SRT CalculatorSRT Calculator

Certifiers’ and Users’ Course

Course Outline (morning)Course Outline (morning)

Regulating Size and Weight Stability related Performance Measures Derivation of SRT Calculator Basic Use of SRT Calculator Test on Basic Use of the Calculator

Course Outline (afternoon)Course Outline (afternoon)

SRT Calculator – Advanced Topics in Loading

SRT Calculator – Advanced Topics in Suspensions

Review

Advanced Users Test

Dimensions and Mass Rules – Dimensions and Mass Rules – Why?Why?

To promote safety Stability Manouevrability Fit on the road

To protect the infrastructure Road damage Bridge damage Fit on the road

Dimensions and Mass Rules – Dimensions and Mass Rules – How?How?

Prescriptive Limits Maximum or minimum mass values Maximum or minimum dimensions

Specify what a vehicle must look like rather than what it needs to be able to do

Prescriptive Limits Prescriptive Limits ProsPros

Simple to regulate Easy to enforce Relatively straightforward

compliance Relatively low cost Usually unambiguous

Prescriptive Limits Prescriptive Limits ConsCons

Not directly linked to the safety or infrastructure protection outcome that is intended

Less safe vehicles may still be legal

Cumbersome – lots of rules

Relatively inflexible

Inhibits innovation

Performance Based StandardsPerformance Based Standards

Performance Standard = Performance Measure + Acceptance Level

Performance Measure - Some quantity that is measured (or calculated) during a specified set of test conditions.

Acceptance Level – Minimum or maximum level required to pass. This may vary with operating environment

Specify what a vehicle must be able to do rather than what it must look like

Performance Based StandardsPerformance Based StandardsExamplesExamples

Basic concept is not new

Braking requirements – Stopping distance from 30km/h or a dry sealed surface shall be less than 7m

Turning circle requirements – a vehicle must be able to complete a 360° turn inside a 25m wall-to wall circle

Performance Based StandardsPerformance Based StandardsProsPros

Directly related to the factors that are to be controlled

Allow for innovation and flexibility in vehicle design

Improve industry understanding of vehicle factors that contribute to safety

Performance Based StandardsPerformance Based StandardsConsCons

More complicated and expensive to assess for compliance

More complex to regulate

Risk of reducing safety by encouraging vehicles to the minimum standard

Risk that the set of PBS is not complete

Performance Measures for Performance Measures for Stability and SafetyStability and Safety

RTAC Study in 1980s to characterise the Canadian HV fleet

Range of measures relating to stability and safety Static Roll Threshold (SRT) Dynamic Load Transfer Ratio (DLTR) Rearward Amplification (RA) Yaw Damping Ratio (YDR) High Speed Transient Offtracking (HSTO) High Speed Steady Offtracking (HSO) Low Speed Offtracking (LSO)

Rollover Related PMsRollover Related PMs

SRT – steady speed cornering Maximum lateral acceleration that a

vehicle can withstand before wheel liftoff

DLTR – evasive manouevre stability Load transfer from one side of the

vehicle to the other during a high speed lane change

Fleet Distribution of SRTFleet Distribution of SRT

SRT Distribution of Fleet

0

5

10

15

20

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1

Static Roll Threshold (g)

Per

cen

t

Crashed Vehicles Crashed Vehicles Distribution of SRTDistribution of SRT

SRT Distribution of Crashed Vehicles

0

5

10

15

20

25

30

35

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1

Static Roll Threshold (g)

Per

cen

t

Relative Crash Rate as a Relative Crash Rate as a Function of SRTFunction of SRT

Relative Crash Rate vs SRT

0

1

2

3

4

5

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

Static Roll Threshold (g)

Re

lati

ve

Cra

sh

Ra

te

SRT ConclusionsSRT Conclusions

Fleet distribution bi-modal

15% fleet have SRT < 0.35g

40% crashed vehicles have SRT < 0.35g

Improving performance of the worst vehicles will have a significant impact on crash rates

Fleet Distribution of DLTRFleet Distribution of DLTR

DLTR Distribution of the Fleet

0

2

4

6

8

10

12

14

16

18

0.05 0.15 0.25 0.35 0.45 0.55 0.65

DLTR

Crashed Vehicles Crashed Vehicles Distribution of DLTRDistribution of DLTR

DLTR Distribution of Crashed Vehicles

0

5

10

15

20

25

30

0.1 0.2 0.3 0.4 0.5 0.6 0.7

DLTR

Relative Crash Rate as a Relative Crash Rate as a Function of DLTRFunction of DLTR

