
The quality of a city depends on things like
*) The average travel time
*) The amount of residential and yard space per person
*) The amount of public park space
Most cities are poorly designed in this regard and hence new cities may emerge that are built from scratch. These cities will take advantage of possibilities offered by electric driverless cars prefabricated housing, and factories where you can manufacture things for yourself.
Population Population Area Travel Travel density (millions) (km^{2}) time means (people/ha) (mins) Manila 430 1.65 38.6 30 Taxi Delhi 255 11.0 431 30 Bus Paris 215 2.27 105 30 Subway Seoul 130 10.4 605 30 Subway New York City 104 8.18 784 30 Subway San Francisco 67 .81 121 30 Subway Boston 51 .65 125 30 Subway Isla Vista 48 .023 4.8 5 Walk, bike Pasadena 24 .140 59.5 10 Car Beverly Hills 23 .347 14.8 10 Car Iowa City 10 .068 64.8 10 Walk, bikeElectic cars outperform public transportation for travel time and energy use. New York City is a catastrophic case that illustrates the weaknesses of public transportation. To get anywhere you have to:
This often takes more than 30 minutes, plus the subway routes are awkwardly designed.
Consider two constrating city designes
Design 1) Everyone has a yard adjacent to a park and no upstairs neighbors.
The house has a garage with an electric car.
Design 2) Everyone lives in skycrapers
Being able to drive an electric car right up to your residence dramatically reduces travel time.
Lawns and parks are good for social interaction, especially for families with children. Skyscrapers are poor in this regard.
A high population density can be achieved even if everyone has a yard.
For example, suppose a citizen has on average:
*) A residence of 30 square meters.
*) A yard of 20 square meters.
*) The residence is adjacent to a park with 30 square meters per person.
*) Road space of 20 square meters per person.
These residences are larger than typical New York City apartments and they achieve a respectable population density of 10000 people/km^{2}.
A city with sensible traffic flow can achieve a large population and a small travel time. For example,
City radius = R = 3 km Average travel speed = V = 15 meters/second Average travel time = T = R/V = 3.3 minutes City population density = D = 10000 people/km^{2} = 1 person every 10 meters^{2} City population = P = πDR^{2}=280000 peopleIt helps to centralize. 4 points of focus of a city are the college, the pub district, the shopping district, and the K12 school. These can be placed in the city center and the residences and businesses radiate out from the center.
Electric cars outperform gasoline cars in all aspects except range. They're simpler, more powerful, quieter, and more flexible, plus in time the cost of batteries will decrease and the range problem will be solved.
The range of an electric car depends on the battery price and is typically .03 kilometers per battery dollar. The value for battery energy/$ increases with time and in the future range won't be a problem. The battery tends to be around 1/3 the cost of the car. For a typical car,
Battery energy/mass = e_{m} = .60 MJoules/kg Battery energy/$ = e_{$} =.0070 MJoules/$ Battery mass = M_{b} = 100 kg Battery energy = E = M_{b} e_{m} = 60 MJoules Battery cost = P = E /e_{$} = 8570 $ Range = X = 273 km At a city speed of 17 m/s Range/$ = X_{$} = X/P = .032 km/$
The range is limited by air drag and rolling drag. Rolling drag dominates at low speed and air drag dominates at high speed, and at the critical "drag speed" V_{d} they are equal, typically around 17 m/s. For a typical car,
Car mass = M = 1200 kg Gravity constant = g = 9.8 m/s^{2} Tire rolling drag coeff = C_{r} =.0075 Rolling drag force = F_{r} = C_{r} M g = 88 Newtons Air drag coefficient = C_{a} = .25 Air density = D = 1.22 kg/meter^{3} Air drag crosssection = A = 2.0 m^{2} Car velocity = V = 17 m/s (City speed. 38 mph) Air drag force = F_{a} = ½C_{a}ADV^{2} = 88 Newtons Total drag force = F = F_{r} + F_{a} = 176 Newtons Drag speed = V_{d} = 17 m/s Speed for which air drag equals rolling drag Car electrical efficiency = Q = .80 Battery energy = E = 60 MJoules Work done from drag = EQ = F X = C_{r} M g [1 + (V/V_{d})^{2}] X Range = X = EQ/(C_{r}Mg)/[1+(V/V_{d})^{2}] = 272 kmThe range is determined by equating the work from drag with the energy delivered by the battery. E Q = F X.
