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 implementation 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.

All statements below are verified against the current source code (Physics/Source/LibHve/Dymesh.cpp, Physics/Source/Simon/PHYMODEL.CPP, Physics/Source/Simon/Road.cpp, Physics/Source/Simon/Tire.cpp, Physics/Source/Simon/suspension.cpp, Physics/Source/Simon/MATRIX.CPP).

Enabling the model¶

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

Level	Setting	Where	Code
Event	Use DyMESH	DyMESH Options dialog	`DyMeshIsTrue`
Event	Include Environment	DyMESH Options dialog	`DyMeshOptions.UseEnvironment`
Event	Environment start time reached	DyMESH Options dialog	`tSim >= tDymeshEnvMin` (`calcFloat[7]`)
Wheel	Wheel is Displaced	Set-up → Wheels → Damage tab	`IsDisplaced`
Wheel	Use DyMesh	Set-up → Wheels → Damage tab	`DyMeshWheelIsUsed[veh][axle][side]`
Wheel	Use DyMesh Environment	Set-up → Wheels → Damage tab	`DyMeshWheelEnvIsUsed[veh][axle][side]`
Wheel	Wheel damage start time reached	Set-up → Wheels → Damage tab	`tSim >= MovedWheelT[veh][axle][side]`

Notes:

If Include Environment is off, or the environment has no tessellated mesh (Environment.EnvironMesh empty), the environment start time is internally set to 1.0e8 s so environment contact never occurs (PHYINPUT.CPP, LoadSimControlData()).
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 (EvtWheelDisplacementPage.cpp).

The wheel as a DyMESH object¶

InitializeDyMeshWheels() and calcWheelMesh() (Dymesh.cpp) build one mesh per selected wheel:

Object table. DyMESH object indices 0..NumVehicles-1 are the vehicles, index NumVehicles is the environment (EnvironIndex), and indices NumVehicles+1... are the wheels (WheelIndex). Each wheel keeps a stable index DyMeshWheelNdx[veh][axle][side].
Geometry. A closed cylinder with NUM_DYMESH_WHEEL_INC = 80 angular slices: 6·80 + 2 = 482 vertices and 12·80 = 960 triangles. From the hub outward: two hub-center vertices, two rim disk rings at the rim radius (parsed from the tire size designation), two near-rim rings at (wheelRad + 4·0.98·tireRad)/5, and two tread-edge rings at 0.98·tireRad, where tireRad is the tire static loaded radius (tireSLR). Dual tires are modeled as one wide cylinder (width = tireWidth + TireSpace).
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	`tireRad/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. GetRestitutionCoef() (Dymesh.cpp) selects the vs.-environment value whenever the contact partner is the environment. Friction for any wheel contact is a fixed 0.75 in GetFrictionCoef(); the environment material's friction is not used for wheels.

The environment as a DyMESH object¶

The GUI tessellates the environment geometry into Environment.EnvironMesh (HVEINV-64/EnvironMesh.cpp); DyMeshInitialize() copies its vertices and faces into the EnvironIndex mesh slot, with per-vertex A/B stiffness taken from the environment surface materials.
The environment is immutable: it never deforms, and ReboundDamagedVerts() 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 in UpdateVehicleExtents(), +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 (Daux() in PHYMODEL.CPP) treats the environment as the last collision partner of every vehicle:

Proximity test. CollisionTest(i, j) builds bounding spheres — one for the sprung mass and one per active DyMESH wheel — and marks WheelInterference[veh][axle][side] for each wheel sphere that touches the partner.
Body contact. DyMesh(vehicle, environment) runs for the sprung-mass mesh.
Wheel contact. DyMeshWheels() loops over the interfering wheels that pass the enable and time gates. For each wheel:
GetWheelMatrices() forms the wheel's transform from its vehicle-fixed center WheelCoord, camber Gamma, spin -Omega, and steer Delta, plus their rates — the mesh physically spins, so vertex velocities include tread surface speed and friction acts in the correct direction.
UpdateWheelMesh() places the (damaged and undamaged) wheel mesh in vehicle space.
DyMesh(environment, wheel) runs the standard DyMESH contact algorithm (contact search, penetration, node force F = (A + B·δ + C·δ² + D·δ³)·area, restitution, friction), with two wheel-specific rules:
- a blown tire's stiffness multiplier is applied to the wheel mesh (ReDefineVertStiffness());
- 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 (SlaveNodeForce(), Dymesh.cpp). Longitudinal and lateral forces still come from every vertex, so a rim striking a curb face pushes back horizontally.
AddWheelForceToSprungMass() accumulates the wheel force into FsumColWheel[veh][axle][side].
UpdateWheelMeshDamage() maps the deformed mesh back into wheel space (persisting damage across steps) and sums the wheel-fixed force and the camber/spin/steer moments; it also records the largest vertex movement, MaxContactDispl.
DyMeshWheelDispl() applies the permanent wheel displacement/bending model (see the Version 3 chapter); displacement is horizontal (x, y) only, since vertical wheel motion is a suspension degree of freedom.
Smoothing. SmoothCollisionForce() averages each wheel's force and moment with the previous step's values (two-point moving average). The smoothed previous vertical force, FsumColWheelPrev[..][2], 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 (`FsumCol`)
Wheel collision Mz (yaw)	Directly onto the sprung mass (`TsumCol`)
Wheel collision Fz	Into the unsprung-mass equation of motion (`MATRIX.CPP`), i.e., through the suspension
Spin moment (My′)	Into the wheel-spin equation as a collision torque (`TORQUE.CPP`)
Camber / steer moments	Permanent camber/steer change via `DyMeshWheelDispl()`
Permanent x/y displacement	Added to `WheelCoord` each step (`WHEELPOS.CPP`), with solid-axle side coupling

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

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 code therefore hands authority from one model to the other in three coordinated pieces, all gated on DyMeshWheelEnvIsUsed && tSim >= tDymeshEnvMin && tSim >= MovedWheelT.

1. Tire deflection rate limiting (`TireDefl()`, `Road.cpp`)¶

The point-contact model computes the radial deflection trh 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 trh is limited per timestep:

trh may not exceed TireDeltPrev + TireDelt (last step's deflection plus the tire's secondary-stiffness breakpoint deflection);
if the tire carried no deflection on the previous step, trh 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 (`TireDefl()`, `Road.cpp`)¶

After the radial force TireFr is computed, it is blended with the DyMESH result using three reference quantities:

PrevFzDyMESH — the previous step's smoothed DyMESH vertical wheel force (−FsumColWheelPrev[..][2]), divided by the number of tires at the wheel;
TestWt — the static load carried at that wheel (static suspension force minus wheel weight, and minus half the solid-axle mass where applicable);
TestWt2 — 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	`PrevFzDyMESH + TireFr`
Tire force below DyMESH force, at/above static load	`PrevFzDyMESH + TestWt`
Tire force ≥ DyMESH force, DyMESH force ≥ static load	`PrevFzDyMESH + min(TestWt, TestWt2)`
Tire force ≥ DyMESH force, DyMESH force < static load (and > 0)	`PrevFzDyMESH + min(TestWt, TireFr)`
Deflection > 15% of tire radius while DyMESH is carrying load	`min(TireFr, PrevFzDyMESH)`, or 0 if DyMESH force ≤ 0

The intent in every branch 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 (trh = TireFr/Kt, 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 (`Tire()`, `Tire.cpp`)¶

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 cos(GammaGround) < MIN_INCLINATION (inclination beyond ≈80°). For a DyMESH environment wheel they are instead faded smoothly: each of TireFxp, TireFyp, TireFzp, the plough forces, slips, and the roll moment is scaled by

factor = 2 / ( cos(GammaGround)/MIN_INCLINATION + MIN_INCLINATION/cos(GammaGround) )

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 (FsumColWheelOut) and wheel-fixed moments (SumWheelMomentOut) 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 (rim and tread values) under tireDyMeshWheelStiffA/B (PHYINPUT.CPP).

Quick reference¶

Constant / parameter	Value / source	Meaning
`NUM_DYMESH_WHEEL_INC`	80	Angular slices 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
`MIN_INCLINATION`	0.17365 (cos ≈ 80°)	Shear-fade threshold
Environment depth padding	60–120 in	Prevents ghosting through flat terrain
Environment start time	DyMESH Options (`calcFloat[7]`)	Earliest wheel/body vs. environment contact