Calculations

Here are some maths things to work out how far Ben's car will go.

I have estimated the weight of the car at 1090kg.
This the weight with the internal combustion engine and associated systems still attached. When that is removed and batteries etc. installed it will be considerably heavier, however for the purposes of an estimate the original weights work fine.

The first thing to do is work out the Drag Force. This is the basically the external forces acting on the car that absorb more energy. So that is wind resistance and tyre drag.

First you've got the drag coefficient and for Ben's car that is 0.4
The drag coefficient is to do with the aerodynamics of the car body, wind resistance really

Then you've got the frontal area of the car which is 2.11m squared.
The frontal area will increase the wind resistance as it has a larger area to act on.

Next is the vehicle mass which is 1090kg and that is equal to 10682N
N stands for Newtons. We'll come back to the mass later.

Now to calculate the Drag Force we use the following equation.

F_Drag = Cd x A x V2
V2 is supposed to be V squared

F_Drag just means Drag Force

Cd is the drag coefficient which is 0.4

A is the frontal area which is 2.11m2

V is the speed in meters per second

So we need to calculate the speed we are traveling at. Lets say we will be traveling at an average speed like 56km/hr (this equation can be used for any vehicle weight traveling at any speed, you just have to change the values)

Convert 56km/hr to meters per second(m/s)

to do this

56 x 1000/3600 = 15.56 m/s

15.56=V

Now input all the values into the equation

F_Drag = Cd x A x V2

F_Drag = 0.4 x 2.11 x 15.56squared = 203.4N this is the total air drag force acting against Ben's car as it travels at 56km/hr.

One more thing we have to add the tyre drag into the equation and generally tyre drag is about 1.3% of the vehicles weigth which is 10682N

so.... 10682 x 1.3/100 = 138.9N

138.9 + 203.4 = 547.6N this is the total drag force that acts against the car as it travels at 56km/hr.

Now to find out the amoun of power it is going to take to move the car, we will calculate this in watts or w. We use the equation
Power = Force x Speed or P = F_Drag x V

so...P = 547.6 x 15.56 = 8520.6w
547.6 is the drag force and 15.56 is the speed in meters per second

To find out what horse power this is 1hp = 746w
so... 8520.6/746 = 11.42hp

Now to calculate the energy consumption rate if the car is travelling at 56km/hr

so.... 8520.6/56 = 152wh/Km this is the amount of energy consumed per km.

Now how will this affect our range, it all depends on what type of battery pack we work with.
Hypothetically we will say that we will have a 144 voly system. That will be 12, 12 volt batteries rated at 150Ah wired in series to give you 144 volts of energy. A 12 volt battery rated at 150Ah will give you 1800 watts of energy. You multiply 12 x 150 to obatin the wattage of the battery.
So the packs energy will be 1800 x 12 = 21600w or 21.6Kw

However lead acid batteries should only be discharged to 50% of their capacity to avoid damaging them so this gives us an actual battery pack of 10.8Kw

So to calculate the range we will have if we were to drive at a constant speed of 56km/hr on a flat road we simply divide the packs capacity by the consumption rate which is 152wh/km

so.... 10800/152 = 71km will be the range of this car, of course in reality the car weigth will be greater and there will be other influencing factors such as climbing inclines and driving at lower speeds, the stop start driving style of town driving, this will all lead to a lesser range. However these are the kind of equations we will be working with initially to determine the needs of our car. There is also a mathematical modeling program called MATLAB that we should get a copy of. It makes the calculations a hell of lot easier, quicker and more accurate.