The drag speed V_{d} is determined by setting F_{r} = F_{a}.
Drag speed = V_{d} = [C_{r} M g / (½ C_{a} D A)]^{½} = 4.01 [C_{r} M /(C_{a} A)]^{½} = 17.0 meters/second
The battery is the dominant cost in an electric car.
Engine Battery Battery Battery Battery Battery Battery Battery Car Car Car power power energy mass cost mass range cost kWatt kWatt MJoule kg MJ/kg kW/kg $ MJ/$ kg km $ Tesla S P85D 568 397 306 540 .57 .74 44000 .0070 2239 426 115000 Ford Focus Electric 107 92 82.8 295 .281 .31 12000 .0069 1674 122 22495 Nissan Leaf 80 80 76.7 218 .35 .37 5500 .0139 1493 172 22360 Mitsubishi iMiEV 47 47 58 201 .288 .23 1080 100 16345
An electric aircraft uses 7 times more energy than an electric car in terms of energy/distance/mass. Electric aircraft have a cruising speed of 50 m/s and electric cars in cities move at around 15 m/s.
Typical values for electric aircraft and cars are:
Electric aircraft speed = 50 m/s Electric aircraft power/mass = 50 Watts/kg Electric aircraft energy/distance/mass= e_{air}= 1.0 Joules/m/kg Electric aircraft flying time = T =3600 seconds Electric aircraft range = X = 180 km Gravity constant = g = 9.8 m/s^{2} Electric car mass = M Electric car rolling drag coefficient = C_{r} = .0075 Electric car rolling drag = F_{r} = C_{r} M g Electric car total drag = F = 2 F_{r} (Assume rolling drag = air drag) Electric car energy/distance/mass = e_{car}= 2 C_{r} g = .147 Joules/m/kg Aircraft energy / Car energy = e_{air} / e_{car} = 6.8
The performance of a car depends on its power source. Lithium batteries have a substantially lower value for energy/mass than gasoline.
Energy/Mass Power/mass Energy/$ Recharge Max MJoule/kg kWatt/kg MJoule/$ time charges Diesel fuel 48  41  Lithium battery .60 .75 .007 hour 10^{4} Lithiumion supercapacitor .054 15 seconds 10^{5} Supercapacitor .016 8 .00005 seconds 10^{6} Aluminum electrolyte capacitor .010 10 .0001 seconds ∞Electric motors can reach a power/mass of 10 kWatts/kg.
Electric motors and gasoline motors have a similar power/mass.
MJ/kg kWatt/kg kWatts kg Supercapacitor, Liion .054 15 Electric motor, maximum  10 200 19.9 EMRAX268 Brushless AC Turbofan jet engine  10.0 83.2 8.32 GE90115B Brayton Electric motor, DC  7.8 1.04 .133 ElectriFly GPMG5220 brushless DC Gasoline engine (BMW) 7.5 690 BMV V10 3L P84/5 2005 Model aircraft engine  2.8 Battery, lithiumion .75 1.5 Fuel cell, Honda  1.0 Typical diesel V8 turbo  .65 Solar cell, space station  .077
Typical car tires have a rolling drag coefficient of .01 and specialized tires can achieve lower values.
