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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.
Weight
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.
Rules Of Thumb:
- A subcompact car (Geo Metro, etc) will have an original curb weight under 2000lbs.
- A typical compact sedan, wagon, or sporty car will have an original curb weight between 2000 and 3000 pounds.
- A midsize car, pickup or minivan's original curb weight will be 3000 to 4000 pounds.
- Large cars and trucks have original curb weights in excess of 4000 pounds.
- A high trim line model can weigh several hundred pounds more than a base model of the same car
- Earlier model years of a car can be lighter than later model years due to "feature creep".
- You will be able to remove around 20 percent of the car's original curb weight in take-off components, such as the engine, gas tank, etc. More extreme measures such as body and interior modifications could buy you another 5 to 10 percent.
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.
| Weights used for my calculations |
|---|
| Total Weight (Mass) | Wtot | 1450kg (3200lbs) | Kilograms (1 kilogram equals 2.2 pounds) |
Motor Characteristics
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.
Rules Of Thumb:
- Figure on using a motor with a continuous rating of least one horse power for every 200 pounds of weight on the car if you want to be able to drive at freeway speeds. An 8-inch ADC motor rated for about 20 horsepower. The 9-inch ADC is rated for about 30 horsepower.
- An electric motor's peak horsepower is three times its rated horsepower in a typical EV conversion. This will be sustainable for several minutes or more, which is plenty long enough to accelerate to freeway speed or to climb a steep hill. The motor controller that you use will likely be the limiting factor in effective peak horsepower of the motor, due to the controller's voltage and current ratings.
- Don't use a motor with less than 3000 RPM rating. You won't encounter this with purpose-build series-wound DC motors, but you might with more exotic motor designs, or with older motors and motors that were not originally designed for use in an EV. With the gear ratios in a typical car's drivetrain, the motor will reach 3000 RPM by the time you reach freeway speed.
- Don't use a motor that is rated for less than 96 volts for a car that will travel at freeway speeds. It is common practice to exceed the rated voltage by 10 to 20 percent in a homebuilt EV, but don't push it. EV drag racers often exceed their motors' rated voltages by double or triple, but they also only run for a few seconds at a time, and they do occasionally toast a motor.
- For a given basic motor design, larger ones tend to have better peak efficiencies, but at the same time can be less efficient under light loads.
- It takes about 10 horsepower to propel a small car at 55mph. This translates to someplace around 20 foot pounds of torque at the motor, with typical sized tires and gear ratios.
The commonly quoted properties for any electric motor are:
- Voltage rating: The maximum voltage that the motor has been designed for. Input voltage and motor RPM are roughly proportional, so you need to make sure that this rating sufficient to allow you to achieve the speeds you want the car to drive at.
- RPM rating: Again, make sure it is sufficient for achieving the speeds that you want the car to drive at. You can calculate motor RPM, knowing the size of your drive wheels and the overall gear ratio of the drivetrain.
- Continuous Horsepower rating: The maximum output power that the motor can continuously deliver. Note that the peak horsepower that an electric motor can deliver on an intermittent basis is easily several times what the rated horsepower is.
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
- Current Curve: This shows the input current to the motor in relation to the output torque. This curve will be roughly linear. The inverse slope of this line represents the "torque constant" for the motor. This curve will not cross "0" amps at the zero torque point on the chart. The current draw at zero torque is known as the idle current of the motor. This is the minimum amount of current that will allow the motor to run.
- Efficiency Curve: This curve shows the overall efficiency of the motor in converting electrical power (watts, or volts multiplied by amps) into mechanical power (watts, or horsepower). For most DC motors, this curve will peak in the middle of the motor's curve aroiund a few thousand RPM, and it will drop off drastically at the high RPM and high torque ends of the chart. A good DC motor will have 85 percent or better peak efficiency, and the "flatter" the efficiency curve is, the better.
- RPM Curve: This curve relates the output RPM of the motor to the input voltage. The higher the input voltage of the motor, the higher the RPM will be. Note however that load on the motor will affect RPM as well, and this in turn can affect the effective voltage across the motor. The more you load the motor, the more it will draw down the voltage across it. However, as voltage across the motor drops under load, its current draw increases. In other words, as you load down a motor, its RPM goes down and its torque increases.
- Power Curve: This curve is can be thought of as a function of the RPM curve and input torque. Mechanical power (watts, or horsepower) is proportional to speed multiplied by torque.
| 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) |
Drivetrain Characteristics
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.
Rules of Thumb:
- A typical manual transmission or transaxle is about 95% efficient.
