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

Electric vehicles
Hydroponics
City design
Prefab homes
Electric bikes
Electric flying cars

A city built from scratch can solve problems that existing cities can't. Using driverless electric vehicles, prefabricated housing, and hydroponics, the following are possible:

Electric vehicles outperform gasoline vehicles in all regards except range, and if you splurge on the battery you can have the range (plus ludicrous power). They are simpler, cheaper, more powerful, quieter, and longer-lasting than gasoline cars. Electric motors can be put on anything, which has triggered a proliferation of novel electric vehicles such as bikes, kick scooters, skates, uniwheels, and compact cars. This decreases travel time, especially if the road system has compact electric vehicles in mind.

Travel time can be decreased using autopilot cars, which can coordinate with a central computer to minimize traffic.

Prefabricated houses decrease housing cost and increase flexibility in changing residences. They can be assembled like legos into large structures.

Using intelligent design, residential and public space per person can be optimized, and it can be arranged so that everyone has a yard bordering a park.

Hydroponics gives 100 times the yield of soil agriculture, and 40 square meters of hydroponics is enough to sustain a person.

A flying car powered by lithium-ion batteries can fly for 45 minutes and cover 100 km.

The average American home uses 1500 Watts of electricity. Solar cells average 50 Watts/meter2 and this power can be provided by 30 meters2 of cells.

1500 Watts of power for 1 day is 130 MegaJoules. Lithium-ion batteries cost 100 $/MegaJoule and this energy can be provided by a $13000 battery.

A compact entertainment district enhances socialization. The district should have an indoor and outdoor park surrounded by establishments such as bars, restaurants, etc.

Electric vehicles decrease dependence on foreign oil.

We expand on each of these points in the sections below.


City design

The quality of a city depends on things such as
*) The travel time to cross the city.
*) The amount of residential and yard space per person.
*) The amount of public park space per person. Yards bordering a park are especially valuable.

Most cities are poorly designed in this regard, motivating the creation of new cities from scratch. These cities can take advantage of possibilities offered by electric driverless cars, prefabricated housing, hydroponics, and factories where you can manufacture stuff for yourself.

The following table shows the population density and typical travel time for various cities.

           Population  Population  Area  Travel  Travel
            density    (millions)  (km2)  time   means
          (people/km2)                   (mins)

Manila         43000     1.65      38.6     30    Taxi
Delhi          25500    11.0      431       30    Bus
Paris          21500     2.27     105       30    Subway
Seoul          13000    10.4      605       30    Subway
New York City  10400     8.18     784       30    Subway
San Francisco   6700      .81     121       30    Subway
Boston          5100      .65     125       30    Subway
Isla Vista      4800      .023      4.8      5    Walk, bike
Pasadena        2400      .140     59.5     10    Car
Beverly Hills   2300      .347     14.8     10    Car
Iowa City       1000      .068     64.8     10    Walk, bike

New York City is a catastrophic case that illustrates the weaknesses of public transportation. To get somewhere you have to:
*) Take the elevator from whatever 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. London can be even worse than New York because because the subway stations are further apart and deeper underground.


Houses vs. skyscrapers

Living in houses vs. skyscrapers has constrasting strengths and weaknesses.

                       House    Skyscraper

Patio                    *          *
Rooftop                  *
Basement                 *
Yard                     *
Garage                   *               Being able to drive directly to your house decreases travel time
Bordering park           *
High-altitude view                  *
High population density             *
Sunlight                 *
If houses are designed well they can achive a high population density. We show an example in the next section.
Pizza houses

Houses can achieve a high population density if designed intelligently. The design goals are:

*) Maximize house area
*) Maximize window size
*) Maximize yard area
*) Have the yard border a park
*) Make the windows as far as possible from the windows of other houses.

A house can be placed either at the edge of a yard or at the center. Placing it at the edge maximizes the continuity of the yard, which is especially important for small yards.

A design with these goals in mind is the "pizza design", where each pizza slice is a house, each house has a yard, and the space between houses is a public park. The park has paths so that light electric vehicles can drive directly to the houses. Each pizza has 6 houses (slices). Pizzas are arranged hexagonally to maximize the yard and park space.

Since a pizza house doesn't have any upstairs or downstairs neighbors it can have a rooftop, a basement, and a yard. A skyscraper apartment can't have this.

The following table shows the population density for various sized houses. Pizza houses can exceed the population density of cities such as Manhattan and Paris.

House      Slice    Yard    Park   Total   Area per  Population density
size       radius  radius  radius  radius   person
           meters  meters  meters  meters  meters2      people/km2

Studio       3       2       2       7       23          43000
1-bedroom    4       3       3      10       47          21000
2-bedroom    6       4       4      14       93          10700
3-bedroom    8       5       4      17      137           7300


Slices per pizza     =  N  =  6
Slice radius         =  r             Radius of the house slice
Yard radius          =  Y             Distance that the yard extends from the house
Park radius          =  P             Distance from the edge of the yard to the park midpoint
Total radius         =  R  = r+Y+P    Distance from the house center to the park midpoint
Circle packing factor=  C  = π/(2√3) = .9069     Optimum packing efficiency for circles
Total area per person=  A  =  C π R2 N-1
Population density   =  D  =  A-1

House size

A pizza house can have a large area if you include the basement, roof, and yard. If the basement extends to halfway between houses then the total area of a studio-sized house is:

        meters2
House       5
Roof        5
Yard        8
Basement   25
Total      43

City quality

The larger the house the better, and the larger the population density the better (shorter travel time). We define a measure of overall city quality as house size times population density.