Mass of car = M Gravity coefficient = g = 9.8 meters/second^{2} Car downward force = F_{g} = M g Rolling drag coefficient = C_{r} Rolling drag = F_{r} = C_{} F_{g}The tires with the lowest rolling drag coefficient are:
Tire Rolling drag coefficient Bridgestone B381 .00615 Michelin Symmetry .00650 Michelin Tiger Paw .00683 Bridgestone Dueller .00700 BFGoodrich Rugged Trail .00709 Michelin LTX .00754 Goodyear Integrity .00758 Railroad .00035 Steel wheels on steel rails Racing bicycle tires .0025 8 bars of pressure Typical bicycle tires .004 18wheeler truck tires .005 Typical car tire .01Data
The cost of transport depends on the drag force per person.
Drag force = F Distance traveled = X Energy expended = E = F X Number of people = N Energy/distance/person = Z = E/X/N = F/N Drag speed = V_{d} (Speed for which rolling drag = air drag)For typical vehicles,
Mass C_{r} Area C_{d} Drag speed People Force/person Force/person kg m^{2} m/s at 15 m/s at 30 m/s Electric bike 20 .003 .7 1.0 2.6 1 99 387 Electric scooter 120 .005 1.0 1.0 4.0 1 147 550 Electric car, lightweight 600 .0075 2.0 .20 14.3 1 105 269 Electric car, middleweight 1200 .0075 2.5 .25 15.7 1 180 437 Electric car, heavyweight 1800 .0075 3.0 .3 15.9 1 262 632 Bus 10000 .005 8.0 .6 15.7 60 23.1 56.0 Subway car 34000 .00035 10.0 .6 6.3 100 9.7 34.4 18wheel truck 36000 .005 8.0 .6 24.6 1 2422 4397 Aircraft, 747 220128     480 625The force/person for the 747 aircraft is for a cruising speed of Mach .9 and an altitude of 12 km.
We assume that each person adds 80 kg to the mass of the vehicle.
Buses use 5 times less energy as cars but only if they are full
Within cities, cars have faster travel times than buses, especially if parking is abundant or the cars are selfdriving. Buses are more suited to intercity transport.
Trains use 2 times less energy than buses but they are highly inflexible.
Acceleration depends on the size of the battery, and supercapacitors can add an extra boost. For a typical car that accelerates from 0 to 100 km/h (37.8 m/s) in 8 seconds, the size of the battery required is:
Car mass = M = 1200 kg Target speed = V = 27.8 m/s (100 km/h. Speed at end of acceleration) Kinetic energy = E = ½ M V^{2} = 464000 Joules Time = T = 8 seconds (Time to accelerate from rest to speed V) Engine efficiency = Q = .8 Power = P = E/T = 58000 Watts Battey power/mass = p = 750 Watts/kg Battery mass = M_{B} = P / (Q p) = 112 kg Battery cost/mass = c = 86 $/kg Battery cost = C = 9600 $
Supercapacitors are ideal for recovering breaking energy because they can be charged/discharged more times than batteries. To capture the energy from breaking from freeway speed, on order of 27 kg of supercapacotors are required.
Car mass = M = 1200 kg Car velocity = V = 27.8 m/s Car kinetic energy = E =464000 Joules Supercapacitor energy/mass = e = 16000 Joules/kg Supercapacitor mass = E/e = 29 kg
The principal challenge for flying cars is noise. There is no such thing as a quiet flying car.
Fixed wing flight is at least 6 times more efficient than helicopter flight.
The larger the propeller the less noise. The sound power of a propeller scales as the 5th power of tip speed. A flying car should have a propeller as large as possible. A single large propeller is better than multiple small propellers.
A ducted (shielded) propeller is substantially quieter than an unshielded propeller, and is more efficient in producing thrust.
Electric aircraft are substantially simpler and safer than gasoline aircraft.
