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NEM3101 Engineering Analysis and Modelling Dr M.Sek
Week 4 tasks
Numerical integration and differentiation. Power demand on an automotive engine.
Notes on numerical integration and differentiation can be found by following the links at:
You work for a Formula 1 team. You happen to obtain a record of velocity versus elapsed time during a lap test for the car of your competitor. No other information is available due to commercial-inconfidence restrictions.
The knowledge about the power of the competitor's car engine would allow your team to fine-tune the power characteristics of your car engine to exceed that of the competitor's.
You are given a task of estimating the power characteristics of their engine.
On the website, under the heading Sample data files: Car speed vs time data, there is a a twocolumn text file, containing a record of speed of an accelerating vehicle (in km/h), starting from a stationary position. Values in the first column are the elapsed time from the start (in seconds) and the corresponding values of velocity (km/h) are in the second column. To save the file right-click on the link and select 'Save target as'.
1 Make appropriate analysis of how to determine the power that the vehicle power drive must supply at each point of time to produce that velocity profile. First, neglect aerodynamic drag, rolling resistance and other friction losses If you need to assume some values, do so.
2 At each point of time determine the distance from the start that the vehicle has travelled. This requires numerical integration, such as trapezoidal integration.
3 Determine the acceleration the vehicle is subjected to at each point of time. This requires numerical differentiation. Finite difference formulae can be found at:
4 Calculate the power demand at each point of time.
5 Now consider the rolling resistance and aerodynamic drag with a rolling friction coefficient and aerodynamic drag coefficient typical to vehicles. What is the drive power at each point of time now? Make assumptions and select values from a realistic range as required.
Submit your progress work at the end of the Lab session and the completed work before the start of your next Lab session in Week 5
Make hard copies of plots showing the results and bring them to the Lab in Week 5.
Relationship between the position, velocity and acceleration
Position x
v ? ? x?
dv d 2x
a ? ? 2 ? ?x??dt dt

Position x dx ? v dt
x2 t 2
? dx ? ? v dt
x1 t1
Distance travelled
t 2
x2 ? x1 ? ? v dt Area under v
New position
t 2
x2 ? x1 ? ? v dt
t1 ? f(t)

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