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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)

Orville and Wilbur Wright

Orville Wright
Wilbur Wright

The Wright brothers designed, manufactured, and sold their own line of bicycles and used the profits to fund their aircraft research.

They began by designing wings and gliders.

They were the first to use wind tunnels to test wings. Their wing design eclipsed the European designs.

They innovated the design of steering and stability systems

They advanced the design of propellers.

First flight
82nd flight: 2.75 miles and 304 seconds

Orville was injured in a crash and a passenger was killed
The original aircraft


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.


Engines


Turboprop

In a turboprop, incoming air is compressed by a fan and then mixed with fuel. The exploding air powers a crankshaft that turns the propeller. This is the most efficient engine up to Mach .5.


Turbofan
In a turbofan the exploding fuel+air mixture powers a fan. Some of the incoming air is reacted with fuel and most of it is bypassed, channelled instead to the fan and propelled aftward.

Turbofans are the most efficient kind of engine from Mach .5 to 1.0. All commercial aircraft that fly close to Mach 1 are turbofans.


Turbojet

A turbojet uses most of its intake air for combustion and most of the thrust comes from jet action rather than from a fan. Such engines can go beyond Mach 1.


Afterburner

F/A-18 Hornet
SR-71 Blackbird
SR-71 Blackbird engine test

A turbofan in afterburner mode injects fuel aft of the fan. The fuel explodes and adds thrust. This enables an aircraft to go beyond Mach 1.


Ramjet

If the aircraft is moving faster than Mach 1 then the incoming air doesn't need to be compressed with a fan. The ram pressure from slowing down the air in the combustion chamber is enough.

Ramjets work up to Mach 6, at which point the incoming compressed air becomes too hot.

Ramjets are simpler than turbofans because they don't have any moving parts. They are often used for missiles.


Scramjet

NASA X-23
Turbofan, ramjet, scramjet

In a scramjet the incoming air is compressed enough to make it explodable but not enough to slow it down below Mach 1. Such an engine sidesteps the heating concern of a ramjet and can go up to Mach 15.


SR-71 Blackbird engine


de Laval nozzle

In a de Laval nozzle, incomming subsonic air accelerates as it approaches the nozzle. The nozzle is shaped so that the air becomes supersonic at the narrowest point, after which it continues accelerating as it expands aftward.


Specific impulse

Exhaust velocity  =  V
Gravity constant  =  g
Specific impulse  =  I  =  V/g

Air compression

A jet engine compresses air before mixing it with fuel. For adiabatic compression,

Adiabatic index =  A  =  1.4      (for air)
Density         =  D
Pressure        =  P  ≈  DA  ≈  D T
Temperature     =  T  ≈  DA-1
The larger the air density the more efficient the engine. Increased density comes with increased temperature and the performance of an engine is determined by the quality of the high-temperature alloys.

The following table shows the properties of an adiabatically compressed gas in relative units and in Kelvin. In practice the gas compression is not adiabatic and the pressure and temperature values are larger.

Density  Pressure   Temperature   Temperature
                                   (Kelvin)
   1      1             1            250         Ambient air at 10 km altitude
   2      2.64          1.32         330
   3      4.66          1.55         388
   4      6.96          1.74         435
   6     12.3           2.05         512
   8     18.4           2.30         574
  12     32.4           2.70         675
  16     48.5           3.03         758
  24     85.6           3.57         891
  32    128.0           4.0         1000
Aircraft engines:
                                   Pressure ratio

Airbus A350   Rolls-Royce Trent XWB     52
Boeing 747    General Electric CF6      42
Boeing 777    General Electric GE90     42
Airbus A380   Rolls-Royce Trent 900     39
F-15          General Electric F110     30
Concorde      Rolls-Royce 593           15.5

Bird flight

Flapping the wings propels the bird upward and then the bird glides downward until the next flap. Forward propulsion comes more from gravitational descent than from flapping.


Flight lab


Wings

Construct a wing and a wind tunnel and measure the following:

Wing drag force       =  Fdrag  =  Rearward force on the wing
Wing lift force       =  Flift  =  Upward lift force on the wing
Wing lift coefficient =  Qlift  =  Flift / Fdrag
The larger the value of Qlift the better. You can measure the lift coefficient by measuring wing forces as above or you can measure the glide ratio, discussed below.

