Rotor — Robotics/Rotorcraft

Rotor

Robotics / Rotorcraft

The thrust and torque a propeller or rotor of a given size produces at a given rotational speed and air density, as a force and a moment in body axes.

One rotor's thrust and torque, with k_T = C_T·R²·π·R² and k_Q = −C_Q·R³·π·R²:

• T = (k_T·Ω²)·ρ, so thrust does not care which way the rotor turns
• M_z = ρ·(k_Q·Ω·|Ω|), which does – a rotor spun backwards reverses its torque, and that is how a quadcopter's counter-rotating pairs cancel

Without flap effects the disc does not tilt, so F = [0; 0; −T] and M = [0; 0; M_z].

Ports

• Omega – Ω, the rotor's rotational speed in rad/s, [1,1]. Its sign is the sense of rotation and reaches the torque only.
• rho – ρ, the air density, [1,1], in kg/m³ or slug/ft³.
• Fxyz – the force in body axes, a [3,1] column in N or lbf.
• Mxyz – the moment in body axes, a [3,1] column in N·m or lbf·ft.

Parameters

• Units – Metric (MKS), English (velocity in ft/s) or English (velocity in kts). The arithmetic is unit-consistent in both systems, so the first two run the same numbers; kts is the only one that converts anything – the body velocity, by 1852/3600/0.3048 ≈ 1.68781 ft/s per knot.
• Coefficient Source – where the two coefficients come from:
  • Dialog – the two values below, used as given
  • Compute using BEMT – blade element momentum theory over the blade geometry below, solved once when the configuration is loaded, so the export carries the resulting pair as constants
• Thrust Coefficient – C_T, used when the source is Dialog.
• Torque Coefficient – C_Q, used when the source is Dialog.
• Number Of Blades – N_b, used by the momentum solver (through the solidity σ = N_b·c/(π·R) and Prandtl's tip loss) and by nothing else when the source is Dialog.
• Blade Radius – R, in the length unit; it sets the whole scale of the block, thrust going as R⁴ and torque as R⁵.
• Blade Chord – c, in the length unit.
• Hinge Offset – e, the flapping hinge's distance from the shaft, in the length unit; at least zero and less than the radius, and read only by the momentum solver here.
• Lift Curve Slope – the blade section's lift slope per radian.
• Mean Drag Coefficient – c_d0, the profile drag the momentum solver adds to the torque coefficient as σ·c_d0/8. It reaches nothing else.
• Twist Distribution – Linear or Ideal, which decides the one blade pitch the block uses: (2/3)·θ_root + (1/2)·θ_twist on a Linear blade, θ_tip on an Ideal one.
• Blade Root Angle – θ_root, in radians (Linear twist).
• Blade Twist Angle – θ_twist, in radians (Linear twist).
• Blade Tip Angle – θ_tip, in radians (Ideal twist).
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. Every parameter is baked into the arithmetic at export, the two coefficients included – so a core exported with Compute using BEMT carries the pair the solver found and does not re-solve anything at run time.

The three HDL targets are simulation-only: a division and a signed square does not belong in a Q16.16 datapath, so they compute in real and quantize only at the ports – which also bounds what can cross one, ±32768. PLC Structured Text has no ATAN2 in IEC 61131-3, so where one is needed it is rebuilt from ATAN(y/x) with the quadrant reconstruction.

Simulink bridge

Import and export, mapped to Aerospace Blockset's aerolibrotordyn/Rotor. Units → units, Coefficient Source → CTCQMode, Thrust Coefficient → CT, Torque Coefficient → CQ, Number Of Blades → Nb, Blade Radius → radius, Blade Chord → chord, Hinge Offset → hingeOffset, Lift Curve Slope → clalpha, Mean Drag Coefficient → cd0, Twist Distribution → twistType, Blade Root Angle → thetaRoot, Blade Twist Angle → thetaTwist and Blade Tip Angle → thetaTip; every combo is Simulink's own list, so the mapping is lossless. Three Simulink parameters are always written fixed, because each of them MOVES A PORT and a fixed port list cannot follow one: modelMode = Without flap effects (with them the block gains a body velocity and a body angular rate input – that is the Rotor With Flap Effects block), controlInput = off (it adds a collective pitch input) and CTout = off (it adds two coefficient outputs). Simulink's third CT and CQ source, Ports, is not offered for the same reason. The Simulink block has no SampleTime (measured), so the rate stays on the ICore side.

Notes

• Algebraic and stateless; nonlinear, so no state space.
• Measured, not derived. Every rule above was read off Aerospace Blockset R2026a's own block, which is a built-in block type whose source does not ship, and the transcription agrees with it to 1e-16 on about 1600 random states.
• A negative density is not refused here. The Simulink block stops the run on one ("Density must be greater than or equal to 0"); this block computes with what it is given, which at ρ < 0 is a thrust pointing the other way.
• The momentum solver runs once per configuration load, not per sample: 100 blade elements, Newton from λ = 0.001 to a step under 1e-6, at most 100 iterations.