gta 307 minimum horizontal radius (rev.02)

Global Transport AtlasSeries 3 - Comparative Geometrics

307 Minimum horizontal radius (Revision .05)

GTA series 3 / 307 rev. 05 January 2016 Page 307 / 1

What it is

There are different types of minimum horizontal radius. These include:

1. Minimum radius whilst maintaining normal (negative) crossfall (= adverse camber)

2. Minimum radius to avoid need for transition curves

3. Minimum radius where superelevation equals normal crossfall

4. Minimum radius for an upper limit of superelevation

5. Minimum radius for aesthetics

This note refers to the minimum radius for an upper limit of superelevation.

These minimum values are usually associated with circular curves. There are other types of horizontal curve.

The conventional theory

The most accepted theory relates the horizontal radius to speed, superelevation and side friction. It imagines

a vehicle travelling along a curve on an inclined slope. It assumes that the horizontal element of the

centrifugal force equals the resisting force provided by friction at the road surface between the vehicle tyres

and the road. The formula is:

R = V2 / 127 * (e + f)

Easa and Dabbour (Ref. 1643) say this is one type of vehicle stability model, and call it the "point-mass" (PM)

model.

Where the conventional theory is applied

This formula can be found in reference works from a number of countries, such as the UK (168 / 1986), the

USA (ref. 831 /2011), Nigeria (ref. 1505 / 2013), and New Zealand (80 / 2003), Ecuador (1746 / 2013), and

e.g. for bikeways in USA ((ref. 1919).

Parameter Symbol Units

R horizontal radius metres

Vspeed (usually, design

speed)km/hr

e superelevation metres / m

f lateral friction (no units)

307 - Minimum horizontal radius for maximum superelevation


Global Transport Atlas

Series 3- Comparative Geometrics

row country year ref.no. e 40 50 60 70 80 90 100 110 120 note

a Switzerland 1991 732 7% 45 75 120 175 240 320 420 525 650

b Multi-country 2010 1887 7% 34 53 91 148 219 319 414 des. min.

c Multi-country 2010 1887 7% 30 47 71 102 153 236 342 abs. min.

d Argentina 2010 1860 6% 210 290 395 515 645 785 935 1095 1270 des. min.

e Germany 2008 1615 6% 280 370 470 720 900

f UK 1974 167 7% 130 230 350 510 min.

g UK 1974 167 7% 120 150 300 normal

Radius and vehicle type:

h Multi-country 2002 1968 7% 70 116 181 258 363 trucks

i Multi-country 2014 2182 6% 41 73 bicycles

e = superelevation

Row a, Swiss values taken as benchmark values

Row b, c: from Austroads

Row e: usage factor 0.4

Row f: for rural roads

Row g: for urban roads

Row h: desirable minimum for trucks

Some values for minimum horizontal radius

Notes

DISCUSSION

The following sections cover:

Where the conventional theory is modified

Where the conventional theory may be weak

Alternative theories

Health warning

Comment

References

Cover note and disclaimer

History and change log for this note


GTA series 3 / 307 rev. 05 January 2016 07 / 3



Permitted degree of use

In Germany (e.g. ref. 1615) a "permitted degree of use" factor is applied to values for side friction. This factor

varies with road type.

Desirable and minimum values

The Austroads multi-country standard (ref. 1887) refers to desirable and absolute minimum values, which

are calculated from values of desirable and maximum side friction.

In Argentina (ref. 1860) the theory is modified in the sense that it refers to four different values for minimum

radius:

Rmin (abs) - absolute minimum radius, where e, f are at their maximum values and V is guideline speed

Rmin (des) - desirable minimum radius where e, is at maximum value, f is zero and V := VMM (average

free flow speed)

Rmin (BR) - minimum radius with crossfall removed (e+f = 0,02 - I assume f is zero - and V := VMM)

Rmin (BN) - minimum radius with normal crossfall (e+f = 0,015 and V is guideline speed

Permitted values of side friction and superelevation

Countries often have different ideas about which values of lateral friction and superelevation are to be used in

design (and so in the conventional formula).

Steep downgrades

Austroads (ref. 1887) says that "On steep downgrades there is a greater chance of some drivers tending to

overdrive horizontal curves. Therefore, the minimum curve radius .... should be increased by 10% for each 1%

increase in grade over 3%, (using a particular formula)

Road type

Some countries provide separate recommendations for regional, urban and rural roads. For urban roads for

example, permitted superelevation is often lower than for other roads.

