Military

World military budget

             B$/yr   % GDP                        B$/yr   % GDP

World        1676     2.3           Japan          40.9   1.0
USA           597     3.3           Germany        39.4   1.2
China         215     1.9           South Korea    36.4   2.6
Saudi Arabia   87.2  13.7           Brazil         24.6   1.4
Russia         66.4   5.4           Italy          23.8   1.3
UK             55.5   2.0           Australia      23.6   1.9
India          51.3   2.3           UAE            22.8   5.7
France         50.9   2.1           Israel         16.1   5.4

Military equipment

Ronald Reagan, Kitty Hawk, and Abraham Lincoln (front to back)

Virginia class nuclear submarine
Virginia class: the "North Dakota"

      Nuclear  Diesel  Aircraft   Military   F-22  F-35  B-2  Combat   Nuclear
       subs     subs   carriers  Satellites                  aircraft  devices

Total     148   228       20     320        184         20  20089    15913
USA        72             10     123        184   71    20   3680     7100
Russia     45    18        1      74                         1337     7700
UK         11              1       7              18*         278      225
France     10              1       8                          395      300
China       9    46        1      68                         2571      260
India       1    13        2       5                          928      110
Japan            17                4               5*         777       TC
Israel            3                8              33*         440       80
Italy             6        2       6               8*         258
Germany           4                7                          245
S. Korea         12                                           587       TC
Egypt                                                         569
N. Korea                                                      563        8
Taiwan            2                1                          485
Pakistan          5                                           460      120
Iran              3                                           337
Turkey           14                1               6*         335
S. Arabia                                                     313       TC
Syria                                                         277
Greece            8                                           244
Ukraine                                                       203
UAE                                2                          175
Spain             4                                           166
Australia         6                1              72*         146
Myanmar                                                       155       TC
Thailand                   1                                  143
Sweden            5                                           134
Singapore         4                                           126
Argentina         3                                           123       TC
Kazakhstan                                                    122
Algeria           4                                           120
Poland            5                                           113       TC
Finland                                                       107
Canada            4                1                           95
Chile             4                1
Netherlands       4                               10*
Norway            6                                4*
Mexico                             1                                    TC
Spain                              2
Brazil            5        1                                            TC
Malaysia          2
Portugal          2
Romania           1
Vietnam           1
Colombia          2
Ecuador           2
Indonesia         2
Peru              6
S. Africa         3
Venezuela         2

*:  On order
TC: Does not possess nuclear devices but is technologically capable of building them
The aircraft with stealth technology are the F-22, F-35, and B-2.
For the "combat aircraft" column, only countries with at least 100 combat aircraft are listed.
Data
Air Force
       F-22 F-35 F-15 F-16 F-18 F-4 F-5 F-2 MiG31 MiG25 MiG29 MiG29 MiG21 Su35 Su30  J7 J10

USA     195 121  449  983   885         561
Russia                                       152         252              48
China                                                                     24        728 240
Japan        42* 154             71      64
S. Korea     40*  58  169        71 158
India                                          5               108   245       241
Singapore         40   60            27
Taiwan                115            23
Thailand               53            30
Indonesia              16             2
Malaysia                      8      18
Philip.
Total                4500
*: On order

Submarines

Virginia class nuclear submarine
Virginia class: the "North Dakota"

                  Speed  Power   Mass  Depth  Len   Wid   Hei  Drag  Year   #   Power
                  km/h   MWatts  Mkg     m     m     m     m

USA     Virginia     46   30      7.9   240  115    10.0             2004  13   Nuclear
USA     Ohio         46   45     18.8   240  170    13    10.8  .73  1981  18   Nuclear
USA     Los Angeles  37   26      6.9   290  110    10     9.4  .63  1976  36   Nuclear
Russia  Akula        65   32     13.8   520  113.3  13.6   9.7  .55  1986  10   Nuclear
Russia  Oscar        59   73.1   19.4        155    18.2   9   1.02  1981   5   Nuclear
Russia  Borey        56          24     450  170    13.5  10         2010   3   Nuclear
Russia  Delta 4      44.4               320                          1981   7   Nuclear
UK      Vanguard     46   41     15.9        149.9  12.8  12         1993   4   Nuclear
France  Triomphant   46          14.3   400  138    12.5  10.6       1997   4   Nuclear
India   Arihant      44   83     ~7     300  112    11    10   1.73  2016   1   Nuclear
China   Type 93      55.6         7.0        110    11     7.5       2006   5   Nuclear
China   Type 95                                                      2015   5   Nuclear
China   Type 94                  11          135    12.5             2007   4   Nuclear

India   Shishumar    41   10.6    1.85  260   64.4                   1986   4   Diesel electric. German
Germany Type 212     37    2.85   1.83  700   57.2   7     6         2002  10   AIP, Fuel cell
India   Kalvari      37           1.87        61.7   6.2   5.8       2016   1   AIP, Fuel cell
Japan   Soryu        37    6.0    4.2         84.0   9.1   8.5       2009   9   AIP, Stirling
Japan   Oyashio      37    5.78   4.0         81.7   8.9   7.4  .20  1998  11   Diesel electric
Australia  Collins   37    5.37   3.41 >180   77.4   7.8   7    .23  1996   6   Diesel electric
India   Sindhughosh  31   10.2    3.08  300          9.9   6.6  .36  1986   9   Diesel electric. Kilo class
Taiwan  Hai Lung     22           2.66  300   66.9   8.4   6.7       1987   2   Diesel electric. Dutch Zwaardvis class
"Depth" refers to the "Test depth", which is typically 2/3 of the crush depth.
"Drag" is the drag coefficient defined below.
Submarine speed
Height           =  H
Width            =  W
Cross section    =  A  =  π H W / 4
Water density    =  D  =  1025 km/meter3       Typical for seawater
Speed            =  V
Drag coefficient =  C
Propeller power  =  P  =  ½ C D A V3

Submarines by country

      Nuclear  Diesel  Aircraft
       subs     subs   carriers

Total     148   228       20
USA        72             10
Russia     45    18        1
UK         11              1
France     10              1
China       9    46        1
India       1    13        2
Japan            17
Turkey           14
S. Korea         12
Greece            8
Italy             6        2
Norway            6
Peru              6
Australia         6
Pakistan          5
Sweden            5
Brazil            5        1
Poland            5
Germany           4
Singapore         4
Spain             4
Algeria           4
Canada            4
Chile             4
Netherlands       4
S. Africa         3
Israel            3
Iran              3
Argentina         3
Taiwan            2
Malaysia          2
Portugal          2
Colombia          2
Ecuador           2
Indonesia         2
Venezuela         2
Romania           1
Vietnam           1

Torpedoes
                  Speed   Range   Mass  Warhead  Length  Diam   Depth  Year  Fuel
                  km/h     km     ton     ton    meter   meter  meter

UK      Spearfish  150     54     1.85    .30     7.0    .533          1992  Otto fuel 2
China   Yu-6       120.4   45                            .533          2012  Otto fuel 2
USA     Mark 48    102     38     1.68    .29     5.8    .53     800   2008  Otto fuel 2
Germany DM2A4       92.6   50             .26     6.6    .533                Silver zinc battery
USA     Mark 54     74.1           .276   .044    2.72   .324          2004  Otto fuel 2
S Korea White Shark 63     30     1.1             2.7    .48           2004
Inaia   Varunastra  74     40      1.5    .25      7.0   .533    400   2016  Electric

