TRANSPIRE DYNAMICS · FLIGHT DYNAMICS CONCEPT SERIES · PART II SIX DEGREES OF FREEDOM · ROTOR WAKE FLOWFIELD TRANSPIREDYNAMICS.COM

UH-60 in three dimensions:
the air it moves

Part I covered the longitudinal slice — climb, dive, speed. This page flies the full six-degree-of-freedom aircraft and — the real point — shows you the flowfield: the column of air the rotor drives downward, how it skews back in forward flight, and splashes outward near the ground.

6-DOF RIGID BODY LIVE WAKE PARTICLES YOU CAN STILL CRASH
◂ Part I — Longitudinal flight dynamics
SEC 01 · THE SIMULATOR

Full-motion model, live wake

Below is a six-degree-of-freedom UH-60A: position and attitude in all axes, articulated-rotor flapping response, real tail rotor side force, fuselage and fin aerodynamics, wheel contact. The blue-shaded particles are air, advected through an analytic model of the rotor's induced-velocity field. Drag to orbit the camera, scroll to zoom. Cockpit units are U.S. standard: knots, feet, ft/min.

WHY IT DRIFTSThe main rotor turns counter-clockwise viewed from above. Torque reaction yaws the nose right, so the tail rotor thrusts to the right to hold heading — and that side force shoves the whole aircraft right. Pilots hold a touch of left cyclic; the UH-60 hovers slightly left-skid-low. Watch for it in the hover demo, then try the same with SAS off.
UH-60 · 6-DOF · ρ = 0.00238 SLUG/FT³ (SL STD) · GW 17,000 LB
TRIM: P 0.0° / R 0.0°
Feedback v1.17.11

Disclaimer

This is an independent educational concept demonstrator by Transpire Dynamics LLC. It is not affiliated with, endorsed by, or certified by the U.S. Army, Sikorsky, Lockheed Martin, or the U.S. Department of Defense.

All aerodynamic parameters are derived from publicly available, open-domain literature. Models are physics-based and derived from first principles, but optimized for real-time computation and not intended for full engineering analysis. High-fidelity work requires dedicated offline simulation tools.

transpiredynamics.com →

ft
kts
deg
COL 50%
CYC 0 / 0
PED 0
Phase demonstrations — press one, then watch the message bar ENGINES: ON — governor holds NR ≈ 100%
SEC 02 · THE FLOWFIELD

Where the lift comes from: a river of air

A hovering Black Hawk at 17,000 lb pumps roughly two tons of air per second downward at about 40 ft/s through the disk, doubling to ~80 ft/s in the developed wake below. That column is the wake the particles trace. Everything strange about helicopters — translational lift, ground effect, settling with power — is this column behaving differently.

AHOVER — THE COLUMN

Out of ground effect the wake is a near-vertical tube, contracting to about 71% of rotor radius as it accelerates (mass conservation: faster flow, narrower tube). Air above the disk is drawn in from everywhere, like a sink drain.

BGROUND EFFECT — THE SPLASH

Within about one rotor diameter of the surface the column has nowhere to go and splashes radially outward — the outwash that flattens grass and pelts ground crews. The cushion of redirected air cuts induced power; the aircraft hovers cheaper. Watch particles fan out along the pad.

CFORWARD FLIGHT — THE SKEW

With airspeed, the wake blows backward like smoke from a moving chimney. The skew angle grows with speed; past ~20 kt the disk continuously meets fresh, undisturbed air — effective translational lift. The helix of tip vortices trails behind like a wake behind a boat.

DVORTEX RING STATE — THE DOUGHNUT

Descend into your own column near its speed and the wake stops leaving: it recirculates in a torus around the disk edge. Thrust becomes erratic, adding collective feeds the ring. The escape is forward cyclic — fly into clean air. Watch the particles loop.

