
Electric vehicles outperform gasoline vehicles in all regards except range, and if you splurge on the battery you can have the range (and ludicrous power). Electric vehicles are more powerful, quieter, simpler, more flexible, and cheaper than gasoline vehicles, and you can put an electric motor on anything, even a rollerblade. Electric power is ideal for compact and cheap city cars.
Air drag determines a vehicle's top speed and energy usage, and this determines the minimum battery size.
Air density = D = 1.22 kg/meter^{3} Air drag area = A Speed = V Air drag force = F = ½ A D V^{2} Air drag power = P = ½ A D V^{3} = F V Range = X Energy used = E = F X Battery mass = M Battery cost = S Battery energy/mass= e = E/M = .8 MJoules/kg Battery power/mass = p = P/M = 1600 Watts/kg Battery energy/$ = s = S/M = .010 MJoules/$A compact car designed for city speeds doesn't need much power. Example values for various electric vehicles:
Speed Power Force Force/prsn People Range Drag area m/s kWatt Newton Newton km m^{2} Skate 10 .18 18 18 1 5 .3 Kick scooter 10 .18 18 18 1 5 .3 Bike 15 .82 55 55 1 8 .4 Car, small, city speed 20 4.9 244 244 1 10 1 Car, large, freeway speed 30 33 1100 1100 1 15 2 Bus, freeway speed 30 99 3290 46 72 15 6 Train car, freeway speed 30 99 3290 27 120 15 6 Airbus A380 251 251000 1000000 1840 544 10000 160 1 Horsepower = 746 WattsEnergy usage is proportional to the drag force per person. If a bus is full it is 5 times more efficient than a compact car, but buses are rarely full and usually slow.
Buses and trains are substantially more efficient than planes and they should be favored over short flights.
"Power" is the minimum power required for the given speed.
We assume a minimalist battery  the smallest battery that can provide the given power. We then calculate the energy for this battery using the battery parameters and we caculate a range using this energy. Larger range can be achieved with a larger battery. Since a minimalist battery is cheap, a larger battery is usually feasible.
The drag parameter is obtained from an analysis of commercial vehicles. Data
Battery cost as a function of power is 20 Watts/$. A 1 kWatt bike battery costs $50, a 10 kWatt city car battery costs $500, and a 100 kWatt freeway car battery costs $5000. For city vehicles the battery is a small fraction of the vehicle cost and for freeway vehicles it's a significant cost.
A flying car powered by lithiumion batteries can fly for 45 minutes and cover 100 km. The minimum price of the car is set by the battery. The smallest battery capable of powering a 1person car costs $8000.
Flying cars will be capable of vertical takeoff and landing and will have 2, 3, or 4 rotors. The rotor number is determined by a tradeoff between efficiency (fewer rotors is better) vs. stability and failsafe (more rotors is better). The car will also have a wing to help with horizontal flight.
The properites of flying cars are determined by the properties of lithiumion batteries and rotors. In the sections below we use these to construct a concrete design for a flying car.
The design of the car depends on the physics of rotors. For a rotor,
Power required to hover = Constant * LiftForce^{3/2} / RotorRadiusThe larger the rotor radius the better, so long as it's not so large as t dominate the mass of the car. We choose the design so that the total mass in rotors is half the mass of the pilot.
The most efficient copter has one lift rotor (a "monocopter"). Increasing the number of rotors while preserving the total rotor mass means that each rotor becomes smaller, hence it takes more power to fly.
Increasing the rotor number increases stability and redundancy. Most drones use 4, 6, or 8 rotors. 4 rotors offers good stability and failsafe and there is no point to a flying car with more than 4 rotors. Flying cars can be expected to have 2, 3, or 4 rotors.
The flight time is proportional to the battery mass, hence the battery should be as large as possible but not so large so as to dominate the car mass. We choose a design with a battery mass equal to the pilot mass. With this mass, the battery power is twice that required to hover, and so power isn't a problem.
Stateoftheart lithiumion batteries have an energy/mass of .8 MJoules/kg and can fly a car for 44 minutes. In the future, lithiumsulfur batteries will take over with an energy/mass of 1.4 MJoules/kg.
We outline a design using 2 large lift rotors plus a few small stability rotors, with the following masses:
Flying car mass = 120 kg (Excluding battery and pilot) Battery mass = 100 kg Pilot mass = 80 kg Total car mass = 300 kg Total aircraft mass = M = 300 kg (Includes passenger) # of large rotors = N = 2 Rotor radius = R = 1.5 meters Gravity constant = g = 9.8 meters/second^{2} Rotor force = F = Mg/N =1470 Newtons Rotor quality = q = 1.02 Air density = D = 1.22 kg/meter^{3} Rotor power = P_{r}=(qDR)^{1}F^{3/2}= 30.2 kWatts Hover power = P_{h}= N P_{r} = 60.4 kWatts Hover power/mass = P/M = 101 Watts/kg battery mass = m = 100 kg Battery power/mass = p =1200 Watts/kg Battery power = P_{b}= p m = 120 kWatts Battery energy/mass = e = .8 MJoules/kg Battery energy = E = e m = 80 MJoules Battery $/energy = c = 100 $/MJoule Battery cost = C = c E =8000 $ Hover time = T = E/P_{h} =2650 seconds = 44 minutesThe properties of propellers are discussed in the propeller section. The rotor tip speed is
Rotor lift/drag = Q = 5.5 Rotor tip speed = V = PQ/F = 113 m/sThe ideal horizontal cruise speed is around 1/3 of the rotor tip speed. If we assume a cruise speed of 40 meters/second and a flight time of 44 minutes then the range is 106 km.
Electric bike motors use either 36, 48, or 72 Volts. The following table shows how to build a battery pack for each motor power.
Power Volts Cells Series Parallel Current Cell Cell Cell Cell Cell kWatt Amperes Amperes Amphours $ type ID# .5 36 10 .75 36 10 10 1 21 25 2.1 4 A LG HD4 1.5 48 13 13 1 31 30 2.0 4.5 A Sony VTC4 3 72 20 20 1 42 60 4.5 4.5 C Basen 6 72 40 20 2 83 120 4.5 4.5 C Basen 12 72 80 20 3 167 180 4.5 4.5 C Basen Cells Total number of cells, equal to the number of cells connected in series times the number of cells connected in parallel. Series Number of cells connected in series. For example, 20 batteries with 3.6 volts each connected in series produces a voltage of 72 Volts. Parallel Number of cells connected in parallel. Current Current required to provide given power Cell Maximum current of a cell