Combat aircraft

F-22 Raptor
F-35 Lightning
F-15 Eagle

F-15 Eagle cockpit
F-16 Falcon
MiG-25 Foxbat

               Speed  Mass  Takeoff  Ceiling  Thrust  Range  Cost  Number Year Stealth
               Mach   ton     ton      km       kN     km     M$

SR-71 Blackbird  3.3   30.6   78.0     25.9    302    5400          32   1966
MiG-25 Foxbat    2.83  20.0   36.7     20.7    200.2  1730        1186   1970
MiG-31 Foxhound  2.83  21.8   46.2     20.6    304    1450         519   1981
F-22A Raptor     2.51  19.7   38.0     19.8    312    2960   150   195   2005   *
F-15 Eagle       2.5   12.7   30.8     20.0    211.4  4000    28   192   1976
MiG-29 Fulcrum   2.25  11.0   20.0     18.0    162.8  1430    29  1600   1982
Su-35            2.25  18.4   34.5     18.0    284    3600    40    48   1988
F-4 Phantom II   2.23  13.8   28.0     18.3           1500        5195   1958
Chengdu J-10     2.2    9.8   19.3     18.0    130    1850    28   400   2005
F-16 Falcon      2.0    8.6   19.2     15.2    127    1200    15   957   1978
Chengdu J-7      2.0    5.3    9.1     17.5     64.7   850        2400   1966
Dassault Rafale  1.8   10.3   24.5     15.2    151.2  3700    79   152   2001
Euro Typhoon     1.75  11.0   23.5     19.8    180    2900    90   478   2003
F-35A Lightning  1.61  13.2   31.8     15.2    191    2220    85    77   2006   *
B-52              .99  83.2  220       15.0    608   14080    84   744   1952
B-2 Bomber        .95  71.7  170.6     15.2    308   11100   740    21   1997   *
A-10C Warthog     .83  11.3   23.0     13.7     80.6  1200    19   291   1972
Drone RQ-180          ~15              18.3          ~2200               2015   *
Drone X-47B       .95   6.4   20.2     12.2           3890           2   2011   *  Carrier
Drone Avenger     .70          8.3     15.2     17.8  2900    12     3   2009   *
Drone RQ-4        .60   6.8   14.6     18.3     34   22800   131    42   1998
Drone Reaper      .34   2.2    4.8     15.2      5.0  1852    17   163   2007
Drone RQ-170                           15                           20   2007   *

India HAL AMCA   2.5   14.0   36.0     18.0    250    2800     ?     0   2023   *
India HAL FGFA   2.3   18.0   35.0     20.0    352    3500     ?     0  >2020   *
Mitsubishi F-3   2.25   9.7     ?        ?      98.1  3200     ?     1   2024   *
Chengdu J-20     2.0   19.4   36.3       ?     359.8     ?   110     4   2018   *
Sukhoi PAK FA    2.0   18.0   35.0     20.0    334    3500    50     6   2018   *
Shenyang J-31    1.8   17.6   25.0       ?     200    4000     ?     0   2018   *

Mach 1 = 295 m/s
5th generation fighters: F-22, F-35, X-2, HAL AMCA, J-20, J-31, Sukhoi PAK FA

An aircraft moving at Mach 2 and turning with a radius of 1.2 km has a g force of 7 g's.


Drones

X-47B
X-47B

RQ-170 Sentinel
MQ-9 Reaper


Missiles

Air to air missiles

F-22 and the AIM-120
AIM-9
Astra
Predator and Hellfire
Helfire in a transparent case

                Mach   Range  Missile  Warhead  Year  Engine
                        km      kg       kg

Russia  R-37      6      400    600      60    1989   Solid rocket
Japan   AAM-4     5      100    224       ?    1999   Ramjet
India   Astra     4.5+   110    154      15    2010   Solid rocket
EU      Meteor    4+     200    185       ?    2012   Ramjet
Russia  R-77-PD   4      200    175      22.5  1994   Ramjet
USA     AIM-120D  4      180    152      18    2008   Solid rocket
Israel  Derby-IR  4      100    118      23           Solid rocket
Israel  Rafael    4       50    118      23    1990   Solid rocket
France  MICA      4       50    112      12    1996   Solid rocket
Israel  Python 5  4       20    105      11           Solid rocket
Russia  K-100     3.3    400    748      50    2010   Solid rocket
UK      ASRAAM    3+      50     88      10    1998   Solid rocket
Germany IRIS-T    3       25     87.4          2005   Solid rocket
USA     AIM-9X    2.5+    35     86       9    2003   Solid rocket
USA     Hellfire  1.3      8     49       9    1984   Solid rocket  AGM-114

Ground to air missiles

David's Sling
Terminal High Altitude Area Defense (THAAD)

SM-3
SM-3
Chu-SAM
RIM-174

                 Mach   Range  Missile  Warhead  Year  Engine     Stages   Anti
                         km      kg       kg                              missile

USA     SM-3      15.2   2500   1500       0    2009   Solid rocket  4       *
Israel  Arrow      9      150   1300     150    2000   Solid rocket  2
USA     THAAD      8.24   200    900       0    2008   Solid rocket          *
USA     David      7.5    300                   2016   Solid rocket          *
Russia  S-400      6.8    400   1835     180    2007   Solid rocket          *
India   Prithvi    5     2000   5600            2006   Solid, liquid 2       *
India   AAD Ashwin 4.5    200   1200       0    2007   Solid rocket  1
Taiwan  Sky Bow 2  4.5    150   1135      90    1998   Solid rocket
China   HQ-9       4.2    200   1300     180    1997   Solid rocket  2
USA     Patriot 3  4.1     35    700      90    2000   Solid rocket          *
China   KS-1       4.1     50    900     100    2006   Solid rocket          *
USA     RIM-174    3.5    460   1500      64    2013   Solid rocket  2
India   Barak 8    2      100    275      60    1015   Solid rocket  2
Japan   Chu-SAM                  570      73    2003   Solid rocket
Korea   KM-SAM             40    400            2015   Solid rocket

Ground to ground missiles

Tomahawk
Tomahawk

                Mach   Range  Missile  Warhead  Year  Engine        Launch
                        km      kg       kg                         platform

USA     Tomahawk   .84  2500   1600     450    1983   Turbofan      Ground
USA     AGM-129    .75  3700   1300     130    1990   Turbofan      B-52 Bomber
USA     AGM-86     .73  2400   1430    1361    1980   Turbofan      B-52 Bomber

Hypersonic missiles

HTV-2
X-51
DARPA Falcon HTV-3

                   Speed   Mass  Payload  Range  Year
                   mach    tons   tons     km

USA      SR-72         6                          Future. Successor to the SR-71 Blackbird
USA      HSSW          6                    900   Future. High Speed Strike Weaspon
USA      HTV-2        20           5500   17000   2 Test flights
USA      X-41          8           450            Future
USA      X-51          5.1  1.8             740   2013    Tested. 21 km altitude. Will become the HSSW
Russia   Object 4202  10                          Tested
India    HSTDV        12                          Future
China    Wu-14        10                          2014   7 tests.  also called the DZ-ZF
The SR-72 has two engines: a ramjet for below Mach 3 and a ramjet/scramjet for above Mach 3. The engines share an intake and thrust nozzle.
Intercontinental ballistic missiles

