Drone Flight Time Calculator

For equal, separate rotor disks, total area is $A=N\pi D^2/4$. Steady hover requires $T=mg$. Conservation of mass, momentum and energy gives disk induced speed $v_i=\sqrt{T/(2\rho A)}$ and ideal power $P_i=Tv_i$. The ERAU helicopter chapter develops these relations. The same multicopter form appears in Deliparaschos et al., attached PDF p. 22, Eq. (8).

Rotor shaft power is $P_s=P_i/FM$, where figure of merit includes non-ideal induced and blade profile losses. Battery propulsion power is $P_s/\eta_d$; auxiliary battery-side power is added separately. Thus $P_h=P_i/(FM\eta_d)+P_{aux}$.

Rated pack energy is $E_n=V_nQ$ with capacity in Ah and energy in Wh. Usable mission energy is $E_u=uE_n$, and hover endurance is $t_h=E_u/P_h$ in hours. The single usable-energy fraction includes reserve and battery derating. It is not multiplied by a separate battery efficiency here.

Maximum thrust is $T_{max}=NF_{motor}$ and available thrust-to-weight is $T_{max}/(mg)$. For selected ratio $R$, the thrust-based mass limit is $m_T=T_{max}/(Rg)$. For target duration $t_r$, the allowable battery power is $E_u/t_r$. Subtract auxiliaries, convert the remaining power to ideal rotor power, and invert momentum theory to obtain $m_E=[(E_u/t_r-P_{aux})FM\eta_d\sqrt{2\rho A}]^{2/3}/g$. A nonpositive remaining power gives zero supported mass.

The governing mass limit is $\min(m_T,m_E)$. Total payload budget is that limit minus aircraft-and-battery mass, bounded below by zero. Signed headroom additionally subtracts the current payload. The payload sweep holds battery, geometry and efficiencies fixed.

Hover feasibility, payload limits and the highlighted payload curve include the theoretical boundary $T_{max}=mg$. At a target thrust-to-weight ratio of 1, that boundary leaves zero thrust or control margin. Choose a ratio above 1 and retain margin for practical operation.

• Steady, level hover in still air and outside ground effect; standard gravity is 9.80665 m/s².
• Rotors share thrust equally, have equal diameters and separate disks. Coaxial wake interference, fuselage download and unusual layouts are excluded.
• Figure of merit and motor/ESC efficiency are constant at the evaluated loads. Their defaults, 0.60 and 0.85, are illustrative assumptions, not measured performance of a named aircraft.
• Battery mass, nominal voltage and capacity are independent inputs. Changing capacity does not automatically change mass.
• The usable-energy fraction includes reserve and battery losses once. Auxiliary power is measured at the flight battery, including converter losses.
• Maximum motor thrust must be appropriate to the propeller, voltage, density and sustainable operating conditions. It is a user-supplied test value.
• A required thrust-to-weight ratio of 2 is an illustrative design target, not a certification or flight-safety requirement.

Use for preliminary multicopter hover sizing and comparisons near a known hover operating point. The payload budget covers thrust and estimated hover duration only. It does not establish structural capacity, centre-of-gravity limits, motor/ESC thermal limits, battery current capability or permitted takeoff mass.

Constant figure of merit is a local approximation: blade pitch, Reynolds number and operating load can change efficiency. The payload sweep is therefore a sensitivity estimate, not a replacement for a measured motor/propeller map. Current is an average at nominal voltage; low-voltage current and cutoff may be more restrictive.

Forward flight may consume less power than hover at modest speed, while racing, wind, climb and manoeuvres may consume much more. No mission or cruise correction is inferred. Ground effect, coaxial disks and overlapping disks are outside the model.

Reference checks cover published ideal hover power, published mass accounting and a manufacturer battery energy specification. They do not constitute measured flight-time validation for an arbitrary drone. The Deliparaschos paper gives inconsistent battery voltages in its text and Table 4; its approximate eight-minute endurance is not used as a numerical reference.