This page lists the various input parameters you need in order to be able to perform mathematical calculations to figure range, acceleration, hill climbing ability and top speed.
Note that in figuring this input data, you will have to look up information, make some educated estimates, and maybe make a few A before B before A calculations. I just did my best, you will have to as well.
Also provided are some "rules of thumb", useful for those of us who hate math, and for validating estimates and calculations. The numbers I provide at the end of each section are what I am using on the EV Performance Analysis page in my calculations.
you need to know the weight of the car as an EV. Weight factors into all calculations for the performance of an EV (or any car): Range, Acceleration, hill climb angle, and top speed.
Figuring the car's weight as an EV is a matter of taking the car's original curb weight and subtracting the weight of the removed internal combustion components, and then adding the weight of the batteries (discussed later) and electric propulsion components. See the EV Reference Material for help in figuring out this information. You can make estimates, or weigh everything that you add or remove, as I am doing. Look at the EV Chassis Selection page for a table of curb weights for some of the cars I considered.
I have removed about 520 pounds of weight from my MR2. Its original curb weight was 2265 pounds. See the EV Weight Change Page for details. The take-offs represent about 23 percent of the car's weight. I expect the final product to weigh about 3200 pounds: 1700 pounds for the chassis, 1100 pounds of batteries, (See the battery characteristics section for where I got this number), and another 300 pounds or so for everything else). This represents a gain of about 43% over the car's original curb weight on top of the stripped-down weight of the chassis.
EV electric motors have several properties that need to be considered when being evaluated. These values should be available from the manufacturer.
For calculating the expected range of an EV, the most interesting aspect of a motor is going to be the efficiency of the motor, measured at the load point for which you are calculating your car's range. For calculating hill climb angle, acceleration and top speed, the peak horsepower of the motor is the primary consideration.
The commonly quoted properties for any electric motor are:
There are also several less-commonly quoted properties of an electric motor which are very valuable when deciding on a motor for your EV. These values are often plotted together on the same chart. An example for the Advanced DC nine inch motor (the one I am using) is shown below. This chart will be for a given input voltage, and will have output Torque on the X axis, and a separate Y axis for each curve.
|Advanced DC nine-inch motor torque curve. Image credit: EVParts.com and Advanced DC motors.|
Image credit: http://www.adcmotors.com and http://evparts.com
|Motor Characteristics used for my calculations|
|ADC 9" Rated Voltage||Mvmax||120 V||Volts|
|ADC 9" Rated RPM||Mrpmmax||5000 rpm||Revolutions per Minute|
|ADC 9" Rated Power||Mpcon||22000 W (30hp)||Watts (746 watts equals 1 horsepower)|
|ADC 9" Peak Power (500A controller limited)||Mppk||64000 W (85hp)||Watts (746 watts equals 1 horsepower)|
|ADC 9" Efficiency (at 20lb/ft of torque)||Effmot||0.88||None|
|ADC 9" Torque Constant||Mtc||0.312 Nm/A (0.23LbFt/A)||Newton-Meters per Ampere (1 newton meter equals 0.74 foot pounds)|
If you are performing a typical EV conversion like I am, you will be mating an electric motor up to your vehicle's original transmission, and the remainder of your vehicle's drivetrain (driveshafts, axles, differential, wheel bearings, etc) will be unchanged. (See my Motor And Adapter Plate page for more information about this, and see my MR2 EV Transmission Modification page for details on how to ensure you get maximum efficiency out of the transmission.
In order to calculate the overall range of the car, you have to take into account the efficiency of the drivetrain. It is difficult to measure the overall efficiency of a drivetrain under normal operating conditions, but there are a few places online and in books (such as those recommended in the EV Reference Material page) that provide drivetrain efficieny numbers. I will repeat those generalizations again here, and infer some additional ones based on the relative complexity of the different types of car drivetrains. Common sense says that the fewer moving parts you have, the better. Every set of gears, and every bearing, universal joint, seal, and shifting fork causes friction. Parts turning while bathed in oil will churn it about and lose energy. Driveshafts lose energy at their universal joints and splines, and due to vibration that inevitably occurs as they spin.
In order to figure acceleration and hill climbing ability, and to figure top speed, you will need to know the overall (motor-to-wheels) gear ratios of your drivetrain. Figure the ratios by multiplying each gear ratio in the transmission by the gear ratio of the differential. These ratios are commonly available in the car's user's manual and/or service manual, or enthusiasts can provide the information online. Sometimes different axle ratios and different transmission options were available, so be sure you know which one you have.
Given the above generalizations, you can start to make a basic analysis of the drivetrain.
