IS 12793 (2012): Motorcycles — Measurment Method for ...

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IS 12793 (2012): Motorcycles — Measurment Method forLocation of Centre of Gravity [TED 4: Automotive BrakingSystems]

IS 12793 : 1989

w&T mm

Indian Standard

AUTOMOTIVE VEHICLES - TWO WHEELERS, CENTRE OF GRAVITY - METHOD OF

DETERMINATION

UDC 629’118’3 : 531’24

@ BIS 1991

BUREAU OF INDIAN STANDARDS MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

Mfzrch 1991 i

Price Group 2

--

Automotive Vehicle Testing and Performance Evaluation Sectional Committee, TED 008

FOREWORD

This Indian Standard was adopted by the Bureau of Indian Standards on 18 August 1989, after the draft finalized by the Automotive Vehicle Testing and Performance Evaluation Sectional Committee had been approved by the Transport Engineering Division Council.

IS 12793:1989

Indian Standard

AUTOMOTIVE VEHICLES - TWO WHEELERS, CENTRE OF GRAVITY - METHOD OF

DETERMINATION I SCOPE

1.1 This Indian Standard specifies the method for determining the position and height of centre of gravity ( C.G. ) of two wheeled vehicles like mopeds, motorcycles, scooters, etc.

2 TERMS AND DEFINITIONS

For the purpose of this Indian Standard following terms and definitions shall apply,

2.1 Position of Centre of Gravity

The position of centre of gravity on a horizontal plane shall be defined on the longitudinal axis and on the transverse axis as follows ( see Fig. 1 ).

2.1.1 Position of centre of gravity along the longitudinal axis is defined as the least distance of centre of gravity in mm from the transverse vertical plane passing through the centre of the front wheel of the test vehicle. This is represented by ‘X’ in Fig. 1.

2.1.2 Position of centre of gravity along transverse axis of the vehicle is defined as the least distance of centre of a gravity in mm from a longitudinal median plane passing through the longi- tudinal centre lme of the two wheeler. rThe position of centre of gravity may be on left or right hand side of the lonaitudinal vertical olane with reference to driver when seated in driving seat. This is represented buy ‘Y’ in Fig. 1. A

2.2 Height of Centre of Gravity

It is the height of centre of gravity in mm from the supporting surface, when the vehicle on a plain level horizontal surface. This is represented by ‘2’ in Fig. 1.

is placed

VERTICAL PLANE PASSING

\

THROUGH LONGITUDINAL CENTRE OF THE VEHICLE

HORIZONTAL PLAN THROUGH CENTRE 0

2 = Height of C.G. from ground level X = Distance of C.G. from front axle along longitudinal axis

Y = Distance of C.G. from centre line along transverse axis

FIG. 1 CENTRE OF GRAVITY FOR Two WHEELER

1

IS 12793 : 1989

3 MATHEMATICAL EXPRESSION FOR LOCATING THE POSITION AND HEIGHT OF CENTRE OF GRAVITY

The following abbreviations have been used while deriving the formulae for determining the position and height of centre of gravity for two wheelers:

Ml = mass on front wheel ( kg ), w, = mass on rear wheel ( kg ), W = vehicle kerb weight ( kg ), W3 = front wheel loading when rear wheel has been lifted ( kg ), L = wheel base ( mm ), X = distance of C.G. along the longitudinal axis of the vehicle from the centre of the front

wheel ( mm > ( see 2.1.1 ), Y = distance of C.G. along the transverse axis of the vehicle towards left hand side or right

hand side from the longitudinal axis of the vehicle ( mm ) ( see 2.1.2 ), 2 = height of C.G. on vertical axis from the ground level ( mm ) ( see 2.2 ),

r1 = rolling radius of front wheel ( mm ),

r3 = rolling radius of rear wheel ( mm ), rl = rz = r ( when radius of two wheels is equal ), and V = height of lift of rear wheel of the vehicle from the ground level ( mm ).

3.1 Position of C.G. Along Longitudinal Axis of Test Vehicle ( X ) from Centre of Front Wheel

FIG. 2 POSITRON OF CENTRE OF GRAVITY

Taking moments about A,

wx= W,L

x- w235

W

. . . (i)

3.2 Position of C.G. on Transverse Axis of Test Vehicle ( Y )

The exact location of C.G. on transverse axis may not be practically found out because of the fact that it is not feasible in practice to measure the near side and off side weight of the two wheeler separately. However, to a great degree of approximation, the same may be considered to be situated on the longitudinal axis of the test vehicle for all practical purposes ( that is Y = 0 ).

