Main site of science textbooks
Crowdfunding site for the free
online science textbooks project

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

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


A city built from scratch based on driverless electric vehicles, prefabricated housing, and hydroponics solves problems that existing cities can't, such as:

Decreased travel time.
Increased residential and public space per person.
Decreased housing prices and flexibility in changing residences.
Decreased noise pollution with electric vehicles.
Decreased dependence on foreign oil.
Feed everyone using hydroponics.

Electric cars outperform gasoline cars in all ways except range and are ideal for compact city cars. Electric motors can also be put on anything, such as a bike, a kick scooter, or rollerblades.

Battery technology is now prime time and and is capable of powering a flying car for 30 minutes.

Prefabricated homes can cost as little as $5000, are transportable, and can be assembled like legos into larger structures. A city can be built from scratch in a short time using prefabricated homes.

Hydroponics yield is 100 times larger than soil yield and 40 square meters of hydroponics is sufficient to sustain a person.

In the sections below we expand on each of these points.


Electric vehicles

Electric vehicles outperform gasoline vehicles in all regards except range, and if you splurge on the battery you can have the range. Electric vehicles are more powerful, quieter, simpler, more flexible, and cheaper than gasoline cars, and you can put an electric motor on anything, even a rollerblade. Electric power is ideal for compact and cheap city car.


Air drag

Air drag determines a vehicle's top speed and energy usage, and this determines the battery size.

Air density        =  D  =  1.22 kg/meter3
Air drag area      =  A
Speed              =  V
Air drag force     =  F  =  ½ A D V2
Air drag power     =  P  =  ½ A D V3
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     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
Energy 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

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.


City 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
Pasadena        24      .140     59.5     10    Car
Beverly Hills   23      .347     14.8     10    Car
Iowa City       10      .068     64.8     10    Walk, bike
Isla Vista      48      .023      4.8      5    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 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.

Consider two contrasting city designs:
Design 1) Everyone has a yard adjacent to a park and no upstairs neighbors. The house has a garage with a electric driverless car.
Design 2) Everyone lives in skycrapers

Lawns and parks are good for social interaction, especially for families with children. Skyscrapers are poor in this regard.

Being able to drive an electric car right up to your residence dramatically reduces travel time.

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.
Hydroponics

Hydroponics is the technique of growing plants in water rather than soil, where the water is fertilized with nutrients. THis substantiall increases the yield.

The principal technical challenge for a hydroponics system is to supply the roots with oxygen, which requires a water flow system. These are called "grow kits".

Data for this chapter come from from Wikipedia and from Christopher Willis' article on hydroponics.


Hydroponic system

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

An example hydroponic system consists of:

                               $     Amazon link

Grow kit, 90 sites            160    *
LED grow light, 1000 Watts    140    *
Fertilizer, 10 kg             130    *
Mirror film, 400 square feet   24    *
Greenhouse                    120    *
Total                         600

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

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.
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 cheapest source of macronutrients is cheese and peanuts.
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.
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
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

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

Deformation

The deformation of a solid is characterized by shear strain, tensile strain, and bulk compression.

Tensile strain
Shear strain
Bulk compression

Tensile strength relates to the strength of wires.

Two vices pull on a wire

Shear strength relates to the strength of beams and columns.

Bending of a beam
Buckling of a column
Human humerus

The maximum force on a beam is determined by the shear strength.

F  =  Maximum force applied to the center of a beam before it breaks
X  =  Beam length
Y  =  Beam thickness
Z  =  Beam height
x  =  Deflection of the beam at the center when under force "F"

ShearStrength  =  3 F X / (2 Y Z2)
If a column is short then it squashes before it buckles and if it is long then it buckles before it squashes.

A column's resistance to squashing is determined by the Bulk strength.

