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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
CR2032         3.                                                             Most common button cell
CR1216          .33                                                           Smallest button cell

Apple Watch 4  4.0                                            .29
iPhoneXR 6"   41                                             2.94             Machine = .194 kg
iPhoneXSM 6"  44                                             3.17             Machine = .208 kg
iPhoneXS 6"   36                                             2.66             Machine = .177 kg
iPhone8+ 6"   27                                             2.79             Machine = .202 kg
iPhone8  5"   25                                             1.82             Machine = .148 kg
iPhone7+ 6"   40                                             2.90             Machine = .188 kg
iPhone7  5"   27                                             1.96             Machine = .138 kg
iPad Mini 8"  70                                             5.12             Machine = .30  kg
iPad Pro 10" 111                                             8.13             Machine = .47  kg
Mac Air 11"  137                                                              Machine = 1.08 kg
Mac Air 13"  194                                                              Machine = 1.34 kg
MacBook 12"  149                                                              Machine =  .92 kg
Mac Pro 13"  209                                                              Machine = 1.37 kg
Mac Pro 15"  301                                                              Machine = 1.83 kg

              Energy  Power  Lifetime
              kJoule  Watts   hours

iPhone 8  5"    25     .50    14
iPhone 8+ 6"    27     .54    14
iPad Mini 8"    70    1.9     10
iPad Pro 10"   111    3.1     10
Mac Air  11"   137    3.8     10
Mac Air  13"   194    5.4     10
Mac Pro  13"   209    5.8     10
Mac Pro  15"   301    8.4     10

Battery energy and power

Voltage          =  V         Volts
Charge           =  C         Coulombs
Time             =  T         seconds
Electric current =  I  = C/T  Amperes (Amps)
Electric power   =  P  =  VI  Watts
Energy           =  E  =  PT  Joules
                       =  CV  Joules
Battery energy is often given in "Watt hours" or "Ampere hours".

1 Watt hour = 3600 Joules = 1 Watt * 3600 seconds

1 Amp hour = 3600 Coulombs = 1 Coulombs/second * 3600 seconds

A battery with a voltage of 3.7 Volts that delivers 1 Ampere for 1 hour has an energy of
Energy = 1 Ampere * 3.7 Volts * 3600 seconds = 13320 Joules


Battery types
              Energy/Mass  Power/Mass  Recharge  Year  Anode  Cathode   Market fraction of
               MJoule/kg    Watt/kg                                     Lithium-ion batteries

Lithium air          6.12               No     Future  Li    O2
Aluminum air         4.68     200       No     1970    Al    O2
Lithium thionyl      2.00     700       No     1973    Li    SOCl2
Zinc air             1.59               No     1932    Zn    O2
Lithium-ion sulfur   1.44     670       Yes    Future  Li    S               0
Lithium metal        1.01     400       No     1976    Li    MnO2
Lithium-ion CoNiAlO2  .79               Yes    1999    Li    CoNiAlO2         .10
Lithium-ion CoNiMnO2  .74    1200       Yes    2008    Li    CoNiMnO2         .29
Lithium-ion CoO2      .70     200       Yes    1991    Li    CoO2             .29
Lithium-ion Mn2O4     .54    1200       Yes    1999    Li    Mn2O4            .10
Lithium-ion FePO4     .47    1200       Yes    1996    Li    FePO4            .22
Alkaline              .40               Yes    1992    Zn    MnO2
NiMH                  .34    1000       Yes    1990    MH    NiO(OH)
Lead acid             .15     180       Yes    1881    Pb    PbO2
NiCd                  .14     200       Yes    1960    Cd    NiO(OH)

History
                  MJoules/kg   Recharge

1932  Zinc air          1.59     N
1949  Alkaline           .59     N
1973  Lithium thionyl   1.8      N
1976  LiMnO2            1.01     N
1989  LiFeS2            1.07     N
1989  Aluminum air      4.68     N
Lab   Lithium air       6.1      N

1881  Lead acid          .14     Y
1901  NiFe               .09     Y
1960  NiCd               .14     Y
1975  NiH2               .23     Y
1991  Lithium-ion        .95     Y
1992  Rechargeable alk.  .4      Y
Lab   Lithium sulfur    1.44     Y

Energy storage

Pumped hydro reservoir

The largest energy storage stations are "pumped hydro" stations, where water is pumped to an elevated reservoir when energy is available and returned to the lower reservoir when energy is needed. The cheapest system types are pumped hydro and underground compressed air. For small-scale energy storage such as homes, batteries are the cheapest option. The types of energy storage are:

                   Cost    Cost   Efficiency   Cycles
                   kJ/$   Watt/$

Pumped hydro         26       .7      .8       Infinite    Pump water to an elevated reservoir
Air, underground     60      1.0      .7       Infinite    Compress air
Air, above ground     9       .5      .7       Infinite    Compress air
Battery, Li-ion      10     10        .9       1000
Battery, Lead acid   10     10        .9       1000
Flywheel               .45    .5      .85      Infinite
Gasoline          30000      2.0      .35      -           Using a generator with 2 Watts/$
Solar cell            -       .5      -        -
Wind turbine          -       .25     -        -           Blade diameter = 2.5 meters

The largest energy storage systems for each type of storage are:

                                         GWatt hours

California, San Luis        Pumped hydro    126
Tennessee, Raccoon Mtn.     Pumped hydro     36
Virginia, Bath County       Pumped hydro     31
California, Kern County     Compressed air    3
Alabama, McIntosh CAES      Compressed iar    2.9
Arizona, Solana             Thermal salt      1.7
Spain, Andasol              Thermal salt      1.03
Australia, Hornsdale        Battery, Li-ion    .129
California, Primus Power    Battery, ZnCl      .075
Japan, Hokkaido Project     Battery, Li-ion    .060
China, National Wind        Battery, Li-ion    .036
New York, Beacon            Flywheel           .005

The average American home uses 1400 Watts of electricity. 1 GWatt hour is enough to power 30000 homes for 1 day.

