GCE A/L Engineering Technology cheat sheet

Orthographic projection in first-angle places the view of the object's top below the front view; third-angle places it above - Sinhala/Tamil A/L papers commonly use first angle (ISO-E).

Line conventions (ISO 128): continuous thick = visible edges; continuous thin = dimension, extension and hatching lines; dashed = hidden edges; chain thin = centre lines and pitch circles.

Dimensioning rules: dimension to visible outlines only, never to hidden lines; place the smallest dimension nearest the feature; use one arrowhead where space is tight and a leader with a dot for circles.

Scale formula: representative fraction RF = drawing length / actual length; a 1:50 plan of a 6 m wall is drawn 120 mm long.

Section views use uniformly spaced 45° hatching thin lines; adjacent parts are hatched in opposite directions; shafts, bolts and ribs are not hatched when cut longitudinally.

Geometric construction: to bisect an angle, strike equal arcs from both arms and intersect; the perpendicular bisector of a chord passes through the circle centre.

Title block essentials: drawing number, part name, material, scale, projection symbol, tolerance class, date and drafter/checker signatures.

Auxiliary views are projected perpendicular to an inclined surface to show its true shape; a surface appears true size only when parallel to the plane of projection.

Stress σ = F/A; strain ε = ΔL/L; Young's modulus E = σ/ε in the elastic region (mild steel ≈ 200 GPa, aluminium ≈ 70 GPa, cast iron ≈ 100–150 GPa).

Ductility is measured by percentage elongation and reduction in area; brittleness shows near-zero elongation and a sudden fracture with no necking.

Hardness scales: Brinell (HBW, 10 mm ball), Vickers (HV, pyramid, covers all hardness ranges), Rockwell C (HRC, hard steels) - conversions are approximate only.

Carbon steel classes: low carbon ≤0.25 % C (ductile, weldable), medium 0.25–0.6 % C (hardenable), high >0.6 % C (springs, tools); cast iron typically 2–4 % C.

Heat treatment: annealing softens and relieves stress; normalising refines grain; quenching forms martensite; tempering restores toughness after quenching.

Non-ferrous: aluminium alloys (high strength-to-weight, oxide film corrosion resistance), copper (excellent conductivity), brass = Cu+Zn, bronze = Cu+Sn.

Polymers: thermoplastics soften on reheating and are recyclable (PE, PVC, ABS); thermosets cross-link permanently (epoxy, bakelite, polyester resin).

Composite rule of mixtures: E_c ≈ V_f·E_f + V_m·E_m, so fibre volume fraction and fibre orientation govern strength and stiffness.

Equilibrium of a coplanar force system: ΣFx = 0, ΣFy = 0, ΣM = 0 about any point; three non-parallel non-concurrent forces must be concurrent.

Moment M = F × perpendicular distance; a couple has equal, opposite, parallel forces and a moment independent of the reference point.

Friction: limiting friction F = μN; angle of friction φ = tan⁻¹μ; on an incline motion starts when tan θ = μ.

Centroid of a triangle lies at one-third height from the base; rectangle at mid-height; semicircle at 4r/3π from the diameter.

Second moment of area: rectangle I = bd³/12 about the centroidal axis; parallel-axis theorem I = I_G + A·d².

Bending equation σ/y = M/I = E/R; maximum bending stress occurs at the greatest distance y from the neutral axis.

Torsion: T/J = τ/r = Gθ/L; for a solid circular shaft J = πd⁴/32, so τ_max = 16T/πd³.

Kinematics: v = u + at, s = ut + ½at², v² = u² + 2as; for a projectile, range R = u²sin2θ/g is maximum at 45°.

Ohm's law V = IR; power P = VI = I²R = V²/R; series resistances add, parallel conductances add (1/R_T = Σ1/R).

Kirchhoff's laws: KCL - sum of currents at a node is zero; KVL - sum of emfs and p.d.s around a closed loop is zero.

