DyMESH Wheel vs. Environment¶

This chapter describes the wheel vs. environment extension of the DyMESH Wheels collision model: each selected wheel's cylindrical mesh collides with the environment (terrain) mesh as a full DyMESH contact pair. Wheel-to-curb strikes, ditch impacts, and ground contact during rollover are then computed by the DyMESH contact algorithm rather than by the point-contact tire model alone, which loses validity at large camber angles and large radial deflections.

Because the tire is now touching the ground through two models at once — the classic radial-spring tire model and the DyMESH wheel mesh — the model includes an explicit handoff between the two so the ground force is not double-counted. That handoff is described in detail in The handoff between the tire model and DyMESH, which is the heart of this chapter.

The description below reflects the behavior of the current version of HVE.

Enabling the model¶

Wheel vs. environment contact runs for a given wheel only when all of the following are true:

Level	Setting	Where
Event	Use DyMESH	DyMESH Options dialog
Event	Include Environment	DyMESH Options dialog
Event	Environment start time reached	DyMESH Options dialog
Wheel	Wheel is Displaced	Set-up → Wheels → Damage tab
Wheel	Use DyMesh	Set-up → Wheels → Damage tab
Wheel	Use DyMesh Environment	Set-up → Wheels → Damage tab
Wheel	Wheel damage start time reached	Set-up → Wheels → Damage tab

Notes:

If Include Environment is off, or the environment has no tessellated mesh, wheel-environment contact never occurs.
With Auto Start checked on the Damage tab, the wheel participates immediately; with an explicit start time the wheel joins the collision model only after that time.
The Use DyMesh Environment checkbox is enabled in the dialog only when the wheel is displaced, DyMESH is on, Use DyMesh is checked, and the event's Include Environment is on.

The wheel as a DyMESH object¶

During initialization one mesh is built per selected wheel:

Object list. The DyMESH objects are ordered vehicles first, then the environment, then the wheels. Each selected wheel keeps a stable object index for the whole run.
Geometry. A closed cylinder with 80 angular slices: \(6\times80 + 2 = 482\) vertices and \(12\times80 = 960\) triangles. From the hub outward: two hub-center vertices, two rim disk rings at the rim radius \(r_\mathrm{rim}\) (parsed from the tire size designation), two near-rim rings at \(r_\mathrm{near} = \left[\,r_\mathrm{rim} + 4\,(0.98\,r_\mathrm{tire})\,\right]/5\) — that is, four-fifths of the way out from the rim radius to the tread radius — and two tread-edge rings at \(0.98\,r_\mathrm{tire}\), where \(r_\mathrm{tire}\) is the tire static loaded radius. Dual tires are modeled as one wide cylinder whose width is the tire width plus the dual-tire spacing.
Vertex materials. Each vertex carries an A (constant) and B (linear) stiffness, a friction coefficient, two restitution coefficients, and a saturation deflection:

Region	B stiffness	Friction	Restitution vs. vehicle	Restitution vs. environment	Saturation
Hub / rim disks	Wheel Displacement Rate ÷ wheel disc area	0.55	0.05	0.05	wheel width
Near-rim rings	average of rim and tread stiffness	0.75	0.05	0.05	wheel width
Tread ring	tire Initial Ride Rate ÷ contact-patch area	0.75	0.05	1.00	static loaded radius ÷ 4

Restitution here controls permanent deformation: a coefficient of 1.0 springs the vertex fully back each step (elastic), while 0.05 retains ~95% of the crush (plastic). Against the environment the tread is therefore fully elastic — the tire does not accumulate crush from ground contact — while the rim deforms permanently, as a real wheel does. The vs.-environment restitution value is selected automatically whenever the contact partner is the environment. Friction for any wheel contact is a fixed 0.75 for the tread and near-rim vertices (0.55 for the rim disks); the environment material's own friction value is not used for wheels.

The environment as a DyMESH object¶

The GUI tessellates the environment geometry into an environment mesh; at initialization its vertices and faces are copied into the environment object slot, with per-vertex A/B stiffness taken from the environment surface materials.
The environment is immutable: it never deforms, and the rebound (unloading) pass skips it entirely.
A flat terrain is treated as a solid block of earth, not a thin shell: its bounding extents are padded downward — 60 in when the object extents are updated, and 120 in in the polygon-search bounding boxes — so a wheel cannot pass through a zero-thickness ground plane between timesteps.