You will have to adjust the wing's "angle of attack" to get the optimal lift coefficient.


Gliders

Build a glider using any materials available and try to minimze the glide angle, which is defined as the change in height divided by the change in lateral distance. Try different kinds of designs and see if you can optimize the design.

To measure the glide ratio, launch the glider with zero initial velocity from a height close to the ceiling and measure how far it travels before hitting the floor.

Z  =  Glide ratio  =  Distance traveled / Initial height
The larger the glide ratio the better.

The glide ratio is equal to the lift coefficient.

Z  =  Qlift

Propellers

First electric helicopter, 2011

Construct a propeller powered by a rubber band and construct a helicopter to support the propeller. Place the helicopter on the ground and engage the propeller and measure the maximum height that the helicopter reaches.

Maximum height of the helicopter  =  H
The larger the value of H the better.
Propeller aircraft

The propeller provides forward force and the wing provides upward force.

Combine a glider with a rubber-band-powered propeller to form a propeller aircraft. Release it from at rest on the ground and measure the distance it flies.

Distance the plane flies  =  X
The larger the value of X the better.

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.
Helicopter drones

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)


                Drone  Battery  Drone  Battery  Battery  Drone  Drone  Flight  Price  Wireless
                mass   energy           mass             power          time           range
                 kg    MJoule   MJ/kg    kg      MJ/kg   Watt    W/kg  minutes   $      km

Mota Jetjat Nano .011    .00160  .145                     3.3    303      8      40    .02
ByRobot Fighter  .030    .0040   .133                     6.7    222     10     120    .1
Blade mQX        .0751   .0067   .089                    11.2    149     10     115
XDrone Zepto     .082    .0067   .081                     4.6     56     24      40    .05
Walkera QR Y100  .146    .0213   .146   .0413    .52     17.8    122     20     100    .1
MJX Bugs 3       .485    .0480   .099                    44.4     92     18     100    .5
DJI Mavic Pro    .725    .157    .217   .24      .65    109      150     24    1000   7.0
XK Detect X380C 1.18     .216    .183                   120      102     30     522   1.0
Xiaomi Mi       1.376    .319    .214                   197      143     27     380   1.0
DJI Phantom 4   1.38     .293    .212   .426     .69    174      126     28    1000   5.0
XK X500         1.8      .288    .160                   160       89     30     303   1.0
JYU Spider X    2.1      .360    .171   .812     .44    200       95     30     155   4.0
MD4-1000        2.65    1.039    .392                   197       74     88    2000    .5
DJI Inspire     2.935    .360    .123   .67      .54    333      114     18    2000   7.0
Altura Zenith   3.5     1.327    .379                   491      140     45    2000   1.0
Walkera QR X800 3.9      .799    .205  1.134     .70    222       57     60    2700   2.0
AEE F100        6.0     1.598    .266                   380       63     70   58000  10.0
Chaos HL48      6.8     1.758    .259                   651       96     45   20000  20.0
MD4-3000       10.4     2.80     .269                  1037      100     45           4.0
Ehang 184     200      51.8      .259                 37500      188     23  300000   3.5
Airbus EFan                                              60
The minimum power requirement for quadcopter flight is of order 60 Watts/kg.
1 MJ = 1 MJoule = 106 Joules

Electric power outperformes gasoline power in all categories except energy density. Electric motors are lighter, simpler, cheaper, more flexible, and more reliable than combustion motors.


Fixed-wing drones
            Drone  Battery  Drone  Drone  Drone  Flight  Cost  Wireless  Wing  Wing  Cruise   Max   Flight
            mass   energy    E/M   power          time          range    area  span  speed   speed  range
             kg    MJoule   MJ/kg  Watts  W/kg   minutes  $       km      m2    m     m/s     m/s    km

Sky Hawk       .355  .0346  .097    19.2  54.1     30     400    1.0           1.0
Chaipirinha    .62   .088   .142                          154                   .85
AgDrone       2.25   .639   .284   161    71.7     66            4.5            .124  46.7     82    50
Trimble UX5   2.5    .320   .128   107    42.7     50   10000    2.5     .34    .10   80             60
Airbus E-Fan 450  104.4     .232 29000    64.4     60                          9.5    44.4     61.1 160
Sun Flyer   1225