- A typical automatic transmission is around 85% efficient. Don't go there.
- A typical solid rear axle is about 97% efficient, including the wheel bearings.
- A typical differential unit in a car with independent suspension is 98% efficient.
- A typical driveshaft (with two universal or CV joints and a spline of some sort) is 99% efficient. This can get better if the driveshaft is nearly straight (requiring no flexing of its CV/universal joints) and worse if those universal joints are running at a significant angle.
- Wheel bearings lose about 0.5% per axle. (I will account for brake drag in the rolling resistance section.)
- A typical overall gear ratio in 1st gear for a car is about 12 to 1.
- A typical overall gear ratio in 4th gear for a car is about 4 to 1.
Given the above generalizations, you can start to make a basic analysis of the drivetrain.
- The Toyota MR2: Mid engine, rear drive. A simple, lightweight drivetrain.
- Manual transaxle: 95%
- Driveshafts(2): 98%
- Driven rear wheels: 0.995
- Undriven front axle: 0.995
- Total drivetrain efficiency: 0.95 * 0.98 * 0.995 *0.995 == 0.9217 or 92.2% efficient.
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 |
|---|
| Overall Efficiency | Effdt | 0.92 | None |
| Highest gear ratio (Low gear) | Dgrhi | 13 | None |
| Lowest gear ratio (High gear) | Dgrlo | 4 | None |
Electrical System
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.
Rules of Thumb:
- Modern PWM (Pulse-Width-Modulated) Motor Controllers such as the ubiquitous Curtis and the high-performance Zilla (See the links on the EV Reference Material page) are amazingly efficient. A safe assumption is that they will exceed 98% efficiency under typical road use. (Note that if they were not that efficient, they would require a huge heat sink to dissipate the heat generated.)
- Lead acid batteries and properly-sized power cabling have very low internal resistance, but can still lose about 1% of power as heat.
- An estimate as to continuous power draw of all 12-volt automotive accessories (lights, fans, radio, etc) on a car is 250 to 500 watts. If the car has minimal accessories, use the low figure. If it has a lot of add-ons in addition to the normal stuff, use the high end. Even 500 watts is a tiny amount compared to the many kilowatts of power that the motor will draw.
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 |
|---|
| Overall Efficiency | Effel | 0.95 | None |
| Controller maximum current | Ccmax | 500A | Amperes |
| Controller maximum voltage | Cvmax | 144V | Volts |
Battery Characteristics
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.
Lead Acid Battery Properties:
- Flooded and regular sealed lead acid batteries such as the Trojan T-875 and TE-35 have an energy density (in Watt-Hours of energy per Pound) of about 20Wh/Lb.
- AGM-Type lead acid batteries such as Optima deep cycle batteries will have an energy density (in Watt-Hours per Pound) of about 15Wh/Lb.
- An EV using lead acid batteries should have at least 1/3 of its overall weight in batteries.
- Lead Acid batteries have an annoying habit of having their effective energy capacity reduced exponentially with a linear increase in current draw. This can be modelled using a formula called Peukert's law. Typically manufacturers give effective capacity at several different power output levels for a given battery type. This effect can easily halve (or worse) the effective capacity of lead acid batteries in an EV application.
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 volts | Bv | 128V | Volts |
| Battery Energy Capacity (20 hour rating) | Be | 24kwh | kilowatt hours |
| Battery Energy Capacity (75 amp load rating) | Be | 14kwh | kilowatt hours |
Aerodynamic Drag
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.
Rules Of Thumb:
- The smaller the car, the better.
- Hard Top sports cars, and hatchbacks are among the most aerodynamic cars available.
- For any given age of car, Japanese cars will tend to be better than European, which tend to be better than American
- Newer cars are generally more aerodynamic than older ones
- Station wagons and pickup trucks of a given size are similar in overall drag, so I have heard.
- Convertibles will have significantly worse drag compared to the hard top version of the car.
- Don't go by what looks more aerodynamic; two very similar looking cars can have substantially different aerodynamic properties.
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) |
Rolling Resistance
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.
Rules Of Thumb:
- The more worn a tire is, the less rolling resistance it will have
- Larger diameter tires have less rolling resistance than smaller tires
- Narrower tires have less rolling resistance than wide tires
- Higher pressure in the tires results in less rolling resistance
- Typical tires have a rolling resistance of 1 to 2 percent.
- "Low Rolling Resistance" tires are usually quoted as having 0.6 to 1 percent rolling resistance.
- Brake friction can add another 0.25 percent of the car's weight in drag.
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 |
