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City design
Driverless electric cars and prefab homes
Dr. Jay Maron

Electric cars
Electric flying cars
Electric bikes
City design
Prefab houses


Electric cars

Range

Tesla Model S

Electric cars outperform gasoline cars in all regards except range. They're simpler, more powerful, quieter, and more flexible than gasoline cars.

The range of an electric car depends on the battery price and is typically .032 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 =  em           =  .60 MJoules/kg
Battery energy/$    =  e$           =.0070 MJoules/$
Battery mass        =  Mb           =  100 kg
Battery energy      =  E  =  Mb em  =   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" Vd they are equal, typically around 17 m/s.


Energy cost

The energy expended by an electric vehicle is determined by the drag force.

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 = Vd (Speed for which rolling drag = air drag) For typical vehicles,
              Force/prsn  Force/prsn  Mass  Cr  Area  Cd  Drag speed   People
              at 15 m/s   at 30 m/s
                 m/s          m/s      kg            m2           m/s

Electric bike      99       387         20  .004      .7   1.0     2.6      1
Electric car      105       269        600  .0075    2.0    .3    14.3      1
Bus                23.1      56      10000  .005     8.0    .6    15.7     60
Subway car          9.7      34      34000  .00035  10.0    .6     6.3    100
18-wheel truck   2422      4400      36000  .005     8.0    .6    24.6      1
The 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 self-driving. Buses are more suited to inter-city transport.

Trains use 2 times less energy than buses but they are highly inflexible.


Energy source

Tesla Roadster

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       104
Supercapacitor                  .016      8          .00005   seconds    106
Aluminum electrolyte capacitor  .010     10          .0001    seconds     ∞
Electric motors can reach a power/mass of 10 kWatts/kg.
Supercapacitors are a rapidly-improving technology and lithium batteries are a mature technology.
Motors

Electric motors and gasoline motors have a similar power/mass.

                        MJ/kg  kWatt/kg  kWatts  kg

Supercapacitor, Li-ion    .054  15
Electric motor, maximum   -     10       200     19.9    EMRAX268 Brushless AC
Turbofan jet engine       -     10.0      83.2    8.32   GE90-115B 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, lithium-ion      .75    1.5
Fuel cell, Honda          -      1.0
Typical diesel V8 turbo   -       .65
Solar cell, space station -       .077

Electric car vs. electric aircraft

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=  eair= 1.0 Joules/m/kg
Electric aircraft flying time         =  T  =3600 seconds
Electric aircraft range               =  X  = 180 km
Gravity constant                      =  g  = 9.8 m/s2
Electric car mass                     =  M
Electric car rolling drag coefficient =  Cr = .0075
Electric car rolling drag             =  Fr =  Cr M g
Electric car total drag               =  F  =  2 Fr        (Assume rolling drag = air drag)
Electric car energy/distance/mass     =  ecar=  2 Cr g  =  .147 Joules/m/kg
Aircraft energy / Car energy          =  eair / ecar  =  6.8

Drag speed

For a typical car,

Car mass                   =  M           = 1200 kg
Gravity constant           =  g           =  9.8 m/s2
Tire rolling drag coeff    =  Cr          =.0075
Rolling drag force         =  Fr = Cr M g =   88 Newtons

Air drag coefficient       =  Ca          =  .25
Air density                =  D           = 1.22 kg/meter3
Air drag cross-section     =  A           =  2.0 m2
Car velocity               =  V           =   17 m/s      (City speed. 38 mph)
Air drag force             =  Fa = ½CaADV2 =  88 Newtons

Total drag force           =  F  = Fr + Fa = 176 Newtons
Drag speed                 =  Vd           =  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     =  Cr M g [1 + (V/Vd)2] X
Range                      =  X  = EQ/(CrMg)/[1+(V/Vd)2] =  272 km
The range is determined by equating the work from drag with the energy delivered by the battery.   E Q = F X.

The drag speed Vd is determined by setting Fr = Fa.

Drag speed  =  Vd  =  [Cr M g / (½ Ca D A)]½  =  4.01 [Cr M /(Ca A)]½  =  17.0 meters/second

Acceleration

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 V2  =  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      =  MB =  P / (Q p)   =   112 kg
Battery cost/mass =  c             =    86 $/kg
Battery cost      =  C             =  9600 $

Recovering breaking energy

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

Flying cars

Fantrainer
Fantrainer
Terra Fugia

Optica
Ducted fan

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 cross-section, 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


Electric bikes

Electric bikes are easy to make. All you have to do is replace a conventional wheel with an electric wheel and attach a battery pack. Electric wheels come in kits and you can make the battery pack yourself. Example configurations for various motor powers:

Power    Max    Range   Motor   Battery   Battery
power   speed           cost     cost     energy
kWatt    mph    miles    $         $      MJoule

   .75   30      10     160       40       .5
  1.5    35      20     240       60      1.2
  3      45      40     570      100      1.8
  6      55      80    1150      200      3.6
The bikes have one electric wheel and one conventional wheel, except for 6 kWatt bike, which has 2 electric wheels with 3 kWatt each.