Power

For a typical drone,

Drone mass             =  M
Battery mass           =  Mbat
Payload mass           =  Mpay
Climbing speed         =  Vcli
Max horizontal speed   =  Vmax
Hover constant         =  H            =  60 Watts/kg       Power/mass required to hover
Hover power            =  Phov=  H M
Hover power for payload=  Ppay=  H Mpay
Gravity constant       =  g            =  9.8 m/s
Power to climb         =  Pcli=  M g V
Drag coefficient       =  C
Air density            =  D            = 1.22 kg/meter3
Drone cross-section    =  A
Drag power             =  Pdrag= ½ C D A V3
If the climbing power is equal to the hover power,
V = H / g  =  6 meters/second
If the climbing power is equal to the drag power,
M g V = ½ C D A V3

V  =  [2Mg/(CDA)]½  =  4.0 [M/(CA)]½ meters/second
              Drone  Battery  Load   Hover  Load  Climb   Power   P/M  Climb Speed  Thrust
               kg      kg      kg    Watt   Watt  Watt    Watt    W/kg  m/s   m/s   Newtons

Nihui NH-010     .0168  .0047    -       6.7                 6.7  1426   -     -
Walkera QR Y100  .146   .0413    -      17.8         35.5   53.3  1291   -     -
DJI Mavic Pro    .725   .24      -     109                 109     454   5    18
DJI Phantom 4   1.38    .426     .462  174    58     81    232     545   6    20
JYU Spider X    2.1     .812    2.3    200   219    103    419     516   5     8
MD4-1000        2.65            1.2    197    89    195    286           7.5  12     118
DJI Inspire 1   2.935   .67     1.7    333   193    144    526     785   5    22
AEE F100        6.0             2.5    300                 380                28
Chaos HL48      6.8             6.8    651   651          1302
MD4-3000       10.4             4.6   1037         1019   1496          10           280
Ehang         200             100    37500                                    28

Drone   kg     Drone mass without payload
Battery kg     Battery mass
Load    kg     Maximum payload for hovering
Hover   Watt   Power required to hover without payload
Load    Watt   Power used for the payload only
Climb   Watt   Climbing power  =  Mass * ClimbVelocity * Gravityconstant
Power   Watt   Total power  =  Hover power + Load power
P/M     W/kg   Power/Mass for the battery
Climb   m/s    Maximum climbing speed
Speed   m/s    Maximum horizontal speed
Thrust  Newton Maximum thrust
The JYU Spider X has the largest value for (payload mass) / (drone mass). The battery power/mass is
Battery power/mass  =  Phov ⋅ (M + Mpay) / M / Mbat  =  516 Watts/kg

Noise

Noise power is proportional to the rotor tip speed to the fifth power. The more rotors and the more blades per rotor, the less noise produced.


Flying electric car

Current technological limits are:

Battery energy/mass  =  ebat     =  .80  MJoule/kg
Capacitor energy/mass=  ecap     =  .016 MJoule/kg
Battery power/mass   =  pbat     = 1600  Watt/kg
Capacitor power/mass =  pcap     = 8000  Watt/kg
Motor power/mass     =  pmot     = 8000  Watt/kg
Rotor quality        =  q        = 1.25
The larger the rotor, the larger the value of thrust/power and the smaller the noise. We use 2 power rotors, each with a radius of 2 meters.
Rotor parameter =  C  =       3  kg/meter3
Rotor radius    =  R  =       2  meters
Rotor mass      =  M  =  C R3 = 24  kg

There are 2 large rotors mounted left and right and 2 small rotors mounted front and back. All are horizontal and the large rotors can tilt forward, like an Osprey.

The structure connecting the large rotors is a wing, and it extends beyond the rotors.