Single-phase AC: V_rms = V_peak/√2; impedance Z = √(R² + (X_L − X_C)²); resonance at f = 1/(2π√(LC)).

Three-phase star: V_line = √3·V_phase, I_line = I_phase; delta: V_line = V_phase, I_line = √3·I_phase.

Transformer: V₂/V₁ = N₂/N₁ = I₁/I₂; ideal transformer has no losses and power in equals power out.

Semiconductor devices: diode conducts when forward biased above ≈0.7 V (Si); a bridge rectifier gives full-wave DC; a Zener diode regulates voltage in reverse breakdown.

Transistor as a switch: cut-off (V_BE < 0.7 V, no collector current) and saturation (V_CE ≈ 0.2 V); β = I_C/I_B.

Electrical machines: DC motor speed falls as load rises; induction motor slip s = (N_s − N)/N_s, synchronous speed N_s = 120f/p.

First law for a closed system: Q − W = ΔU; for a steady-flow open system: q − w = Δh + Δke + Δpe.

Ideal gas: pV = mRT; R = 287 J/kg·K for air; cp − cv = R and γ = cp/cv = 1.4 for air.

Absolute temperature must be used in gas laws: T(K) = T(°C) + 273.15.

Carnot efficiency η = 1 − T_cold/T_hot (absolute temperatures); no real engine between the same limits can exceed it.

Otto cycle efficiency η = 1 − 1/r^(γ−1), where r is the compression ratio; Diesel cycle efficiency also depends on the cut-off ratio.

Polytropic process: pVⁿ = C; work = (p₁V₁ − p₂V₂)/(n − 1) for n ≠ 1; n = 1 is isothermal, n = γ is isentropic.

Heat transfer: conduction Q/t = kAΔT/L; Stefan–Boltzmann radiation P = εσAT⁴; convection depends on the film coefficient h.

Boiler/steam terms: sensible heat raises water to saturation, latent heat converts it to dry saturated steam, superheat is added above saturation temperature.

Cutting speed V = πDN/1000 (m/min) with D in mm and N in rev/min; feed is in mm/rev and depth of cut in mm.

Turning time = L/(f·N) where L is the tool travel including approach and overrun; drilling time uses feed per revolution and hole depth plus point allowance.

Casting: shrinkage allowance is added to the pattern (grey cast iron ≈ 10 mm/m, steel ≈ 20 mm/m); draft angle eases pattern withdrawal.

Welding: arc welding uses a consumable or non-consumable electrode; V-groove butt joints need root gap and included angle for penetration; brazing joins below 450 °C without melting the parent metal.

Sheet metal: blank size = developed length of the neutral axis; bend allowance uses the neutral-axis radius, not the inside radius.

Limits and fits (ISO): clearance fit - hole minimum larger than shaft maximum; interference fit - shaft larger than hole; transition may be either.

Hole basis is preferred: H for the hole, and shaft letters a–h give clearance, j–n transition, p–zc interference.

Machine tools: a lathe produces cylindrical surfaces, a milling machine flat surfaces and slots, a shaping machine flat surfaces by reciprocating single-point tool.

Vernier calliper: least count = 1 main scale division − 1 vernier division; typical 0.02 mm when 50 vernier divisions span 49 main divisions.

Micrometer least count = pitch/number of thimble divisions, typically 0.5 mm/50 = 0.01 mm; zero error must be added or subtracted.

Errors: systematic (calibration, zero error) can be corrected; random errors are reduced by averaging repeated readings.

Accuracy is closeness to the true value; precision is repeatability of readings - a precise instrument can still be inaccurate.

Sensitivity is output change per unit input (e.g. mV/°C for a thermocouple); resolution is the smallest detectable change.

Transducers: thermocouple (Seebeck emf), RTD/thermistor (resistance change), strain gauge (gauge factor ΔR/R = G·ε), LVDT (displacement).

Control: open loop has no feedback; closed loop compares feedback with set point and the error drives the controller; PID combines proportional, integral and derivative action.