A  =  Area of the column
B  =  Bulk strength of the column
F  =  Force required to squash a column
   =  B A
A column's resistance to buckling is determined by the Young's modulus. Suppose a column is a hollow cylinder.
L  =  Length of the column
R  =  Outer radius of the column
r  =  Inner radius of the column   (r=0 if the cylinder is not hollow)
Y  =  Young's modulus
Q  =  Dimensionless effective length of the column
   =   .5      if both ends are fixed
   =  2        if one end is fixed and the other end is free to move laterally
   =  1        if both ends are pinned  (hinged and free to rotate)
   =   .699    if one end is fixed and the other is pinned
F  =  Force required to buckle the column
   =  ½ π3 Y (R4-r4) / (Q L)2
If a column's buckling limit is equal to its squashing limit then (assume r=0)
R/L  =  (Q/π) * (2B/Y)1/2

Building materials

The figure of merit for materials for beams and columns is:

Tensile strength  =  y             Pressure required to break the material
Young's modulus   =  Y             A measure of a material's rigidity
Density           =  D
Beam quality      =  y D-2
Column quality    =  Y D-2


             Density  Tensile   Young's   Beam    Column   Compression
                      strength  modulus  quality  quality   strength
             g/cm^3     GPa       GPa                         GPa

Balsa            .12     .020     3.7   1.39     257
Cedar            .34     .054     8.2    .47      71
Pine             .37     .063     9.0    .46      66
Mahogany         .67     .124    10.8    .28      24
Spruce, red      .41     .072    10.7    .43      64
Walnut, black    .56     .104    11.8    .33      38
Oak, swamp       .79     .124    14.5    .20      23
Hickory          .81     .144    15.2    .22      23
Bamboo           .85     .169    20      .23      28
Ironwood        1.1      .181    21      .15      17

Magnesium alloy 1.8      .25     45      .077     13.9
Aluminum + Be   2.27     .41     70      .080     13.6
Aluminum alloy  2.8      .40     70      .051      8.9
Titanium alloy  4.6     1.20    120      .057      5.7
Steel + CoNi    8.6     2.07    211      .028      2.9
Moly + WHa     14.3     1.8     330      .009      1.6

Polyamide       1.14     .11      4.5    .085      3.5
Polyimide       1.42     .085     2.5    .042      1.2
Acrylic         1.18     .07      3.2    .050      2.3
Polycarbonate   1.21     .07      2.6    .048      1.8
Carbon fiber    1.75    3.0

Quartzite                .025
Granite         2.7      .020                                 .13
Basalt          2.9      .020
Marble                   .015
Limestone       2.7      .015                                 .06
Gneiss                   .015
Shale           2.5      .007
Cement                   .0035                                .02
Slate                    .0035                                .095
Concrete                 .003                                 .015
Brick                    .003                                 .08
Sandstone       2.3      .002                                 .06
Wood is better than metal because of its lower density, but metal is easier to make into hollow tubes.

For metal, wood, and plastic, the tensile strength is similar to the compression stength. For rock the tensile strength is much less than the tensile strength.


Flying electric cars

Design

The larger the propeller radius, the less power that is required to fly. One hence makes the propeller as large as possible, subject to the constraint that if the propeller is too large, the mass is too large.

The most efficient copter has one large rotor for lift plus a small rotor for stability (a "monocopter"). If we increase the number of lift rotors while preserving the total rotor mass then the radius of each rotor is smaller and it takes more power to fly.

Increasing the rotor number increases stability and redundancy. Most drones use 4, 6, or 8 rotors. We construct a design for a flying car using 2 large rotors and 2 small rotors. The large rotors carry most of the weight and the small rotors add stability and failsafe.

The large propellers are mounted forward and aft and the foward propeller tilts forward for horizontal flight. The small propellers are to the right and left.

We assume the total vehicle mass is 400 kg and we use the properties of propellers to calculate the power required to hover. We use a peak power that is comfortably larger than the hover power. The battery mass required to supply this power is 1/4 the total vehicle mass.

