Aero & Endurance Estimator · The Gideon Corp.

Preset / Geometry Source

No STL loaded. Showing parametric model built from the inputs below.

Airframe

Airframe mass (no payload)

Payload mass

Configuration

Prop diameter

Aerodynamics

Frame drag coefficient C_d

Frontal area

Max pitch attitude

Propulsion

Figure of merit FM

Motor efficiency η_m

ESC efficiency η_esc

Download / interference k

Battery

Capacity

Cells (series)

C-rating (continuous)

Usable fraction

Environment & Systems

Density altitude

Avionics / payload power

Flow overlay: illustrative, not CFD

drag to orbit · wheel to zoom

Power vs airspeed min P = best endurance · min P/V = best range

Trade study

What this tool computes, and how far to trust it

This is a screening estimator for electric UAS in steady flight, low subsonic, ISA atmosphere: multirotors (quad / hex / X8) in hover and forward flight, and fixed-wing cruise (Fulmar X-class preset is an electric analog of a fuel aircraft, so its real fuel endurance is far longer). Every model used is named below. Transition flight, launch/recovery, gusts/wind, battery sag, and motor thermal limits are not modelled.

Models used

Quantity	Model	Notes
Hover induced power	P_ideal = T^1.5/√(2ρA)	Actuator-disk momentum theory, per rotor.
Profile + non-ideal losses	P_shaft = P_ideal/FM	Figure of merit, typical 0.65 to 0.75 for small UAS rotors (default 0.70). Profile power is inside FM, not modelled separately.
Airframe download / rotor interference	T_req = W·(1+k)	Empirical correction, k ≈ 0.05 to 0.12 by rotor spacing/overlap (default 0.08). Applied to the weight-support term in all flight states, slightly conservative in fast forward flight.
Coaxial interference (X8)	P_ind × 1.22	Torque-balanced coax induced-power interference factor ≈1.22 (Leishman); applied only for the X8 configuration.
Induced velocity in forward flight	v_i = v_h²/√(V²+v_i²)	Glauert momentum solution (high-speed approximation), solved by fixed-point iteration. Small-angle: freestream taken as edgewise.
Parasite drag	D = ½ρV²·C_d·A_front	Flat-plate referenced to frontal area; C_d 0.6 to 1.0 typical for open multirotor frames. Frontal area held constant with pitch attitude (simplification).
Total forward-flight power	P_shaft(V) = (T·v_i + D·V)/FM	Energy method; thrust T = √(W²(1+k)² + D²). FM applied as overall rotor efficiency so P(V→0) is exactly the hover model.
Electrical power	P_elec = P_shaft/(η_mη_esc) + P_avionics	Defaults η_m=0.85, η_esc=0.95.
Air density	ρ = 1.225·(1−2.25577·10⁻⁵h)^4.25588	ISA troposphere, density altitude h in metres.
Energy & endurance	t = E·f_usable / P_elec	E = Ah × n_cells × 3.7 V nominal; usable fraction default 0.80. Constant-power discharge (no sag model).
Max speed	min( P-limited, tilt-limited )	P-limited: P_elec(V) = Ah·C·V_pack (battery continuous limit; motor limits not modelled). Tilt-limited: drag = W·tan(θ_max).
Best endurance / best range	argmin P(V) · argmin P(V)/V	Numerical search on the power curve.
Hover throttle	≈ T_hover/T_max	Thrust fraction at the battery power limit, an approximation; real ESC throttle-to-thrust maps are nonlinear.
Fixed-wing drag polar	C_D = C_D0 + C_L²/(π·e·AR)	Parabolic polar; Oswald e default 0.75. C_D0 0.03 to 0.05 typical for small UAS.
Fixed-wing cruise power	P = D·V/η_p	Energy method; propeller efficiency η_p default 0.75, then the motor/ESC chain as above.
Fixed-wing characteristic speeds	V_mp = V_md/3^¼; floor 1.1·V_s	Best endurance at minimum power, best range at minimum drag; the analytic minima are used as validation anchors. No speed is reported below a 10 % stall margin.
Fixed-wing max speed	min( P-limited, V_NE )	Battery continuous power vs the structural never-exceed placard (input). Motor limits not modelled.