Nominal configuration for a quiet flying car:
A single large ducted fan mounted on the rear
50 kWatt engine
Gyrofans and gyroscopes for stability
Wings that fold for driving
Telescoping wing section within the main wing (wings should be as long as possible)
A cockpit with a low crosssection, like a velobike. The passengers sit behind the pilot
Thin tires for a low cross section
A 10 kg vehicle parachute for emergency landing
2 kg parachutes for passengers
A total mass in the range of 500 kg
Prefabricated homes can be made from shipping containers, which are abundant, cheap, and easily delivered.
$ Length Width Height Mass ft ft ft kg 10foot shipping container 1000 10 8 8.5 1300 20foot shipping container 1200 20 8 8.5 2200 40foot shipping container 1500 40 8 8.5 3800 Typical mobile home 90 18
For a 1level prefabricated square bamboo house,
Side length = 8 meters Wall height = 3 meters Floor area = 64 meters^{2} Wall area = 24 meters^{2} Interior walls = 24 meters^{2} Total wall area = 248 meters^{2} Floor, ceiling, 4 walls, and interior walls Wall thickness = .05 meters Wall volume = 12.4 meters^{3} Bamboo density = 350 kg/meter^{2} Bamboo mass = 4.3 tons Carbon mass = 2.2 tons Bamboo carbon frac= .5 House mass = 7.0 tonsA helicopter can carry 12 tons. A prefabricated house can be placed anywhere in the wilderness and multiple modules can be assembled on site.
Prefabricated houses can be helicoptered to wilderness locations and flying cars can be used to reach them.
Mass Payload Power Speed Range Climb Rotor Ceiling Power/Mass (tons) (tons) (MW) (m/s) (km) (m/s) (m) (km) kWatt/kg S64 Aircrane 8.72 9.07 7.11 56 370 6.75 21.95 815 CH47 Chinook 11.15 12.7 7.03 88 741 7.73 18.3 6.1 630 Karman KMAX 2.33 2.72 1.34 51 495 14.71 575 85 gallons/hr
The flight time of a drone is determined by:
*) The battery energy/mass.
*) The power/mass required to hover.
*) The ratio of the battery mass to the drone mass.
Typical parameters for a drone are:
Drone mass = M = 1.0 kg Battery mass = M_{bat} = .5 kg (The battery is the most vital component) Battery energy = E = .38 MJoules Battery energy/mass= e_{bat}= E/M_{bat}= .75 MJoules/kg (Upper range for lithium batteries) Drone energy/mass = e = E/M = .38 MJoules/kg Drone power/mass = p = P/M = 60 Watts/kg (Practical minimum to hover. Independent of mass) Drone power = P = p M = 60 Watts (Power required to hover) Flight time = T = E/P = 6250 seconds = 104 minutesThe flight time in terms of component parameters is
T = (e_{bat}/p) * (M_{bat}/M) Drone Battery Drone Battery Battery Drone Drone Flight Price Wireless mass energy mass power time range kg MJoule MJ/kg kg MJ/kg Watt W/kg minutes $ km Mota Jetjat Nano .011 .00160 .145 3.3 303 8 40 .02 ByRobot Fighter .030 .0040 .133 6.7 222 10 120 .1 Blade mQX .0751 .0067 .089 11.2 149 10 115 XDrone Zepto .082 .0067 .081 4.6 56 24 40 .05 Walkera QR Y100 .146 .0213 .146 .0413 .52 17.8 122 20 100 .1 MJX Bugs 3 .485 .0480 .099 44.4 92 18 100 .5 DJI Mavic Pro .725 .157 .217 .24 .65 109 150 24 1000 7.0 XK Detect X380C 1.18 .216 .183 120 102 30 522 1.0 Xiaomi Mi 1.376 .319 .214 197 143 27 380 1.0 DJI Phantom 4 1.38 .293 .212 .426 .69 174 126 28 1000 5.0 XK X500 1.8 .288 .160 160 89 30 303 1.0 JYU Spider X 2.1 .360 .171 .812 .44 200 95 30 155 4.0 MD41000 2.65 1.039 .392 197 74 88 2000 .5 DJI Inspire 2.935 .360 .123 .67 .54 333 114 18 2000 7.0 Altura Zenith 3.5 1.327 .379 491 140 45 2000 1.0 Walkera QR X800 3.9 .799 .205 1.134 .70 222 57 60 2700 2.0 AEE F100 6.0 1.598 .266 380 63 70 58000 10.0 Chaos HL48 6.8 1.758 .259 651 96 45 20000 20.0 MD43000 10.4 2.80 .269 1037 100 45 4.0 Ehang 184 200 51.8 .259 37500 188 23 300000 3.5 Airbus EFan 60The minimum power requirement for quadcopter flight is of order 60 Watts/kg.