Consideration of comfort

Austroads says that "the desirable maximum values (for side friction) should be used on intermediate and

high-speed roads with uniform traffic flow, on which drivers are not tolerant of discomfort” and that “In ....

mountainous terrain, drivers are more tolerant of discomfort. This permits the absolute maximum values of

side friction to be safely used in the design of horizontal curves".

Type of terrain

Same comment as above under "considerations of comfort"

Type of vehicle

Side friction varies with type of vehicle ( see e.g. table 2.6 in ref. 80). Speed limits (and therefore perhaps

design speed) also vary with type of vehicle.

Type of road surface

Where the conventional theory is modified





Side friction (and so horizontal radius) also varies with type of road surface, see(again). table 2.6 in ref. 80.

Also AASHTO 2011 (ref. 831) says that friction values for gravel surfaces are less than those for paved

surfaces, and gives a chart which shows minimum radius and superelevation for gravel-surfaced roads.

Where the minimum radius is measured

Ref. 831 says (e.g.) that “For consistency with the radius defined for turning roadways and to consider the

motorist operating within the innermost travel lane, the radius used to design horizontal curves should be

measured to the inside edge of the innermost travel lane, particularly for wide roadways with sharp

horizontal curvature"

Aesthetics

Ref. 1887 says:

“In flat terrain, aesthetics may be improved if curves of double the minimum length are provided.

Some road authorities specify that curves on more important two-lane roads should be at least 120 –

150 m long, but curves on mountain roads may be as short as 30 m. On divided roads of high standard,

curves less than 300 m long look too short”.

Where the conventional theory may be weak

The conventional theory may be wrong

In this context, E. Hauer (ref. 765; 1999) says "it is by now clear that there is no premeditated connection

between the reality of crash occurrence on horizontal curves and the procedure used for their design". On the

use of design speed as a parameter, a 1994 paper from the Dutch SWOV Institute (ref. 264) says "Regarding

especially the safety at bends, one could say that the definition of a minimal radius depending on the design

speed is both insufficient and unnecessarily constraining".

The values used to develop horizontal radius may be out of date

Some guidelines use side friction values which are 40 years old or more. For example, Asea and Dabbour

note that "The required increase in minimum radius presented in this paper is based on current design

values of side friction. These values were developed for passenger cars many years ago and should be revised

to account for the characteristics of modern passenger cars and trucks"

The explanation of what is being offered may be misleading

Users of design standards have to be vary careful in how they understand the suggested values. For example

Austroads (ref. 1887) table 7.5 refers to "minimum radius of horizontal curves..." - but these may only be

minimum radius for cars (and not, for example, for trucks)

Other weaknesses

The conventional theory does not work or may be misused:

On low-speed roads, where the vehicle geometrics become a limiting factor

For trucks, where high loads can lead to a higher risk of overturning than of side slipping

On three-dimensional roads, where (for example) a combination of gradient and superelevation can lead

to excessive crossfall (note: all roads are three-dimensional objects).





On all roads where the design values are calculated for cars and where the roads are also used by other

types of vehicle

On unsurfaced and gravel-surfaced roads, where the design values are calculated for asphalt surfaced

roads

Vehicles may follow a sharper alignment than the curve radius

In "Safer Curves on Multiple Lane Roads" (Ref. 1996) , Johan Granlund points out that vehicles do not

always follow the alignment of a curved road, but often change lanes at the same time, and here "when

shifting lane quickly, the vehicle experience a transient “curve radius” much sharper than indicated by the

road curve radius".

The conventional theory only applies to cars and not (e.g.) to trucks

In "Lowered crash risk with banked curves designed for heavy trucks" , (Ref.1997) Mr. Granlund and his

co-authors conclude that (amongst other points) :

For roads where same speed limits apply for both passenger cars and HGV´s, (....) the need for road

superelevation is given by HGV’s rather than by cars. Hence road design codes should use models of

HGV´s rather than of passenger cars.

A conclusion was that the traditional point-mass “car model” can underestimate the superelevation

needed for safe HGV operations.

The position of design control lines can vary, even within one road design project

(Ref. 2133) says that "The horizontal and vertical elements of a road are described in terms of control lines.

Control lines are lines mathematically defined in the horizontal and vertical planes”. The blog post (link 1)

argues that, if you break the location of vertical, superelevation and horizontal (radius) control lines you are

perhaps breaking the theory behind road design, with the possibility that in practice one or other design

parameter will be below minimum requirements.

Different standards may refer to different measures of speed.