First ICBM: SM-65 Atlas, completed in 1958
Titan 2
Peacekeeper
Minuteman 3
Minuteman 3

Trident 2
Peacekeeper
Minuteman 3

                     Payload  Paylod   Range  Mass    Launch   Year
                     (tons)   (Mtons)  (km)   (tons)

USA     Titan 2               9        15000   154     Silo    1962   Inactive
USA     Minuteman 3            .9      13000    35.3   Silo    1970
USA     Trident 2              .95     11300    58.5   Sub     1987
USA     Titan                 3.75     10200   151.1   Silo    1959   Inactive
USA     Peacekeeper           3         9600    96.8   Silo    1983   Inactive
Russia  RS-24                 1.2      12000     49    Road    2007
Russia  Voevoda         8.7   8        11000    211.4  Silo    1986
Russia  Layner                         11000     40    Sub     2011
Russia  RS-28 Sarmat   10              10000   >100    Silo    2020   Liquid rocket
Russia  Bulava                 .9      10000     36.8  Sub     2005
France  M51.1                 1        10000    52     Sub     2006
China   DF-5B                 8        15000    183    Silo    2015
China   DF-5A                 4        15000    183    Silo    1983
China   JL-2                  6        12000     42    Sub     2001
China   DF-5                  5        12000    183    Silo    1971
China   DF-31A                3        12000     42    Road
China   DF-31                 1         8000     42    Road    1999
China   DF-4                  3.3       7000     82    Silo    1974
India   Surya          15              16000     70    Road    2022
India   Agni-VI        10              12000     70    Road    2017
India   Agni-V          6               8000     50    Road    2012
India   K-4             2.5             3500     17    Sub     2016   Solid. Arihant nuclear sub
India   K-15           ~6.5              750      1.0  Sub     2010   Solid. 2 stages. Arihant nuclear sub
Israel  Jericho 3        .75           11500     30    Road    2008
N. Kor. Taepodong-2                     6000     79.2  Pad     2006
Pakis.  Shaheen 3                       2750           Road    2015   Solid. 2 stages.
Pakis.  Shaheen 2                       2000     25    Road    2014   Solid. 2 stages.
Pakis.  Ghauri 2        1.2             1800     17.8  Road
Pakis.  Ghauri 1         .7             1500     15.8  Road    2003   Liquid. 1 stage.
Iran    Shabab 3        1.0             1930                   2003
Payload in "tons" represents the mass of the payload.
Payload in "Mtons" is the nuclear detonation payload in terms of tons of TNT.
Firearms

Walther PPK/E 9 mm
FN SCAR-H 7.6 mm

Barrett M82 13 mm
M2 Bradley, M242 Bushmaster 25 mm
GAU-8 Avenger 30 mm

A-10 Warthog, GAU-8 Avenger
M1 Abrams 120 mm
M777 howitzer 155 mm

M777 Howitzer
U.S.S. Iowa 406 mm

                Bullet  Bullet   Speed   Energy   Barrel    Gun     Fire   Vehicle
                 diam    mass                                       rate    mass
                  mm      kg      m/s    kJoule   meters     kg     Hertz   tons

Walther PPK         5.6    .0020   530       .277   .083       .560
Walther PPK         5.6    .0030   370       .141   .083       .560
Walther PPK/S       7.65   .0050   318       .240   .083       .630
Walther PPK/E       9.0    .0065   323       .338   .083       .665
M4 Carbine          5.56   .0041   936      1.796   .370      2.88    15.8
FN SCAR-H Rifle     7.62   .011    790      3.506   .400      3.58    10.4           20 round magazine
Barrett M82        13.0    .045    908     18.940   .74      14.0                    10 round magazine
Vidhwansak         20      .13     720     33.7    1.0       26                      20x81 mm. 3 round magazine
RT-20              20      .13     850     47       .92      19.2                    1 round magazine
M621 cannon        20      .102   1005     51.5              45.5     13.3           20x102 mm
M61 Vulcan         20      .102   1050     56.2              92      110             20x102. 6 barrels
Oerlikon KBA       25      .184   1335    164      2.888    112       10
M242 Bushmaster    25      .184   1100    111      2.175    119        8.3    27.6   M2 Bradley
GAU-12 Equalizer   25      .184   1040     99.5             122       70       6.3   Harrier 2. 5 barrels
M230 chain gun     30      .395    805    128                55.9     10.4     5.2   Apache. 30x113 mm
Mk44 Bushmaster 2  30      .395   1080    230      2.41     160        3.3    27.6   M2 Bradley. 30x173 mm
GAU-8 Avenger      30      .395   1070    226      2.30     281       70      11.3   A-10 Warthog. 30x173 mm. 7 barrels
Bushmaster III     35             1180                      218        3.3           35x228 mm
Bushmaster IV      40     1.08                              198        3.3           40x365 mm
Rheinmetall 120   120     8.350   1750  12800      6.6     4500         .1    62     M1 Abrams tank
M777 Howitzer     155    48        827  16400      5.08    4200         .083
Iowa Battleship   406   862        820 290000     20.3   121500         .033  45000
2 bore rifle       33.7    .225    460     23.7     .711      4.5                    Historical big-game rifle
Cannonball 6 lb    87     2.72     438    261      2.4
Cannonball 9 lb    96     4.08     440    395      2.7
Cannonball 12 lb  110     5.44     453    558      2.4
Cannonball 18 lb  125     8.16     524   1120      2.6     2060
Cannonball 24 lb  138    10.89     524   1495      3.0     2500
Cannonball 32 lb  152    14.5      518   1945      3.4     2540
Cannonball 36 lb  158    16.33     450   1653      2.9     3250
Cannonball diameters are calculated from the mass assuming a density of 7.9 g/cm3.
For a pistol or rifle, the "vehicle mass" is the mass of the person wielding it. We use the mass of a typical person.
The "Metal Storm" gun has 36 barrels, 5 bullets per barrel, and fires all bullets in .01 seconds. The bullets are stacked in the barrel end-to-end and fired sequentially.

12 pound cannonballs
24 pound cannonballs


Bullet speed

25 mm
25 mm rocket propelled gernade
Excalibur 155 mm

The energy distribution for a 7.62 mm Hawk bullet is

Bullet energy    .32
Hot gas          .34
Barrel heat      .30
Barrel friction  .02
Unburnt powder   .01
To estimate the velocity of a bullet,
Energy efficiency  =  e  =  .32    (Efficiency for converting powder energy to bullet enery)
Bullet mass        =  M
Powder mass        =  m
Powder energy/mass =  Q  =  5.2 MJoules/kg
Bullet velocity    =  V
Bullet energy      =  E  =  ½ M V2  =  e Q m    (Kinetic energy = Efficiency * Powder energy)

V  =  (2 e Q m / M)2  =  1820 (m/M)½  meters/second

Muzzle break

M777 Howitzer
XD-40 V-10

The muzzle break at the end of the barrel deflects gas sideways to reduce recoil.