The drivetrain efficiency on the MR2 is probably about as good as you can get. For most cars, and rear wheel drive trucks, the number should be similar. Note however that if you look at a four wheel drive vehicle the number will get noticeably worse, and if you use an automatic transmission it will really get bad.
|Drivetrain Characteristics used for my calculations|
|Highest gear ratio (Low gear)||Dgrhi||13||None|
|Lowest gear ratio (High gear)||Dgrlo||4||None|
The efficiency of the electrical system is needed for the EV range calculation. Just like the mechanical drivetrain, the electrical system in the car is not 100% efficient. There are losses in the motor controller and batteries due to internal resistance and the inductive properties of the system as the controller operates. 12-volt accessories on the car will draw power that does not end up making the car go forwards, so for my calculations I consider that as a loss of efficiency in the electrical system.
For top speed, acceleration, and hill climb ability, the maximum current and voltage ratings of the motor controller is needed.
So, given the above generalizations, a conservative guess as to the overall efficiency of the electrical system in an EV is 95%.
|Electrical System Characteristics used for my calculations|
|Controller maximum current||Ccmax||500A||Amperes|
|Controller maximum voltage||Cvmax||144V||Volts|
The batteries that you choose to use will (of course) have a big effect on the performance of the car. However, for the typical, non-filthy-rich person, lead-acid batteries are really the only viable option right now. (Look on the EV Reference Material page for links to wikipedia articles on the various battery types)
Battery weight and energy capacity will go straight to figuring range. Battery weight is probably the single biggest factor affecting acceleration and hill climbing ability. Look on the EV Battery Considerations page for more details on selecting the right kind of batteries for you.
Knowing the above properties of Lead Acid batteries, and Knowing what type of battery, and how many you intend to use will allow you to calculate the weight of the battery pack, and to calculate its voltage and total energy capacity. (For the pack energy capacity is most conveniently measured in Kilowatt-Hours). I intend to use a pack of 17 trojan T-875's. This will give me a 136 volt pack with a nominal 24kwH of capacity that weighs 1100 pounds. However considering Peukert's law and the 75-amp capacity rating of these batteries, it is safer to assume that I will be able to get 14KwH of power from the pack, running at highway speeds.
|Battery Characteristics used for my calculations|
|Battery Weight||Wbat||500kg (1100lbs)||Kilograms|
|Battery Energy Capacity (20 hour rating)||Be||24kwh||kilowatt hours|
|Battery Energy Capacity (75 amp load rating)||Be||14kwh||kilowatt hours|
For a car that is travelling at highway speeds, aerodynamic drag is the largest force that must be overcome to keep the car moving. (Hills notwithstanding) The car's aerodynamics have lesser effects as well on top speed and acceleration. The aerodynamic properties of a car body are difficult to measure, but fortunately the information is available for many cars. See the EV Reference Material page for some links.
The overall aerodynamic drag of a car is affected by two things: Shape and Size. A given shape has a measurable property called Cd, or the drag coefficient. Size, for the purpose of aerodynamics, is described as A or frontal surface area. To figure overall drag force on a car, you need to use CdA or the drag coefficient multiplied by the frontal surface area. See the EV Chassis Selection page for some CdA values for cars I considered. See the EV Reference Material page for links to sites that suggest ways to improve aerodynamics of a car.
My Toyota MR2 has a CdA of 0.535m2. It was near the best in the list of cars I was considering. The same year Pontiac Fiero (a very similar looking rear engine sports car) has CdA of 0.63m2, almost 20% worse, even though (to me, anyway) it looks more aerodynamic than the MR2.
|Aerodynamic drag characteristics used for my calculations|
|Drag coefficient times frontal surface area||CdA||0.535m2 (5.76sqft)||square meters (1m2 equals 10.76sqft)|
The rolling resistance of a car is the second biggest source of drag on a car that is travelling at freeway speed, and is probably the largest force acting on it at lower speeds. Therefore, it must be factored into the range calculation, and it has lesser effects on top speed and acceleration, and hill climbing angle. Tire rolling resistance is typically described as a constant force resisting movement of about 1% to 2% of the weight of the car. The tires you choose have a significant effect on this. See the EV Reference Material for more details and suggestions as to what tires are best to use. Brake drag will add a smaller component to the overall rolling resistance.
Given all of this, it is safe to assume 1.5 percent of the car's overall weight in rolling resistance, if you use LRR tires. Otherwise, assume 2 percent.
|Rolling resistance characteristics used for my calculations|
|Total Rolling Resistance (as a proportion of vehicle weight)||Rr||0.015||None|