Electric car modelling using a trapezium rule

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Electric car modelling using the trapezium rule The trapezium rule allows us to numerically estimate integrals. This case study involves the use of the trapezium rule to model the performance of a hypothetical electric car propelled by a DC motor by integrating acceleration to estimate velocity and integrating velocity to estimate distance. The Electric car is powered by a permanent magnet 24 volt DC motor connected to the rear driving wheels by a simple sprocket and chain mechanism with no gearbox. The motor is powered by a set of ten 12V batteries. The motor torque Tm (Nm) can be approximately modelled as Tm = K I, where K is the DC motor torque constant and I is the motor current (A). The Mechanics The model we are dealing with is a simplified version that neglects the rotational inertia of the wheels and other components of the motor system. The torque on the wheel is directly proportional to the motor torque Tm therefore T = Tm = K I can be directly calculated. The forces we will be dealing with are; the forward propulsion force (F) generated by the rear wheels, the gravitational force (W = M g) and the drag force due to friction (Fd). Mathematical Relationships The relationship between acceleration, velocity and distance will help us to model the performance of the car. Relation of force (N) to mass (kg) and acceleration (m/sec2): Relation of velocity (m/sec) to acceleration (m/sec2): Relation of distance (m) to velocity (m/sec): Drag and Wind resistance The effect of wind resistance will be modelled as the additional force which takes effect at velocities greater than v1. According to the equation Fd = Fd0 (1 + b(v �� v1)2) the drag force will increase for velocities v > v1. In this case study there will be a low velocity drag force acting on velocities 20 m/s or less and an

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