Signal conditioning: a Wheatstone bridge converts small resistance changes to voltage; an amplifier raises it to the ADC range; anti-alias filtering precedes sampling.

Concrete mix: nominal 1:2:4 (cement:sand:aggregate) for general work; water-cement ratio ≈0.5 governs strength and workability.

Concrete cube strength is measured at 28 days; characteristic strength is the value below which no more than 5 % of results fall.

Slump test measures workability; compaction factor test is used for drier mixes; curing keeps concrete moist for strength gain.

Reinforcement: steel bars carry tension in concrete; cover protects against corrosion and fire; lap length and anchorage depend on bar diameter and grade.

Soil bearing capacity governs footing size; shallow footings transfer load at low depth, piles transfer it to deeper competent strata by friction or end bearing.

Beam bending: maximum bending moment for a simply supported beam with central point load W is WL/4; with uniformly distributed load w, it is wL²/8.

Surveying: levelling uses a level and staff; reduced level = height of instrument − staff reading; rise and fall method checks ΣBS − ΣFS = last RL − first RL.

Setting out uses a builder's square or the 3-4-5 rule to establish right angles; levels are transferred with a dumpy level or automatic level.

CAD coordinate entry: absolute (x,y), relative (@dx,dy) and polar (@r<θ); object snaps (endpoint, midpoint, centre, intersection) enforce geometric accuracy.

Layers separate line types by function (outline, hidden, centre, dimension) and carry colour, linetype and lineweight; drawing should be done at full size and scaled at plot.

Parametric CAD uses geometric constraints (parallel, tangent, coincident) and dimensional constraints; over-constraining produces conflicts.

Standard sheet sizes ISO A0 = 1 m²; each successive size halves the area, so A4 = 1/16 m² (210 × 297 mm).

Model space holds true-size geometry; paper space/layout holds the title block and viewports at a chosen scale such as 1:10.

Blocks/symbols are reusable definitions; editing the definition updates every insertion, which suits standard fasteners and symbols.

Dimension styles must match the drafting standard in use (arrow type, text height, precision); text height is typically 2.5–3.5 mm on A4.

Plot output: lineweight and linetype scale must be checked in the preview; missing fonts are replaced, so standard fonts should be used.

A project brief defines the problem, client need, constraints and acceptance criteria; the design specification turns these into measurable requirements.

Project phases: identification, research, specification, concept design, detailed design, prototype, test, evaluation, reporting.

Gantt charts show activities against time and reveal the critical path; the critical path is the longest sequence with zero float.

The design process is iterative: evaluate against the specification and return to earlier stages when a criterion is not met.

Testing must state the variable changed, the variable measured and the variables held constant, with repeat readings for reliability.

Costing includes materials, bought-out parts, labour and overhead; a bill of materials lists every part with quantity, material and size.

Risk assessment for a project: identify hazards, rate likelihood and severity, apply controls, and record residual risk.

Reporting: state aim, method, results with units, analysis, sources of error, conclusion and recommendations; cite sources and acknowledge assistance.

Personal protective equipment is the last line of defence: eliminate, substitute, engineer controls, administrate, then PPE.

Electrical safety: isolate, lock off and tag, prove dead with a tester, and earth before work; earth-leakage protection trips at a set residual current.

Machine guarding: fixed guards for permanent hazards, interlocked guards stop the machine when opened; never remove a guard to speed work.

Workshop hazards: eye injury from swarf and grinding, hand injury at the chuck, fumes from welding and solvents - local exhaust ventilation controls fumes.

Fire triangle: fuel, oxygen and heat; Class A solid, B flammable liquid, C gas, D metal fires; water must not be used on electrical or metal fires.

Manual handling: keep the load close, bend the knees, keep the back straight, and team-lift loads beyond the safe individual limit.

Professional ethics: competence within one's training, honesty in reporting results, confidentiality, and reporting unsafe practice.