Electric wheel prices are from Amazon.com.


Electric bike speed limits
             Speed   Power   License
              mph    kWatt   required?

Massachusetts  25     .75    Yes
Connecticut    30    1.5     Yes
Pennsylvania   20     .75    No
Maryland       20     .5     No
Delaware       20     .75    No
DC             20     ?      No
California     28     .75    No
Oregon         20    1.0     No
Washington     20    1.0     No

Travel time

The quality of a city depends on things such as
*) 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)  (km2)  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, bike
Electic 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:
*) Take the elevator from whatevery floor you're on to the ground floor.
*) Walk to the subway
*) Wait for the subway
*) Ride the subway
*) Transfer subways
*) Wait for the subway
*) Ride the subway
*) Walk from the subway station to the destination skyscraper
*) Take the elevator from the ground floor to the destination floor

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/km2.


Travel time

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/km2  =  1 person every 10 meters2
City population         =  P = πDR2=280000 people
It helps to centralize. 4 points of focus of a city are the college, the pub district, the shopping district, and the K-12 school. These can be placed in the city center and the residences and businesses radiate out from the center.
Prefabricated homes

Prefabricated homes cost in the range from 20 to 100 $/foot2. A 400 foot2 minimalistic home costs on order 8000 $.


Shipping containers

Prefabricated homes can be made from shipping containers, which are abundant, cheap, and easily delivered.


                               $   Length  Width  Height  Mass
                                     ft     ft      ft     kg

10-foot shipping container   1000    10      8     8.5    1300
20-foot shipping container   1200    20      8     8.5    2200
40-foot shipping container   1500    40      8     8.5    3800
Typical mobile home                  90     18

Prefabricated bamboo house

For a 1-level prefabricated square bamboo house,

Side length       =    8 meters
Wall height       =    3 meters
Floor area        =   64 meters2
Wall area         =   24 meters2
Interior walls    =   24 meters2
Total wall area   =  248 meters2       Floor, ceiling, 4 walls, and interior walls
Wall thickness    =  .05 meters
Wall volume       = 12.4 meters3
Bamboo density    =  350 kg/meter2
Bamboo mass       =  4.3 tons
Carbon mass       =  2.2 tons
Bamboo carbon frac=   .5
House mass        =  7.0 tons
A helicopter can carry 12 tons. A prefabricated house can be placed anywhere in the wilderness and multiple modules can be assembled on site.
Wilderness

Prefabricated houses can be helicoptered to wilderness locations and flying cars can be used to reach them.


Flying electric cars

Design

We give a sample design for a flying electric car based on current technoly. We assume a 1 person model with 4 rotors.

Battery energy/mass =  e        =    .8  MJoules/kg
Battery power/mass  =  p        =  2000  Watts/kg
Rotor quality       =  q        =  1.25
Vehicle mass        =  M        =   400  kg
Gravity constant    =  g        =   9.8  meters/second2
Number of rotors    =  N        =     4
Rotor force         =  F  = Mg/N=   980  Newtons
Rotor power         =  P
Rotor radius        =  R        =   1.5  meters
Hover force/power   =  Z  = F/P
                          = qRF=  .0599
Hover power         =  Phov     = 65400  Watts
Hover power/mass    =  p  = P/M =   164  Watts/kg
Max power           =  Pmax     =120000  Watts
Battery minimum mass=  Mb =Pmax/p=   60  kg
Battery energy      =  E  =e Mbat=   48  MJoules
Hover time          =  T  = E/P  = 73.4  minutes
Forward rotor power =  Pf       = 64000  Watts
Rear rotor power    =  Pr       = 32000  Watts
Rear rotor power    =  Pl       = 32000  Watts
Rear rotor power    =  Pr       = 32000  Watts
Forward axis power  =  P1       = 10000  Watts
Rear axis power     =  P2       = 10000  Watts
Motor capacity      =  Pmot     =180000  Watts
Motor power/mass    =  pmot     =  8000  Watts/kg
Motor mass          =  Mmot     =  22.5  kg
Rotor mass          =  Mrot     =    40  kg              4 rotors at 10 kg each
Wing mass           =
Freeway speed       =  V        =     30 meters/second
Drag coefficient    =  C        =     .5
Drag cross section  =  A        =      2 meters2
Air density         =  D        =   1.22 kg/meter3
Air drag power      =  Fdrag=  ½ C D A V3  =  16500 Watts
Cabin           50
Battery         60
Motors          22
Rotors          40
Rotor fuselage  50
Cabin fuselage  75
Wing            50
Car axles       20
Wheels          20


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
We choose a design with 4 rotors mounted on a cross above the car, with a forward, aft, left, and right rotor. The left-right cross piece is a wing, and it has an interior telescoping sections that extend the length of the wing when flying. The elements of a 1-person flying car are:
Beam strength

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 H2 S / X

Flying cars

Fantrainer
Fantrainer
Terra Fugia

Optica
Ducted fan

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 cross-section, 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


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