Total aircraft mass =  M        = 400    kg           (Includes passenger)
# of large rotors   =  N        =   2
Rotor radius        =  R        =   1.5  meters
Gravity constant    =  g        =   9.8  meters/second2
Rotor force         =  F = Mg/N =1960    Newtons
Rotor quality       =  q        =   1.02
Air density         =  D        =   1.22 kg/meter3
Rotor power         =  Pr=(qDR)-1F3/2= 46.2  kWatts
Hover power         =  Ph= N Pr =  92.4  kWatts
Peak power          =  P        = 150    kWatts
Battery power/mass  =  p        =1600    Watts/kg
Battery energy/mass =  e        =    .8  MJoules/kg
Battery mass        =  m = P/p  =  94    kg
Battery energy      =  E = e m  =  75    MJoules
Hover time          =  T = E/Ph = 812    seconds  =  14 minutes
The properties of propellers are discussed in the
propeller section. The rotor tip speed is
Rotor lift/drag  =  Q  =  5.5
Rotor tip speed  =  V  =  P Q / F  =  130 m/s
The maximum horizontal speed is around 1/3 of the rotor tip speed. If we assume a horizontal speed of 40 meters/second then the range is 32 km.
Mass

For the large propellers,

Propeller radius          =  R  =  1.5 meters
Propeller mass parameter  =  C  =  5   kg/meter3
Propeller mass            =  M  =  C R3  =  17 kg
For the motors on the large propellers,
Motor power      = 60 kWatts
Motor power/mass =  8 kWatts/kg
Motor mass       =7.5 kg
The masses of the components in kg is
2 large 1.5 meter rotors       32
2 small 1.0 meter rotors       10
2 motors fo rthe large rotors  16
2 motors for the small rotors  10
Battery                       100
Cabin                          50
Fuselage                       50
Pilot                          80
Cargo                          20

Total                         380

Flight time

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       =  Mbat        =  .5 kg           (The battery is the most vital component)
Battery energy     =  E          =  .38 MJoules
Battery energy/mass=  ebat= E/Mbat=  .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 minutes
The flight time in terms of component parameters is
T  =  (ebat/p) * (Mbat/M)

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

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

Batteries

Lithium batteries

The properties of the best commercial lithium ion batteries are:

Energy/Mass     =    .8  Joule/kg
Power/Mass      =   1.6  kWatt/kg
Energy/$        =    .01 MJoule/kg
Density         =   3.5  gram/cm3
Recharges       =1000
Shelf life      =   1.0  year
Voltage         =   3.7  Volt
Max temperature =  60    Celsius
Min temperature = -20    Celsius
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      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

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 order 50 m/s.

Typical values for electric cars and aircraft 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 force

The drag force on an object moving through a fluid is

Velocity             =  V
Fluid density        =  D  =  1.22 kg/m2   (Air at sea level)
Cross-sectional area =  A
Drag coefficient     =  C
Drag force           =  F  =  ½ C A D V2
Drag power           =  P  =  ½ C A D V3  =  F V
Drag parameter       =  K  =  C A
"Terminal velocity" occurs when the drag force equals the gravitational force.
M g  =  ½ C D A V2
Suppose we want to estimate the parachute size required for a soft landing. Let a "soft landing" be the speed reached if you jump from a height of 2 meters, which is Vt = 6 m/s. If a skydiver has a mass of 100 kg then the area of the parachute required for this velocity is 46 meters2, which corresponds to a parachute radius of 3.8 meters.
Drag coefficient

               Drag coefficient

Bicycle car         .076        Velomobile
Tesla Model 3       .21         2017
Toyota Prius        .24         2016
Bullet              .30
Typical car         .33         Cars range from 1/4 to 1/2
Sphere              .47
Typical truck       .6
Formula-1 car       .9          The drag coeffient is high to give it downforce
Bicycle + rider    1.0
Skier              1.0
Wire               1.2