Relative crash rate vs DLTR

0

0.5

1

1.5

2

2.5

3

3.5

0.1 0.2 0.3 0.4 0.5 0.6 0.7

DLTR ConclusionsDLTR Conclusions Fleet distribution tri-modal

increase in crash rate for DLTR > 0.7

limited evidence for significant effect of crash rate for lower DLTR

Note that DLTR and SRT are not independent

Levels for PBSLevels for PBS SRT

From crash data 0.4g-0.45g is desirable Internationally 0.35g minimum is widely

suggested Higher targets affect too many vehicles

and have too big an effect on productivity DLTR

Internationally 0.6 maximum has been suggested but some debate

From crash data 0.67 approximately equivalent effect to 035g SRT in New Zealand

Potential Impact on Crash RatePotential Impact on Crash Rate

15% of vehicles below 0.35g SRT involved in 40% of rollover crashes

Reducing their crash rate to the average could reduce rollover crashes by more than 25%

SRT and DLTR are related. Improving one will improve the other

SRT CalculatorSRT CalculatorDerivation and ValidationDerivation and Validation

Static Roll Threshold (SRT)

Maximum lateral acceleration that a vehicle can withstand during steady speed cornering before the wheels on one side lift off.

Static Roll Threshold DeterminationStatic Roll Threshold Determination

Experimentally through a tilt-table test

Analytically by computer simulation

SRT Calculator

Tilt-Table TestTilt-Table Test

Pros No vehicle

instrumentation req’d No vehicle parameters

req’dCons

Facility cost Testing cost

Accuracy depends on good test procedures

SRT by Computer SimulationSRT by Computer Simulation

Pros Cheaper than physical testing No instrumentation or measurements

required

Cons Detailed vehicle parameters needed Too costly for routine use Skilled analysts required to ensure

accuracy

2D Model – Horizontal Forces2D Model – Horizontal Forces

2D Model – Vertical Forces2D Model – Vertical Forces

Simple 2D Rollover ModelSimple 2D Rollover Model

2H

T SRT

Solving force and moment balance equations gives a simple equation for SRT

2D Model Complications2D Model Complications

Roll angle, , is the result of all the compliances in the vehicle. It is not simple to determine

Two ends of the vehicle are not necessarily the same. Need to consider the interaction between them

Graphical MethodGraphical Method(Winkler et al)(Winkler et al)

Graphical Method with Lash Graphical Method with Lash (Winkler et al)(Winkler et al)

SRT Calculator SRT Calculator Basic Assumptions Basic Assumptions

Applied to a single vehicle unit with no more than two axle groups

Two axle groups are connected by a rigid body i.e. chassis flex is not taken into account

Suspension stiffnesses are approximated as linear i.e. constant rate but suspension lash is taken into account

SRT Calculator SRT Calculator Basic Method Basic Method

Develop equations for graphical method (see Schedule 1 in Dimensions and Mass Rule 41001)

Equations are piecewise linear. Solve for transition points, checking for validity.

SRT is maximum lateral acceleration for which a valid solution exists.

Vehicle Parameters in Equations Vehicle Parameters in Equations

Sprung mass by axle group and Cg height Unsprung mass by axle group and Cg height Tyre vertical stiffness Tyre track width Suspension vertical stiffness Suspension roll stiffness Suspension track width Suspension roll centre height Suspension lash

SRT Calculator Software SRT Calculator Software SpecificationsSpecifications

User inputs known or easily obtained

Web-based software

Three versions Public – on internet Level 1 Certifier – generates

compliance certificates for relatively standard vehicles

Level 2 Certifier – generates compliance certificates

SRT Calculator ImplementationSRT Calculator Implementation

Aim to minimise user data input requirements but maintain enough flexibility to represent key vehicle parameters accurately enough

Assumptions on default parameter values are conservative so that actual SRT will be at least as high as calculator result

Calculator Implementation -Calculator Implementation -continuedcontinued

Vehicle width is assumed to be 2.5m – tyre track width is back-calculated from tyre size and configuration