Rooftops, yards, basements, and bordering parks add to the value of a house and we reflect this by defining a "house quality".

House area/person   =  Ah
Yard area/person    =  Ay
Rooftop area/person =  Ar
Park area/person    =  Ap          (The house's share of the park)
House quality       =  A = Ah + ½ (Ay+Ar+Ap)
Population density  =  P            people/meters2
City quality        =  Q  =  A P    dimensionless


              Population      House      City
               density     area/person  quality
              people/km2  meters2/person

Paris             21500       30          .64
New York City     10400       30          .31
Pizza studio      43000       43         1.8
Pizza 1-bedroom   21000       60         1.3

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.
Electric vehicles

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 vehicles.


Power

To give a sense for the strength of human and electric power,

                          kiloWatts

Human unstrenuous cycling     .1
Human strenuous cycling       .3
Human sprint cycling         1
Typical electric bike        1
Monster electric bike        6
Typical car                100
Electric power opens the way for light cheap city vehicles. Electric power easily has the speed and range for city driving.
Speed

To give a sense for the relationship between power and top speed,

        Power   Speed   Speed
        kWatt    m/s     mph

Bike      .12     7      17     Human unstrenuous cycling
Bike      .25     9      21     Human strenuous cycling
Bike     1       15      33     Human sprint cycling
Bike     2       19      42
Bike     4       24      53

Trike    1       12      26
Trike    4       19      42
Trike   16       30      67

Car     16       26      58     Minimum power for cities
Car     32       33      73     Minimum power for highways
Car     64       41      92     Minimum power for freeways
Car    128       52     116     Typical car
Car    512       82     184     Sports car

Battery

Typical values for a 16 kWatt car battery are:

Energy/Mass   =  e  =  E/M  =   .8   MJoules/kg
Power/Mass    =  p  =  P/M  =  1.2   kWatts/kg
Energy/Cost   =  c  =  E/C  =   .01  MJoules/$
Power/Cost    =  d  =  P/C  =   .012 kWatts/$
Energy/Power  =  D  =  E/P  =   .67  MJoules/kWatt
Mass          =  M  =       = 13     kg
Energy        =  E  =       = 11     MJoules
Power         =  P  =       = 16     kWatts
Cost          =  C  =       = 1330   $

Range

Air drag determines a vehicle's top speed, energy use, and minimum battery power. A 16 kWatt car with a minimalist battery has a range of 30 km when driving at a speed of 20 meters/second.

Air density        =  D                        =  1.22 kg/meter3
Air drag coef.     =  K                        =   .75 meters2
Car speed          =  V                        = 20    meters/second
Air drag force     =  F  =  K D V2  =366    Newtons
Air drag power     =  P  =  K D V3  =  7.3  kWatts
Battery energy     =  E                        = 11    MJoules
Distance traveled  =  X  =  E/F                = 30    km

Energy efficiency

The goal is to minimize the energy cost per person. For an N-person vehicle,

People            =  N
Distance traveled =  X
Air drag force    =  F
Energy            =  E  =  F X
Energy efficiency =  Q  =  E/(NX)  =  F/N
The energy efficiency is equal to the air drag force divided by the number of passengers. Example values for various vehicles:
                        Speed    Power     Force   Force/prsn  People   Range  Drag area
                         m/s     kWatt     Newton    Newton              km     m2

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 Watts
A full bus 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 should be favored over short flights.

Trains are not substantially more efficient than buses and they are far less flexible.


Hydroponics

Hydroponics is the technique of growing plants in water rather than soil, where the water is fertilized with nutrients. Hydroponics can yield 100 times as much food as soil-based agriculture, and a person can be sustained with only 200 square meters of hydroponics.

Hydroponics is easy. One can buy a system that takes care of everything and one need only supply the system with water and fertilizer. One can further improve yield with greenhouses, lighting, and mirrors.


Hydroponic system

Grow kit
Nutrient solution
Mirror foil
LED light
Sturdy greenhouse
Unsturdy greenhouse

A "grow kit" takes care of supplying the plants with water. One need only supply the kit with water and fertilizer. Fertilizer comes in powder form and dissolves in the water. Kits cost $2 per plant site.

Putting a greenhouse around the kit amplifies the yield by allowing one to control temperature and humidity. A greenhouse also allows plants to be grown during the winter.

Mirrors can amplify the sunlight reaching the planet, and mirror film is cheap.

Lights can improve the growth rate and make it possible to grow plants 24 hours.