Rolling drag

Force of the wheel normal to ground  =  Fnormal
Rolling friction coefficient         =  Croll
Rolling friction force               =  Froll  =  Croll Fnormal

Typical car tires have a rolling drag coefficient of .01 and specialized tires can achieve lower values.
                             Croll

Railroad                      .00035     Steel wheels on steel rails
Steel ball bearings on steel  .00125
Racing bicycle tires          .0025      8 bars of pressure
Typical bicycle tires         .004
18-wheeler truck tires        .005
Best car tires                .0075
Typical car tires             .01
Car tires on sand             .3

Rolling friction coefficient
Wheel diameter          =  D
Wheel sinkage depth     =  Z
Rolling coefficient     =  Croll  ≈  (Z/D)½

Energy and power

Energy          =  E          Joules
Time            =  T          seconds
Power           =  P  =  E/T  Watts
Mass            =  M          kilograms
Energy/Mass     =  e  =  E/M  Joules/kilogram
Power/Mass      =  p  =  P/M  Watts/kilogram

Fuel
Black: Carbon    White: Hydrogen    Red: Oxygen

Methane (Natural gas)
Ethane
Propane
Butane (Lighter fluid)
Octane (gasoline)
Dodecane (Kerosene)

Hexadecane (Diesel)
Palmitic acid (fat)
Ethanol (alcohol)

Glucose (sugar)
Fructose (sugar)
Galactose (sugar)
Lactose = Glucose + Galactose
Starch (sugar chain)
Leucine (amino acid)

ATP (Adenosine triphosphate)
Phosphocreatine
Nitrocellulose (smokeless powder)
TNT
HMX (plastic explosive)

Lignin (wood)
Coal

Medival-style black powder
Modern smokeless powder
Capacitor
Lithium-ion battery
Nuclear battery (radioactive plutonium-238)
Nuclear fission
Nuclear fusion
Antimatter


Vehicle power

Tesla Roadster

The energy sources that can be used by vehicles are:

              Energy/Mass   Power/mass   Energy/$   Rechargeable   Charge   Maximum charging
               MJoule/kg     Watt/kg     MJoule/$                  time          cycles

Gasoline            45                   60
Battery, aluminum    4.6       130                      No
Battery, lithium      .8      1600         .010         Yes        1 hour      1000
Supercapacitor        .016    8000         .00005       Yes        Instant     Infinite
Aluminum capacitor    .010   10000         .0001        Yes        Instant     Infinite

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


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

Engine efficiency

Photoelectric cell
Thermoelectric generator
Stirling engine
Stirling engine

Electric car engine  .80
Gasoline engine      .15
Diesel engine        .20
Human muscles        .22
Biomass plant        .25
Natural gas plant    .35
Solar cell           .20     Crystalline type
Solar cell           .40     Multilayer type
Turboprop, Mach .4   .80     Turboprops work up to Mach .5
Turbojet,  Mach .4   .40
Turbofan,  Mach .4   .68
Turbojet,  Mach .9   .77
Turbofan,  Mach .9   .90
For an electric vehicle the overall efficiency is similar to that of a diesel engine.
Overall efficiency  =  Power plant efficiency  *  Vehicle efficiency  =  .35 * .80 =  .28

Fuel efficiency
                       Speed   l/km   l/km/   Passengers
                        m/s           person