For example, both (Ref. 1088, SIECA 2004) and (Ref. 1887 Austroads, 2010) have tables for speed and

minimum horizontal radius - but (Ref. 1088 table 4.10) refers to design speed whereas (1887) refers to

operating speed. Perhaps the theory behind the two tables is different, but at least it makes any comparison

of the values of minimum radius a bit doubtful.

Some engineers apply different design speeds for vertical and horizontal alignment design for

the same section of road

Wolhuter (Ref. 2247) in his discussion on vertical alignment, quotes Transit New Zealand to say that:

“It is good design practice to make the vertical alignment design speed 10 to 15 km/h greater than the

horizontal alignment design speed to provide an additional safety margin (Transit New Zealand,

2002)”





Alternative theories

Bicycle model

Easa and Dabbour (Ref. 1643) describe two other vehicle stability models. One, the "bicycle model" adds

consideration of front and rear tyres (and so two different side friction factors.

Vehicle dynamics model

The second, a vehicle dynamics model from the University of Michigan, " accurately simulates a vehicle

traveling through a user-defined alignment, taking into account vehicle characteristics such as body roll,

pitch, yaw, and lateral weight distribution".

3D design approach

The same authors recommend a 3D approach. In their concluding remarks they say that "current geometric

design guides do not account for 3-D alignments in the calculation of the required minimum radius for

horizontal curves".

A recent paper by Amiridis and Psarianos on 3D road design (ref. 2271) includes an extensive list of

references on 3D design.

Rate of change of acceleration

Kilinc and Taybura (ref. 810 / 1999) describe a method for calculating minimum horizontal radius based on

the limiting values of rate of change of acceleration ("jerk").

Vehicle geometry

On roads with low design speeds, the physical limitations of the road vehicle can be the deciding factor in

determining minimum radius. For example (ref. 80) has a table which gives minimum design radius for

different types of design vehicle.

Risk of vehicles overturning

For example, on motorway slip roads with quite small radius curves and inclined vertical alignment the

minimum radius may be determined by calculation of the risk of high vehicles overturning.

Australia (or rather, Austroads) practice says that (ref. 1968):

"Trucks have a higher centre of gravity than cars. Consequently, the limiting condition for trucks

negotiating a circular curve tends to be rollover rather than skidding".

Austroads then developed a method of calculating horizontal radius for trucks which is based on a measure of

truck rollover which they call "static roll threshold".

Maximum level of centrifugal acceleration

(Ref. 1038) says that “British design practice is based on the fundamental assumption that at absolute

minimum radius the 99th percentile vehicle should not experience more than the maximum level of

centrifugal acceleration acceptable for comfort and safety. This was established at about 0.22 some 70 years

ago and has not been changed since”

….And that centrifugal acceleration is given by : v2 / R where

Parameter Symbol Units

R horizontal radius metres

vspeed (usually, design

speed)m/sec





Health warning

Users have to be vary careful in how they understand the suggested values in any particular standard.

Preferably, each standard should attach a health warning to its suggested values, along the lines of:

“The values for minimum horizontal radius quoted in these guidelines are for cars driving on wet

regional roads in level terrain and with an asphalt or concrete surface, for the quoted values of

superelevation and side friction, and with the usual secondary provisos (car brakes and tyres in good

condition, 90th %ile driver etc.).

The values do not apply to exceptional circumstances; for example, they do not apply to roads which

are on steep gradients, or on structures. They do not apply to three-dimensional roads, to other types

of vehicle, or to other types of road surface (e.g. gravel or high-friction).

It is not sure what the relationship is betwen these values for minimum radius and road safety.

It is also not sure what the relationship is between the historical values for side friction used in

calculating the minimum radius, and the values which might be found today with modern cars, tyres

and road surfaces. In particular the values do not apply to roads with high friction surfaces.”

Comment

The use of different terms for what might be the same thing can lead to confusion. For example the

references have terms such as: normal, desirable, minimum, desirable minimum and absolute minimum.

They could be reduced in number and carefully defined or explained.

It seems likely that collecting the values for minimum horizontal radius quoted in different design standards

provides a set of results which is both over-complicated and over-simple. Over-complicated in the sense that

there should be no need for what appears to be a wide range of values in different countries. For example,

only a few values are used for maximum superelevation, and for similar road surfaces and vehicle types there

need probably only be one set of friction values. And over-simplified in that design standards usually only

refer to cars and surfaced roads.

