# VeSyMA Sign Convention

Sign Conventions, for variables with a positive and negative direction, are common place in the engineering world. VeSyMA is no different, with many commonly used variables adhering to a sign convention. Most of the time, VeSyMA follows the ISO (International Organisation for Standardisation) standard for a variable or quantity where possible. However, ISO standards do not cover all the variables you might encounter when using VeSyMA based vehicle simulations. This post builds on a previous one regarding vehicle coordinate systems.

Here is a list of the most commonly encountered signed variables found in VeSyMA, with their sign convention explained.

Banking: Relative to the forward direction of the road. Banking where the driver’s left side of the road is lower than the right, regardless of turn direction is positive.

Example: Run the function termed “Banking test example” in the text file available for download.

Gradient: Slope of the road, defined as vertical elevation per unit distance. A value of >0 denotes the road is rising as the vehicle drives; a value <0 indicates the road elevation is dropping per forward movement along the road centerline.

Example: Run the function termed “Gradient test example” in the text file available for download.

## Vehicle parameter sign convention

Pitch: Depends upon the vehicle coordinate system. VeSyMA standard is ISO, where vehicle nose down/rear up is considered positive. For both supported non-standard coordinate systems, BRU and SAE (FRD), the opposite (nose up/rear down) is positive.

Example: Run Suspensions.Experiments.OpenLoop.Braking and look at the pitch value as the nose dives.

Roll: Follows the ISO convention by default, so driver’s left up/right down is positive. SAE (FRD) follows the same convention. BRU is opposite (driver’s left down/right up considered positive roll).

Example: Run Suspensions.Experiments.OpenLoop.JTurn, looking at the value of roll as the vehicle completes the left and right hand portions of the test.

Yaw: Like pitch and roll, yaw follows the right hand screw rule. Therefore by default in VeSyMA, vehicle rotation to driver’s left (anti-clockwise in vehicle plan view) is considered positive yaw. Same applies for BRU. SAE (FRD) by virtue of inverting the direction of the z (vertical) axis, leads to a positive yaw value opposite to ISO/BRU.

Example: Suspensions.Experiments.OpenLoop.SteeringRamp puts the vehicle in extended yaw.

Toe: Defined relative to the vehicle, in VeSyMA a wheel where the front is pointing towards the vehicle has a positive toe angle, otherwise known as toe-in. If the wheel is pointing away from the vehicle, the angle will be negative; this is toe-out.

Example: One of the library examples is configured with toe sensors. Run Suspensions.Experiments.PathFollowing.CurvedAndSlopedRoadRearSteer and compare the left and right values as the car turns.

Camber: If the top of the tyre points away the vehicle centerline, then the camber angle is positive. Conversely, negative camber where the top of the tyre is tilted towards the vehicle has a negative angle.

Example: This example is configured with sensors including camber. Run Suspensions.Experiments.PathFollowing.CurvedAndSlopedRoadRearSteer and compare the left and right values as the car turns. Also see VeSyMA.UserGuide.TyreConventions.

Lateral acceleration/velocity: Physically speaking. this denotes the acceleration and velocity towards the centre of the arc the vehicle moves through. Numerically, this follows the coordinate system of the vehicle (ISO by default) convention. Therefore, positive lateral acceleration/speed are associated with left hand turns.

Example: Run Suspensions.Experiments.PathFollowing.DoubleLaneChange, observing how the sign changes as the vehicle turns to the left and the right.

Longitudinal acceleration/velocity: In the same vein as lateral acceleration/velocity, the longitudinal equivalent in VeSyMA follows the direction defined by the vehicle coordinate system. As ISO has the longitudinal axis positive forward, positive acceleration/speed are associated with acceleration increasing the forward velocity of the vehicle.

Example: The test Suspensions.Experiments.OpenLoop.Acceleration provides the best place to observe longitudinal velocity and acceleration as the car accelerates.

Aerodynamic forces: Both drag and downforce are applied with the ISO convention. Intuitively, this means a drag force is negative; downforce is also negative, owing to acting in the opposite direction of the positive ISO z. Handily, this is also consistent with its definition as negative lift.

Example: Use Suspensions.Experiments.OpenLoop.Acceleration to watch the aerodynamic forces build as the vehicle gains velocity.

Pedal travel: Signals from the driver are normalised. A value of 1 means the pedal is depressed, with 0 denoting no input.

Example: Suspensions.Experiments.OpenLoop.Acceleration begins with the driver model on the brake before fully depressing the accelerator pedal.

Steering wheel rotation/torque: Clockwise torque and angle are positive values.

Example: Run Suspensions.Experiments.OpenLoop.SteeringRamp and observe the increasing wheel angle and torque noting their direciton.

## General mechanical sign convention

Shaft rotation: Following the right hand screw rule, positive rotation is defined as anti-clockwise around direction of the positive axis.

Example: Use Suspensions.Experiments.OpenLoop.Acceleration and look at the driveshaft rotations.

## Closing remarks

Like any software package, VeSyMA has its own sign conventions for various quantities. Most of the time, the ISO value is used. Hopefully the quantities listed here are of use in your projects!

Written by: Theodor Ensbury – Project Engineer

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