMF - (I \times r)

\]

Where \( I = \frac{EMF}{R + r} \).

Capacitors

A capacitor stores energy in an electric field. The energy stored is:

\[

E = \frac{1}{2}CV^2

\]

A 100 µF capacitor charged to 28 V stores 0.0392 J of energy. This stored energy is a safety hazard and must be discharged before maintenance.

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2.6 Waves and Sound

Waves are a means of transferring energy without transferring matter.

Wave Properties

• Frequency (f): The number of complete waves passing a point per second, measured in hertz (Hz).
• Wavelength (λ): The distance between two successive identical points on a wave, measured in metres (m).
• Speed (v): The speed at which the wave propagates.

The relationship between these is:

\[

v = f \times \lambda

\]

A sound wave with a frequency of 440 Hz and a wavelength of 0.75 m has a speed of 330 m/s.

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2.7 Aeroplane Aerodynamics and Flight Controls

This section applies the principles of fluid dynamics to the flight of an aeroplane.

Forces in Flight

Four forces act on an aeroplane in flight: lift, weight, thrust, and drag.

• Lift acts perpendicular to the relative airflow.
• Weight acts vertically downwards.
• Thrust acts parallel to the flight path, in the direction of motion.
• Drag acts parallel to the flight path, opposing motion.

Steady Climb

In a steady climb (constant velocity), the net force is zero. Resolving forces parallel and perpendicular to the flight path:

• Parallel to flight path: Thrust = Drag + (Weight × sin(climb angle)). Therefore, Thrust > Drag.
• Perpendicular to flight path: Lift = Weight × cos(climb angle). Therefore, Lift < Weight.

This is a common exam question, and it is important to understand the distinction between the forces resolved along the flight path and those in the vertical direction.

Pitot-Static System

The pitot-static system provides pressure data for the airspeed indicator (ASI), altimeter, and vertical speed indicator (VSI).

• The pitot tube measures total pressure (static + dynamic).
• The static port measures static pressure.
• The ASI measures the difference between the two (dynamic pressure) and converts it to airspeed.
• The altimeter measures static pressure and converts it to altitude based on the International Standard Atmosphere (ISA) model.

System Faults:

• If the pitot tube is blocked (e.g., by ice), the ASI will not respond to changes in airspeed. During a climb, the static pressure decreases, causing the ASI to read as an altimeter (it will show an increase in airspeed).
• If the static port is blocked, the static pressure inside the instruments remains constant. The ASI will read zero when the pitot pressure equals the trapped static pressure, even in a headwind.

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Common Relationships Between Concepts

• Pressure, Force, and Area: These are linked in both statics (stress) and fluid mechanics (hydraulics). Understanding this relationship is key to solving many problems.
• Gas Laws and Absolute Temperature: All gas law calculations require temperatures in kelvin. Failing to convert from Celsius is a common error.
• Bernoulli's Principle and Airspeed: The dynamic pressure measured by the pitot-static system is directly related to airspeed. This connects fluid dynamics to aerodynamics.
• Energy Conservation: Work, kinetic energy, and potential energy are all forms of energy. The principle of conservation of energy links these concepts.
• Thermodynamics and Engine Performance: The gas laws and thermodynamic processes (adiabatic, isentropic) are used to analyse engine cycles and component efficiencies.

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Typical Exam Focus Points

• Unit Conversions: Be proficient in converting between psi and Pa, mm and m, and mm² and m².
• Fundamental Definitions: Know the definitions of SI units (newton, pascal, joule) and the difference between scalar and vector quantities.
• Gas Laws: Be able to apply Boyle's, Charles's, and Gay-Lussac's laws, remembering to use absolute pressures and temperatures in kelvin.
• Hydraulic Calculations: Be able to calculate force, pressure, and area using Pascal's principle, and understand the effect of piston and rod areas on actuator force.
• Stress and Strain: Be able to calculate stress, strain, and elongation using Young's Modulus, and understand the concept of fatigue.
• Ohm's Law and Series Circuits: Be able to calculate resistance, current, and voltage in simple DC circuits, including the effect of internal resistance.
• Bernoulli's Principle: Understand the relationship between velocity and static pressure, and its application in pitot-static systems and venturis.
• Forces in Flight: Understand the force balance in a steady climb and the relationship between thrust, drag, lift, and weight.
• Heat Transfer: Be able to calculate heat energy using specific heat capacity and understand the three modes of heat transfer.
• Rotational Motion: Be able to calculate rotational kinetic energy and torque.