In a tech blog post on the simplification of standards (see here) I wrote:

1. Standards should be prepared on a modular basis, with each module describing a specific parameter

2. There should be one main document for each parameter, with -"modifications" notes issued by

responsible authorities where they feel local circumstances are different

3. Standards should not be duplicated

4. Standards should be related to climate and terrain conditions rather than to administrative boundaries

5. Each module should provide details in terms of the primary influencer, design speed

6. Each module should include comments and / or values in terms of the main secondary influencers, such

as

Road type

Vehicle type

Road surface

Terrain

Climate





80 - New Zealand, shgdm-part-2 Basic design criteria, Transit, 2003

167 - UK, Hobbs, “Traffic planning and engineering” Pergammon Press, 1974

168- UK, O’Flaherty, Traffic planning and engineering; Edward Arnold, 1986

732 - Switzerland, “VSS 640-080 Projektierung, Grundlagen; VSS, 1991

765 - Canada, Ezra Hauer, “Safety in geometric design standards”, 1999

810 - Turkey, Ahmet Sami KILINÇ and Tamer BAYBURA, “Determination of Minimum Horizontal Curve

Radius”; FIG Working Week, 2012

831 - USA, “A policy on the geometric design of highways and streets”; AASHTO, 2011

1038 - UK, C.A. O’Flaherty, “Transport planning and traffic engineering”; Elsevier, 2006

1088 - Multi-country, “Manual Centroamericano De Normas Para El Diseño Geométrico De Las Carreteras

Regionales; SIECA, 2004

1505 - Nigeria, Highway manual part 1 Design / vol. I: geometric design; Federal Ministry of Works, 2013

1615 - Germany, RAA Richtlinien für die Anlage von Autobahnen; fgsv, 2008

1643 - Canada, Easa and Dabbour, “Design radius requirements for simple horizontal curves on 3D

alignments”; Can. J. Civ. Eng.30: 1022–1033, 2003

1746 - Ecuador, NEVI 12 volume 2A norma para estudios y disenos viales ; MTOP, 2013

1860 - Argentina, Normas y Recomendaciones de Diseño Geométrico y Seguridad Vial; DNV, 2010

1887 - multi-country / Austroads, AGRD part 3: Geometric design; Austroads, 2010

1968 - multi-country / Austroads, “Geometric design for trucks - when, where and how?”; Austroads, 2002

1996 - Sweden, Granlund, "Safer Curves on Multiple Lane Roads," Transport Research Arena Europe 2010

1997 - Sweden/Norway, Granlund, Haskanes and Ibrahim, "Lowered crash risk with banked curves designed

for heavy trucks"; HVTT13, San Luis, Argentina, 2014

2133 - Canada, "Geometric Design Manual Part 2", Middlesex County, Ontario, Canada, 2015 (?)

2182 - Multi-country / Austroads, “Cycling aspects of Austroads guides”, Austroads 2014

2271 - Greece, Amiridis and Psarianos, “Three dimensional road design by applying differential geometry and

conventional design approach criteria”, Mathematical Design & Technical Aesthetics, ISSN 2310-2179

(Online) Volume 3, Issue 1 (2015)

Links

Blog post 1 https://comparativegeometrics.wordpress.com/2015/10/01/road-geometric-design-control-

lines/

Blog post 2 https://comparativegeometrics.wordpress.com/2015/11/14/simplification-of-standards-3/

References





Cover notes and Disclaimer

This is a research document. The best efforts have been made to make sure the figures are correct. However no liability

can be taken for any of the details, information or analysis in this document.

The layout, look and feel of this document is copyright.

The photos are generally copyright of REB.

This work is licensed under the Creative Commons Attribution-NoDerivs 3.0 Unported License. To view a copy of this

license, visit http://creativecommons.org/licenses/by-nd/3.0/

History and Change log for this note

First version published December 2014.

Rev. 05 (January 2016) - Added notes on different measures of speed and different speeds for horizontal and vertical

design. Added row h to values table. Modified layout. Added extra note and reference on 3D road design.

Rev. 04 -/-

Rev. 03 (November 2015) - Added note about control lines

Rev. 02 (February 2015) - Added notes on papers by Johan Granlund et al (refs. 1996, 1997).

Contact

We welcome comments on this paper, and also on new

developments in other countries in this field.

Email: [email protected]

Web: http://comparativegeometrics.wordpress.com/

About the contributor

Robert Bartlett, Germany - is an experienced

transportation and urban development studies engineer

with over 25 years of professional experience. Current

engineering work: includes technical research in highway

design standards and applications in areas such as urban

planning and highway engineering. Interests include

applied GIS.

gta 307 minimum horizontal radius (rev.02)

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