3.3 Height of C.G. on Vertical Axis of Test Vehicle ( Z)

The height of a two wheeled vehicle can be experimentally determined by weighing the loads coming on different wheels when any one of the two wheels is resting on the platform of weigh- bridge and other on+ the resting on same level but away from the platform and is lifted through certain height ‘Y’ from ground level.

Let ‘Wa’ be the load coming on front wheel after the rear wheel has been lifted through ‘Y’ and ‘R’ be the reaction at rear wheel after lifting.

R=W-W3

Taking moments about the point K

2

R.(c+d)=W.C c+d=KF=Lcos(@++) AB = Z = centre of gravity of the vehicle from the ground.

when # is small AB coincides with AD. KE= x.c0s(e+4)

AD =AB-DB

f r--r, ) DB=r,+ t .X

IS 12793 : 1989

. ..(i)

AD = Z - [r, -I- ” ( --I) .x

iYD=AD&(B-l-(G) L 1

= Z- t t

rl + ( h--r1 1 x L * II sin ( 0 + * )

=Z.sin(f?+cL)- rl+(rz~rl).X . sin ( e + 4 )

c=KM==KE-ME =KE-HD

= X . cos ( e + 4 ) - [ Z. sin ( 0 + 94 ) - {rl + ( r2Lr1 ). X sin ( e-4 ) I]

c+d=KF= L. cos ( e -t * 1

Substituting ( ii ) and ( iii ) in ( i )

= x . cos ( e + * ) - Z . sin ( 0 + 3 ) + (rl + ( r2Lr’ ) . X 1. sin ( e+ I) ) . . . (ii)

. ..(iii)

FIG. 3 HEIGHT OF CENTRE OF GRAVITY ON VERTICAL AXIS

~.L.cos(~++)=~. X.cos(e+~)--Z.sill(e-TV)+ C

+ r1 + ( “LY1 ) . X } . sin ( sin ( e + 4 > ] dividing both sides by [ W . sin(e+#)l

R .~.COt(8+$)=X,cot(8fYI) __2+ rl+k-)‘l).X IT L 1

or (R.L.X) ______ W .cOt(e+~)~-z+[r,+(_‘TLr’!.X]

3

IS 12793 :1989

or cot(8+(I)+rl+ ( r2 - r1 1

L .X

KF cot ( 6 + !b ) = FJ

z=r1+ (r2L*1) *X + X- c (

~___

If both tyres are of same size having ‘r’ as rolling radius ( r,” = rl = r ) then

Z=r+ X- C

NOTE _ When the vehicle is lifted on the front Oi th: rear whesl the static rolling radicls may hive different values due to the different weight distribution in tilted pXition complred to th: h>rizJ;ltsl position. The effect of this may be ignored.

4 TEST PROCEDURE

4.1 After the vehicle has been prepared according to 4, the following procedure shall be followed for determining the position and height of C.G. of a two wheeled vehicle:

a)

b) d d)

e)

f)

!a

The front and rear wheel loading of the test vehicle shall be measured separately on a weighbridge. These loadings shall be denoted by WI and W, respectively.

The kerb weight of the test vehicle shall be measured and denoted by W.

The wheel base shall be measured and denoted by ‘L’.

The static rolling radius of the wheel of the test vehicle shall be measured and denoted by

rl and r2.

The test vehicle shall be positioned on the platform of the weighbridge in such a way that the front wheel remains on the weighbridge platform whereas the rear wheel remains outside on the same level.

The rear wheel of the vehicle which is outside the weighing platform, shall be lifted slowly by a crane so that the angle through which the vehicle is tilted does not exceed lo” ( Approx )- Note the front wheel loading on the weighbridge in the lifted position. Denote this by W,.

4.2 The position and height of centre of gravity of test vehicle can be worked out from the following formulae:

i> Position of C.G. along longitudinal axis from thecentre of front wheel

ii) Position of C.G. along transverse axis ( Y) from the longitudinal axis of test vehicle is O- ( zero ).

iii) Height of C.G. along vertical axis = B ( if both tyres are of same size )

B = r -!- ( x_ (W;W3)+ JF1_‘”

if the rolling radius of front and rear wheels are rl and r2 respectively.

4

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2. .-* ,._ ._ ,_ _______”

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Dot : No. TED 008 ( 4962 )

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