
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 = M_{bat} = .5 kg (The battery is the most vital component) Battery energy = E = .38 MJoules Battery energy/mass= e_{bat}= E/M_{bat}= .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 minutesThe flight time in terms of component parameters is
T = (e_{bat}/p) * (M_{bat}/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 NH010 .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 MD41000 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 3.5The minimum power requirement for quadcopter flight is of order 60 Watts/kg.
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.
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 EFan 450 104.4 .232 29000 64.4 60 9.5 44.4 61.1 160
Drone mass = M Battery mass = M_{bat} Payload mass = M_{pay} Climbing speed = V_{cli} Max horizontal speed = V_{max} Hover constant = H = 60 Watts/kg Power/mass required to hover Hover power = P_{hov}= H M Hover power for payload= P_{pay}= H M_{pay} Gravity constant = g = 9.8 m/s Power to climb = P_{cli}= M g V Drag coefficient = C Air density = D = 1.22 kg/meter^{3} Drone crosssection = A Drag power = P_{drag}= ½ C D A V^{3}If the climbing power is equal to the hover power,
V = H / g = 6 meters/secondIf the climbing power is equal to the drag power,
M g V = ½ C D A V^{3} 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 MD41000 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 28The JYU Spider X has the largest value for (payload mass) / (drone mass). The battery power/mass is
Battery power/mass = P_{hov} ⋅ (M + M_{pay}) / M / M_{bat} = 516 Watts/kg
mWatt $ Diameter Length Beam Beam mm mm mrad mm Violet .075 70 16.5 170 .5 4 wicked nano Violet .1 10 16.2 laserspointers 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
$ Lumens Diameter Mass Lumens per inch ounce inch^{2} 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
$ GB Sandisk 20 64 Amazon Sandisk 42 128 Amazon Sandisk 76 200 Amazon PNY 87 256 Amazon
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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 Lithiumion battery .75 1.5 .009 .0142 106 Lithium supercapacitor .008 8 .0010 .09 90 Aluminum capacitor .0011 100If the battery and motor have equal power then the battery has a larger mass than the motor.
Mass of motor = M_{mot} Mass of battery = M_{bat} Power = P (Same for both the motor and the battery) Power/mass of motor = p_{mot} = P/M_{mot} = 8.0 kWatt/kg Power/mass of battery = p_{bat} = P/M_{bat} = 1.5 kWatt/kg Battery mass / Motor mass= R =M_{bat}/M_{mot} = p_{mot}/p_{bat} = 5.3The "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 = M_{dro} Motor mass = M_{mot} Motor power/mass = p_{mot} = 8000 Watts/kg Hover minimum power/mass = p_{hov} = 60 Watts/kg Drone power = P_{dro} = p_{mot} M_{mot} Hover minimum power = P_{hov} = p_{hov} M_{dro} Sports prowess = S = P_{dro}/P_{hov} = (p_{mot}/p_{hov}) * (M_{mot}/M_{dro}) = 80 M_{mot}/M_{dro}If S=1 then M_{mot}/M_{dro} = 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 = (p_{bat}/p_{hov}) * (M_{bat}/M_{dro}) = 25 M_{bat}/M_{dro}If M_{bat}/M_{dro} = 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 1.0Supercapacitors 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 = p_{bat} = 1.5 kWatts/kg Supercapacitor power/mass = p_{sup} = 8.0 kWatts/kg Battery power = P Battery mass = M_{bat} = P / p_{bat} Supercapacitor mass = M_{sup} = P / p_{sup} Supercapacitor/Battery mass= R =M_{sup}/ M_{bat} = p_{bat}/p_{sup} = .19The 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 = .015If 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.