A hydroponics system can be ordered online from places such as Amazon and Wallmart, and examples of costs are:

                               $     Amazon link

Grow kit, 11 sites             25    *
Grow kit, 90 sites            160    *
Fertilizer, 10 kg              13    *
LED grow light, 1000 Watts    140    *
Mirror film, 400 square feet   24    *
Greenhouse                    120    *

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

Flying electric cars

The properties of a flying car are determined by the properties of propellers and lithium-ion batteries. Typical parameters for a 1-person car are:

Hovering time      =   25 minutes
Cruise speed       =  100 meters/second
Range              =  155 km
Hovering power     =   40 kWatts
Vehicle mass       =  320 kg
Battery energy/mass=   .8 MJoules/kg
Battery power/mass = 1200 Watts/kg
Battery cost/MJoule=  100 $/MJoule
Battery mass       =   80 kg
Battery energy     =   64 MJoules
Battery power      =   96 kWatts
Battery cost       = 6400 $

For hovering, the more rotors the better. The hovering time scales as rotor number to the 1/6 power. Adding rotors also increases stability and failsafe.


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
        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?

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

Human nutrients

A vitamin pill covers all micronutrients. The macronutrients are:

         Requirement  Centrum
            g/day        g

Protein      50        0
Potassium     3.5      .08
Calcium       1.0      .2
Phosphorus    1.0      .02
Magnesium      .35     .05
Foods with high macronutrient density. Numbers in parts per thousand.
          Phosphorus  Potassium  Calcium  Magnesium  Protein

Sunflower seed  6.6      6.4       .8        3.3       179
Cheddar         5.1      1.0      7.2         .28      283
Peanut          3.8      7.1       .9        1.7       267
Beef            3.0      2.4       .12        .19      247
Turkey          2.1      3.0       .1         .21      293
Egg             1.9      1.3       .53        .12      120
Milk             .9      1.4      1.1         .10       33
Potato           .7      5.4       .15        .28       13
Rice             .7       .8       .11        .23       52
Avocado          .5      4.8       .1         .29       13
The ultimate macronutrient food is sunflower seeds. The cheapest source of macronutrients is cheese and peanuts.
Food cost

We calculate the price for food for 1 year. We assume 2600 calories/day.

              Energy  Price  Efficiency
              Cal/kg  $/kg     Cal/$

Rice (dry)     3330    2.86   1160
Peanut         6000    6.60    910
Sunflower seed 5710   10.00    571
Chicken        2762    5.00    550
Milk            422     .80    530
Mountain Dew    440    1.00    440
Turkey         2429    6.00    404
Cheddar        4040   10.00    404
Beef           3380    9.00    375
Watermellon     300     .83    361
Egg            1400    4.00    350
Potato          930    2.84    327
Mozarella      2780    8.80    315
Palm oil       7353   24.00    306
Corn            860    4.40    195
Apple           579    5.00    115
Cucumber        154    2.00     77
Tomato          249    4.41     56
Lettuce          95    5.57     17
Cherry tomato   176   11.76     14
Rice is the cheapest source of calories and peanuts are the cheapest source of macronutrients. You can feed a person for 2.5 $/day with rice, peanuts, and a vitamin pill.
Thermal insulation

The best insulator is air, which is why fluffy low-density objects like pillows and down coats are effective insulators. The most effective possible coat for cold weather is a full-length leather coat with a fluffy liner. The leather is air-proof and creates a bubble of air and the liner makes the air layer as thick as possible. The stiffness of leather also helps for trapping a large volume of air.

Some common thermal conductivities are:

         Watts/Kelvin/meter

Steel         45
Granite        2.5
Glass           .8
Water           .6
Brick           .5
Plastic         .5
Plexiglass      .2
Wood            .1
Plastic foam    .03
Air             .025
The insulation quality of a material is proportional to the thickness divided by the thermal conductivity.
Thickness                 = X               Meters
Thermal conductivity      = C               Watts/Kelvin/meter
Temperature differential  = T               Kelvin
Heat flux                 = F = CT/X = T/B  Watts/meter2
Insulation quality        = B = X/C         Kelvin meter2/Watt


             Thickness  Thermal conduct    Insulation       Mass/Area
                mm       Watts/K/meter  Kelvin/meter2/Watt  kg/meter2

Leather layer     1         .5                2              1
Fluffy liner      5         .025            200               .1

Human power

To feel toasty warm in 0 Celsius you need an insulation quality at least as large as 1.3 Kelvin Kelvin meter2/Watt, which can only be achieved with fluffy liner. If the liner has the thermal conductivity of air then the thickness required is 3 cm.

Human power               =  P          = 100  Watts
Human surface area        =  A          =   3  meters2
Human heat flux           =  F  =  P/A  =  33  Watts/meter2
Human temperature                       =  37  Celsius
External temperature                    =   0  Celsius
Temperature differential  =  T          =  37  Celsius
Insulation quality        =  B  =  T/F  = 1.1  Kelvin meter2/Watt
Thermal conductivity      =  C          =.025  Watts/Kelvin/meter
Insulation thickness      =  X  =  B C  =.028  meters

Head power

The head generates heavy power and is easy to keep warm. One has to protect this heat with a hat. When resting,

            Power   Surface area   Heat flux
            Watts     meters2      Watts/meter2

Head          20         .13         160
Body         100        3             33

Battery heater

A heater can be constructed with a battery and resistors. A 12 Volt external laptop battery can deliver 18 Watts. For a typical battery,