First aid and reporting: know the location of first-aid kit and emergency stop; all accidents and near misses are recorded in the accident book.

Tolerance notation: limits shown as 25.00/24.95 or 25 ±0.025; ISO symbol H7/g6 gives hole basis clearance with the numeric values from tables.

Geometric tolerancing symbols: flatness, straightness, circularity, cylindricity (form); perpendicularity, parallelism, angularity (orientation); position, concentricity, symmetry (location).

A datum is a theoretically exact reference; the datum feature symbol attaches to the surface that establishes it.

Surface texture: Ra is the arithmetic mean roughness; a 3.2 µm Ra finish is typical turned work, 0.8 µm for ground surfaces.

Screw thread designation M20 × 2.5 means metric thread, 20 mm nominal major diameter, 2.5 mm pitch; a coarse thread omits the pitch.

Welding symbols: a fillet weld is shown by a triangle on the reference line; the arrow side is below the line, the other side above.

Assembly drawings use item numbers and a parts list; working drawings give each part fully dimensioned for manufacture.

CAD file management: revision control, unique drawing numbers, and a checked/approved signature trail prevent manufacturing from obsolete drawings.

Production types: job (one-off, general machines), batch (moderate volume, jigs and fixtures), mass (dedicated lines, high capital).

Lean tools: 5S workplace organisation, kanban pull scheduling, poka-yoke error proofing, and value-stream mapping to remove waste.

Seven wastes: overproduction, waiting, transport, over-processing, inventory, motion and defects.

Quality control: control charts separate common-cause from special-cause variation; sampling plans define accept/reject lots.

Metrology in production: go/no-go gauges check limits quickly; a go gauge must pass the part, a no-go gauge must not enter.

Jigs guide the tool and fixtures hold the work; both reduce setting time and operator dependence in batch production.

Automation levels: fixed (mass), programmable (batch, CNC), flexible (mixed volume) - CNC part programs use G-codes for motion and M-codes for machine functions.

Maintenance: preventive (scheduled), predictive (condition-based), corrective (after failure); total productive maintenance targets zero breakdowns.

Renewable sources: solar photovoltaic (direct electricity), solar thermal (heat), wind (kinetic to electrical), hydro (potential to electrical), biomass and geothermal.

Wind power available in the stream P = ½ρAV³; the Betz limit states no turbine extracts more than 16/27 of that power.

Hydro power P = ρgQHη, so output rises with flow rate and head; pumped storage returns energy at lower efficiency.

Solar panel output depends on irradiance, temperature and tilt; output falls as cell temperature rises above 25 °C.

Fossil plant efficiency: thermal efficiency = net work out / heat energy in; combined cycle raises efficiency by using exhaust heat in a steam cycle.

Energy units: 1 kWh = 3.6 MJ; 1 tonne of oil equivalent ≈ 41.9 GJ; power is energy per unit time (W = J/s).

Energy storage: batteries store electrochemical energy, flywheels kinetic, pumped hydro potential; round-trip efficiency is always below 100 %.

Environmental control: SO₂ and NOₓ from combustion are limited by scrubbers and low-NOₓ burners; CO₂ capture reduces emissions at an energy penalty.

Calibration compares an instrument against a traceable standard and records the error at several points across the range, up and down.

Hysteresis is the difference between readings taken while increasing and decreasing the input; dead band is the input change giving no output change.

Linearity error is the maximum deviation from the best straight line, expressed as a percentage of full-scale output.

Range and span: range is the lower to upper limit, span is the difference between them; accuracy is often quoted as % of span.

Static characteristics: accuracy, precision, sensitivity, resolution, drift, repeatability and hysteresis.

Dynamic characteristics: response time, time constant, and damping - an underdamped instrument oscillates, an overdamped one responds slowly.

Temperature measurement: thermocouple for wide range and fast response, RTD for stability and accuracy, thermistor for high sensitivity over a narrow range.

Pressure measurement: Bourdon tube for gauge pressure, diaphragm and strain-gauge transmitters, manometer for low pressure via ρgh.

