Formula One Race Strategy
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within Formula One racing. Here students learn about the models which are used to develop race strategy, since every F1 team must decide how much fuel their cars will start each race with, and the laps on which they will stop to refuel…
Dropped Load Assessment in Nuclear Industry
This resource, from Mathematics for Engineering Exemplars, introduces mathematical models for the risk assessment of dropped load, which are used to analyse the safety of structures within nuclear power stations. Here students learn about the formulae which engineers use to calculate the maximum dynamic stress and strain produced…
Wind Turbine Power Calculations
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the field of mechanical and electrical engineering in the power industry. When planning a wind farm it is important to know the expected power and energy output of each wind turbine to be able to calculate its economic viability. This…
Forces on Large Steam Turbine Blades
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the mechanical and electrical engineering power industry. Here students learn how statistical models are used to set alarms which detect changes in vibration above normal values. The alarms highlight that something is changing and…
Monitoring Vibration Levels in Steam Turbines
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the mechanical and electrical engineering power industry. Here students learn how statistical models are used to set alarms which detect changes in vibration above normal values. The alarms highlight that something is changing and…
Understanding the Motion of the Wheels
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the field of mechanical engineering and explores the design and construction of wheels, to be used to challenge a land speed record. These principles also apply in engines and gear-boxes, which are typically full of rotating machinery…
The Mathematics of Pumping Water
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when designing a pumping system. The operating pressure of a pumping system can vary due to various factors, so all the relevant operating conditions need to be assessed to ensure the selected pump is capable of achieving the entire operating…
The Mathematics of Simple Beam Deflection
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within a civil engineering environment. Here students apply standard deflection formulae to solve some typical beam deflection design problems. These formulae form the basis of the calculations that would be undertaken in real life for…
Draining Hazardous Liquids During Chemical Processing
This resource, from Mathematics for Engineering Exemplars, shows how to build a mathematical model of liquid draining through a tank and how to use the model to determine the time required for a tank to completely drain. Bernoulli’s conservation of energy equation, which requires integration and differentiation, is applied…
Mathematics behind the Water Network in Rural Mountain Areas
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within public health engineering to supply clean water in a rural mountain area. Here students learn about the formulae used to calculate the optimum size of pipes which will ensure good pressure of water throughout the network. Detailed…
Study of Dynamic Systems in JCB Construction Machinery
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the mechanical and civil engineering industry. Here students learn how calculations for displacement, velocity and acceleration, caused during loading, are used to ensure that they are not so large as to adversely affect the performance…
Suspension System in JCB Construction Machinery
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when designing highway machinery. Because a driver has to remain in the same machine for almost eight hours each day, the vibration amplitudes of the operator’s seat, which should be kept as low as possible, are a key factor when…
Study of the Motion of Knee and Ankle during Cycling
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the field of sports technology to compare the potential for injury to the knee or ankle when cycling and when jogging. Students model a situation involving oscillations, looking at inertial forces, Newton’s Laws of Motion,…
The Study of Root Mean Square (RMS) Value
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within mechanical, electrical and electronics engineering. One of the principal applications of Root Mean Square values is with alternating currents and voltages. This activity demonstrates the calculations required to evaluate RMS using…
The Study of Engineers' Data 1
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when investigating the volume of registration of engineers. Statistical calculations and graphical representations are used to explore the variations, over time, of membership by area of expertise. Detailed notes and examples are provided…
Study of Vibrations in JCB Dieselmax Engines
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when designing and developing engines. As well as considering the power requirements for a given application, the vibration of the system should be considered. The engine installation in a machine must ensure that the natural frequency…
Calculating Power of JCB Dieselmax Engines
This resource from Mathematics for Engineering Exemplars shows the application of mathematics in mechanical engineering and construction machinery. Here students encounter the formulae used to calculate the power of the engine which was used to power the JCB Dieselmax LSR car to a world land speed record of 350mph in August 2006. Detailed…
The Mathematics of Escalators on the London Underground
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics for the operation of escalators on the London underground. Students consider a variety of issues which include passenger numbers and flow, as well as carbon emissions, escalator speed and energy efficiency. Detailed notes and examples…
Underground Storage Tank
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when building an underground storage tank, with an elliptical cross section. Health and safety requirements apply and the depth to which the tank must be buried is established using the 2D geometry of an ellipse, trigonometric functions…
Steam Pipe Insulation
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the field of mechanical engineering. Here students learn that lack of proper insulation results in large energy losses which, over time, cost a lot of money. Models are used to calculate the value of the critical insulation radius…
The Mathematics of Aircraft Navigation
This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the aeronautical industry. Students are given a scenario which involves the recovery of stranded mountaineers by a rescue helicopter and the considerations required for a successful outcome. Trigonometry, formula transposition and…