# Deformable Terrain

## Contents

# Deformable Terrain with ODE Friction VTI

Aside from the deformation parameters, the ODE model requires at minimum a base friction value and rolling resistance value defined on the ODE Surface.

# Deformable Terrain with Universal VTI

The Universal Vehicle Terrain Interaction(VTI) Model requires a slip/normalized force table for both lateral force and longitudinal force defined in JSON, as well as basic rolling resistance values. ANVEL includes a small set of examples for the Universal VTI Model, but those can be combined with users' data to create a more comprehensive data set.

# Pressure-Sinkage Models

For any of the VTI models in ANVEL, the deformation is controlled by a pressure-sinkage relationship that uses one of the following models.

The equation to use depends on the specific use case, but the Bekker, BG, and Upadhyaya parameters may be easier to collect. ANVEL supplies defaults built in for all of the surfaces, but they have not been thoroughly verified.

## Meirion-Griffith/Spenko (MGS) 2010

The Meirion-Griffith/Spenko (MGS) 2010 terrain model is applicable for small, rigid wheels.^{[1]}

Enumeration Value: 1

Parameters:

```
float32 k; //Constant pressure scale factor kPa/m
float32 n; //Sinkage exponent
float32 m; //Radius exponent
Pressure = 1000.0 * k * pow( sinkage, n ) * pow( radius * 2, m );
```

## MGS 2013

The MGS 2013 terrain model is an improved version of 2010 model with contact patch taken into account.^{[2]}

Enumeration Value: 2

Parameters:

```
float32 k; //Constant pressure scale factor
float32 n; //Sinkage exponent
float32 m; //Contact surface exponent
Pressure = 1000.0 * k * pow( sinkage, n ) * pow( wheelWidth* contactPatchLength, m );
```

## MGS 2014 (Dilative Soils)

The MGS 2014 terrain model is applicable to overconsolidated soils which takes an additional weighting factor based on wheel diameter to width ratio.^{[3]}

Enumeration Value: 3

Parameters:

```
float32 k; //Constant
float32 n; //Sinkage exponent
float32 m; //Diameter exponent
float32 a; // Diameter to width based weighting constant (0-1)
float32 Q; //Diameter to width based weighting constant exponent (0-1)
Pressure = 1000.0 * k * pow( sinkage, n ) * pow( radius * 2.0, m ) * pow(a, Q * ((radius*2.0) / wheelWidth) );
```

## Bekker-Wong

The Bekker-Wong terrain model is applicable for use with larger vehicles with moderate levels of sinkage.^{[4]}

Enumeration Value: 4

Parameters:

```
float32 n; //Sinkage exponent
float32 kc; //cohesion coefficient
float32 kPhi; //frictional coefficient
Pressure = 1000.0 * ( ( kv / (min(contactPatchLength, wheelWidth) + kPhi) * pow( sinkage, n);
```

## Bernstein-Goriatchkin

The Bernstein-Goriatchkin terrain model is the basis for most of the other equations.^{[5]}

Enumeration Value: 5

Parameters:

```
float32 k; //scale factor kPa/m
float32 n; //sinkage exponent
Pressure = 1000.0 * (k * pow( sinkage, n ));
```

## Upadhyay

The Upadhyay terrain model is a modified version of the Bekker equation.^{[6]}

Enumeration Value: 6

Parameters:

```
float32 k1;
float32 k2;
float32 n;
Pressure = 1000.0 * (k1 + k2 * wheelWidth) * pow( sinkage / wheelWidth, n );
```

- ↑ "A Modified Pressure-Sinkage Model for Small, Rigid Wheels on Deformable Terrains", Meirion-Griffith, Spenko 2010
- ↑ "A pressure-sinkage model for small-diameter wheels on compactive, deformable terrain", Meirion-Griffith, Spenko 2013
- ↑ "Development and experimental validation of an improved pressure-sinkage model for small-wheeled vehicles on dilative, deformable terrain", G. Meirion-Griffith, C. Nie, M. Spenko 2014
- ↑ "Theory of land locomotion", Bekker 1956
- ↑ Bernstein-Goriatchkin "Probleme zur experimentellen motorpflugmechanik", Der Motorwagen, 1913
- ↑ "Development of a portable instrument to measure soil properties relevant to traction.", Research Report, 1986