Loads: dead (self-weight), live (occupancy), wind and seismic; design compares factored load effects with factored resistance.

Stress in a short axially loaded column σ = P/A; slenderness ratio L/k determines whether buckling governs.

Shear force and bending moment diagrams: shear is zero where the bending moment is maximum; a point load gives a shear jump and a moment kink.

Deflection limits protect finishes and serviceability; deflection rises with span to the fourth power for a uniformly loaded beam (δ = 5wL⁴/384EI).

Brickwork: stretcher, header and English bonds; mortar joint thickness is typically 10 mm; a half-brick wall is not load-bearing for heavy loads.

Timber: grain direction governs strength; moisture content changes cause shrinkage and warping; preservative treatment extends life.

Foundations: strip for walls, pad for columns, raft for weak soils over a large area, piles where a firm stratum is deep.

Construction sequencing: setting out, excavation, foundation, superstructure, services, finishes, with inspection at each hold point.

Cable voltage drop ≈ (2 × I × L × ρ)/A for a single-phase two-wire circuit; the permitted drop is limited by regulation.

Earthing provides a low-impedance path so protective devices operate; the earth-fault loop impedance must be low enough to trip the device in time.

Protective devices: fuses and MCBs for overload and short circuit, RCD for residual current (earth leakage), surge arresters for transient overvoltage.

Cable current rating depends on conductor size, insulation, ambient temperature and installation method (enclosed or clipped).

Power factor correction: capacitors reduce reactive power; corrected kVAR = P(tan φ₁ − tan φ₂), improving supply capacity and reducing losses.

Distribution: generation at medium voltage, step-up transformers for transmission to cut I²R losses, step-down transformers for distribution and use.

Battery: capacity in ampere-hours; series cells add voltage, parallel cells add current capacity; charging efficiency is below 100 %.

Illumination: luminous flux in lumens, illuminance in lux (lumens per m²), efficacy in lumens per watt - LED lamps give the highest efficacy.

Continuity: A₁V₁ = A₂V₂ for incompressible flow; a smaller pipe area gives a higher velocity.

Bernoulli (ideal, horizontal): p/ρg + V²/2g + z = constant; real flow loses head to friction.

Reynolds number Re = ρVD/μ; below ≈2000 flow is laminar, above ≈4000 turbulent, between is transitional.

Pressure in a fluid: p = ρgh; gauge pressure is measured above atmosphere, absolute pressure = gauge + atmospheric.

Archimedes: upthrust equals the weight of fluid displaced; a floating body displaces its own weight of fluid.

Pump power = ρgQH/η; system head includes static lift, friction and velocity head.

Pipe friction head h_f = f(L/D)(V²/2g); friction rises with length and velocity squared and falls with larger diameter.

Flow measurement: orifice plate and venturi use pressure difference; a venturi has lower permanent loss than an orifice for the same flow.

Tensile test gives yield strength, ultimate tensile strength, elongation and Young's modulus from the stress–strain curve.

Proof stress (0.2 % offset) is used for materials with no clear yield point, such as aluminium alloys.

Impact test (Charpy/Izod) measures toughness; a ductile-to-brittle transition appears as test temperature falls in some steels.

Fatigue failure starts at a stress concentration and grows under repeated stress below the static strength; a smooth finish and radius reduce the risk.

Creep is time-dependent deformation under sustained load at high temperature; it limits design of turbine and boiler components.

Corrosion: galvanic corrosion needs two dissimilar metals and an electrolyte; sacrificial anodes protect steel because the anode corrodes instead.

Non-destructive testing: dye penetrant for surface cracks, magnetic particle for surface/near-surface in ferrous metals, ultrasonic and radiography for internal defects.

Hardness test selection: Brinell for castings and coarse structures, Vickers for thin sections and case-hardened layers, Rockwell for rapid production checks.

