About
How ForceSight’s physics works
Hamptonian ForceSight is a physics laboratory for learning. Its numbers are never for planning a real flight — real limits come from the aircraft’s own documentation.
Four kinds of number
calculated The physics model computed it from the inputs: gravity, rotor thrust and torque (blade-element momentum theory), the rigid-body motion (six degrees of freedom, 250 Hz, Runge–Kutta), air density (ISA), battery current and voltage.
approximation A simplified model of something more complex: body drag (constant drag areas), ground effect (Cheeseman–Bennett), the vortex ring state (an empirical curve), gusts and turbulence, ground contact, the battery’s discharge curve. The trends are right; the exact numbers are not.
illustrative Drawn to help you see, from calculated numbers: airflow particles, smoke streamlines, the propeller blur. Not a flow simulation. Fog changes what you see, never how the aircraft flies.
published estimate calibrated Aircraft data: published by the manufacturer (with its source), estimated by us (with the reasoning), or chosen so the model reproduces a published number (hover time, top speed).
Numerical validation
The engine is tested against closed-form physics on every build. The tests check:
- International Standard Atmosphere: density at 0, 1 000 and 3 000 m; density altitude rule of thumb
- Rotor: hover induced velocity equals momentum theory √(T/2ρA); figure of merit below 1
- Rotor: thrust ∝ Ω² and ∝ ρ; climbing reduces thrust; forward flight adds translational lift
- Ground effect matches Cheeseman–Bennett; vortex-ring curve continuous with momentum theory
- Free fall: Δy = ½gt²; terminal velocity √(2mg/ρC_DA); hover on the Moon (W = mg)
- Hover: thrust = weight (±0.5%), rotor speed = calibrated hover speed; RPM ∝ 1/√ρ; RPM ∝ √(total mass)
- Off-centre payload: rotor thrust moment balances the payload moment
- Battery: energy drawn = power × time; matches the calibrated hover power
- Tilt to accelerate: a = g·tan θ; published top speed reached at the assumed tilt while holding height
- Position hold in wind: tan θ = drag / weight; attitude mode drifts downwind
- Yaw: I·ψ̈ = Σ reaction torque, direction from propeller spin
- Quadcopter cannot survive a motor loss; a hexacopter can (failure detection and re-mixing)
- Rewind and replay reproduce a flight exactly (gusts and turbulence included)
- Every aircraft: figure of merit, efficiency and thrust-to-weight in plausible ranges; hover time reproduced
- Fixed wing: lift = weight at trim; best L/D where induced = parasite drag; stall behaviour
- Multirotor trim: power dips with translational lift then rises with drag
- Missions: the server re-flies a recording to the same score; tampered recordings fail
- Motor-failure cases: the stated outcome matches what the simulation does, for several seeds
What the model leaves out
- Rotor–rotor interaction, blade flapping dynamics, unsteady aerodynamics (except the vortex-ring fluctuation).
- Motor electrical dynamics: motors respond with a first-order lag; efficiency is a single number.
- Real flight-controller code: the controller is a teaching cascade (position → velocity → tilt → rate → mixer), not PX4, ArduPilot or DJI firmware.
- Aerodynamic moments of the airframe, humidity, compressibility, and terrain-induced turbulence.
- Ducted rotors (Avata): no duct model; the calibrated efficiency absorbs it.
Sources
- DJI Matrice 30 Series — Specs (manufacturer, accessed 2026-10-14) — Series values (M30 and M30T share an airframe); takeoff weight includes two TB30 batteries.
- DJI Matrice 30 Series — 3D Model (M30T.stp) (manufacturer-cad, accessed 2026-10-14) — Public CAD; propellers ship as swept discs of 405 mm diameter.
- DJI Mavic 3 Classic — Specs (manufacturer, accessed 2026-10-14)
- DJI Mavic 3 Pro — Specs (manufacturer, accessed 2026-10-14)
- DJI Avata — specifications (DroneSpec by Dronedesk) (aggregator, accessed 2026-10-14) — DJI’s own Avata specs page could not be read from this environment; values agree with dealer listings.
- DJI FPV — DJI Support FAQ (manufacturer, accessed 2026-10-14) — Takeoff weight ≈ 795 g and 245 mm diagonal.
- DJI FPV Technical Specifications (Dr. Drone, DJI dealer) (dealer, accessed 2026-10-14)
- DJI Inspire 1 — specifications (DroneSpec by Dronedesk) (aggregator, accessed 2026-10-14) — Discontinued aircraft; DJI’s page no longer lists specifications. Dronedesk warns its pages are auto-generated — treat as secondary.
- DJI Flamewheel F450 ARF Kit (GetFPV) (dealer, accessed 2026-10-14) — Frame 282 g, 450 mm motor-to-motor, recommended takeoff weight 800–1600 g, props 10×4.5 or 8×4.5, 3S–4S.
- Hamptonian AeroNatomy — F450 / Pixhawk 2.4.8 classroom build (classroom, accessed 2026-10-14) — AeroNatomy content/aircraft/f450-pixhawk248. The class kit: 2212-class ≈920–1000 KV motors, 1045 props, 3S LiPo (3300 mAh in the class inventory).
Fleet: DJI Matrice 30T, DJI Mavic 3 Classic, DJI Mavic 3 Pro, DJI Avata, DJI FPV, DJI Inspire 1, F450 quadcopter with Pixhawk 2.4.8. Physics references: Leishman, Principles of Helicopter Aerodynamics; Cheeseman & Bennett (1955); ICAO Doc 7488 (ISA); FAA Pilot’s Handbook of Aeronautical Knowledge.
Credits
- Photographed hangar and airfield, concrete, asphalt and grass: Poly Haven (CC0).
- DJI Matrice 30T geometry: DJI’s public M30 Series 3D model (propellers modelled; no licence terms stated by DJI — used to depict the aircraft for education).
- F450 / Pixhawk parts: Hamptonian AeroNatomy’s digital twin (authored to measured dimensions).
- Other aircraft: study models built to published dimensions — not manufacturer geometry.
- Mission music: composed in code for ForceSight. Reward tracks: supplied by your teacher.
- Narration: ElevenLabs (professional voice), generated for ForceSight.