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)

Capacitors
Voltage          =  V             Volts
Capacitance      =  C             Farads
Total energy     =  E  =  ½ C V2  Joules
Effective        =  Ee =  ¼ C V2  Joules
Not all of the energy in a capacitor is harnessable because the voltage diminishes as the charge diminishes, hence the effective energy is less than the total energy.
Drone power system

One has to choose a wise balance for the masses of the motor, battery, fuselage, and payload. The properties of the electrical components are:

                    Energy/Mass  Power/mass  Energy/$  Power/$  $/Mass
                     MJoule/kg    kWatt/kg   MJoule/$  kWatt/$   $/kg

Electric motor          -         10.0        -        .062     160
Lithium-ion battery     .75        1.5        .009     .0142    106
Lithium supercapacitor  .008       8          .0010    .09       90
Aluminum capacitor      .0011    100
If the battery and motor have equal power then the battery has a larger mass than the motor.
Mass of motor            =  Mmot
Mass of battery          =  Mbat
Power                    =  P             (Same for both the motor and the battery)
Power/mass of motor      =  pmot  =  P/Mmot  =   8.0 kWatt/kg
Power/mass of battery    =  pbat  =  P/Mbat  =   1.5 kWatt/kg
Battery mass / Motor mass=  R    =Mbat/Mmot  =  pmot/pbat  =  5.3
The "sports prowess" of a drone is the drone power divided by the minimum hover power. To fly, this number must be larger than 1.
Drone mass               =  Mdro
Motor mass               =  Mmot
Motor power/mass         =  pmot =  8000 Watts/kg
Hover minimum power/mass =  phov =    60 Watts/kg
Drone power              =  Pdro =  pmot Mmot
Hover minimum power      =  Phov =  phov Mdro
Sports prowess           =  S   =  Pdro/Phov  =  (pmot/phov) * (Mmot/Mdro)  =  80 Mmot/Mdro
If S=1 then Mmot/Mdro = 1/80 and the motor constitutes a negligible fraction of the drone mass. One can afford to increase the motor mass to make a sports drone with S >> 1.

If the motor and battery generate equal power then the sports prowess is

S  =  (pbat/phov) * (Mbat/Mdro)  =  25 Mbat/Mdro
If Mbat/Mdro = ½ then S=12.5, well above the minimum required to hover.

Suppose a drone has a mass of 1 kg. A squash racquet can have a mass of as little as .12 kg. The fuselage mass can be much less than this because a drone doesn't need to be as tough as a squash racquet, hence the fuselage mass is negligible compared to the drone mass. An example configuration is:

              kg

Battery       .5
Motors        .1   To match the battery and motor power, set motor mass / battery mass = 1/5
Rotors       <.05
Fuselage      .1
Camera        .3
Drone total  1.0
Supercapacitors can generate a larger power/mass than batteries and are useful for extreme bursts of power, however their energy density is low compared to batteries and so the burst is short. If the supercapacitor and battery have equal power then
Battery power/mass         =  pbat  =  1.5 kWatts/kg
Supercapacitor power/mass  =  psup  =  8.0 kWatts/kg
Battery power              =  P
Battery mass               =  Mbat  =  P / pbat
Supercapacitor mass        =  Msup  =  P / psup
Supercapacitor/Battery mass=  R     =Msup/ Mbat  =  pbat/psup  =  .19
The supercapacitor is substantially ligher than the battery. By adding a lightweight supercapacitor you can double the power. Since drones already have abundant power, the added mass of the supercapacitor usually makes this not worth it.

If a battery and an aluminum capacitor have equal powers,

Aluminum capacitor mass  /  Battery mass  =  .015
If a battery or supercapacitor is operating at full power then the time required to expend all the energy is
Mass          =  M
Energy        =  E
Power         =  P
Energy/Mass   =  e  =  E/M
Power/Mass    =  p  =  P/M
Discharge time=  T  =  E/P  =  e/p

                     Energy/Mass  Power/Mass   Discharge time   Mass
                      MJoule/kg    kWatt/kg       seconds        kg

Lithium battery         .75          1.5          500           1.0
Supercapacitor          .008         8.0            1.0          .19
Aluminum capacitor      .0011      100               .011        .015
"Mass" is the mass required to provide equal power as a lithium battery of equal mass.
Flight


Lift

Air density            =  D
Velocity               =  V
Wing area              =  Awing
Wing drag coefficient  =  Cwing
Drag force on the wing =  Fdrag = ½ CWing Awing D V2


             Cwing

F-4 Phantom   .021     (subsonic)
Cessna 310    .027
Airbus A380   .027
Boeing 747    .031
F-4 Phantom   .044     (supersonic)

Lift-to-drag ratio
Flift  =  Lift force (upward)
Fdrag  =  Drag force (rearward)
Qlift  =  Lift-to-drag coefficient  =  Flift / Fdrag

              Qlift

U-2            23     High-altitude spy plane
Albatross      20     Largest bird
Gossamer       20     Gossamer albatross, human-powered aircraft  
Hang glider    15
Tern           12
Herring Gull   10
Airbus A380     7.5
Concorde        7.1
Boeing 747      7
Cessna 150      7
Parachute       5
Sparrow         4
Wingsuit        2.5
Flying lemur    ?     Most capable gliding mammal.  2 kg max
Flying squirrel 2.0

Gliding

A glider is an airplane without an engine. The more efficient the glider, the smaller the glide angle. The minimum glide angle is determined by the wing lift/drag coefficient.

Wing lift/drag coefficient =  Qlift  =  Flift / Fdrag
Glider horizontal velocity =  Vx
Glider vertical velocity   =  Vz
Drag force                 =  Fdrag
Gravitational force        =  Fgrav
Lift force                 =  Flift  =  Fgrav
Drag power                 =  Pdrag  =  Fdrag Vx
Power from gravit          =  Pgrav  =  Fgrav Vz
If the glider descends at constant velocity,
Pdrag  =  Pgrav
The goal of a glider is to maximize the glide ratio Vx / Vz.
Vx / Vz  =  (Pdrag / Fdrag)  /  (Pgrav / Fgrav)
         =  Fgrav / Fdrag
         =  Qlift
The glide ratio is equal to the lift coefficient Qlift.

Level flight

D    =  Air density
Awing =  Wing area
Cwing =  Wing drag coefficient
Fdrag =  Drag force on the wing   =  ½ Cwing D Awing V^2
Qwing =  Wing lift coefficient    =  Flift / Fdrag
Flift =  Lift force from the wing =  Qwing Fdrag
M    =  Aircraft mass
Feng  =  Engine force
Fgrav =  Gravity force            =  M g
Pdrag =  Drag power               =  Fdrag V  =  ½ Cwing D Awing V3
V    =  Cruising speed
Agility= Power-to-weight ratio    =  Pdrag / M  =  V g / Q      (derived below)
For flight at constant velocity,
Feng  =  Fdrag              Horizontal force balance

Flift =  Fgrav              Vertical force balance

Agility =  Pdrag   / M
        =  Fdrag V / M
        =  Flift V / M / Q
        =  M g  V / M / Q
        =  V g / Q
We can use this equation to solve for the minimum agility required to fly.
Pdrag  =  M g V / Q  =  ½ Cwing D Awing V3

Agility  =  g3/2 M½ Q-3/2 (½ C D A)
If we assume that mass scales as size cubed and wing area scales as size squared, then
Awing   ~  M2/3

Agility ~  g3/2 M1/6 Q-3/2 C D

Aircraft data

Cessna 150
Boeing 747
Airbus 380

SR-71 Blackbird
U-2 spy plane
Concorde
Concorde temperature at Mach 2

         Vcruise  Vmax  Mass  Takeoff  Ceiling  Density  Force  Wing   Len   Wing   Range
           m/s   m/s   ton    ton      km      kg/m3     kN     m2     m     m      km

Cessna 150    42   56     .60     .73  4.3   .79      1.34   15     7.3  10.1    778
Boeing 747   254  274  178.1   377.8  11.0   .36   1128     525    70.6  64.4  14200
Boeing 787-9 251  262  128.9   254.0  13.1   .26    640     360.5  62.8  60.1  14140
Airbus A380  243  262  276.8   575    13.1   .26   1360     845    72.2  79.8  15200
Concorde     599  605   78.7   190.5  18.3   .115   560     358.2  61.7  25.6   7223
F-22 Raptor  544  740   19.7    38.0  19.8   .091   312      78.0  18.9  13.6   2960
U-2          192  224    6.49   18.1  21.3   .071    84.5    92.9  19.2  31.4  10308
SR-71        954  983   30.6    78.0  25.9   .034   302     170    32.7  16.9   5400
Mach 1 = 298 m/s.