ENGINEER PANEL — THE ANALYTIC WAKE MODEL

The particle field is advected through a superposition of analytic elements, not a CFD solve. The main rotor wake is a Glauert-style skewed cylinder: momentum theory gives the induced velocity at the disk \(v_i\) from

$$ T = 2\rho A\, v_i \sqrt{(V\cos\alpha)^2 + (V\sin\alpha + v_i)^2} $$

solved iteratively, with the wake skew angle measured from the disk normal:

$$ \chi = \tan^{-1}\!\left(\frac{\mu}{\lambda_i + \mu_z}\right), \qquad \mu = \frac{V\cos\alpha}{\Omega R} $$

Inside the skewed cylinder the induced flow ramps from \(v_i\) at the disk to \(2v_i\) in the far wake (momentum doubling), with radius contracting toward \(R/\sqrt{2}\). Above the disk, an inflow sink field draws particles in. Near the ground, an image-disk reflection redirects the column into a radial wall jet \(\propto 1/r\) — the outwash. The VRS torus is superimposed when the descent-rate criterion of Part I is met. The tip-vortex ribbons are prescribed (Landgrebe-style) helices riding the same skew and contraction — geometry, not free filaments.

The architecture exposes a single interface — flow.sample(point) → velocity — so the analytic model can be swapped for a free-vortex filament solver (Biot–Savart over trailed tip vortices) without touching the particle system. That solver is the disabled "v2.1" toggle above. The path-trace overlay releases tracer particles into the same field and draws the trail each one actually travels (pathlines, RK2-advected) — so you watch a parcel of still air wait ahead of the aircraft, get drawn into the disk, and ride the skewed wake aft; in vortex-ring state the traces wind into the recirculating torus.

SEC 03 · LATERAL DYNAMICS

The axes Part I ignored

Longitudinal flight is the easy half. The lateral-directional axes are where a helicopter shows its character — every one of these is in the model and visible in the sim:

01TORQUE ROLL & YAW

Pull collective and the airframe reacts against the rotor: nose yaws right (CCW rotor seen from above), and the tail rotor's answer pushes you sideways. Every power change is a pedal change.

02TRANSLATING TENDENCY

The tail rotor's steady right side force drifts the hover right unless the pilot holds left cyclic — so the rotor disk tilts slightly left and the aircraft hangs left-skid-low. Free, permanent, uncommanded.

03WEATHERVANE & THE BALL

The vertical fin makes the aircraft want to point into the relative wind. Sideslip shows on the slip ball at the bottom of the screen — step on the ball to center it, same rule as airplanes.

04WHY SAS EXISTS

The bare airframe is dynamically unstable — a divergent oscillation a human can't comfortably hand-fly for long. The Stability Augmentation System adds rate damping. Toggle it off above and feel the difference. The FCS row stacks outer loops on top — hover hold (position → velocity → attitude cascade) and airspeed hold — the same architecture real AFCS modes use.

ENGINEER PANEL — 6-DOF EQUATIONS & ROTOR MOMENTS

States: inertial position, attitude quaternion \(q\), body velocities \((u,v,w)\), body rates \((p,q_r,r)\), rotor speed \(\Omega\). Rigid-body dynamics in body axes:

$$ m(\dot{\mathbf{v}} + \boldsymbol{\omega}\times\mathbf{v}) = \mathbf{F}_{rotor} + \mathbf{F}_{tail} + \mathbf{F}_{fus} + m\,\mathbf{g}_b, \qquad \mathbf{I}\dot{\boldsymbol{\omega}} + \boldsymbol{\omega}\times\mathbf{I}\boldsymbol{\omega} = \mathbf{M} $$

with the UH-60's products of inertia retained (\(I_{xz}\neq 0\)). Rotor thrust acts along the tip-path-plane normal; first-order flapping maps cyclic and speed into TPP tilt:

$$ a_1 \approx \underbrace{\frac{2\mu\left(\tfrac{4}{3}\theta_0 - \lambda\right)}{1 - \mu^2/2}}_{\text{blowback}} - B_1, \qquad b_1 \approx \frac{\tfrac{4}{3}\mu\, a_0}{1 + \mu^2/2} + A_1 $$