Generic tyre properties based on size and configuration are used

Standard axle and wheel masses for each vehicle type are assumed

Empty sprung mass Cg height is assumed based on vehicle type

Generic suspension parameters are embedded so that in many cases actual data are not needed

Calculator ValidationCalculator Validation

Tilt table test on a 4-axle trailer

Comparison with results from Yaw-Roll simulations for a selection of vehicles

Validation resultsValidation resultsTilt-table testsTilt-table tests

Tilt table test* Yaw Roll Computer simulation

SRT Calculator Generic steel suspension

SRT Calculator User-defined suspension

0.418 ± 0.006

0.428 0.407 0.415

Validation resultsValidation resultsGeneric SuspensionsGeneric Suspensions

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

YAW ROLL Calculated SRT

Cal

cula

tor

SR

T -

Gen

eric

sus

pens

ion

Validation results Validation results User-Defined SuspensionsUser-Defined Suspensions

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

YAW ROLL Calculated SRT

Cal

cula

tor

SR

T -

Use

r de

fined

sus

pens

ion

Rollover ExampleRollover Example

SRT Requirements in Rule 41001SRT Requirements in Rule 41001

Principle of Safety at Reasonable Cost

SRT level 0.35g

All heavy vehicles of Class NC and Class TD have to comply except for those on the exempt list

SRT Requirements in Rule 41001SRT Requirements in Rule 41001ContinuedContinued

Distinction between compliance and certification

All vehicles listed above must comply

Only vehicles of Class TD with a load height greater than 2.8m need to be certified

Using the SRT CalculatorUsing the SRT CalculatorBasicsBasics

Start the calculator either On the internet at the LTSA site

www.ltsa.govt.nz/srt-calculator Or for certifiers from the Start

menu or the desktop icon – SRT Calculator

Vehicle Type ChoiceVehicle Type Choice

Affects default no of axles and tyre configurations but these can be changed

Affects axle mass values and empty sprung mass Cg height which are embedded values

For a semi-trailer only the rear bogey is analysed and it is treated as if it were an independent vehicle (like a simple trailer)

No of AxlesNo of Axles

Choosing a vehicle type inserts a default number of front and rear axles. These should be changed if necessary

Some basic error checking is done. Eg a semi-trailer must have zero front axles

Main Data Entry PageMain Data Entry Page

Schematic showing vehicle type and axle configuration selected. If wrong go back.

Data entry boxes have pop-up help on labels (not functioning on Netscape 4)

Main Data Entry Page - TyresMain Data Entry Page - Tyres

For each axle tyre size and configuration should be selected

Selection affects unsprung mass (standard wheel masses) value and Cg height

Selection determines track width

Calculator does not allow for the effects of low profile tyres as they are not significant

Main Data Entry Page – Main Data Entry Page – Axle LoadsAxle Loads

For each axle group, gross mass and tare mass must be entered

Calculator automatically calculates payload mass and total mass as numbers are entered

Payloads and totals are not correct until all data have been entered

Main Data Entry Page – Main Data Entry Page – Axle Loads continuedAxle Loads continued

Tare mass values should come from a weighbridge docket or from the manufacturer

The gross mass should be based on either the current RUC value or a higher value specified by the operator

Gross mass should not be the vehicle GVM unless requested by the operator

Distribution of gross mass between axle groups is normally in proportion to the axle group load limits

Main Data Entry Page – Main Data Entry Page – Load CategoriesLoad Categories

This is used to determine the payload Cg height

Mixed Freight – Assumes 70% of load mass is in bottom half of load space and 30% in the top half

Uniform Density – Assumes the payload Cg is at the vertical midpoint of the load space. Expects the load space to be symmetric about a horizontal axis.

Other – Requires the user to calculate the vertical position of the payload Cg. This option is not available to level 1 certifiers

Main Data Entry Page – Main Data Entry Page – Load GeometryLoad Geometry

For load types Mixed and Uniform, the load bed and load height are used to calculate the payload Cg Implicit assumption that the values are

constant along the vehicle but Sloping decks/roofs – use values at

longitudinal midpoint (level 1 certifier) Step decks – can use a weighted

average of values based on load mass carried at each level (level 2 certifier)

Anything more complex use load category “Other” (level 2 certifier)

Main Data Entry Page – Main Data Entry Page – Load Geometry cont’dLoad Geometry cont’d

For load type Other the payload Cg height must be calculated by the user and entered explicitly A load height value must also be

entered but this is only for inclusion on the certificate. It is not used in the calculations

Main Data Entry Page – Main Data Entry Page – Suspension DataSuspension Data

Suspension type selection “generic” suspension data come from

reported measurement results and are at the compliant end of the spectrum, i.e. resultant SRT will be lower

“user defined” requires the user to input suspension parameters. These data must be obtained from the supplier or by measurement and documentary support should be kept.

