COG, Center of gravity of a tractor and its determination methods.

1. Lecture
on
Centre of gravity of wheeled and track type tractors, implement
hitching and weight transfer and its calculation
By:
Er Kishan Kumar Patel
PhD 1 st year (FMPE)
ID: 20192893
SV COLLEGE OF AGRICULTURAL ENGINEERING AND TECHNOLOGY &
RESARCH STATION
INDIRA GANDHI KRISHI VISHWAVIDYALAYA, RAIPUR
2019-20

2. What is center of gravity?
Center of gravity
COG is a point at which the whole of the mass and the weight
of the tractor may be considered to act. its location depends on
the disposition of the various masses that comprise the tractor.
This is the point where all parts of the tractor balance. The
position of the centre of gravity changes of any implement as
add ,removed or changes position.

3. Where is the center of gravity located on a tractor?
Center of gravity of an object determines the stability of that object.
The center of gravity will always seek the lowest position possible
therefore must be taken when loading or hitching to prevent rollover

4. LOCATION OF CENTRE OF GRAVITY IN A TRACTOR

5. The typical tractor has its center of gravity located
between the front and rear wheels behind the midpoint
of the tractors length and above the axle height.

6. If tipping an object lowers the centre of gravity, the object will not return
to its original position.
Center of gravity of an object will always seek the lowest possible
position.
Effect of tilting

7. The external forces acting on a tractor pulling an important can be
quantified and analyzed.
An overturn resulting from the centre of gravity moving outside the
tipping axis.

8. 1. if hitch height is too high, the hitched tractor is not in
equilibrium.
2. hitching at a lower point or weighing the front of the
tractor can prevent unsafe rollover conditions from
occurring.
Hitch height is an important variable in stability-

9. Methods for determine COG
Through the point of suspension. if this
can be repeated using another point of
suspension , another vertical plane is
derived.
Suspension method-1
The point of inter section of these planes
is the centre of gravity of the tractor.
Tractor is initially suspended from a
point on, say the front axle using a crane
hoist taking care that front axle and rear
axle are horizontal, then the center of
gravity will be on the vertical plane
passing.

10.  if a tractor is suspended using ropes
or chain in such a way that one side
is longer than the other.
Suspension method-2
The intersection of the two vertical
planes got in that case gives the
location of the centre of gravity of the
tractor.
The tractor is suspended twice in
such a way that longer side is attached
to the rear axle and reverse in the
second case.

11. Balancing method
It is balanced on the block while
driving forward and then while driving
in the reverse.
The two vertical planes so got give
the location of the centre of gravity of
the track type tractor.
In this case, a large block of
wood of length equal to the overall
width of the tractor and height of
nearly 15 cm is used.
The balancing method can be used to
determine the location of center of
gravity of track type tractors.

12. Weighing method
The weighing method of finding the location of the center of gravity
can be used in the laboratories. A weighing scale can be used to measure
the total weight of tractor and reactions acting on the two wheels.
The weighing method of finding the center of gravity is easily applied.
A vertical plane containing the center of gravity can be determined by the
following equation:
If the front wheel of the tractor are raised a distance y2 and Rf´
determined, another plane containing the centre of gravity may be
obtained from the same equation

13. The intersection of these two planes will locate the centre of gravity G.
This location can be satisfactorily indicated by chalking the lines of the
planes on the side of the tractor.
It should be pointed out that x1´ can be determined approximately by:

14. Following parameters are measured before taking the tractor to a
weighing balance:
•Wheelbase of the tractor
•Radius of front and rear wheels
•Height of the centers of front and rear wheels from the ground
When on the weighing balance, the parameters noted are:
•Total weight of the tractor
•Weight coming on the front and rear tyres.
Procedure for determining the centre of gravity of a tractor by
weighing method:
These parameters are also measured when the front wheels are lifted by a
height ‘h’.

15. the front wheel of the tractor are raised distance Y2 and R’f is determined
by weighing.
Wx’2-R´f X´1 = 0
From fig.
tan β1 = x4 / y3
tan β1 = (x2 - x3) / y3
y3 = (x2 – x3) / tan β1
so, a vertical transverse plane containing C.G. can be determine by using
above equation
Wx2-Rf X1=0
or
From Fig.

