A Handling Quality Metric 
A Given: Instability is A Bad Thing Instability implies response is unbounded with time; in vehicle control terms, an uncommanded spin Spins not preferred because they may lead to tripped rollover by presenting the vehicle sideways to obstacles/terrain Four states possible for systems generally[1,2]: 

Asymptotic Stability Neutral Stability Divergent Instability Oscillatory Instability 

[1] Fundamentals of Vehicle Dynamics, Gillespie, p402 [2] The Multibody Systems Approach to Vehicle Dynamics, Blundell & Harty, p172 [3] Race Car Vehicle Dynamics, Milliken & Milliken, p245 

Understeer/Oversteer aSAE Understeer guarantees stability in absence of driver SAE Oversteer does not predFrom Fundamentals of Vehicle Dynamics, Gille

r Vehicle Dynamics, Milliken & Milliken, p245

Divergent Instability Better Surrogate for Tripped Roll

A Given: Instability is A Bad Thing

Handling Metric Context 
Lateral Acceleration Very Noisy Measurement noise very high on lugged tires with non-deformable terrain 

Polynomial Fit ArVehicle motion is the forces divided by reluto move (mass, inertiTires are often represcalled “Magic Formul

There is no good reapolynomial to the dat

[4] Newton’s 2nd Law 

[5] Tyre Modelling for Use in Vehicle Dynamics Pacejka

Discerning Turning Point Unsatisfactory Experime

L t l A l ti V

N

Measurement Noise 

Y X D C Bx E 

  sin arctan 

^ 

 

a ¬ 
The Fixed Steer Test Extremely repeatable and requires no special facilities other than a consistent surface Unlike constant radius test, it is not a test of the steering robot quality, driver skill, etc While not directly comparable to other tests (none are directly comparable with each other), will nevertheless expose a vehicle that seeks to spin (“divergent”)

Yaw Rate Gives CYaw rate is rotation vData not so susceptib(magenta) when comacceleration (green) Mount location insenreadings anywhere o

Fixed Steer is Repeatable, Driver-Independent and gives 

The Fixed Steer Test Ya

Another Possible Test Protocol 

D t t tib
Yaw Rate is Directly Connected to Lateral Acceler

A Geometric Connection 

“Non Spin” (aka No-Slip, Steady State) Yaw rate connects to Lateral Acceleration simplyA “geometric” vehicle will have a yaw rate which is identical to a neutral steer v[3] Race Car Vehicle Dynamics, Milliken & Milliken, p159 

U

δ

r

L

 
Visually a Strong Difference – No Filtering/Processing 

Divergent Spin Condition Instability is shown by a large cha(slope) of the plot for a small spe

vertical”

Detecting Divergence – Fixed Steer Results 

0.5g Hyperbola Measured 

Yaw Rate vs Vehicle Speed

Extrapolated line from on-center fit – 5 seconds after 2m/s (5 repeats) 

No Spin Condition Plotting yaw rate against vehicle speed will show its character compared to a “geometric” vehiclePlotting 0.5g*9.81ms-2/Vehicle Speed(ms-1) gives a “0.5g 

Hyperbola” to determine test end 

Convergent vehicles typically keep a “substantially constant” slope of yaw rate with speed 
• Divergent response – trace “becomes steep” 

below 0.5g Hyperbola – divergence obvious 

• Extremely convergent veh

horizontal 

• Both vehicles very consis

Proposed Test Shows Large Difference 

• Divergent response trace “becomes steep” becom Extremely convergen

200ft Fixed Steer – Divergent/Convergent 

Left Turn 

Right Turn 
• Shows loss of path follow

–

“path error” (vehicle is le

Shows Both Divergence and Path Error Plainl

Shows loss of path f f path o

200ft Fixed Steer – Divergent/Convergent 

• Note very large increase in yaw rate for 1mph 

speed change (~0.5 m/s) 

Left Turn 

Right Turn 
• Difference still clear - divergent configuration is 

obvious (vehicle tips onto outriggers on right turn) 

• Excellent repeatability always 

Robust against Test Radius 

• Difference still clear divergent configuration c is

50ft Fixed Steer – Divergent/Convergent 

• Convergence remains cle

0.5g hyperbola for 50ft dia

• Path following less compr

Left Turn 

Right Turn 
Numerically Robust With Typical Data (20 Vehicle S

Plot 5 repeats in each direction For each repeat 

Fit on-center slope Fit limit slope 

Average on-center slopes between repeats Average limit slopes between repeats Evaluate relationship of averaged limit slope to averaged on-center slope Pass-fail criterion? 

Ratio preferred over arithmetical difference 

–

less sensitive to radius 

Plot 5 repeats in each direc

tion

Suggested Detail - Provisional 

0.5g Hyp

Measured Yaw Rate vs Vehicle Speed 

Fitted line on-center 5 seconds of data beyond 2 m/s 
Divergent Response Stands Out in Blind, Automated P

Sample Metric 

– Fleet Review (40/50ft) 

• 200

everatio 

• 100

somtwo 

• 100

goobetwand 

• All v

exce

• Not 

und

01234
• Test end detection – characteristic goes 

through 0.55g hyperbola or significant deceleration 

Process Automates Well 

• Test end detection characteristic g ristic

Process Automation 

• Limit identification – 0.5

crossing or maximum inAcceleration (some veh0.5g) 

• Fit window controllable 

examples so far Test end autodetected 

W ll

examples so far
100ft Data Comparison Expand Vehicle set 

eg Historic 

Test robustness of processing Refine Pass/Fail criteria Formalize Process Receive Inputs from others 

Early Promise Needs Verification & Formalizati

100ft D t C

Next Steps 
Method developed on first principles/best-practices Better Surrogate for Tripped Rollover Risk Repeatable methods with minimal test errors Drives predictable vehicle handling designs Discriminates and identifies unpredictable behaviors 

Superior Alternative to Understeer Bias 

M th d d l

Summary 
• What other signatures can the data show? 

• Fails to reach 0.5g • Convergent oversteer 

Other Numerical Measures of Interest to Manufacturers a

• What other signatures can the data show?

Broad Picture of Vehicle 

• Lack of symmetry left-to-right 

“Club-like” thickening of data 

associated with tire saturation 
• Vehicle 1 

Appendix – Real Vehicle Data – 50ft 

• Vehicle 1

Appendix – Real Vehicle Data – 50ft 

• Vehicle 2 
• Vehicle 3 

Appendix – Real Vehicle Data – 50ft 

• Vehicle 3

Appendix – Real Vehicle Data – 50ft 

• Vehicle 4 
• Vehicle 5 

Appendix – Real Vehicle Data – 50ft 

• Vehicle 5

Appendix – Real Vehicle Data – 50ft 

• Vehicle 6 
• Vehicle 7 

Appendix – Real Vehicle Data – 50ft 

• Vehicle 7

Appendix – Real Vehicle Data – 50ft 

• Vehicle 8 
• Vehicle 9 

Appendix – Real Vehicle Data – 50ft 

• Vehicle 9

Appendix – Real Vehicle Data – 50ft 

• Vehicle 10 
• Vehicle 11 

Appendix – Real Vehicle Data – 50ft 

• Vehicle 11

Appendix – Real Vehicle Data – 50ft 

• Vehicle 12 
Appendix – Real Vehicle Data – 50ft 

Appendix – Real Vehicle Data – 50ft 

• Summary • Ratio and Delta measures 

(ratio plot shown) 

• All vehicles converge exc