Oxy-acetylene flame types: neutral (≈3200 °C, steel welding), oxidising (excess oxygen, brass brazing), carburising (excess acetylene, hard surfacing).

Arc welding polarity: DC electrode negative gives deeper penetration, electrode positive gives better cleaning action on aluminium.

Weld defects: porosity from gas entrapment, slag inclusion from poor cleaning, lack of fusion from low current, undercut from excessive current.

Forging shapes metal by compressive force above recrystallisation temperature; it improves grain flow and strength along the shape.

Rolling, extrusion and drawing are continuous forming processes; extrusion pushes metal through a die, drawing pulls it through.

Press work: blanking cuts the outline, piercing cuts a hole, deep drawing forms a cup; clearance between punch and die controls edge quality.

Soldering and brazing rely on capillary action and flux to remove oxide; the joint is not a fusion weld and the parent metal does not melt.

Heat-affected zone in welding is un-melted parent metal altered by heat; rapid cooling can harden it and cause cracking in high-carbon steels.

Hierarchy of control is applied before work starts; a safe system of work and permit-to-work are required for high-risk tasks.

Risk rating = likelihood × severity; controls reduce one or both, and residual risk must be recorded and accepted by an authorised person.

Hand tool and portable tool safety: inspect before use, use the correct tool for the task, disconnect power before changing blades or bits.

Lifting equipment and slings must be rated, inspected and marked with safe working load; never exceed the SWL and keep people clear of the lift.

Hazardous substances require a safety data sheet, labelling, ventilation and correct storage; solvents must not be used near ignition sources.

Noise control: reduce at source, enclose, then use hearing protection; exposure limits are set as daily average levels.

Documentation: drawings, method statements, risk assessments and inspection records form the quality and safety trail; changes need authorisation.

Professional responsibility includes refusing unsafe work, reporting defects, maintaining competence and respecting confidentiality of designs.

Specification criteria should be measurable, e.g. 'withstands 50 N without permanent deformation' rather than 'must be strong'.

Concept selection uses a weighted decision matrix: score each concept against criteria, multiply by weight and sum to compare objectively.

Prototype testing records the test conditions, instrument used and uncertainty; results are compared with the specification, not with opinion.

Analysis of results: tabulate readings, calculate means, plot graphs with labelled axes and units, and identify trends and anomalies.

Sources of error are classified as measurement, procedural or environmental; each should be discussed with its effect on the result.

Evaluation covers function, safety, cost, environmental impact and manufacturability, and states improvements for a future version.

Technical communication: use SI units, correct significant figures, labelled diagrams, and a conclusion that answers the original aim.

Project records: a logbook with dated entries, design sketches and test data supports the final report and demonstrates the work was your own.

Isometric axes are at 30° to the horizontal; true lengths are drawn along the axes and isometric scale = 0.816 × true length for the isometric projection.

In isometric drawing, circles appear as ellipses; the major axis is about 1.22 × diameter and the minor axis about 0.71 × diameter.

Oblique projection shows the front face true shape with receding edges at an angle, usually 45°, and half scale for cavalier/cabinet distinction.

Development of a right cylinder: rectangle of width πD and height equal to the cylinder length.

Development of a right cone: sector of radius equal to slant height, with sector angle θ = 360° × (base radius / slant height).

Intersection of two cylinders produces a curve found by projecting common points from plan to elevation; it is needed for sheet-metal fabrication.

Thread representation: external threads shown by a thick major diameter and thin minor diameter line; internal threads hidden or sectioned.

Springs, gears and knurling use conventional representations rather than true projections to keep drawings clear.

Ammeters are connected in series and have low resistance; voltmeters in parallel with high resistance; a multimeter selects the function and range.

An analogue meter's figure of merit is the current for full-scale deflection; a shunt extends current range, a multiplier extends voltage range.

Wheatstone bridge balances when R₁/R₂ = R₃/R₄; at balance no current flows through the galvanometer.

Oscilloscope: time base sets the horizontal scale in s/div, volts/div sets vertical scale; frequency = 1/period read from the trace.