Voltage         =  V          =  12  Volts
Max current     =  I          = 1.5  Amperes
Max power       =  P  =  V I  =  18  Watts
Battery cost    =  C          =  20  $
Battery energy  =  E          = 133  kJoules
Battery cost/$  =  c  =  C/E  =   7  kJoules/$
Operating time  =  T  =  E/P  =7390  seconds  =  2.1 hours
The value of the resistor is chosen to deliver the desired power. For example,
Voltage     =  V  =  I R  =   12  Volts          Ohm's law
Resistance  =  R          =  100  Ohms
Current     =  I          =  .12  Amperes
Power       =  P          =  1.4  Watts
The resistors should be "power resistors", which are large. If each resistor dissipates 1.4 Watts then the battery can support 12 resistors. The resistors should be wired in parallel. Duct tape is useful for holding the resistors and wires together to create a "resistor scarf".
Solar cells

A typical solar farm costs 5 $/Watt and produces 30 MWatts/km2, and America's electricity requirement can be satisfied by a farm that is 5% the size of Arizona. The largest farms are:

                                       GWatts  km2  MWatts/km2  B$  $/Watt

California   Solar Star                   .58   13    45
California   Topaz                        .55   25    22      2.5   4.5    Thin film CdTe
California   Desert Sunlight              .55   16    34                   Thin film CdTe
China        Longyangxia Dam              .32    9    36
California   Cal. Valley Solar Ranch      .29    8    36      1.6   5.5    Silicon crystal
Arizona      Agua Caliente Solar Project  .29   10    29      1.8   6.2    Thin film CdTe


       Solar power capacity (GWatts)

World         139
Germany        38.2
China          28.2
Japan          23.3
Italy          18.5
USA            18.3
France          5.7
Spain           5.4
UK              5.1
Australia       4.1

American solar farms tend to be in California or Arizona where sunlight is abundant. We calculate the payback time for a typical 1 meter2 solar cell in Arizona.

Solar cell efficiency         =  e             =  .20               Converting solar to electric energy
Arizona solar intensity, peak =  Ipeak          = 1000 Watts         Noon in mid-summer
Arizona solar intensity, ave. =  Iave           =  250 Watts         Averaged over day and night
Solar cell peak power         =  Ppeak =  e Ipeak=  200 Watts
Solar cell average power      =  Pave  =  e Iave =   50 Watts
Solar cell operation time     =  T              =  2.3 years         Payback time
Solar cell energy generated   =  E    =  Pave T = 3622 MJoules
Electricity cost per Joule    =  Qelec          =2.8⋅10-8 $/Joule  =  .10 $/kWh
Value of electricity generated=  Celec =  E Qelec=  100 $
Solar cell cost               =  Ccell           =  100 $
Solar cell cost per peak Watt =  Qcell =Ccell/Ppeak= .50 $/Watt
Setting the cost of the solar cell equal to the value of the energy generated,
Ccell  =  Celec  =  e Iave T Qelec

Payback time  =  T  =  Ccell / (e Iave Qelec)  =  2.3 years
A solar farm in Arizona large enough to supply all of America's electricity is a square 120 km on a side, which is 5% of the area of Arizona.
U.S. total power                =  3000 GWatts
U.S. electric power             =   500 GWatts
U.S. solar power                =    21 GWatts
U.S. power/person               =  9400 Watts
U.S. population                 =   320 million
Solar farm power per area       =    35 MWatts/km2     (Typical solar farm)
Solar farm area                 = 14300 km2
Arizona area                    =295234 km2
Solar farm side length          =   120 km             (Assume a square)

Silver is the most reflective metal

The types of solar cells are:

Technology         Efficiency  $/Watt  Market frac   Key element   Element cost ($/kWatt)

Thin film Ga As           .29                        Gallium
Crystalline Si (mono)     .25     .50     .36        Silver        48
Crystalline Si (poly)     .20     .50     .55        Silver       100
Thin film Cu In Ga Se     .20             .02        Indium
Thin film Cd Te           .16             .051       Tellurium      5
Thin film Amorphous Si    .11             .02        -
Multi junction            .41                        Gallium
World record              .44


Energy cost of silicon crystal= 39.6  MJ/kg
Electricity cost              =   36  MJ/$
Silicon crystal cost          =  1.1  $/kg
Monocrystal silicon           =  6.0  kg/kWatt
Monocrystal silicon cost      =  6.6  $/kWatt
Crystal silicon thickness     =  .18  mm
Thin film (CdTe) tellurium    = .093  kg/kWatt     =  4.6 $/kWatt
Silicon-monocrystal silver    =  .05  kg/kWatt     =   48 $/kWatt  =   100 $/kg  =  .0096kg/m2
Silicon-polycrystal silver    =  .10  kg/kWatt     =  100 $/kWatt  =  1000 $/kg  =  .020 kg/m2
Price of silver               =  264  $/kg

Inverter

A solar cell system requires an inverter to convert DC to AC power. For a 1 meter2 cell,

Solar cell efficiency               =  e
Peak power                          =  Ppeak =  e Ipeak    =  200 Watts
Cost of inverter per peak Watt      =  Qinv  =  .15 $/Watt
Cost of inverter                    =  Cinv  =  Qinv Ppeak  =  15 $
Cost of solar cell                  =  Ccell               = 100 $
Total system cost                   =  Ctotal              = 200 $
The the inverter costs less than the solar cell.
Benches

Not all benches are created equal. Care must be taken in designing a bench that is comfortable.

