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65 Posts
Discussion Starter · #1 ·
I want a book with equations and explanations. I want as many ways to approach the DIY EV equations as possible. You know, stuff like 1/2mv^2 + ... [I forget the other terms, but aerodynamics, the little bit of rolling resistance, etc.]. I want equations/explanations of power, energy, and range. I wanna be able to plug equations and values into a spreadsheet, make some graphs, and feel like I've gotta handle on this EV stuff. I don't want assumptions and fluff. If it also has stuff on controller theory and whatnot, that's fine.


65 Posts
Discussion Starter · #3 ·
I liked this one. There may be more recent editions or others by now. Basic physics texts can help. And there may be schools in your area.

Build Your Own Electric Vehicle by Bob Brant

Also, you can find a lot here
I just ordered the 2007 or 2008 (?) edition of that book.

The EV info has two guidelines for the first two steps of sizing your battery pack:
Step 1:
"The voltage should be chosen to match the power requirement of the vehicle at the required top speed. For example most DC motorbike conversions will require a minimum voltage of approximately 72V to be able to travel at 60+mph (100km/h) while a pick-up conversion would most likely require 144V to maintain the same speed.

The first step in sizing your pack is to determine your top speed requirements and look at the voltage of other similar sized conversion needed to achieve that speed."

Step 2:
"As a general guide motor bikes will generally use 75-150Wh/mile, cars may use around 200-400 and pick-ups and heavy vehicles around 400-600Wh/mile ..."

I'd like to calculate those values instead of estimating them.

Admin: 'one of many'
4,838 Posts
Everything that went into my spreadsheet came from this forum. I searched about for any references and asked a few questions and worked out the equations as I went along.

Everytime I found something that might be useful I made a note and put it in my spreadsheet until I had enough to get something useable.
I included little tables of air density at various temperatures, for aerodynamic drag, and for rolling resistance of different tyres on different surfaces.


Power consumption of aerodynamic drag
= 1/2 x air density x V³ x frontal area x Cd [notice that that is a V cubed in there]

Power consumption of rolling resistance
= Crr x Mv x V

air density (rho) = 1.29 at 0
Mv = Mass of vehicle (kg)
V = Velocity (metres/second)
Crr = Coefficient of rolling resistance, 0.03 for car tyre on asphalt
Cd Coefficient of drag, around 0.6 for an open top car and 0.3-0.35 for average modern car.

The combination of these two will tell you how much power, in Watts, your car needs to keep moving at a specific velocity on level ground in still air at
0ºC with ordinary car tyres on asphalt.

Dividing your W(power) by your mph gives you Wh/mile

Energy consumption = Wh/mile

Using your required range you can determine the battery capacity.

Energy Consumption x Range
eg: 200Wh/m x 40mile range = 8000Wh or 8kWh
However you only have an 80% Depth of Discharge (DoD) so you require a 10kWh pack.

Pack capacity
Cell voltage x ah rating x number of cells
3.2v x 100ah x 30
9600Wh @ 96v

You can vary the number and size of cells until you get the power and range you require.

You can also look up the mass, in kg, of the range of cells and include that in the overall mass of the vehicle.

This is what my spread sheet looked like when I did a quick calculation for my tractor.
Using LiFeP04 cells:

Using Lead Acid:

I have since extended the spreadsheet to include gear ratio calculations (that are not linked to the above sheets) and weight distribution (that is linked) to determine front rear weight and centre of gravity.

1,378 Posts
A good proxy for energy use is fuel economy. Figure it takes about 1000 pounds to equal a gallon of gasoline (or about 100 kg of lead acid to equate to a liter of gasoline). Even if you go full bore with computations, this can offer a sanity check. Credit for this idea goes to Killacycle owner Bill Dube . Let's try a few computations, they are consistent with your quote below:

1000 kg of Optima lead acid batteries ~= 7 kWhr of usable energy

10 mpg vehicle => 7 kWh / 10 mi = 700 wh/mi
15 mpg vehicle => 7 kWh / 15 mi = 470 wh/mi
20 mpg vehicle => 7 kWhr / 20 m = 350 Wh/mi
30 mpg vehicle => 7 kWhr / 30 m = 230 Wh/mi
40 mpg vehicle => 7 kWhr / 40 m = 180 Wh/mi
50 mpg vehicle => 7 kWhr / 50 m = 140 Wh/mi
70 mpg vehicle => 7 kWhr / 70 m = 100 Wh/mi
100 mpg vehicle => 7 kWhr / 100 m = 70 Wh/mi

Of course, YMMV.
... "As a general guide motor bikes will generally use 75-150Wh/mile, cars may use around 200-400 and pick-ups and heavy vehicles around 400-600Wh/mile ..."

I'd like to calculate those values instead of estimating them.

102 Posts

I bought the Second Edition of this, and can't recommend it. The content may be good, but unfortunately the editing is extremely poor. For example, on one page I found the same paragraph in two different sections (but only relevant to the second). Also (it may have been the same page) there's a diagram showing a basic setup for switching between AC and DC drive-trains, and the diagram has the AC and DC motors switched so it doesn't match the text (or make sense) at all.

These are not the only things I found wrong, they're just the ones I remember...

But it does have lots of formulae :)
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