Digital meter resolution is the smallest display increment; accuracy includes gain and offset errors and is quoted as ±(% reading + counts).

Current measurement with a clamp meter uses the magnetic field of the conductor and needs no circuit break; it suits AC and, with Hall sensors, DC.

Energy measurement: a kWh meter integrates power over time; power P = VI cos φ for AC, where cos φ is the power factor.

Instrument loading: a low-resistance voltmeter or high-resistance ammeter disturbs the circuit and causes a measurement error.

Concrete cube test: 150 mm cubes cured and crushed at 7 and 28 days; 7-day strength is typically about two-thirds of 28-day strength.

Workability tests: slump for normal mixes, compaction factor for low-workability mixes, Vebe for very dry mixes.

Aggregate grading affects workability and strength; a well-graded mix has fewer voids and needs less cement paste.

Steel tensile test gives yield and ultimate strength; reinforcement grade is denoted by characteristic yield strength, e.g. 460 N/mm².

Bitumen for roads is graded by penetration or viscosity; the test temperature must be stated because bitumen is temperature sensitive.

Soil compaction: the Proctor test finds the optimum moisture content giving maximum dry density; density is checked in the field.

Concrete cover and compaction protect reinforcement; honeycombing indicates poor compaction or mix segregation and must be repaired.

Quality records: cube results, slump readings and steel test certificates form the inspection trail for each pour.

Logic gates: AND (output 1 only if all inputs 1), OR (1 if any input 1), NOT (inverts), NAND and NOR are universal gates.

Boolean identities: A + A·B = A, A + Ā = 1, A·Ā = 0; De Morgan: (A·B)' = A' + B' and (A + B)' = A'·B'.

Combinational circuits: half adder sum = A ⊕ B, carry = A·B; a full adder also accepts a carry-in.

Sequential circuits have memory: an SR latch holds state, a D flip-flop stores one bit on the clock edge, a counter chains flip-flops.

Operational amplifier: inverting gain = −R_f/R_in, non-inverting gain = 1 + R_f/R_in; the ideal op-amp has infinite input impedance and zero output impedance.

Filters: a low-pass RC filter has cut-off frequency f_c = 1/(2πRC); above it the output falls at 20 dB per decade.

Rectification: half-wave gives one pulse per cycle, full-wave two; a smoothing capacitor reduces ripple, and ripple falls as C and load resistance rise.

Digital-to-analogue conversion uses a weighted resistor or R-2R ladder; resolution in volts = full-scale/2ⁿ for an n-bit converter.

Lever: effort × effort arm = load × load arm; mechanical advantage = load/effort, velocity ratio = effort distance/load distance.

Pulley systems: velocity ratio equals the number of rope sections supporting the load; efficiency = MA/VR × 100 %.

Gear train: speed ratio = product of driven teeth / product of driver teeth; a worm drive gives high reduction in one stage.

Screw jack: velocity ratio = 2πL/p, where L is the lever length and p the thread pitch.

Truss analysis by method of joints: at a joint with two unknown members and no external load, both are zero-force members if the joint has only two non-collinear members.

A simply supported beam with uniformly distributed load w over span L has maximum shear wL/2 at the supports and maximum moment wL²/8 at mid-span.

Combined stress: principal stresses from σ and τ are σ/2 ± √((σ/2)² + τ²); maximum shear stress = √((σ/2)² + τ²).

Strain energy in axial loading U = P²L/2AE; resilience is the energy absorbed within the elastic limit.

Vapour-compression cycle: compression, condensation, expansion through a throttle, evaporation; COP = refrigeration effect / work input.

Carnot COP for a refrigerator = T_cold/(T_hot − T_cold) with absolute temperatures; real COP is always lower.

Refrigerant leaves the evaporator as low-pressure dry vapour and leaves the condenser as high-pressure liquid; the throttle causes a pressure drop with no work.