The higher the back of the bench, the better. Best of all is if the bench can support the back of your head.
Benches with curvature are more comfortable than flat benches.
There should be space underneath the bench for your feet.
There should be a canopy for rain, with side walls to shield against wind.
There should be benches in the sun for cold weather and benches in the shade for hot weather.
Benches should have arm rests.


Acknowledgements

We give thanks to Broadway Presbyterian Church, Starbucks, and Morning 2 Midnight.


Appendix

Lithium-ion batteries

The properties of the best commercial lithium ion batteries are:

Energy/Mass     =    .8  Joule/kg
Power/Mass      =  1200  Watt/kg
Energy/$        =    .01 MJoule/kg
Density         =   3.5  gram/cm3
Recharges       =1000
Shelf life      =   1.0  year
Voltage         =   3.7  Volt
Energy/Mass and Power/Mass are an engineering tradeoff. One can be increased at the expense of the other.
Battery sizes

Energies and powers are for lithium batteries, which have a voltage of 3.7 Volts. The "ID #" is often used instead of cell size.

Cell   Energy  Power  Current  Mass  Diameter  Length  Charge   Price    ID #
size   kJoule  Watt   Ampere   gram     mm       mm    AmpHour    $

D       107     220     60     138      32       67     8.0      13      32650
C        67     220     60      92      26       50     5.0       8      26650, 25500
B        58     160     45      72      22       60     4.5       5      21700, 20700
A        47     110     30      49      18       50     3.5       3      18650
AA        9      22      6      15      14       53      .70      1      14500
AAA       4.7    11      3       7.6    10       44      .35       .5    10440
AAAA      2.3     6      1.5     3.8     8       42      .17       .25   75400

Battery packs

A single battery is a "cell" and a set of cells is a "pack". Packs are used to multiply the energy and power of cells.

Battery packs are notorous for catching fire, but cell technology has reached the point where it's now possible to make safe battery packs, and the design is simple enough so that anyone can construct their own packs.

Cells can be combined in series and/or parallel. Connecting in series multiples voltage, and voltage is helpful for achieving high power in a motor.

Connecting in series is easier than in parallel. If it's possible to achieve the required power without parallelization then one should do so, and this is usually possible with modern cells.

Series packs have the advantage that the cells can easily be extracted and charged individually, and cells can be interchanged between packs. One can also construct a set of series packs and swap them in like gun clips.

High power electric bikes use a voltage of 72 Volts. If we use one series array of C cells then a pack provides 4440 Watts and 1.2 MJoules. Any electric device requiring less than this much power can be powered by a series pack.

The properties of a modern high-power cell are:

Type         =  "C"
Voltage      =   3.7 Volts
Energy       =  60   kJoules
Power        = 155   Watts
Mass         =  92   grams
Energy/mass  = 650   kJoules/kg
Power/mass   =1680   Watts/kg
Current      =  42   Amperes
Manufacturer = "Basen"
When the cells are connected in series the values for voltage and power are:
Cells   Voltage    Power
         Volts     kWatts

   1      3.7        .15
   2      7.4        .30
   3     11          .45     Electric kick scooter
   4     15          .60
   6     24          .90     Electric bike
  10     36         1.5
  20     72         3.0      Compact electric car
  96    356        15.0      Large electric car

Battery pack strategy

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 max   Cell    Cell  Cell  Cell brand
kWatt                                  Amperes  Amperes  Amphours   $    type

   .75  36     10      10       1         21      30       2.0      5     A    Sony VTC4
  1.5   48     13      13       1         31      60       4.5      8     C    Basen
  3     72     20      20       1         42      60       4.5      8     C    Basen
  6     72     40      20       2         83     120       4.5      8     C    Basen
 12     72     80      20       3        167     180       4.5      8     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
Cellmax   Maximum current of a cell

Nutrient solution

1 kg of nutrient powder is mixed with ton of water. The composition of a typical nutrient solution is

        Parts per million

Potassium       160
Nitrogen        150
Calcium         100
Phosphorus       40
Sulfur           40
Magnesium        30
Iron              2
Manganese          .5
Zinc               .3
Boron              .2
Copper             .1
Molybdenum         .075
Source
Crop yield
             Yield      Yield     Energy
           kCal/m2/yr  kg/m2/yr   Cal/kg

Potato          48        52       923
Onion           20        50       400
Tomato cherry   17.2      98       176
Blueberry       13.8      24       573
Cucumber        12.6      82       154
Tomato          12.4      50       249
Lettuce          7.0      74        95

Hydroponic yield vs. field yield

Hydroponics offers gains over field agriculture in many categories. The following table shows the amplification for each category in terms of hydroponic yield over field yield. The total amplification is the product of the amplification from each category.