The simulation loop¶

Each derivative evaluation of the vehicle dynamics model treats the environment as the last collision partner of every vehicle, in this order:

Proximity test. Bounding spheres are built — one for the sprung mass and one per active DyMESH wheel — and each wheel sphere that touches the partner is flagged as interfering.
Body contact. The standard DyMESH contact runs for the sprung-mass mesh against the environment.
Wheel contact. The wheel loop runs over the interfering wheels that pass the enable and time gates. For each wheel:
The wheel's transform is formed from its vehicle-fixed center position, camber angle, spin angle (the negative of the accumulated wheel rotation), and steer angle, plus their rates — the mesh physically spins, so vertex velocities include tread surface speed and friction acts in the correct direction.
The damaged and undamaged wheel meshes are placed in vehicle space.
The standard DyMESH contact algorithm is run between the environment and the wheel mesh (contact search, penetration, node force \(F = \left(A + B\,\delta + C\,\delta^{2} + D\,\delta^{3}\right) A_v\), restitution, friction), with two wheel-specific rules:
- a blown tire's stiffness multiplier is applied to the wheel mesh;
- hub, rim, and near-rim vertices produce no vertical force — their earth-fixed z force component is zeroed, so only the tread ring carries vertical load. Longitudinal and lateral forces still come from every vertex, so a rim striking a curb face pushes back horizontally.
The resulting wheel force is accumulated into the vehicle's wheel collision force totals.
The deformed mesh is mapped back into wheel space (persisting damage across steps) and the wheel-fixed force and the camber/spin/steer moments are summed. The largest movement of any wheel-mesh vertex during the step — the maximum wheel-mesh contact movement — is also recorded.
The permanent wheel displacement/bending model is applied, capped by that contact movement (see the Version 3 chapter); displacement is horizontal (x, y) only, since vertical wheel motion is a suspension degree of freedom.
Smoothing. Each wheel's force and moment is averaged with the previous step's values (two-point moving average). The smoothed previous vertical force is what the tire-model handoff (below) reads.

Force paths into the vehicle dynamics¶

Quantity	Path
Wheel collision Fx, Fy	Directly onto the sprung mass
Wheel collision Mz (yaw)	Directly onto the sprung mass
Wheel collision Fz	Into the unsprung-mass equation of motion, i.e., through the suspension
Spin moment (My′)	Into the wheel-spin equation as a collision torque
Camber / steer moments	Permanent camber/steer change via the wheel displacement model
Permanent x/y displacement	Added to the wheel's vehicle-fixed center position each step, with solid-axle side coupling

Because collision loads can legitimately exceed the normal suspension limits, the excessive-deflection, excessive-velocity, and excessive-force suspension error stops are suppressed for DyMESH wheels, as is the excessive-tire-deflection stop in the tire/terrain model.

The handoff between the tire model and DyMESH¶

With wheel vs. environment active, the same tire touches the ground through two models. Left uncorrected, the radial-spring tire force and the DyMESH tread force would both push the vehicle up and the total would be roughly double the correct load. The model therefore hands authority from one model to the other in three coordinated pieces, all gated on the wheel having Use DyMesh Environment selected and on both the event's environment start time and the wheel's damage start time having been reached.

1. Tire deflection rate limiting¶

The point-contact model computes the radial tire deflection \(\delta_\mathrm{tire}\) geometrically from the terrain under the wheel center. During a hard vertical event (curb face, ditch wall, rollover touchdown) that geometric deflection can jump in a single timestep. When the wheel is a DyMESH environment wheel, the growth of \(\delta_\mathrm{tire}\) is limited per timestep:

\(\delta_\mathrm{tire}\) may not exceed last step's deflection plus the tire's secondary-stiffness breakpoint deflection;
if the tire carried no deflection on the previous step, \(\delta_\mathrm{tire}\) is forced to zero — a suddenly deep penetration produces no point-contact force at all, and the DyMESH wheel mesh carries the impact instead.

The tire radius used by the rest of the tire model is recomputed from the limited deflection, keeping the two models geometrically consistent.

2. Vertical force blending¶

After the radial tire force \(F_\mathrm{tire}\) is computed, it is blended with the DyMESH result using three reference quantities:

\(F_\mathrm{DyMESH}\) — the previous step's smoothed DyMESH vertical wheel force (taken with the sign convention that upward ground reaction is positive), divided by the number of tires at the wheel;
\(W_\mathrm{static}\) — the static load carried at that wheel (static suspension force minus wheel weight, and minus half the solid-axle mass where applicable);
\(F_\mathrm{spring}\) — last step's deflection times the current radial stiffness (the force the tire spring "should" be carrying).