Psychrometry: dry-bulb temperature, wet-bulb temperature and relative humidity define air condition; dew point is where condensation begins.

Cooling load comes from occupants, lighting, equipment, solar gain and infiltration; latent load is the moisture removed.

Air conditioning processes: sensible cooling, dehumidification below dew point, humidification by steam or spray, and heating.

Heat pump COP = heating effect / work input = COP_refrigeration + 1 in the same cycle.

Insulation reduces heat gain by conduction; the overall heat-transfer coefficient U combines surface films and layer resistances.

Vernier height gauge measures height from a surface plate; a surface plate provides a true reference plane for marking out and inspection.

Angle measurement: a sine bar gives sin θ = h/L where h is the slip gauge height and L the distance between rollers.

Slip gauges are wrung together to build a dimension; select the minimum number of slips by removing the largest possible sizes first.

Limits and fits calculations: for H7/g6, allowance = minimum hole − maximum shaft; the fit is clearance when allowance is positive.

Surface roughness Ra is the arithmetic mean deviation from the mean line; Rz is the average peak-to-valley height of sampled lengths.

Go/no-go gauges: the go gauge checks the maximum material condition and must enter; the no-go checks the least material condition and must not.

Coordinate measuring machines measure in three axes with a probe; they give form and position as well as size.

Calibration records must be traceable to a national standard and state the uncertainty, otherwise the measurement is not defensible.

DC generator emf E = (pΦNZ)/60A, where p is pole pairs, Φ flux per pole, N speed, Z conductors and A parallel paths.

DC motor torque T = kΦI_a; speed falls with load because armature drop and armature reaction reduce flux effect.

Starting a DC motor requires a starter to limit armature current, since at standstill the back emf is zero and I = V/R_a is large.

Three-phase induction motor: rotating field speed N_s = 120f/p; slip is small at full load (typically 2–5 %).

Single-phase induction motors need a starting winding or capacitor to create a rotating field; they are used for small loads.

Transformer losses: copper loss varies with load squared, iron loss is nearly constant; maximum efficiency occurs when copper loss equals iron loss.

Motor protection: overload relay for sustained overcurrent, fuse or MCB for short circuit, and thermal protection embedded in the winding.

Variable-speed drives rectify and invert the supply to control frequency, so motor speed changes with frequency while torque capability is managed.

Level survey: height of instrument HI = RL of benchmark + backsight; RL of a point = HI − intermediate or foresight reading.

Rise and fall method: rise when the next staff reading is smaller, fall when larger; arithmetic check ΣBS − ΣFS = Σrise − Σfall = last RL − first RL.

The collimation method (height of instrument) is quicker but gives no check on intermediate sights.

Traverse: bearings are measured from north; interior angle sum of a closed polygon = (n − 2) × 180°.

Compass bearings: whole-circle bearing is measured clockwise from north; a magnetic bearing differs from true bearing by magnetic declination.

Setting out a right angle uses the 3-4-5 triangle or a theodolite turned through 90°; long lines need a check on the diagonal.

Contours join points of equal level; closely spaced contours indicate steep ground, widely spaced contours gentle ground.

Volumes from spot levels use the trapezoidal or prismoidal rule; the prismoidal rule is more accurate for varying cross-sections.

Every project activity requires a risk assessment before work begins; the assessment is reviewed when the method or conditions change.

Ethical reporting means presenting all results, including those that do not support the hypothesis, and stating limitations honestly.

Data protection and confidentiality: client drawings and test data are not shared without permission.

Plagiarism is avoided by citing sources and by keeping dated design records that show your own contribution.

Teamwork: agree roles, record decisions, and ensure each member can explain the whole design, not only their part.

Environmental responsibility: choose recyclable materials, minimise waste in manufacture and consider energy use over the product life.

Professional bodies set codes of conduct covering competence, public safety, integrity and sustainability; membership is not a licence to exceed competence.

Final report structure: title, summary, aim, background research, design, method, results, discussion, conclusion, references and appendices.