Plant density               8          In terms of plants/meter2
Crops per year              4
Crop variety                2
Temperature contro l        2
LED lighting                2
Carbon dioxide enhancement  1.5

Hydroponic physics

Soil mass yield             =   1  grams/meter2/day      Data
Hydroponic mass yield       = 100  grams/meter2/day      Data
Typical food energy density =1000  Calorie/kg             (Potato = 930 Cal/kg)
Hydroponic calorie yield    = 100  Calorie/meter2/day
Calorie requirement per day =2600  Calorie/day
Hydroponic area/person      =  26  meters2     (Area required to sustain one person)

Hydroponic yield/growsite   =   4  kg
Electricity cost            =  30  MJoules/$
Minimum water flow rate     =  .5  Litre/minute
Optimal water flow rate     =   1  Litre/minute
Maximum water flow rate     =   2  Litre/minute
Maximum pipe length         =  10  meters                      (If longer, nitrogen becomes depleted)

Grow kit cost              =   2  $/growsite
Largest kit size           =  72  growsites
Nutrient solution cost     =  13  $/kg       (solid form)
Water requirement          = 500  kg of water per kg of solid nutrient fertilizer
LED lamp cost              =   7  Watts/$
Mirror film cost           = 1.5  meter2/$
Transparent acrylic sheets =  32  $/meter2
Greenhouse cost (sturdy)   =.016  meters3/$        (Plexiglass. Survives high wind)
Greenhouse cost (unsturdy) =.18   meters3/$        (Plastic. Cannot survive high wind)

O2 solubility in H2O, 10 C  =11.2  mg/Litre
O2 solubility in H2O, 20 C  = 9.1  mg/Litre
O2 solubility in H2O, 30 C  = 7.2  mg/Litre
O2 density in the atmosphere= 280  mg/Litre
The water pipes should exclude light to prevent algae growth.
Artificial light

The most efficient plant for converting sunlight to food energy is sugar cane, which has an efficiency of 7%. If LED lights are used to grow food for 1 person then the electrical power required is:

LED light efficiency       =  Ql          =  .2
Sugar cane efficinecy      =  Qc          =  .07
Plant efficiency           =  Qp          =  .5        Efficiency relative to sugar cane
Total efficiency           =  Q  = QlQcQp =  .007
Human power                =  P           =  120 Watts
LED power                  =  p  = P/Q    =17000 Watts
Electric energy/dollar     =  c           =   40 MJoules/$
Electricity cost for 1 year=  C           =12750 $

The sun

Arizona solar intensity, peak  =1000  Watts/meter2   (Noon in mid-summer)
Arizona solar intensity, ave.  = 250  Watts/meter2   (Averaged over day and night)
Manhattan solar intensity, ave.= 155  Watts/meter2
Electricity cost per Joule     =  36  MJoules/$
Energy in one day              =13.4  MJoules/day/meter2
Cost for one day               = .37  $/day/meter2

Cooling

A greenhouse can be cooled by evaporating water.

Melting energy of water at 0 Celsius        =     334  kJ/kg
Vaporization energy of water at 100 Celsius =    2257  kJ/kg
Energy to raise water from 0 to 30 Celsius  =     126  kJ/kg
Total energy for melting ice                =    2717  kJ/kg

Calories
1 Calorie                   =  4184 Joules
Daily requirement for men   =  2600 Calories
Daily requirement for women =  2000 Calories

Gigafactory

The Gigafactory in Nevada has a production target for 2020 of:

Battery production   =  200 TeraJoules/year
Energy of one car    =  310 MJoules           (Tesla Model S)
Cars supplied/year   =  .64 million
The Solar City Factory produces solar panels.
Panel production  =  1.0 GWatts/year
Panel duty factor =  .25        (Average solar intensity over peak solar intensity)
Effective power production  =  .25 GWatts/year

Electricity cost
Cost of electricity       =  30  MJoules/$
Crop time                 =   3  Mseconds  =  40 days
Lamp power                =1000  Watts
Lamp energy per crop      =   3  GJoules/crop
Lamp energy cost per crop = 100  $/crop

Fertilizer composition

The following table shows the elemental composition of a typical hydroponic nutrient solution in parts per million.

Nitrogen     600
Calcium      400
Sulfur       400
Potassium    250
Magnesium     80
Phosphorus    80
Iron           4
Boron          2
Nickel         1
Manganese       .8
Zinc            .5
Copper          .5
Molybdenum      .01
Hydroponic fertilizer can be purchased in solid form for $12/kg on Amazon.com. One kg of solid fertilizer supplies 500 kg of water.
Citrus growing regions


Hovering flight

Hovering propeller

For propellers,

Rotor radius     =  R
Air density      =  D  =  1.22 kg/meter3 at sea level
Rotor tip speed  =  V
Rotor width param=  Cr
Rotor lift force =  F =  D Cr R2 V2
Rotor drag force =  F
Rotor lift/drag  =  Qr =  F / F
Rotor power      =  P  =  F V  =  F V / Qr
Rotor force/power=  Z  =  F/ P
                       =  Qr / V
                       =  R F D½ Cr½ Qr
                       =  R F D½ qr
Rotor quality    =  qr =  Qr Cr½
The physical parameters of a propeller are {Qr,Cr,qr}, with typical values of
Qr = 5.5
Cr =  .045
qr = 1.17
Most propellers have 2 blades and some have 3. If there are 4 or more blades then qr declines.

