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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
Nihui NH-010     .0168   .00200  .119   .0047    .43      6.7    397      5      24    .03
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
SKRC D20         .092    .0080   .087                    11.1    121     12      20    .3
SKRC Q16         .111    .0067   .060                     7.4     67     15      40    .2
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
Bayangtoys X16   .50     .088    .176                    92      183     16     110    .8
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
Ehang 184     200      51.8      .259                 37500      188     23  300000   3.5
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

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
                Mass    Hover  Battery  Battery  Payload  Climb   Max speed  Power/mass
                 kg     Watts    MJ       kg       kg      m/s       m/s      Watts/kg

DJI Mavic Pro      .725   109    .157    .24                5       17.9
Phantom 4         1.38    174    .293    .426               6       20
JYU Spider X      2.1     200    .360    .812       2.3     5        8         516
MD4-1000          2.65    197   1.039               1.2             12
AEE F100          6.0     380   1.598               2.5             27.7
Ehang wingspan  200     37500  51.8                99.8             28
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

Lasers
      mWatt    $   Diameter  Length  Beam  Beam
                      mm       mm    mrad   mm

Violet   .075   70   16.5     170     .5    4   wicked nano
Violet   .1     10   16.2                       lasers-pointers
Violet   .2     20   20       112               laserpointerpro
Violet   .5     30   24       148               laserpointerpro
Violet  1.0    100   24       180               laserpointerpro
Blue     .2     65                              freemascot.com
Blue    1.0     70                              freemascot.com


Color   Wavelength (nm)

Violet    405
Blue      445
Green     532
Yellow    589
Red       635

Flashlights
                   $  Lumens  Diameter  Mass    Lumens per
                                inch    ounce     inch2

Thrunite Ti4T       36   300    .55               1260
Thrunite Ti4        24   252    .55
ThorFire PF4        20   210    .6
Nitecore MT06       23   165    .55
Revtronic pocket    14   105    .6
Thrunite Archer 2A  36   500    .87     2.1        840
Revtronic 650       35   650   1.0
Fenix UC35          90   960   1.0
Barska TC1200      106  1200   1.0                1530
Fenix TK16          92  1000   1.3
Streamlight HL3     78  1100   1.6      7.1
Litecore TM03      158  2800   1.6                1390

MicroSD memory
           $   GB

Sandisk   20   64      Amazon
Sandisk   42  128      Amazon
Sandisk   76  200      Amazon
PNY       87  256      Amazon

Laptops
                $  RAM  Drive  Size Thick CPUs GHz    Pixels   Pounds  Op

Asus T100HA     183   4    64  10.1   .7   4  1.4     1280  800  2.2  W10 Newegg  Detach
Asus T100HA     220   4    64  10.1   .7   4  1.4     1280  800  2.2  W10 Amazon  Detach
Asus T101HA     300   4   128  10.1   .74     1.4                     W10 Adorama Detach
Asus T102HA     400   4   128  10.1        4  ?       1280  800  1.7  W10
Asus E200HA     200   4    32  11.5   .7   4  1.4     1366  768  2.2  W10 Amazon
Asus TP200SA    250   4    64  11.6   .73                             W10         Convert
Asus T200SA     350   4    64  11.6   .73  4  1.6                     W10 Asus

HP 11-y020wm    240   4    32   ?    thin     1.6                     W10 Amazon refurb
Lenovo x120e    140   4+4 128  11.6  brick    1.5     1366  768       W10 Newegg
Toshiba         210   4   128  11.6        4  2.7                         Amazon
Lenovo N22      194   4    64  11.6   .9   2  1.6     1366  768  2.7      Amazon
HP Elitebook    320   8   128  11.6               3i5                     Best Buy

HP 2740P        102   4    64  12.1           2.5  i5                     Newegg
HP Elitebook    210   8   120  12.1  1.1      2.1                2.6      Amazon
Asus Zenbook 3 1100  16  1024  12.5   .46     2.0                         Asus UX390UA

Dell Latitude   205   8   128  12.5           2.7                         Amazon
HP Elitebook    252   8   256  12.5           2.5  i5                     Newegg
Dell Latitude   350  16   256  12.5        2  2.5 2i5 1366  768  3.2      Best Buy
Dell Latitude   380  16   256  12.5               3i5                     Best Buy

Dell Latitude   303   8   240  13.3               2i5                     Best Buy
Dell Latitude   407  16   256  13.3               3i5                     Best Buy

Asus UX360CA    745   8   512  13.3   .54    M6Y75               2.9  W10
Asus UX303UA    750   8   256  13.3   .8   2  2.3
Asus UX305CA    730   8   512  13.3   .5              1920 1080  2.6  W10
Asus UX306UA   1000  16   512  13.3                              2.9  W10
Asus UX305UA          8   512  13.3   .63    i7 6500U 1920 1080  2.9  W10
Asus UX303UB   1050  16   512  13.3   .76
*: ebay
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.
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