The “user defined” option is not available to level 1 certifiers

Main Data Entry Page – Main Data Entry Page – Suspension Data cont’dSuspension Data cont’d

Suspension track width and lash can be easily measured

Values can be entered for both “generic” and “user defined” suspension types

NB: Lash is the movement at the axle not at the spring hanger

Ensure correct units are used

Main Data Entry Page – Main Data Entry Page – Suspension Data cont’dSuspension Data cont’d

“Generic” displays the embedded suspension parameter values. These cannot be changed by the user

Two types of generic air suspension Low roll stiffness type High roll stiffness type

High roll stiffness type uses the axle as an anti-roll bar. This requires that: Suspension has beam axle(s) Trailing arms are rigidly connected to the

beam axle(s) If in doubt assume low roll stiffness type

High roll stiffness type High roll stiffness type air suspensionair suspension

Main Data Entry Page – Main Data Entry Page – Suspension Data for User definedSuspension Data for User defined

“User defined” requires suspension parameters to be entered.

Care is required to ensure: Correct units Roll stiffness is per axle Spring stiffness is per spring

assuming two springs per axle Roll centre height is measured

from the axle centre with +ve upwards

Main Data Entry Page – Main Data Entry Page – Calculate SRTCalculate SRT

Some error checking is done on data entry but most is done when calculation is initiated

Masses are limited to a maximum Vehicle Axle Index of 1.1.

All input data is checked against upper and lower limits

Equation solver assumes small roll angles (<20°) and this is checked

If SRT is less than 0.35g, the calculator determines the reduced load height or reduced mass needed to achieve 0.35g

SRT Results SRT Results

Calculated SRT is shown

If below 0.35g reduced mass and reduced height to pass is shown

Can use “back” button to return, modify inputs and recalculate or

Certifiers can login to generate certificate

SRT Greater than 0.35gSRT Greater than 0.35g

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5 10 15 20 25 30 35

Gross Mass (tonnes)

Lo

ad

He

igh

t (m

)SRT = 0.35g

SRT Less than 0.35gSRT Less than 0.35g

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5 10 15 20 25 30 35

Gross Mass (tonnes)

Lo

ad

He

igh

t (m

)SRT = 0.35g

Certificate Pages Certificate Pages

After login certificate data page Info required for certificate – has no

effect on calculations Certifier details embedded in

personalized copy of software “Generate Certificate” button creates

a certificate in a format suitable for A4 printing

Certificate includes all input data and hence can be used to replicate results

Attach SRT Cert to LT 400

Advanced topics in loading Advanced topics in loading Removable bodiesRemovable bodies

Eg stock-crates Option 1: Consider body as part of

payload Option 2: Consider body as part of tare

mass With load category “Other” option 1 is best Otherwise need to consider overall effect.

Empty sprung mass Cg is assumed to be 0.56m above axle centre for a truck and 1.25m above the axle centre for a trailer. Which option is more realistic?

Advanced topics in loading Advanced topics in loading Sloping Load Beds Sloping Load Beds

Determine longitudinal position of Cg

Measure (or calculate) load bed height and load height at this location

Advanced topics in loading Advanced topics in loading Variable height decks Variable height decks

Load bed height = Weighted average of the different heights using the proportion of payload mass carried as the weighting

Alternatively can use load category “Other” and calculate the Cg of the payload explicitly

Advanced topics in loading Advanced topics in loading No horizontal axis of symmetryNo horizontal axis of symmetry

Use load category “Other” and calculate payload Cg height

Advanced topics in loading Advanced topics in loading Unit LoadsUnit Loads

Use load category “Other” and calculate payload Cg height Use worst case typical load Possible approaches include:

Obtain Cg heights from equipment suppliers Obtain maximum cross-slope capabilityfrom suppliers and calculate

