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For a successful Electric Vehicle design, certain basic minimum specifications need to be met. These specifications are dependant on the vehicle use. If what we are talking about is a fully functional vehicle, then the minimum power needed can be determined. Whatever the configuration, you have to have enough voltage to push the current you need to get the torque you need at the required speed to overcome the losses of tire and wind resistance, and do the work needed to push the vehicle uphill and to increase speed. The needed voltage quickly increases with increased torque and increased speed.
First of all, the vehicle needs to maintain 65 mph on a level freeway. Also the vehicle needs to maintain a minimum of 55 mph up a 6% grade which is the maximum freeway grade. These are continuous requirements. In addition, The vehicle needs to be able to accelerate up Laural Street. The peak slope of Laural Street is about a 21% grade. Therefore, from 0 to 25 mph, the vehicle needs to generate enough torque to create a forward thrust at least one-quarter of the gross vehicle weight. In addition is a minimum acceleration of 1.1 mph/sec that needs a force equal to 5% of the vehicle's weight. This is a short term or intermittent requirement and should not last more then 5 minutes. The other option is to use gears to get the needed torque for going up a hill and/or accelerating. Vehicles must have the ability to accelerate up the grades given to safely drive in traffic.
Therefore we will start with a vehicle with a total gross weight of 3000 lb (including passengers & load), with tires with a rolling resistance of 1% of the vehicles weight [typical radial-ply, high pressure tires], and with a frontal area of 20 square feet and coefficient of drag of about .5, the following suggested values should apply:
speed max grade accel. tire wind total horse equiv. mph grade force force force force force power power 5 25% 750 lb 150 lb. 30 lb. 1 lb. 931 lb. 12.4 9.3 kW 25 18% 540 lb 150 lb. 30 lb. 16 lb. 736 lb. 49.1 36.6 kW 40 12% 350 lb 150 lb. 30 lb. 42 lb. 582 lb. 62.0 46.3 kW 55 6% 180 lb 150 lb. 30 lb. 79 lb. 439 lb. 64.3 48.0 kW 70 0% 200 lb 150 lb. 30 lb. 127 lb. 307 lb. 57.4 42.8 kW
Note that the 931 lb of force is temporary. At any rate, running at this force requires a lot of current and that tends to greatly heat the motor. So when going up a very steep hill, watch your temperature and use a lower gear if necessary.
Going up a 6% freeway, however, may last for 20 minutes. During this time, motor temperature and battery voltage need to be carefully monitored. Under a load like this, motors tend to overheat, and batteries exhaust themselves very quickly. Going up a 6% grade at 55 mph for 20 minutes is a vertical climb of more than 5,000 feet. This is about the limit for a single charge of a lead-acid battery in a typical electric vehicle in where the batteries are half the weight of the vehicle. Vehicles in which the batteries are most of the weight of the vehicle, can go higher.
And, of course, the steady freeway at 70 mph may last as much as an hour or more. In other words, this is a continuous specification. Obviously, at this speed, the batteries would have to be charged about every 45 minutes. In other words, 50 miles is a typical range of an electric vehicle using lead-acid batteries running level at freeway speed. Of course a vehicle with a lower drag coefficient will go further on a charge, as will a vehicle driven slower. At 55 mph or less, on a level freeway, the time between recharges should increase to over an hour, and the range should increase to more than 60 miles.
With the limited power available from the Advanced D.C. FB1-4001 9.1 inch motor, it is necessary to pick a gear ratio high enough to get up hills, but low enough to be able to travel at a reasonable speed. The gear ratio is between the motor and the tires. Also note the thermal limitation of high current. Maximum continuous current ranges from about 160 to 200 amps depending on motor speed and ambient temperature. For minutes, maximum current ranges from about 280 to 460 amps. Higher currents for less then a minute are possible, but not recomended.
Of course current and its corresponding torque are reduced by decreasing motor voltage. Thus at any speed, the force can be any value from zero to the maximum shown. What is necessary is that enough force is available to keep the vehicle moving at a safe speed.
gear ratio = 6 input output Torque current motor power power force speed lb-ft amps RPM KW Hp lb mph 10 100 8000 14.4 15.2 57 100 20 150 6500 21.6 24.8 114 81 30 190 5600 27.4 32.0 171 70 50 280 4600 40.3 43.8 286 58 70 350 4000 50.4 53.3 400 50 100 460 3500 66.2 66.6 571 44 140 600 3000 86.4 80.0 800 38 gear ratio = 8 input output Torque current motor power power force speed lb-ft amps RPM KW Hp lb mph 10 100 8000 14.4 15.2 76 75 20 150 6500 21.6 24.8 152 61 30 190 5600 27.4 32.0 228 53 50 280 4600 40.3 43.8 381 43 70 350 4000 50.4 53.3 533 38 100 460 3500 66.2 66.6 762 33 140 600 3000 86.4 80.0 1066 28
But none of these configurations really give enough power to meet the minimum vehicle specification over the entire operating range as shown in Table 1. Using gears can help cover the full range. A gear ratio of 8:1 or higher can be used with steep hills or driveways to reduce needed current and a gear ratio of about 6:1 can be used on freeways to keep the motor RPM down. Note that the motor is most efficient [between 80% and 88%] at moderate currents.