The blend then works case by case:

Case	Resulting radial force
Tire force below both the DyMESH force and static load	\(F_\mathrm{DyMESH} + F_\mathrm{tire}\)
Tire force below DyMESH force, at/above static load	\(F_\mathrm{DyMESH} + W_\mathrm{static}\)
Tire force ≥ DyMESH force, DyMESH force ≥ static load	\(F_\mathrm{DyMESH} + \min(W_\mathrm{static}, F_\mathrm{spring})\)
Tire force ≥ DyMESH force, DyMESH force < static load (and > 0)	\(F_\mathrm{DyMESH} + \min(W_\mathrm{static}, F_\mathrm{tire})\)
Deflection > 15% of tire radius while DyMESH is carrying load	\(\min(F_\mathrm{tire}, F_\mathrm{DyMESH})\), or 0 if the DyMESH force ≤ 0

The intent in every case is the same: the DyMESH force is authoritative, and the point-contact tire model contributes at most its static share on top of it. In quiet rolling (DyMESH force ≈ 0) the ladder reduces to the ordinary tire force; in a hard strike the DyMESH force dominates and the tire spring is prevented from stacking a second full reaction on top.

Two additional rules close the loop:

beyond the maximum roll angle the radial tire force is zeroed entirely — the DyMESH mesh is then the only ground contact;
the final blended force is converted back into an equivalent deflection, \(\delta_\mathrm{tire} = F_\mathrm{tire}/K_t\) using the radial tire stiffness \(K_t\), capped at the tire's maximum deflection, so that outputs and the next step's rate limiter see a consistent state.

3. Shear-force fade near rollover¶

The friction-circle tire model produces Fx/Fy from slip at the contact patch — meaningless once the wheel plane approaches the ground plane. For a non-DyMESH wheel, tire forces are simply zeroed when the cosine of the wheel-to-ground inclination angle \(\gamma_g\) falls below the minimum-inclination threshold \(c_\mathrm{min} = 0.17365\) (inclination beyond ≈80°). For a DyMESH environment wheel they are instead faded smoothly: each of the contact-patch forces \(F_x\), \(F_y\) and \(F_z\), the plough forces, the slips, and the roll moment is scaled by

\[ f = \frac{2}{\dfrac{\cos\gamma_g}{c_\mathrm{min}} + \dfrac{c_\mathrm{min}}{\cos\gamma_g}} \qquad (\text{Eq. 1}) \]

which equals 1.0 exactly at the threshold and falls toward 0 as the tire goes flat. This avoids the force discontinuity of the hard cutoff while the DyMESH tread/rim contact takes over the shear loads through its own friction model.

Summary of the handoff¶

Regime	Ground normal force	Ground shear force
Normal rolling	Tire model (DyMESH ≈ 0)	Tire model
Curb/obstacle strike	DyMESH tread force + capped tire share	Tire model + DyMESH friction
Near/at rollover (>~80° inclination)	DyMESH tread force (tire force faded/zeroed)	DyMESH friction (tire forces faded)

Outputs¶

The per-wheel collision impulses (Fx Imp, Fy Imp, Fz Imp, Mx Imp, My Imp, Mz Imp) appear in the Key Results output, and the smoothed wheel collision forces and wheel-fixed moments drive the Output vs. Time wheel channels.
The program-data output tables list each DyMESH wheel's mesh size and its first/last vertex A and B stiffnesses (the rim and tread values).

Quick reference¶

Parameter	Value / source	Meaning
Angular slices	80	Angular increments in the wheel mesh
Wheel mesh size	482 verts / 960 triangles	Per wheel
Tread radius	0.98 × static loaded radius	Outer ring radius
Tread restitution vs. environment	1.0	Fully elastic (no permanent tire crush)
Rim restitution	0.05	Plastic (permanent rim deformation)
Wheel contact friction	0.75 (tread/near-rim), 0.55 (rim disks)	Fixed values
Rim B stiffness	Displacement Rate ÷ wheel disc area	From Damage tab
Tread B stiffness	Initial Ride Rate ÷ contact-patch area	From tire data
Minimum-inclination threshold	0.17365 (cos ≈ 80°)	Shear-fade threshold
Environment depth padding	60–120 in	Prevents ghosting through flat terrain
Environment start time	DyMESH Options dialog	Earliest wheel/body vs. environment contact

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