Mass              =  M         =400 kg
Gravity constant  =  g         =  9.8  m/s
Number of rotors  =  N         =  2
Rotor force       =  F  = Mg/N = 1960  Newtons
Rotor efficiency  =  q         =  1.02
Air density       =  D         =  1.22
Rotor radius      =  R         =  2.0  meter
Rotor force/power =  Z  = F/P  =  q D R F  =  .056
Rotor power       =  Prot      =  34.7 kWatt
Total hover power =  Phov      =  70   kWatt
Maximum power     =  Pmax      = 100   kWatt
Battery mass      =  Mbat      =  60   kg
Capacitor mass    =  Mcap      =   5   kg
We choose a design with 4 rotors mounted on a cross above the car, with a forward, aft, left, and right rotor. The forward-aft rotor distance is larger than the left-right rotor distance. The left-right cross section is a wing, and it has an interior telescoping sections that extend the length of the wing when flying. The elements of a 1-person flying car are:

Mass                =  M        =  400 kg
Gravity constant    =  g
Force               =  F  = Mg  =  4000 Newtons
Number of rotors    =  N
Rotor radius        =  R        =  1.5 meters
Hover force/power   =  Z  =qR(F/N)=  .0593
Hover power         =  P        =  67450 Watts
Hover power/mass    =  p        =  169 Watts/kg

Beam strength

The maximum force on a beam is:

Beam length     =  L
Beam height     =  H
Beam width      =  W
Shear strength  =  S
Density         =  D
Mass            =  M
Breaking force  =  F  =  (2/3) W H2 S / X





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.
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

Fuel

Most fuels are combinations of carbon, hydrogen, and oxygen, and are collectively called "hydrocarbons".

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


ATP (Adenosine triphosphate)


Phosphate
ADP (adenosine diphosphate)
ATP (adenosine triphosphaste)

The ATP molecule is a cannon and a phosphate ion is a cannonball. The cannonball powers enzyme action. The fact that the phosphate is large makes it easy to harness for energy. The cannon has to be substantially larger than the cannonball, which is why the ATP molecule is large.

ATP                       →  ADP + Phosphate + Energy       Use ATP to power enzymes
ADP + Phosphate + Energy  →  ATP                            Creation of ATP from ADP
ATP is assembled by the ATP-synthase enzyme. ATP and ATP-synthase are common to all Earth life. Mitochondria convert sugar or fat into ATP and then ATP is used to power enzymes. ATP has substantially less energy/mass than sugar or fat, which is why ATP is only generated as needed.

ATP synthase
ATP synthase
ATP synthase

Video of the ATP-synthase enzyme.        Discussion of the physics of ATP


Creatine

Creatine
Phosphocreatine
Creatine kinase enzyme catalyst

When ATP is depleted it can be regenerated anaerobically with creatine phosphate.

Phosphocreatine + ADP   →   Creatine + ATP
The reaction is reversible. If ATP isn't needed then the energy is converted back to phosphocreatine.

Creatine has half the mass of ATP and so it offers a more lightweight way to store energy.


Lactic acid

When creatine phosphate is depleted then energy can be generated anaerobically using the lactic acid cycle. This produces less energy than aerobic respiration.

Glucose + Oxygen  →  30 ATP of energy     (Aerobic respiration)
Glucose           →   2 ATP of energy     (Anaerobic respiration)
During maximum exertion,
Time before ATP is exhausted                       =   2 seconds
Time before creatine phosphate is exhausted        =  10 seconds
Time before lactic acid becomes uncomfortably high =  90 seconds

ATP energy and power

Energy to form ATP from ADP         =.063  MJoules/mole  =  .653 eV  =  .124 MJoules/kg
Energy yield for (ATP -> ADP)       =.029  MJoules/mole  =  .301 eV  =  .057 MJoules/kg
Energy from phosphocreatine         =.029  MJoules/mole  =  .301 eV  =  .137 MJoules/kg
1 MJoule/mole                                            =10.36  eV
Typical ATP cycle time when at rest =  35  seconds
Human ATP content                   =  .1  moles         =  .051 kg
Human Phosphocreatine mass fraction       =.0090 kg/kg
Human ATP mass fraction             =  f  =.0031 kg/kg
ATP energy/mass                     =  e  = .057 MJoules/kg
Human maximum power/mass            =  p  =   20 Watts/kg
Human time to burn through all ATP  =  T  = fe/P  =  8.8 seconds
Molecular mass of ATP               = 507.2 grams
Molecular mass of ADP               = 427.2 grams
Molecular mass of Phosphate         =  95.0 grams
Molecular mass of H2O               =  18.0 grams
Molecular mass of OH-               =  17.0 grams
Molecular mass of H+                =   1.0 grams
Molecular mass of Creatine          = 131.1 grams
Molecular mass of Phosphocreatine   = 211.1 grams