Walk                    1.4     .0065  .0065   1         60 Watts
Run                             .009   .009    1
Bike                    4.4     .0032  .0032   1
Bike, aerodynamic      13.9     .0005  .0005   1
Car, solar power                .067   .067    1
Car, electric, Tesla            .015   .004    4
Car, electric, GEM NER 10.8     .012   .003    4
Car, electric, GE EV1           .026   .006    4
Car, electric, Volt             .026   .006    4
Car, VW Bluemotion              .038   .010    4
Car, Honda Insight              .049   .012    4
Car, Toyota Prius               .051   .013    4
Car, Cadillac Wagon             .17    .028    6         6.2L engine
Car, Bugatti Veyron             .24    .12     2
Train, Switzerland              .17    .0026  65
Train, Japan                    .65    .011   59
Plane, Dieselis        44.4     .019   .010    2
Plane, Pipistrel Sinus 62.5     .048   .024    2
Plane, Tecnam Sierra   65.8     .072   .036    2
Plane, DynAero MCR-4S  61.1     .088   .022    4         100 hp
Plane, Boeing 747-400                 3.1    660
Plane, Concorde                      16.6    128
Plane, Airbus A380                    3.0    835
Ship, Queen Elizabeth        300       .17  1777
Ship, Cargo            12.8 1070       -       -         Emma Maersk. 170000 tons
Helicopter, Sikorsky   72.2    1.43    .12    12         Model S-76
1 litre gasoline = 31.7 MJoules
U.S. transportation averages
                  MJ/km/    Passengers
                  person    per vehicle

Train, Switzerland  .085       65
Train, Japan        .35        59
Car, electric      1.2          1.5
Train, city        1.60        30.9
Train, intercity   1.65        24.5
Motorcycle         1.61         1.16
Air                1.85        99.3
Car, gasoline      2.32         1.55
Bus                2.78         9.2
Taxi              10.3          1.55

Freight
                  MJ/km/ton

Ship, U.S. local    .16
Ship, ocean cargo   .22     Emma Maersk. 170000 tons
Train               .21
Truck              2.43
Air                6.9

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.
Lithium content of batteries
Battery lithium content    =    .023 kg/MJoule
Lithium price              =  20     $/kg
Battery lithium $/MJoule   =    .46  $/MJoule
Battery total $/MJoule     = 100     $/MJoule
CO2 per MJoule             =  42     kg/MJoules      (to produce lithium-ion batteries)

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


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
ce1.html 0;256;0c
Spices

Turmeric: curcumin
Cumin: cuminaldehyde
Chili: capsaicin
Mustard: allyl isotyiolcyanate

Bay: myrcene
Garlic and onion: allicin
Clove: eugenol

Raspberry ketone
Tangerine: tangeritin
Lemon: citral
Lemon peel: limonene

Chocolate: theobromine
Smoke: guaiacol
Cardamom: terpineol
Wintergreen: methyl salicylate

Hydrogen   White
Carbon     Black
Nitrogen   Blue
Oxygen     Red
Sulfur     Yellow
        Scoville scale (relative capsaicin content)

Ghost pepper    1000000
Trinidad        1000000      Trinidad moruga scorpion
Naga Morich     1000000
Habanero         250000
Cayenne           40000
Tabasco           40000
Jalapeno           6000
Pimento             400


Molecule        Relative hotness

Rresiniferatoxin   16000
Tinyatoxin          5300
Capsaicin             16         Chili pepper
Nonivamide             9.2       Chili pepper
Shogaol                 .16      Ginger
Piperine                .1       Black pepper
Gingerol                .06      Ginger
Capsiate                .016     Chili pepper
Caraway: carvone
Black tea: theaflavin
Cinnamon: cinnamaldehyde
Citrus: hesperidin
Fruit: quercetin

Mint: menthol
Juniper: pinene
Saffron: picrocrocin
Saffron: safranal
Wine: tannic acid

Black pepper: piperine
Oregano: carvacrol
Sesame: sesamol
Curry leaf: girinimbine
Aloe emodin
Whiskey lactone


Signalling molecules

Alcohol
Caffeine
Tetrahydrocannabinol
Nicotine

Adrenaline
Noadrenaline
Dopamine
Seratonin

Aspirin
Ibuprofen
Hydrocodone
Morphone

Vitamin A (beta carotene)
Vitamin A (retinol)
Vitamin C (ascorbic acid
Vitamin D (cholecalciferol)


Main page

Support the free online science textbooks project






© Jason Maron, all rights reserved.