16. Some assumptions while doing this analysis were:
1.The displacement of the point of contact of rear wheel on the ground
as the front wheels are lifted is negligible.
2.There is no deformation of the pneumatic tyre at the point of contact
i.e. height of centre of rear wheel is same as the radius of the rear
wheel.
Hence the height of CG from the ground is given by
where dr is the diameter of the rear wheel.
And cos β1 = x2´/ x3
Or x3 = x2´/ cos β1

17. Hitching system
• The tractor hitch system is that essential element of the tractor which binds the
prime mover and the implement into a single working unit.
• In three-point hitch attaches the implement to the tractor so that the orientation of
the implement is fixed with respect to the tractor and the arm position of the hitch.
• The primary benefit to the three-point hitch system to transfer the weight and
resistance of an implement to the drive wheels of the tractor.
• Three-point linkage most often refers to the way plough and other implements are
attached to an agricultural tractor . Three-point attachment is a way of joining any
implement to the tractor.

18. Hitch System Components
Three types of hitching possible with three point hitch system are free
float (towed), semi-mounting, and fully mounting.
Three point hitch system is the only hitch system now available for all
implements except trailers and combines.

19. Important Features of Hitching System
Depth Control
The depth control is achieved by sensing a force, which is proportional to the
implement draft, by a variety of systems for upper or lower links.
One; the accurate control of a preset tool depth is necessary at all times regardless of
implement draft (position control)
two: the tool depth vary in different soil-draft-load conditions to maintain constant
draft load on tractor (draft control).
the basic function that must be accomplished by the sensing mechanism is to create a
movement which is directly proportional to draft.
The motion of sensing mechanism is then used by hydraulic system in such a way that
implement is lifted if the draft is more than preset draft and implement is lowered if the
draft is less than the preset draft.

20. Draft Control
Position Control
This is a type of restrained link system in which depth of implement is automatically
adjusted to maintain a preselected constant draft. If soil resistance is uniform, depth
fluctuations caused by irregular ground are less with automatic draft control than with
automatic position control
In this system, a constant depth of ploughing is maintained by automatic adjustment of
tractor. In this system the control valve can be operated directly by the driver to raise
lower or hold an implement, mounted on the linkage at any chosen height.
The sensing mechanism for depth is many a times a cam on rock-shaft.
The motion of rock-shaft is then used by hydraulic system in such a way that the
implement is lifted if the depth is more than the preset depth and the implement is
lowered if the depth is less than the preset depth.

21. Horizontal hitching of pull type implement
• For hitching, its location can be assumed to be one-fourth of the width
of cut over from landside and little behind the rear edge of the share.
line of pull is determine by location at H and location of drawbar hitch
point F as pull members are laterally rigid.

22. Vertical hitching of pull type implements

23. Weight transfer and its calculation
• For a tractor under dynamic or in operating conditions , the
weight on the wheels be different from the static values.
These changes are termed as ‘weight transfer’.
• Weight transfer is a normal outcome of the action of the
forces generated on the tractor chassis by the ground and
by the implement.
• It occurs whenever and how the tractor is loaded, including
the ‘no’ load case where there is some weight transfer due
to the torque on the rear wheels required to propel the
tractor against the rolling resistance of all the wheels

24. Referring to (Fig) and considering tractor as a free body, the algebraic
sum of all forces acting parallel or perpendicular to the direction of
motion as well as the algebraic sum of moments about any point must be
separately zero.
∑H = 0, ∑V= 0, ∑ M = 0
H is the horizontal force, V is the vertical force, M is the moment and 
is angle between pull (P) and horizontal,

25. H = F-P cos α = 0 … (1)
Where, F is frictional force
V = R1 + R2 – W-P sin α = 0 … (2)
Taking moments about the point A
∑M = WX1 – Y1 P cos α – SP sin α – R1 X2 = 0 … (3)
Solving equation (3) for R1
Now
And

26. The stability of the tractor in the vertical plane is determined by R1 and
the tractive capacity by R2

27. References
http://ecoursesonline.iasri.res.in/mod/page/view.php?id=489
Elements of agricultural engineering by Dr. Jagdishwar sahay
http://www.agricultureinindia.net/machinery/farm-tractor/traction-and-traction-theory-used-
in-tractors-agriculture/16191
Tractors and their power units by John B. Liljedahl , Paul K. Turnquist, David W. Smith and
Makoto Hoki