The parameters are not independent. They're related through the blade aspect ratio.

K  ≈  Aspect ratio
Cr ≈  K
Qr ≈  K
qr ≈  K½

Hovering time
Aircraft mass        =  M
Gravity              =  g
Aircraft force       =  F =  M g
Rotor radius         =  R                  ~  M1/3
Hovering force/power =  Z  =  qr D½ R F  ~  M-1/6
Hovering power/mass  =  p  =  g / Z        ~  M1/6
Aircraft energy/mass =  e                  ~  M0
Hovering time        =  T  =  e / p        ~  M-1/6

Drive propeller

A drive propeller has to move substantially faster than the aircraft to be effective. This distinguishes it from a hovering propeller, which is designed to minimze propeller speed.

Rotor radius      =  R
Air density       =  D  =  1.22 kg/meter3
Aircraft speed    =  U
Rotor speed coef. =  s
Rotor tip speed   =  V  =  s U
Rotor lift force  =  F
Rotor drag force  =  F
Rotor lift/drag   =  Qr =  F / F
Rotor power       =  P  =  F V  =  F V / Q
Rotor force/power =  Z  =  Q / V
Typically, Q ~ 5.5 and s ~ 3.
Power/Mass ratio

A commonly-appearing quantity is the power/mass ratio, which is inversely proportional to the force/power ratio.

Mass              =  M
Gravity           =  g
Rotor quality     =  q
Hover force       =  F  =  M g
Hover power       =  P
Force/Power ratio =  Z  =  F/P
Power/Mass ratio  =  p  =  P/M  =  g/Z

Typical parameters
Air density       =  Dair=  1.22
Seawater density  =  Dwater= 1025
Gravity           =  g   =  9.8     meters/second2
Wing drag coef.   =  Cw  =   .03
Wing Lift/drag    =  Qw  =  7
Rotor lift/drag   =  Qr  =  5.5
Rotor width param =  Cr  =   .045
Rotor quality     =  qr  =  1.17  =  Qr Cr½
Rotor force/power =  Zr
Rotor agility     =  pr  =  g/Zr
Wing agility      =  pw

Propeller-driven level flight
Aircraft mass        =  M
Gravity              =  g
Air density          =  D  =  1.22 kg/meter3
Aircraft speed       =  U
Rotor speed coef.    =  s
Rotor tip speed      =  V  =  s U
Aircraft lift force  =  F  =  M g
Rotor lift force     =  F
Wing lift/drag       =  Qw =  F / F
Rotor drag force     =  F
Rotor lift/drag      =  Qr =  F / F
Rotor power          =  P  =  F V  =  F V / Qr  =  F V / (Qr Qw)
Aircraft force/power =  Z  =  F / P  =  [Qr Qw / s] / U
There is a tradeoff between Qr and s.
Soundproofing


Transmission through a wall

The left column is the change in decibel level provided by soundproofing.

Decibels

  25   Normal speech can be understood quite easily and distinctly through wall
  30   Loud speech can be understood fairly well, normal speech heard but not understood
  35   Loud speech audible but not intelligible
  45   Loud speech not audible
  50   Very loud sounds such as musical instruments or a stereo can be faintly heard;
  60   Most sounds inaudible
Table for the reduction in intensity of sound for various kinds of walls. Values in decibels.
33  Typical interior wall
46  6 inch hollow concrete masonry
50  10 inch hollow concrete masonry

Wall thickness

Sound transmission through the wall depends on the thickness of the wall.


L       =  Thickness of a wall
Dair    =  Density of air
Dwall   =  Density of wall material
P       =  Characteristic pressure fluctuation of a sound wave striking the wall
V       =  Characterstic velocity fluctuation of a sound wave striking the wall
T       =  Wave period
F       =  Wave frequency
        =  1/T
Vwall   =  Characteristic recoil velocity of a wall upon being struck by a sound wave

V^2  ~  P / Dair
The impulse per area delivered to the wall is
Impulse / Area  ~  P T
                ~  Dair T V^2
The impulse per area is equal to the momentum per area delivered to the wall
Dair T V^2  ~  Dwall L Vwall

Vwall  ~  (Dair/Dwall) V^2 / (LF)
The wall recoil generates a sound wave on the other side of the wall with a characteristic fluctuation magnitude of Vwall. The decibel level is proportional to the logarithm of the velocity.
log(Vwall)  =  Constant - log(L) - log(F)
The change in decibel level is proportional to the logarithm of the wall thickness. It's better to divide a wall into many layers rather than having one solid wall.

The change in decibel level is proportional to the logarithm of the frequency. Low-frequency waves are difficult to block.


Impact transmission


If a sound wave strikes a wall then only a small fraction of the energy is transmitted through the wall. If an object strikes the wall then a substantial amount of energy is transmitted through the wall. Carpets are a big help for soundproofing.


Noise

Noise is often characterized with a power spectrum because the properties of soundproofing depend on frequency. It is easier to stop high-frequency noise than low-frequency noise.


Anechoic chamber

f-16 in an anechoic test chamber

The walls of an anechoic chamber absorb all sound.