Altitude

Commercial airplanes fly at high altitude where the air is thin. The thinner the air, the less the drag force and the less the energy required to travel a given distance.

                Altitude   Density
                  (km)     (kg/m3)

Sea level          0       1.22
Cessna 150         3.0      .79
Boeing 747        11.0      .36
Airbus A380       13.1      .26
Concorde          18.3      .115
F-22 Raptor       19.8      .091
U-2               21.3      .071
SR-71 Blackbird   25.9      .034

Solar powered aircraft
                Cruise  Max  Ceiling  Mass  Cruise  Motor  Solar  Cells  Battery
                 m/s    m/s    kW     tons    kw     kW    cells   m2     tons
                                                            kW

Aquila           35.8          27.4     .40   5.0                          .2
Solar Impulse 2  25.0   38.9   12      2.3           52     66    269.5    .633

The Loon balloon is 15 meters wide, 12 meters, tall, and .076 mm thick. The solar panels generate 100 Watts and the payload is 10 kg. It is too large to be self-propelled and relies and buoyancy modulation and air currents to maneuver.


History
1961  Piggott accomplishes the first human-powered flight, covering a distance
      of 650 meters.
1977  The "Gossomer Condor 2" flies 2172 meters in a figure-eight and wins
      the Kremer Prize.  It was built by Paul MacCready and piloted by amateur
      cyclist and hang-glider pilot Bryan Allen. 
      It cruised at 5.0 m/s with a power of 260 Watts.
1988  The MIT Daedalus 88 piloted by Kanellos Kanellopoulos flies from Crete
      to Santorini (115.11 km), setting the distance record, which still stands.
Human-powered helicopters can only reach a height of 3 meters and can only hover for 20 seconds.

Agility
               Mass    Power   Agility
               (kg)    (kW)   (Watts/kg)

Human             75    2500     33
BMW i8          1485     170    114
Cessna 150       600      75    125
Airbus A380   276000   49000    178
Formula-1 car    642     619    964
SR-71          30600   33000   1078
F-22 Raptor    19700   33000   1675
If you put a wing on a BMW i8, it would be able to go fast enough to take off.
Wing shape
Xwing =  Length of the wing, from the fuselage to the tip
Ywing =  Wing dimension in the direction of flight,
        measured along the point of attachment with the fuselage
Awing =  Wing area
Rwing =  Wing aspect ratio   =  Xwing / Ywing
Qlift =  Wing lift-drag ratio


         QLift  Rwing     Wing     Xwing
                           area
                           (m2)        (m)
U-2         23     10.6                        High-altitude spy plane
Albatros    20                       1.7       Largest bird
Gossamer    20             41.34    14.6       Gossamer albatross, human-powered aircraft  
Airbus A380  7.5    7.5   845       36.3
Concorde     7.1          358.2     11.4
Boeing 747   7      7.9   525       29.3
Cessna 150   7             15        4.5
Wingsuit     2.5    1       2        1.0
QLift tends to be proportional to Rwing.

Wingtip vortex

A wingtip creates a vortex as it moves. Birds fly in a "V" formation to use the updraft from their neighbor's wingtip vortex.


Flight on other worlds

The minimum agility required to fly scales as

Agility  ~  g3/2 M1/6 Q-3/2 Cwing D
We can normalize the Earth to 1 and estimate the minimum agility for other planets. For example,
MarsAgility / EarthAgility  =  (MarsGravity / EarthGravity)3/2 * (MarsDensity / EarthDensity)


        Gravity  Atmosphere   Agility     Power/     Maximum
                  density     normalized   mass      mass for
        (m/s^2)   (kg/m^3)    to Earth   (Watts/kg)  flight (kg)

Earth     9.78      1.22       1.0        400              20
Mars      3.8        .020      1.89       756                .44
Titan     1.35      5.3         .025       10        >1000000
Venus     8.87     67           .12        48        >1000000
Pandora   7.8       1.46        .65       261             265
For the "Power/mass" column we assume that the power required for human flight is 400 Watts and estimate the power required for flight on other planets.

On Titan you can fly with a wingsuit. A creature as massive as a whale can fly.

"Pandora" is the fictional moon from the film "Avatar".

The largest flying birds on the Earth have a mass of 20 kg. We can use the agility scaling to estimate the maximum mass for flight on other planets.

Agility ~  g3/2 M1/6 Q-3/2 Cwing D

M       ~  g-9  D3

Downforce

The wing on a Formula-1 car is an upside-down aircraft wing that generates downforce, to help with friction.

M   =  Mass
V   =  Velocity
A   =  Acceleration (in any direction)
Cfri=  Friction coefficient
C  =  Wing coefficient for downforce
Fgrav=  Gravitational force on the car
                =  M g
F  =  Downforce from the wing
    =  M g C V2
Ffri=  Maximum friction force
    =  Cfri (Fgrav + F)
    =  Cfri M g (1 + C V2)
A formula-1 car generates 1 g of downforce at 50 m/s, hence C = 1/502. At the top speed of 100 m/s the downforce is 4 g. The maximum accelerations incurred by the driver are of order 5 g.

The maximum cornering speed for a circle of radius R is:

Ffri  =  M V2/R  =  M g Cfri (1 + V2/Cfri2)

V2 = g R Cfri / (1 - R/Cfri2)

Angle of attack

The angle of attack is the angle of the plane's noze with respect to level fight. As the angle of attack increases the lift increases, with an accompanying increase in drag. If the angle of attack is too high then lift drops and the plane stalls.


