# Unit 46

### Unit introduction

This unit will develop learners’ knowledge of mathematical and scientific principles and their application in the vehicle technology environment. This can be in a variety of vocational areas, such as the fine detail needed in the calculations in motorsport or the crucial calculations required when working with large commercial vehicles.

Learners will carry out data collection and manipulation in vehicle-related areas such as speed, acceleration and power. They will complete a variety of practical activities, including carrying out an engine performance test and comparing the outcomes to scientific calculations.

Note that the use of ‘e.g.’ in the content is to give an indication and illustration of the breadth and depth of the area or topic. As such, not all content that follows an ‘e.g.’ needs to be taught or assessed.

### Learning outcomes

On completion of this unit a learner should:

• Be able to apply mathematical and statistical methods to vehicle-related tasks
• Be able to apply fundamental algebraic laws and trigonometric ratios to solve vehicle-related tasks
• Be able to apply scientific principles related to heat, force and machines to solve vehicle-related tasks
• Be able to carry out engine testing and apply scientific principles to determine vehicle and engine

### Unit content

• Be able to apply mathematical and statistical methods to vehicle-related tasks

Data for vehicle-related tasks: data, e.g. engine speed, stopping distance, miles per gallon, brake pad life, vehicle speed, acceleration, wheel bearing life; sources, e.g. manufacturers, workshop experiments, publicly available figures (such as media, internet); considerations, e.g. types of error, accuracy, representation

Mathematical methods: methods, e.g. addition, subtraction, multiplication, division, use of brackets, order, estimation techniques, use of calculators, expressing numbers using standard form and scientific notation                                       2

Data manipulation and graphical representation: data represented in graphical format, e.g. bar charts, pie charts, frequency distributions, class boundaries and class width, frequency table, variables (discrete and continuous); histogram (continuous and discrete variants); cumulative frequency curves

Statistical information: arithmetic mean; median; mode; discrete and grouped data

• Be able to apply fundamental algebraic laws and trigonometric ratios to solve vehicle-related tasks

Linear equations and graphs: linear equations, e.g. y = mx + c; straight-line graph (coordinates on a pair of labelled Cartesian axes, positive or negative gradient, intercept, plot of a straight line); quadratic graph y = ax2 + bx + c

Factorisation and quadratics: multiply expressions in brackets by a number, symbol or by another expression in a bracket; by extraction of a common factor; quadratic expressions; roots of an equation, e.g. quadratic equations with real roots by factorisation, and by the use of formula

Trigonometric ratios: basic ratios, e.g. sine, cosine, tangent;

Vehicle-related tasks: algebraic application, e.g. Ohm’s law, pair of simultaneous linear equations in two unknowns (two linear or one linear and one quadratic), acceleration 30 to 50 mph, time taken to cover a given distance when subjected to constant acceleration, volume and area of combined shapes,

e.g. swept, clearance volume, loading capacity, workshop areas; trigonometric application, e.g. steering and suspension angles, valve timing, wiper motion angles

• Be able to apply scientific principles related to heat, force and machines to solve vehicle-related tasks

Force: laws of friction; friction in a clutch; stress and strain; Young’s modulus; forces in tension/compression; vehicle component subjected to tension/ compression, e.g. tie rod, cylinder head bolt, push rod, valve stem, piston, connecting rod, braking components

Heat: gas laws, e.g. Boyle’s law, Charles’ law, general gas equation pV = c , ideal gas equation pV = mRT; change of dimension, e.g. linear, superficial, cubical, heat dissipation; pressure, e.g. hydraulic, gas; gauge pressure, atmospheric pressure

Machines: ratios, e.g. steering box, gear ratio, final drive ratio, compression ratio; vehicle mechanism, e.g. alternator and power steering, pulleys, winches, levers, brake operation, cylinder, gearbox

• Be able to carry out engine testing and apply scientific principles to determine vehicle and engine performance

Vehicle performance: equations of motion; Newton’s laws; performance,

e.g. work, power, velocity, acceleration, retardation

Engine testing: safe use of equipment, e.g. rolling road, dynamometer rig, engine analyser; collection of data, e.g. torque, power (indicated and brake), fuel consumption

Engine performance: performance to report on, e.g. torque, power (indicated and brake), mechanical efficiency, thermal efficiency, volumetric efficiency, specific fuel consumption, brake mean effective pressure, indicated mean effective pressure; presentation within report, e.g. engine indicator diagrams, calculations using data (such as efficiency, frictional loss, temperature variations)