Cg height

Advanced topics in suspensions Advanced topics in suspensions

Generic suspensionsGeneric suspensions

Parameter values derived from UMTRI factbook and based on measurements but do not represent any actual suspension

Parameters selected to be at the more compliant end of the spectrum and thus give conservative estimates of SRT

Provision for users to enter measured values for suspension track width and axle lash

Generic Total Roll StiffnessGeneric Total Roll Stiffness

Generic steer axle 130000 Nm/radian

Generic steel 520000 Nm/radian

Generic air (high stiffness) 780000 NM/radian

Generic air (low stiffness) 280000 NM/radian

Composite Roll Stiffness

100

300

500

700

900

1100

Co

mp

os

ite

Ro

ll S

tiff

ne

ss

(0

00

s N

m/r

ad

ian

)

Air suspensions (high roll stif fness type)

Air suspensions (low roll stif fness type)

Walking beam suspensions

4-spring suspensions

Front suspensions

Single axle leafspring suspensions

Generic Suspension Vertical StiffnessGeneric Suspension Vertical Stiffness

Generic steer axle 185000 N/m

Generic steel 1000000 N/m

Generic air 350000 N/m

Vertical Spring Stiffness

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Sp

rin

g S

tiff

ne

ss

(0

00

s N

/m)

Air suspensions

Walking beam suspensions

4-spring suspensions

Front suspensions

Single axle leafspring suspensions

Generic Roll Centre HeightsGeneric Roll Centre Heights

These are from the ground

Standard wheel approx 0.5m radius

Generic steer axle 0.48m

Generic steel 0.7m

Generic air 0.7m

Roll Centre Height above Ground

Air suspensions

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

Ro

ll c

en

tre

he

igh

t (m

)

4-spring suspensions

Single axle leaf spring suspensions

Walking beam suspensions

Front suspensions

Advanced topics in suspensions Advanced topics in suspensions

User defined suspensionsUser defined suspensions Must enter suspension make and model for

traceability Three key parameters needed

Composite roll stiffness Spring vertical stiffness Roll centre height

To determine these requires sophisticated measurement techniques and analysis

Thus the key data must be provided by the suspension supplier who must take responsibility for its accuracy and validity

User defined suspensionsUser defined suspensionsConversions Conversions

Composite roll stiffness = auxiliary roll stiffness + roll stiffness from springs

Any two of the above (with spring track width) can be used to calculate the third

th track widsuspension the t and

stiffness spring the k where2

.tk Springs from Stiffness Roll

s

2s

User defined suspensionsUser defined suspensionsConversions continuedConversions continued

For steel suspensions (with no anti-roll bar) auxiliary roll stiffness is usually relatively small (5-10% of total)

For low roll stiffness air suspensions (trailing arms bushed on axle or no beam axle), the auxiliary roll stiffness is also relatively small

For high roll stiffness air suspensions (trailing arms rigidly clamped or welded to the axle), the auxiliary roll stiffness is high (80% or more of the total roll stiffness)

Composite Roll Stiffness Composite Roll Stiffness

Input value is per axle assuming all axles in the group of equal stiffness

Manufacturer value may be per axle group. If this is the case, halve the value for a tandem and one-third it for a tridem.

Roll stiffness is required in Nm/radian. It may be supplied in in-lb/degree. To convert multiply by 6.47

Input value is per radian. Supplied data may be per degree. Make sure and convert if necessary.

Spring Stiffness Spring Stiffness

Input value is per spring assuming two springs/axle and all springs of equal stiffness

For one spring/axle suspensions (eg “camelback” type) halve the spring stiffness values

For unequal stiffness springs, average the spring stiffness. If unequal load share, use load share weightings to calculate weighted average

Vertical stiffness is required in N/m. It may be provided in lb/in. To convert multiply by 175.13

Roll Centre Height Roll Centre Height

Input value measured from axle centre not the ground, i.e. independent of tyre size.

Influenced by all linkages in suspension

Determination by measurement is quite complex

Advanced topics in suspensions Advanced topics in suspensions Effects of Parameter ChangesEffects of Parameter Changes

Increased roll stiffness improves SRT

If roll stiffness (relative to load) differs between ends of vehicle, increasing the stiffness of the softer one has more effect

Large axle lash values have a negative impact on SRT

Higher roll centres lead to a better SRT

Improvements of the order of 10-15% are possible with suspension improvements