World War 2 bombers

Avro Lancaster
B-29 Superfortress
Heinkel He 177

Handley Page Halifax
B-17 Flying Fortress
B-17 Flying Fortress

focke-Wulf Condor
Mitsubishi Ki-67
Mitsubishi G4M

Yokosuka Ginga
Tupolev Tu-2

                            Max    Mass   Max   Bombs  Max   Engine   Range    #    Year
                           speed          mass         alt                   Built
                            kph    ton    ton    ton   km    kWatt     km

UK       Avro Lancaster        454  16.6   32.7  10.0   6.5   4x 954   4073   7377  1942
USA      B-29 Superfortress    574  33.8   60.6   9.0   9.7   4x1640   5230   3970  1944
Germany  Heinkel He 177        565  16.8   32.0   7.2   8.0   2x2133   1540   1169  1942
UK       Short Stirling        454  21.3   31.8   6.4   5.0   4x1025   3750   2371  1939
UK       Handley Page Halifax  454  17.7   24.7   5.9   7.3   4x1205   3000   6176  1940
Germany  Fokke-Wulf Condor     360  17.0   24.5   5.4   6.0   4x 895   3560    276  1937
Soviet   Tupolev Tu-2          528   7.6   11.8   3.8   9.0   2x1380   2020   2257  1942
USA      B-17 Flying Fortress  462  16.4   29.7   3.6  10.5   4x 895   3219  12731  1938
Japan    Mitsubishi Ki-67      537   8.6   13.8   1.6   9.5   2x1417   3800    767  1942
Soviet   Petlyakov Pe-2        580   5.9    8.9   1.6   8.8   2x 903   1160  11427  1941
Japan    Yokosuka P1Y Ginga    547   7.3   13.5   1.0   9.4   2x1361   5370   1102  1944
Japan    Mitsubishi G4M        428   6.7   12.9   1.0   8.5   2x1141   2852   2435  1941

Curtis LeMay: Flying fighters is fun. Flying bombers is important.

World War 2 heavy fighters

A-20 Havoc
F7F Tigercat
P-38 Lightning

P-61
P-38
Airspeed chart

Fairey Firefly
Beaufighter
Mosquito
Fairey Fulmar
Defiant

Messerschmitt 410
Heinkel He-219
Junkers Ju-88

Do-217
Me-110

Kawasaki Ki-45
J1N

Gloster Meteor
Me-262 Swallow
Heinkel He-162

                       Max   Climb  Mass   Max   Bombs  Max   Engine   Range   #   Year
                      speed                mass         alt                  Built
                       kph    m/s   ton    ton    ton   km    kWatt     km

USA    P51 Black Widow  589  12.9  10.6   16.2   2.9   10.6  2x1680   982    706  1944
USA    A-20 Havoc       546  10.2   6.8   12.3    .9    7.2  2x1200  1690   7478  1941
USA    F7F Tigercat     740  23     7.4   11.7    .9   12.3  2x1566  1900    364  1944
USA    P-38 Lightning   667  24.1   5.8    9.8   2.3   13.0  2x1193        10037  1941
UK     Fairey Firefly   509   8.8   4.4    6.4    .9    8.5  1x1290  2090   1702  1943
UK     Mosquito         668  14.5   6.5   11.0   1.8   11.0  2x1103  2400   7781  1941
UK     Beaufighter      515   8.2   7.1   11.5    .3    5.8  2x1200  2816   5928  1940
UK     Fairie Fulmar    438         3.2    4.6    .1    8.3  1x 970  1255    600  1940
UK     Defiant          489   9.0   2.8    3.9   0      9.2  1x 768   749   1064  1939
Japan  Dragon Slayer    540  11.7   4.0    5.5   0     10.0  2x 783         1701  1941  Ki-45
Japan  Flying Dragon    537   6.9   8.6   13.8   1.6    9.5  2x1417  3800    767  1942  Ki-67
Japan  J1N Moonlight    507   8.7   4.5    8.2   0           2x 840  2545    479  1942
Ger.   Hornet           624   9.3   6.2   10.8   1.0   10.0  2x1287  2300   1189  1943
Ger.   Flying Pencil    557   3.5   9.1   16.7   4.0    7.4  2x1287  2145   1925  1941  Do-217
Ger.   Heinkel He-219   616               13.6   0      9.3  2x1324  1540    300  1943
Ger.   Junkers Ju-88    360        11.1   12.7   0      5.5  2x1044  1580  15183  1939
Ger.   Me-110           595  12.5          7.8   0     11.0  2x1085   900   6170  1937
SU     Petlyakov Pe-3   530  12.5   5.9    8.0    .7    9.1  2x 820  1500    360  1941
UK     Gloster Meteor   965  35.6   4.8    7.1    .9   13.1   Jet     965   3947  1944
Ger.   Me-262 Swallow   900 ~25     3.8    7.1   1.0   11.5   Jet    1050   1430  1944
Ger.   Heinkel He-162   840  23.4   1.7    2.8   0     12.0   Jet     975    320  1945

Me-262 Swallow jet  =  2x 8.8 kNewtons
Heinkel He-162 jet  =  1x 7.8 kNewtons
Gloster Meteor jet  =  2x16.0 kNewtons

World War 2 light fighters

P-39 Airacobra
P-40 Warhawk
P-43 Lancer

P-47 Thunderbolt
P-51 Mustang
P-63 Kingcobra

F2A Buffalo
F4F
F4U

F6F Hellcat
F8F Bearcat

Ki-27
Ki-43
Ki-44

Ki-61
Ki-84
Ki-100

A5M
Mitsubishi A6M Zero
A6M2

J2M
N1K

Hawker Tempest
Hawker Hurricane
Hawker Typhoon

Submarine Seafire
Submarine Spitfire

Fw-190
Bf-109

YaK-1
Yak-7
Yak-9
Polykarpov I-16

MiG-3
LaGG-3
La-5
La-7

                       Max   Climb  Mass   Max   Bombs  Max   Engine   Range   #    Year
                      speed                mass         alt                  Built
                       kph    m/s   ton    ton    ton   km    kWatt     km

USA    P-39 Airacobra   626  19.3   3.0    3.8    .2   10.7  1x 894   840   9588  1941
USA    P-63 Kingcobra   660  12.7   3.1    4.9    .7   13.1  1x1340   725   3303  1943
USA    F2A Buffalo      517  12.4   2.1    3.2   0     10.1  1x 890  1553    509  1939
USA    P-40 Warhawk     580  11.0   2.8    4.0    .9    8.8  1x 858  1100  13738  1939
USA    P-51 Mustang     703  16.3   3.5    5.5    .5   12.8  1x1111  2755 >15000  1942
USA    F4F Wildcat      515  11.2   2.7    4.0   0     10.4  1x 900  1337   7885  1940
USA    F6F Hellcat      629  17.8   4.2    7.0   1.8   11.4  1x1491  1520  12275  1943
USA    F8F Bearcat      730  23.2   3.2    6.1    .5   12.4  1x1678  1778   1265  1945
USA    P-43 Lancer      573  13.0   2.7    3.8   0     11.0  1x 895  1046    272  1941
USA    P-47 Thunderbolt 713  16.2   4.5    7.9   1.1   13.1  1x1938  1290  15677  1942
USA    F4U Corsair      717  22.1   4.2    5.6   1.8   12.6  1x1775  1617  12571  1942
Japan  Zero             534  15.7   1.7    2.8    .3   10.0  1x 700  3104  10939  1940
Japan  N1K Strong Wind  658  20.3   2.7    4.9    .5   10.8  1x1380  1716   1532  1943
Japan  Ki-84 "Gale"     686  18.3   2.7    4.2    .7   11.8  1x1522  2168   3514  1943
Japan  Ki-61            580  15.2   2.6    3.5    .5   11.6  1x 864   580   3078  1942
Japan  Ki-100           580  13.9   2.5    3.5   0     11.0  1x1120  2200    396  1945
Japan  A5M              440         1.2    1.8   0      9.8  1x 585  1200   1094  1936
Japan  A6M2             436  12.4   1.9    2.9    .1   10.0  1x 709  1782    327  1942
Japan  J2M Thunderbolt  655  23.4   2.8    3.2    .1   11.4  1x1379   560    671  1942
Japan  Ki-27            470  15.3   1.1    1.8    .1   12.2  1x 485   627   3368  1937
Japan  Ki-43            530         1.9    2.9    .5   11.2  1x 858  1760   5919  1941
Japan  Ki-44            605  19.5   2.1    3.0   0     11.2  1x1133         1225  1942
UK     Hawker Hurricane 547  14.1   2.6    4.0    .5   11.0  1x 883   965  14583  1943
UK     Hawker Tempest   700  23.9   4.2    6.2    .9   11.1  1x1625  1190   1702  1944
UK     Hawker Typhoon   663  13.6   4.0    6.0    .9   10.7  1x1685   821   3317  1941
UK   Submarine Seafire  578  13.4   2.8    3.5          9.8  1x1182   825   2334  1942
UK   Submarine Spitfire 595  13.2   2.3    3.0   0     11.1  1x1096   756  20351  1938
Ger.   Fw-190           685  17.0   3.5    4.8    .5   12.0  1x1287   835 >20000  1941
Ger.   Bf-109           640  17.0   2.2    3.4    .3   12.0  1x1085   850  34826  1937
SU     MiG-3            640  13.0   2.7    3.4    .2   12.0  1x 993   820   3172  1941
SU     Yak-1            592  15.4   2.4    2.9   0     10.0  1x 880   700   8700  1940
SU     Yak-3            655  18.5   2.1    2.7   0     10.7  1x 970   650   4848  1944
SU     Yak-7            571  12.0   2.4    2.9   0      9.5  1x 780   643   6399  1942
SU     Yak-9            672  16.7   2.5    3.2   0     10.6  1x1120   675  16769  1942
SU     LaGG-3           575  14.9   2.2    3.2    .2    9.7  1x 924  1000   6528  1941
SU     La-5             648  16.7   2.6    3.4    .2   11.0  1x1385   765   9920  1942
SU     La-7             661  15.7   3.3           .2   10.4  1x1230   665   5753  1944
SU     Polykarpov I-16  525  14.7   1.5    2.1    .5   14.7  1x 820   700   8644  1934