The most common batteries used for home-built electric vehicles are of the deep cycle lead-acid type. These batteries usually weigh between 60 and 90 pounds. The most common configurations are 6, 8 and 12 volt.
Voltage Current Time Power Power Weight volts amps minutes Watts HP lbs US-145 6 125 79 750 1.0 70 US-125 6 125 67 750 1.0 67 17-4-1 8 125 67 1000 1.3 unk. US8VGC 8 100 50 800 1.1 65 US-185 12 125 54 1500 2.0 111 EV-145 12 100 72 1200 1.6 87
In other words, each battery can deliver the electrical equivalent of about a horsepower for about an hour. The US-185 can deliver almost 2 horsepower for about 54 minutes. These batteries can deliver about four times that power for a short period of time, perhaps 7 to 11 minutes. After that, the batteries would have to be recharged. Note that the times are for new batteries and that lead-acid batteries should NOT be completely discharged. Therefore at these discharge rates, the run time should be less than 80% of the times shown. When more power is needed, current increases and time available is greatly reduced. Remember that new batteries correctly cycled can deliver more power and energy then old batteries and that warm batteries can deliver more power and energy then cold batteries. Discharging the batteries more than 60% shortens their life. Discharging the batteries more than 80% significantly shortens their life.
Typical home-built electric vehicles use 12 to 30 batteries. Typical total voltages range from 72 volts (low performance or light weight vehicles) to over 196 volts (high performance or heavy vehicles). Most common configurations are 120 volt and 144 volt vehicles. (Controllers for voltages over 144 are much more expensive.)
Number of Current Time Power Horse Energy Total batteries amps minutes KW Power KW-Hr Weight US-145 24 125 79 18.0 24.1 23.7 1680 lb. US-125 24 125 67 18.0 24.1 20.1 1600 lb. 17-4-1 18 125 67 18.0 24.1 20.1 not given US8VGC 18 100 66 14.4 19.3 15.8 1170 lb. US-185 12 125 54 18.0 24.1 16.2 1332 lb. EV-145 12 100 50 14.4 19.3 12.0 1044 lb.
Other battery types can give more power and/or more energy per pound then lead-acid, but they are much more expensive. Note that speed is dependent on power, and range is dependent on energy.
In summary of the above example, a plot was made of the above data to see the relationship between the force needed to move the vehicle, and the force available from the motor. In this example, the gross weight of the vehicle is 3000 lb, the vehicle has tires make 800 revolutions per mile and have a rolling resistance equal to 1% of the vehicle weight, the vehicle has a frontal area of 20 square feet with a coefficient of drag of 0.5. The motor is an Advanced DC FB1-4001 electric motor connected to 144 volt battery through a 500 A controller that limits the maximum current to 480 amps. The available force from the motor is plotted at the wheels with gear ratios of 6, 8 and 10. A plot of the force needed to move the vehicle at a steady speed on a level road is plotted. A plot of the force needed to move the vehicle at a steady speed up a 6% grade is also plotted. For reference, the maximum force needed to accelerate at 1.1 mph/sec up different grades as defined in table 1 is also plotted. Note that the maximum continuous current to the motor should not exceed 190 amps. A current of 350 amps for more than 5 minutes will overheat the motor. The maximum controller current of 480 amps should used for only a minute or two.
In the above graph, this simulation shows that a gear ratio of 6:1 will allow the vehicle to eventually reach 70 mph on a level road. With a grade of 6%, the vehicle will slow down to 57 mph. With higher gear ratios, these speeds will be reduced. A gear ratio of 6:1 will allow the vehicle to accelerate up a 12% grade at speeds less then 40 mph. A gear ratio of 10:1 will allow the vehicle to accelerate up 25% grade at speeds less then 25 mph. The time going up steep grades must be limited because of full current heating. The driver should try to keep the force below the 6th mark on any curve for continuous driving. [Maximum controller current is 500 A, but more the maximum continuous motor current is about 200 A.] Note that less battery voltage will shift the curves to the left, and more battery voltage will shift the curves to the right. In any design, you need sufficint battery voltage to push the current you need to get the torque you need to get the force you need to maintain your desired speed. The is especially true when going up hills and/or acellerating. Of couse the battery must be able to supply the needed current.
This page is given as a worksheet, a starting point for estimating performance of a new electric vehicle before it is built. As expected, more weight will decrease performance. A smaller battery will significantly decrease speed and range. A smaller motor will decrease maximum speed. Remember that a motor only converts electric power into mechanical power. The battery must be large enough to convert chemical energy into electric energy fast enough to provide the maximum power the motor needs. The battery must be large enough to contain sufficient energy to go the distance.