Electric power outperformes gasoline power in all categories except energy density. Electric motors are lighter, simpler, cheaper, more flexible, and more reliable than combustion motors.
Drone Battery Drone Drone Drone Flight Cost Wireless Wing Wing Cruise Max Flight mass energy E/M power time range area span speed speed range kg MJoule MJ/kg Watts W/kg minutes $ km m2 m m/s m/s km Sky Hawk .355 .0346 .097 19.2 54.1 30 400 1.0 1.0 Chaipirinha .62 .088 .142 154 .85 AgDrone 2.25 .639 .284 161 71.7 66 4.5 .124 46.7 82 50 Trimble UX5 2.5 .320 .128 107 42.7 50 10000 2.5 .34 .10 80 60 Airbus EFan 450 104.4 .232 29000 64.4 60 9.5 44.4 61.1 160 Sun Flyer 1225
The goal of a propeller is to maximize the power/mass ratio.
A propeller test consists of measuring the lift force, the power, and the tip speed (F,P,V), and this can be used to determine the rotor quality parameters (Q,q,W).
Mass = M Rotor radius = R Rotor lift/drag = Q = F / F_{d} Air density = D = 1.22 kg/meter^{3} Rotor lift param = W = F D^{1} R^{2} V^{2} Rotor tip speed = V Rotor lift force = F = D W R^{2} V^{2} Rotor drag force = F_{d} Rotor power = P = F_{d} V = F V / Q Rotor quality = q = Q W^{½} D^{½} = F^{3/2} P^{1} R^{1} Rotor force/power= Z = F / P = Q / V = D^{½} W^{½} Q R F^{½} = q R F^{½} Rotor Radius Z Force Power Rotors Blades Freq V q W Q m N/W N W /rotor Hz m/s 10 inch .127 .078 2.94 37.5 1 2 72 57.5 1.06 .045 4.48 10 inch .127 .056 9.8 176 1 2 131 104.5 1.37 .046 5.85 9x47SF .114 .129 1.06 8 1 2 50 35.8 1.17 .052 4.62 9x47SF .114 .0427 11.5 269 1 2 166.7 119.4 1.27 .051 5.10 10x47SF .127 .186 .696 4 1 2 33.3 26.6 1.22 .050 4.95 10x47SF .127 .0405 16.8 414 1 2 166.7 133.0 1.31 .048 5.39 11x47SF .140 .161 .960 6 1 2 33.3 29.3 1.13 .047 4.72 11x47SF .140 .0381 23.1 607 1 2 166.7 146.6 1.45 .045 5.59 12x38SF .152 .160 1.20 7 1 2 33.3 31.8 1.15 .042 5.09 12x38SF .152 .0381 28.4 745 1 2 166.7 159.2 1.34 .040 6.07 13 inch .165 .081 5.81 72 1 2 1.18 Walkera QR X800 .193 .172 9.56 55.5 4 2 2.76 Chaos HL48 .203 .102 8.33 81.4 8 3 1.45 Ehang .80 .052 245 4688 8 2 1.02 Phurba 1.6 .115 1200 10435 4 2 1.4For drones, the force and power are for one propeller.