Quantity

Model

Notes

Hover induced power

P_ideal = T^1.5/√(2ρA)

Actuator-disk momentum theory, per rotor.

Profile + non-ideal losses

P_shaft = P_ideal/FM

Figure of merit, typical 0.65 to 0.75 for small UAS rotors (default 0.70). Profile power is inside FM, not modelled separately.

Airframe download / rotor interference

T_req = W·(1+k)

Empirical correction, k ≈ 0.05 to 0.12 by rotor spacing/overlap (default 0.08). Applied to the weight-support term in all flight states, slightly conservative in fast forward flight.

Coaxial interference (X8)

P_ind × 1.22

Torque-balanced coax induced-power interference factor ≈1.22 (Leishman); applied only for the X8 configuration.

Induced velocity in forward flight

v_i = v_h²/√(V²+v_i²)

Glauert momentum solution (high-speed approximation), solved by fixed-point iteration. Small-angle: freestream taken as edgewise.

Parasite drag

D = ½ρV²·C_d·A_front

Flat-plate referenced to frontal area; C_d 0.6 to 1.0 typical for open multirotor frames. Frontal area held constant with pitch attitude (simplification).

Total forward-flight power

P_shaft(V) = (T·v_i + D·V)/FM

Energy method; thrust T = √(W²(1+k)² + D²). FM applied as overall rotor efficiency so P(V→0) is exactly the hover model.

Electrical power

P_elec = P_shaft/(η_mη_esc) + P_avionics

Defaults η_m=0.85, η_esc=0.95.

Air density

ρ = 1.225·(1−2.25577·10⁻⁵h)^4.25588

ISA troposphere, density altitude h in metres.

Energy & endurance

t = E·f_usable / P_elec

E = Ah × n_cells × 3.7 V nominal; usable fraction default 0.80. Constant-power discharge (no sag model).

Max speed

min( P-limited, tilt-limited )

P-limited: P_elec(V) = Ah·C·V_pack (battery continuous limit; motor limits not modelled). Tilt-limited: drag = W·tan(θ_max).

Best endurance / best range

argmin P(V) · argmin P(V)/V

Numerical search on the power curve.

Hover throttle

≈ T_hover/T_max

Thrust fraction at the battery power limit, an approximation; real ESC throttle-to-thrust maps are nonlinear.

Fixed-wing drag polar

C_D = C_D0 + C_L²/(π·e·AR)

Parabolic polar; Oswald e default 0.75. C_D0 0.03 to 0.05 typical for small UAS.

Fixed-wing cruise power

P = D·V/η_p

Energy method; propeller efficiency η_p default 0.75, then the motor/ESC chain as above.

Fixed-wing characteristic speeds

V_mp = V_md/3^¼; floor 1.1·V_s

Best endurance at minimum power, best range at minimum drag; the analytic minima are used as validation anchors. No speed is reported below a 10 % stall margin.

Fixed-wing max speed

min( P-limited, V_NE )

Battery continuous power vs the structural never-exceed placard (input). Motor limits not modelled.

Valid range & expected error

Steady flight, electric UAS 0.5 to 30 kg, sea level to ~5 000 m density altitude, airspeeds below ~50 m/s. Against flight-test data for vehicles in this class, momentum-theory and drag-polar screening of this kind typically lands within ±15 to 25 % on power and endurance (multirotor hover and fixed-wing cruise alike), and is weaker (±25 to 40 %) on max speed, which is dominated by the drag estimate and unmodelled motor limits. Trends and sensitivities (the trade-study sweeps) are considerably more reliable than absolute values.

STL frontal area

When an STL is uploaded, frontal area is estimated by orthographic projection: the mesh is rendered front-on to an offscreen buffer and covered pixels are integrated. Propellers are usually absent from CAD exports, so the form value may still be the better number for drag; the toggle in the input panel chooses which is used. If projection fails the STL is used for visualization only and the form value applies.

Validation report

Test

Result

Detail

The same physics code shipped in this file is also executed by _build/run_validation.mjs under Node, which writes _build/validation.md.

Screening estimator for early design-space exploration. Not a substitute for high-fidelity CFD, wind-tunnel, or flight test. Streamlines are illustrative.

The Gideon Corp. · Sovereign operator at mission speed.