The absorbers are pointy to minimize the reflection of sound.

The information rate for sound is kilobytes/second and the rate for vision is megabytes/second.


Transport cost

Leitras velomobile
Loremo
Edison 2
BMW i8

The Saab 900, last of the boxy cars
Lamborghini Diablo
Ford Escape Hybrid
Hummer H2

              Speed    Power    Force   Force   Force   Mass   Drag    Drag   Area  Drag  Roll  Year  100kph
                               (total) (fluid)  (roll)        (data)  (specs)       coef  coef         time
               m/s     kWatt     kN      kN      kN     ton     m2      m2     m2                        s

eSkate            5.3       .11    .021    .013   .008    .08    .76                1.0   .01
eScooter Zoomair  7.2       .25    .035    .027   .008    .08    .85                1.0   .01
Bike             10         .30    .035    .030   .005    .10    .49                1.0   .005
Bike             18        1.78    .103    .098   .005    .10    .50                1.0   .005
eBike 250 Watt    8.9       .25    .028    .023   .005    .10    .48                1.0   .005
eBike 750 Watt   10.6       .75    .071    .066   .005    .10    .96                1.0   .005
eBike 1 kWatt    12.5      1.0     .080    .075   .005    .10    .79                1.0   .005
eBike 1.5 kWatt  15.3      1.5     .098    .093   .005    .10    .65                1.0   .005
eBike 3 kWatt    16.7      3.0     .180    .175   .005    .10   1.03                1.0   .005
eBike Stealth H  22.2      5.2     .234    .228   .006    .12    .76                1.0   .005
eBike Wolverine  29.2      7.0     .240    .234   .006    .12    .45                1.0   .005
Bike, record     22.9      3.66    .160    .155   .005    .10    .48                1.0   .005
Bike, steamline  38.7      3.66    .095    .090   .005    .10    .099                .11  .005

Loremo           27.8     45      1.62    1.58    .035    .47   3.39   .25    1.25   .20  .0075   2009
Mitsubishi MiEV  36.1     47      1.30    1.22    .081   1.08   1.53                 .35  .0075   2011
Aptera 2         38.1     82      2.15    2.09    .062    .82   2.36   .19    1.27   .15  .0075   2011
Nissan Leaf SL   41.7     80      1.92    1.81    .114   1.52   1.71   .72    2.50   .29  .0075   2012  10.1
Volkswagen XL1   43.9*    55      1.25    1.19    .060    .80   1.01   .28    1.47   .19  .0075   2013  11.9
Chevrolet Volt   45.3    210      4.64    4.52    .121   1.61   3.61   .62    2.21   .28  .0075   2014   7.3
Saab 900         58.3    137      2.35    2.25    .100   1.34   1.09   .66    1.94   .34  .0075   1995   7.7
Tesla S P85 249+ 69.2*   568      8.21    8.06    .150   2.00   2.76   .58    2.40   .24  .0075   2012   3.0
BMW i8           69.4*   260      3.75    3.63    .116   1.54   1.24   .55    2.11   .26  .0075   2015   4.4
Nissan GTR       87.2    357      4.09    3.96    .130   1.74    .85   .56    2.09   .27  .0075   2008   3.4
Lamborghini Dia  90.3    362      4.01    3.89    .118   1.58    .78   .57    1.85   .31  .0075   1995
Porsche 918      94.4    661      7.00    6.88    .124   1.66   1.27                 .29  .0075
LaFerrari        96.9    708      7.31    7.19    .119   1.58   1.26                      .0075
Lamborghini SV   97.2    559      5.75    5.62    .130   1.73    .98                      .0075
Bugatti Veyron  119.7    883      7.38    7.24    .142   1.89    .83   .74                .0075   2005
Hummer H2                242                      .218   2.90         2.46    4.32   .57  .0075   2003
Formula 1                                         .053    .702                       .9   .0075   2017

Bus (2 decks)            138                            12.6                              .005    2012
Subway (R160)    24.7    448                            38.6                              .0004   2006

Airbus A380     320   435200   1360    1360                    21.8
F-22 Raptor     740   231000    312     312                      .93
Blackbird SR71 1100   332000    302     302                      .41

Skydive, min     40       30       .75     .75    0       .075   .77                1.0   0
Skydive, max    124      101       .75     .75    0       .075   .080               1.0   0

Sub, human power  4.1      1.78    .434                          .051
Blue Whale       13.9   3750    270                             2.74
Sub, nuke        17.4  30000   1724                            11.2                            Virginia Class

*:               The top speed is electronically limited
Drag (data)      Drag parameter obtained from the power and top speed
Data (specs)     Drag parameter from Wikipedia
Force (total)    Total drag force  =  Fluid drag force +  Roll drag force
Force (fluid)    Fluid drag force
Force (roll)     Roll drag force
Area             Cross section from Wikipedia
Drag coef        Drag coefficient from Wikipedia
Roll coef        Roll coefficient. Assume .0075 for cars and .005 for bikes.
100kph time      Time to accelerate to 100 kph
For the skydiver, the minimum speed is for a maximum cross section (spread eagled) and the maximum speed is for a minimum cross section (dive).

Cycling power

Wiki: Energy efficiency in transportation


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