For small scale energy storage such as an off-grid home, a generator can help. They typically cost ½ $/Watt.

Data on cost of energy storage


Home energy system

A house can use either grid electricity, a gasoline generator, or a system of solar cells and batteries. Grid electricity is cheapest, gasoline is slightly more expensive, and solar cells and batteries are much more expensive.

House, electrical power         =  1000 Watts          Typical for a small house
Energy for one day              =    86 MJoules
Li-ion battery Energy/$         =   .01 MJoule/$
Generator efficiency            =    .3
Generator cost                  =     2 Watts/$
Solar cell cost                 =    .5 Watts/$
Solar cell average power        =    50 Watts/meter2
Cost of grid electricity        =    36 MJoules/$
Gasoline energy per mass        =    48 MJoules/kg
Gasoline cost per mass          =    .5 $/kg
Gasoline energy per dollar      =    96 MJoules/$
Cost, 1 year of grid electricity=   870 $
Cost, 1 year of gasoline        =  1090 $              1 year of gasoline to supply a 1 kWatt generator
Cost, 1000 Watt generator       =   500 $
Cost, 1000 Watt solar cell      =  2000 $
Cost, battery, 1 day of energy  =  8600 $              1 Day at 1 kWatt

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

Metals for an electric economy

Cobalt is the dominant cost for lithium-ion batteries, and copper is the dominant cost for solar cells, wind turbines, and electric motors.

Lithium-ion batteries can be made with or without cobalt, although cobalt is required if you want large energy/mass.

The critical metals are copper, lithium, cobalt, nickel, neodymium, silver, and rare Earths. Cobalt and rare Earths are a concern because they're scarse (42% of cobalt goes to batteries) and because they come from politically unstable regions.

The metal content of various devices is:

           Cost  Mining  Reserves   Battery   Battery   SolarCell  SolarCell    Wind    Wind   Motor     Motor
           $/kg  Bkg/yr    Bkg     kg/MJoule  $/MJoule  kg/kWatt    $/kWatt   kg/kWatt  $/kW  kg/kWatt  $/kWatt

Lithium     20      .6      30       .023      .46        -            -        -        -      -         -
Cobalt      30      .12      7       .20      6.0         -            -        -        -      -         -
Nickel      15     2.2      80       .20      3.0         -            -        -        -      -         -
Copper       6    18       700       -         -         5            30       4       24       .036      .22
Neodymium   25      .01       .6     -         -          -            -        .014     .28    .0062     .16
Silver     450      .026      .53    -         -          .034        15        -        -      -         -

Batteries, lithium, and cobalt

All lithium-ion batteries contain lithium and most contain an equal number of lithium and cobalt atoms. Lithium-ion batteries typically contain an equal number of lithium and cobalt atoms. A cobalt atom is substantially more massive than a lithium atom and so batteries have much more cobalt mass than lithium mass. Cobalt reserves are smaller than lithium reserves and so we will run out of cobalt before we run out of lithium.

For a typical car battery, the cobalt cost is:

Energy                  =  100  MJoules
Cobalt cost per MJoule  =  6.0  $/MJoule
Cobalt cost             =  600  $

If we make 1 billion electric cars then the total cobalt mass is:

Energy                  =  100  MJoules
Cobalt mass per MJoule  =   .2  kg
Cobalt mass per car     =   20  kg
Number of cars          =    1  billion cars
Total cobalt mass       =   20  Bkg
Cobalt mining           =  .12  Bkg/year
Cobalt reserves         =    7  Bkg

The cobalt required far exceeds annual mining and it even exceeds reserves. Not all batteries will be able to have cobalt.


Lithium-ion batteries

All lithium-ion batteries contain lithium and they can also contain cobalt, manganese, nickel, and aluminum. Only lithium (20 $/kg) and cobalt (30 $/kg) are expensive enough to matter. Batteries with high energy/mass require cobalt. The battery types are:

                      Energy/Mass  Market  Commer-
                       MJoule/kg    frac   cialized

Lithium-ion  LiS         1.44       0       Future
Lithium-ion  LiCoO2       .95       .29     1991
Lithium-ion  LiNiCoAlO2   .79       .10     1999
Lithium-ion  LiNiCoMnO2   .74       .29     2008
Lithium-ion  LiMn2O4      .54       .10     1999
Lithium-ion  LiFePO4      .47       .22     1996

Alkaline                  .40               1992
Nickel metal hydride      .34               1990
Lead acid                 .15               1881
Nickel cadmium            .14               1960

Lithium-iBatteries typically cost 100 $/MJ. "Market fraction" is for lithium-ion batteries only.


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