World War 2 aircraft carriers

U.S. Essex Class
U.S. Independence Class

Shokaku Class
Hiyo Class
Chitose Class

Unryu Class
Zuiho Class

       Class        Speed   Power  Length  Displace  Planes     #     Year
                     kph    MWatt    m       kton             built

USA    Essex         60.6   110     263      47       100      24     1942
USA    Independence  58      75     190      11        33       9     1942
Japan  Shokaku       63.9   120     257.5    32.1      72       2     1941
Japan  Hiyo          47.2    42     219.3    24.2      53       3     1944
Japan  Unryu         63     113     227.4    17.8      65       3     1944
Japan  Chitose       53.5    42.4   192.5    15.5      30       2     1944
Japan  Zuiho         52      39     205.5    11.4      30       2     1940

Explosives

Medieval-style black powder
Modern smokeless powder

                   MJoules  Speed   Density  C  H  N  O
                     /kg    (km/s)  (g/cm3)

Bombardier beetle      .4                                 Hydroquinone + H2O2 + protein catalyst
Ammonium nitrate      2.0    2.55    1.12    0  4  2  3
Black powder          2.6     .6     1.65                 Used before 1884
Smokeless powder      5.2    6.4     1.4     6  9  1  7   Used after 1884. Nitrocellulose
TNT                   4.7    6.9     1.65    7  5  3  6   Trinitrotoluene
PETN                  5.8    8.35    1.77    5  8  4 12
Dynamite              5.9    7.2     1.48    3  5  3  9   75% Nitroglycerine + stabilizer
Composition 4         6.3    8.04    1.59    3  6  6  6   91% RDX. "Plastic explosive"
PLX                   6.5            1.14    1  3  1  2   95% CH3NO2 + 5% C2H4(NH2)2
Nitroglycerine        7.2    8.1     1.59    3  5  3  9   Unstable
RDX (Hexagen)         7.5    8.7     1.78    3  6  6  6
HMX (Octogen)         8.0    9.1     1.86    4  8  8  8
Dinitrodiazeno.       9.2   10.0     1.98    4  0  8  8
Octanitrocubane      11.2   10.6     1.95    8  0  8 16
Gasoline + Oxygen    10.4                    8 18  0 13
Hydrogen + Oxygen    13.16                   0  2  0  1
Uranium bomb     219000
Hydrogen bomb        10 mil
Antimatter        90000 mil

Speed: Detonation speed
C:     Carbon atoms
H:     Hydrogen atoms
N:     Nitrogen atoms
O:     Oxygen atoms
Nitrocellulose
TNT
RDX
HMX
PETN
Octanitrocubane

Nitrocellulose
TNT
RDX
HMX
PETN
Octanitrocubane

Dinitrodiazenofuroxan
Nitromethane

~808  Qing Xuzi publishes a formula resembling gunpower, consisting of
      6 parts sulfur, 6 parts saltpeter, and 1 part birthwort herb (for carbon).
~850  Incendiary property of gunpower discovered
1132  "Fire lances" used in the siege of De'an, China
1220  al-Rammah of Syria publishes "Military Horsemanship and Ingenious War
        Devices", describes the purification of potassium nitrate by
        adding potassium carbonate with boiling water, to precipitate out
        magnesium carbonate and calcium carbonate.
1241  Mongols use firearms at the Battle of Mohi, Hungary
1338  Battle of Arnemuiden.  First naval battle involving cannons.
1346  Cannons used in the Siege of Calais and the Battle of Crecy
1540  Biringuccio publishes "De la pirotechnia", giving recipes for gunpowder
1610  First flintlock rifle
1661  Boyle publishes "The Sceptical Chymist", a treatise on the
      distinction between chemistry and alchemy.  It contains some of the
      earliest modern ideas of atoms, molecules, and chemical reaction,
      and marks the beginning of the history of modern chemistry.
1669  Phosphorus discovered
1774  Lavoisier appointed to develop the French gunpowder program.  By 1788
         French gunpowder was the best in the world.
1832  Braconnot synthesizes the first nitrocellulose (guncotton)
1846  Nitrocellulose published
1847  Sobrero discovers nitroglycerine
1862  LeConte publishes simple recipes for producing potassium nitrate.
1865  Abel develops a safe synthesis of nitrocellulose
1867  Nobel develops dynamite, the first explosive more powerful than black powder
      It uses diatomaceous earth to stabilize nitroglycerine
1884  Vieille invents smokeless gunpowder (nitrocellulose), which is 3 times
         more powerful than black powder and less of a nuisance on the battlefield.
1902  TNT first used in the military.  TNT is much safer than dynamite
1930  RDX appears in military applications
1942  Napalm developed
1949  Discovery that HMX can be synthesized from RDX
1956  C-4 explosive developed (based on RDX)
1999  Eaton and Zhang synthesize octanitrocubane and heptanitrocubane

Above 550 Celsius, potassium nitrate decomposes. 2 KNO3 ↔ 2 KNO2 + O2.

