Electric car modelling using a trapezium rule

Electric car mouldingling using the trapezium rule

The trapezium rule allows us to numerically estimate integrals.
This case subject involves the use of the trapezium rule to model the performance of a hypothetical electric car propelled by a DC move by integrating acceleration to estimate pep pill and integrating pep pill to estimate outperform.

The Electric car is powered by a permanent magnet 24 volt DC motor connected to the rear driving rolls by a simple sprocket and chain mechanism with no gearbox. The motor is powered by a set of ten dollar bill 12V batteries.

The motor torque Tm (Nm) can be near 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 therefrom T = Tm = K I can be directly calculated.

The enduringnesss we will be dealing with are; the former propulsion persuasiveness (F) generated by the rear wheels, the gravitational force (W = M g) and the drag force due to friction (Fd).

numeric Relationships

The relationship between acceleration, hurrying and distance will answer us to model the performance of the car.





Relation of force (N) to people (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 granting immunity


The inwardness 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 report there will be a low velocity drag force acting on velocities 20 m/s or less and an additional force when the velocity exceeds the threshold velocity v1 of 20 m/s.

Aim
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