Radius Mass m grams .12 11 .127 6.5 .171 39.7 .193 40
For a typical drone,
Drone mass = M Battery mass = M_{bat} Payload mass = M_{pay} Climbing speed = V_{cli} Max horizontal speed = V_{max} Hover constant = H = 60 Watts/kg Power/mass required to hover Hover power = P_{hov}= H M Hover power for payload= P_{pay}= H M_{pay} Gravity constant = g = 9.8 m/s Power to climb = P_{cli}= M g V Drag coefficient = C Air density = D = 1.22 kg/meter^{3} Drone crosssection = A Drag power = P_{drag}= ½ C D A V^{3}If the climbing power is equal to the hover power,
V = H / g = 6 meters/secondIf the climbing power is equal to the drag power,
M g V = ½ C D A V^{3} V = [2Mg/(CDA)]^{½} = 4.0 [M/(CA)]^{½} meters/second
Drone Battery Load Hover Load Climb Power P/M Climb Speed Thrust kg kg kg Watt Watt Watt Watt W/kg m/s m/s Newtons Nihui NH010 .0168 .0047  6.7 6.7 1426   Walkera QR Y100 .146 .0413  17.8 35.5 53.3 1291   DJI Mavic Pro .725 .24  109 109 454 5 18 DJI Phantom 4 1.38 .426 .462 174 58 81 232 545 6 20 JYU Spider X 2.1 .812 2.3 200 219 103 419 516 5 8 MD41000 2.65 1.2 197 89 195 286 7.5 12 118 DJI Inspire 1 2.935 .67 1.7 333 193 144 526 785 5 22 AEE F100 6.0 2.5 300 380 28 Chaos HL48 6.8 6.8 651 651 1302 MD43000 10.4 4.6 1037 1019 1496 10 280 Ehang 200 100 37500 28 Drone kg Drone mass without payload Battery kg Battery mass Load kg Maximum payload for hovering Hover Watt Power required to hover without payload Load Watt Power used for the payload only Climb Watt Climbing power = Mass * ClimbVelocity * Gravityconstant Power Watt Total power = Hover power + Load power P/M W/kg Power/Mass for the battery Climb m/s Maximum climbing speed Speed m/s Maximum horizontal speed Thrust Newton Maximum thrustThe JYU Spider X has the largest value for (payload mass) / (drone mass). The battery power/mass is
Battery power/mass = P_{hov} ⋅ (M + M_{pay}) / M / M_{bat} = 516 Watts/kg
Noise power is proportional to the rotor tip speed to the fifth power. The more rotors and the more blades per rotor, the less noise produced.
We give a sample design for a flying electric car based on current technological capabilities. We choose a design with 4 rotors mounted on a cross above the car, with a forward, aft, left, and right rotor. The forwardaft rotor distance is larger than the leftright rotor distance. The leftright cross section is a wing, and it has an interior telescoping sections that extend the length of the wing when flying. The elements of a 1person flying car are:
kg Passenger Cabin Battery Motors Rotors Cross structure Wing Car axels Wheels Battery energy/mass = e = .8 MJoules/kg Battery power/mass = p = 2000 Watts/kg Rotor quality = q = 1.25 Mass = M = 400 kg Gravity constant = g Force = F = Mg = 4000 Newtons Number of rotors = N Rotor radius = R = 1.5 meters Hover force/power = Z =qR(F/N)^{½}= .0593 Hover power = P = 67450 Watts Hover power/mass = p = 169 Watts/kg
Rotors = 4 Blades/Rotor = 3 Rotor radius = 1.6 meters Payload = 100 kg One person plus luggage Fuselage mass = 125 kg Battery mass = 75 kg Total mass = 300 kg Hover = 100 Watts/kg Hover power =30000 Watts Total power =60000 Watts Battery = 800 Watts/kg Battery mass = 75 kg
The maximum force on a beam is:
Beam length = L Beam height = H Beam width = W Shear strength = S Density = D Mass = M Breaking force = F = (2/3) W H^{2} S / X
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