Hub pitch/roll moments combine thrust-vector tilt and hinge-offset stiffness (articulated head, \(e \approx 4.7\%R\)):

$$ M = \left(T h + \tfrac{N_b}{2} K_\beta \right)\beta_{tilt}, \qquad K_\beta = \tfrac{3}{2}\, \tfrac{e}{R}\, I_b\, \Omega^2 $$

Tail rotor thrust (pedal-commanded, momentum theory at the 20°-canted tail disk) acts at the tail position: yaw moment from its arm, a right side force, a small vertical lift component from the cant, and a roll moment from its height above the CG. Fuselage drag is a diagonal flat-plate matrix \((f_x, f_y, f_z) = (3.0, 9.3, 7.9)\,\mathrm{m}^2\); fin and stabilator add linear side-force and pitch stiffness with dynamic pressure. SAS is plain rate feedback \( \Delta A_1 = -k_p p,\ \Delta B_1 = k_q q_r,\ \Delta \theta_{ped} = -k_r r\).

SEC 04 · MODEL CONSTANTS

What the sim believes

QuantityU.S.SI
Gross weight17,000 lb7,700 kg
Main rotor radius R26.8 ft8.18 m
Disk area A2,260 ft²210 m²
Disk loading7.5 lb/ft²36.0 kg/m²
Rotor speed Ω (100% NR)258 RPM27.0 rad/s
Tip speed725 ft/s221 m/s
Solidity σ / blades0.083 · 4 blades · CCW from above
Hover induced velocity v_h39.7 ft/s12.1 m/s
Inertia Ixx / Iyy / Izz4,660 / 38,500 / 36,800 slug·ft²6,320 / 52,200 / 49,900 kg·m²
Product of inertia Ixz1,880 slug·ft²2,550 kg·m²
Tail rotor arm / cant32.5 ft · 20° up9.9 m
Power limit (xmsn)3,400 shp2.54 MW
Parasite area f (fwd)32.3 ft²3.0 m²

Approximations: first-order flapping (no lag/torsion DOF), prescribed rather than free wake, flat-plate fuselage aero, point-contact gear, standard-day sea level air. Inertias are public UH-60A values rounded. This is a concept trainer, not an engineering simulator.

SEC 05 · KNOWN LIMITATIONS

What we know isn't right yet

Every simplification is stated. These are active items we're aware of and plan to address and improve.

1WAKE COLUMN RADIAL DISTRIBUTION

Particle density below the disk should visually fill the full rotor-disc diameter with helical structure at the rim. The current radial profile and seeding still produce a slightly narrower-than-real column in some viewing conditions. Tuning in progress.

2TIP-VORTEX HELICAL VISIBILITY

The tip-vortex sheet should produce visible helical particle ribbons at the slipstream boundary (like condensation trails in humid conditions). Swirl magnitude and profile may need further tuning to consistently show this structure across flight regimes.

3PRESCRIBED WAKE GEOMETRY

Wake axis and contraction are analytic (Landgrebe-style), not self-interacting. This means blade-vortex interactions, wake distortion in maneuvers, and the complex near-wake rollup are not captured. The v2.1 free-vortex filament solver will address this.

4NO COMPRESSIBILITY

Advancing blade tip Mach effects are absent. At high forward speed the retreating blade stall and advancing blade shock are not modeled — limits fidelity above ~140 kt.

5FLAT-PLATE FUSELAGE

Fuselage aerodynamics use a diagonal flat-plate drag matrix. No angle-of-attack-resolved lift/side-force, no interference with the rotor wake, no download on the fuselage from the rotor.

6NO BLADE FLEXIBILITY

Rigid blades with first-order flapping only. No lead-lag, no torsion DOF. This omits blade sailing, resonance, and elastic twist effects.

7GROUND CONTACT MODEL

Three-point spring-damper gear. No oleo stroke dynamics, no tire slip model, no ground resonance potential. Adequate for the flight regime but not for detailed ground handling.

8STANDARD-DAY ONLY

Sea-level ISA (ρ = 1.225 kg/m³). No altitude, temperature, or humidity effects on performance. No density altitude calculation.