Black powder           =  .75 KNO3  +  .19 Carbon  +  .06 Sulfur
1 kg TNT equivalent    =   4.184   MJ
Fission bomb           =   9.20e13 J     =  22000 tons of TNT equivalent
Fission bomb           =   420     kg
Fission bomb           =   2.19e11 J/kg
Fusion bomb maximum    =   2.51e13 J/kg   (Maximum theoretical efficiency)
Fusion bomb practical  =   1.0 e13 J/kg   (Practical efficiency achieved in real bombs)

Black powder

Sulfur
Sulfur
Saltpeter
Saltpeter

Charcoal
Icing sugar and KNO3
Mortar and pestle
Mortar and pestle

Potassium nitrate  KNO3     75%       (Saltpeter)
Charcoal           C7H4O    15%
Sulfur             S        10%

Oversimplified equation:  2 KNO3 + 3 C + S  →  K2S + N2 + 3 CO2

Realistic equation:       6 KNO3 + C7H4O + 2 S  →  KCO3 + K2SO4 + K2S + 4 CO2 + 2 CO + 2 H2O + 3 N2
Nitrite (NO3) is the oxidizer and sulfur lowers the ignition temperature.
Fuel air explosives
                   MJoules
                     /kg

Black powder           2.6
Smokeless powder       5.2
HMX (Octogen)          8.0
Gasoline + Oxygen     10.4
Hydrogen + Oxygen     13.16
Uranium bomb      219000
Hydrogen bomb         10 mil
Antimatter         90000 mil

        Mass   Energy    Energy/Mass
         kg      MJ         MJ/kg

MOAB    9800   46000        4.7               8500 kg of fuel

Phosphorus
White phosphorus
White, red, violet, and black phosphorus
Red phosphorus

Violet phosphorus
Black phosphorus
Black phosphorus

Form      Ignition    Density
          (Celsius)

White        30        1.83
Red         240        1.88
Violet      300        2.36
Black                  2.69
Red phosphorus is formed by heating white phosphorus to 250 Celsius or by exposing it to sunlight. Violet phosphorus is formed by heating red phosphorus to 550 Celsius. Black phosphorus is formed by heating white phosphorus at a pressure of 12000 atmospheres. Black phosphorus is least reactive form and it is stable below 550 Celsius.
Matches

Striking surface
P4S3

The safety match was invented in 1844 by Pasch. The match head cannot ignite by itself. Ignitition is achieved by striking it on a rough surface that contains red phosphorus. When the match is struck, potassium chlorate in the match head mixes with red phosphorus in the abrasive to produce a mixture that is easily ignited by friction. Antimony trisulfide is added to increase the burn rate.

Match head                 Fraction             Striking surface   Fraction

Potassium chlorate    KClO3  .50                Red phosphorus      .5
Silicon filler        Si     .4                 Abrasive            .25
Sulfur                S      small              Binder              .16
Antimony3 trisulfide  Sb2S3  small              Neutralizer         .05
Neutralizer                  small              Carbon              .04
Glue                         small
A "strike anywhere" match has phosphorus in the match head in the form of phosphorus sesquisulfide (P4S3) and doesn't need red phosphorus in the striking surface. P4S3 has an ignition temperature of 100 Celsius.
Flint

Before the invention of iron, fires were started by striking flint (quartz) with pyrite to generate sparks. Flintlock rifles work by striking flint with iron. With the discovery of cerium, ferrocerium replaced iron and modern butane lighters use ferrocerium, which is still referred to as "flint".

Cerium        .38      Ignition temperature of 165 Celsius
Lanthanum     .22
Iron          .19
Neodymium2    .04
Praseodymium  .04
Magnesium     .04

Nitrous oxide engine

Nitrous oxide is stored as a cryogenic liquid and injected along with gaoline into the combustion chamber. Upon heating to 300 Celsius the nitrous oxide decomposes into nitrogen and oxygen gas and releases energy. The oxygen fraction in this gas is higher than that in air (1/3 vs. .21) and the higher faction allows for more fuel to be consumed per cylinder firing.

Air density                  =  .00122 g/cm3
Nitrous oxide gas density    =  .00198 g/cm3
Diesel density               =  .832   g/cm3
Gasoline density             =  .745   g/cm3
Diesel energy/mass           =  43.1   MJoules/kg
Gasoline energy/mass         =  43.2   MJoules/kg
Nitrous oxide boiling point  = -88.5   Celsius
Air oxygen fraction          =  .21
Nitrous oxide oxygen fraction=  .33
Nitrous oxide decompose temp =  300    Celsius
Nitrous oxide liquid pressure=   52.4  Bars     Pressure required to liquefy N2O at room temperature

Bombardier beetle

Hydroquinone
P-quinone

Hydroquinone and peroxide are stored in 2 separate compartments are pumped into the reaction chamber where they explode with the help of protein catalysts. The explosion vaporizes 1/5 of the liquid and expels the rest as a boiling drop of water, and the p-quinone in the liquid damages the foe's eyes. The energy of expulsion pumps new material into the reaction chamber and the process repeats at a rate of 500 pulses per second and a total of 70 pulses. The beetle has enough ammunition for 20 barrages.

2 H2O2  →  2 H2O +  O2           (with protein catalyst)
C6H4(OH)2  →  C6H4O2 + H2        (with protein catalyst)
O2 + 2 H2  →  2 H2O

Firing rate                     = 500 pulses/second
Number of pulses in one barrage =  70
Firing time                     = .14 seconds
Number of barrages              =  20

Flame speed

A turbojet engine compresses air before burning it to increase the flame speed and make it burn explosively. A ramjet engine moving supersonically doesn't need a turbine to achieve compression.

Turbojet
Ramjet

Airbus A350 compression ratio  =  52
Air density at sea level       = 1    bar
Air density at 15 km altitude  =  .25 bar
Air density in A350 engine     =  13  bar
From the thermal flame theory of Mallard and Le Chatelier,
Temperature of burnt material    =  Tb
Temperature of unburnt material  =  Tu
Temperature of ignition          =  Ti
Fuel density                     =  Dfuel
Oxygen density                   =  Doxygen
Reaction coefficient             =  C
Reaction rate                    =  R  =  C Dfuel Doxygen
Thermal diffusivity              =  Q  = 1.9⋅10-5 m2/s
Flame speed                      =  V

V2  =  Q C Dfuel Doxygen (Tb - Ti) / (Ti - Tu)

Shocks

Spherical implosion
Mach < 1,    Mach = 1,     Mach > 1

If the pressure front moves supersonically then the front forms a discontinuous shock, where the pressure makes a sudden jump as the shock passes.


Energy boost

Metal powder is often included with explosives.

        Energy/mass    Energy/mass
        not including  including
        oxygen         oxygen
        (MJoule/kg)    (MJoule/kg)

Hydrogen    113.4      12.7
Gasoline     46.0      10.2
Beryllium    64.3      23.2
Aluminum     29.3      15.5                                      
Magnesium    24.5      14.8                                      
Carbon       12.0       3.3
Lithium       6.9       3.2
Iron          6.6       4.6                                      
Copper        2.0       1.6

Fireworks

Li
B
Na
Mg
K
Ca
Fe

Cu
Zn
As
Sr
Sb
Rb
Pb

BaCl (green), CuCl (blue), SrCl (red)
Zero gravity
Bunsen burner, O2 increases rightward
Methane


Oxygen candle

Sodium chlorate

An oxygen candle is a mixture of sodium chlorate and iron powder, which when ignited smolders at 600 Celsius and produces oxygen at a rate of 6.5 man-hours of oxygen per kilogram of mixture. Thermal decomposition releases the oxygen and the burning iron provides the heat. The products of the reaction are NaCl and iron oxide.


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