The Transport Treasure News Letter Center e of Gravity
ISSUE: 20090426-01-ENG
Dear reader, In front of you is The Transport Treasure, the first news letter issued by The Works international. The Transport Treasure provides you with industry news, new developments, operational aspects and engineering solutions. The Transport Treasure is a monthly appearing news letter. This month we will be covering the topic “Center of Gravity” or simply CoG. The CoG is a widely misunderstood concept that has lead and still leads to incidents and accidents.
CoG x
Wl Wt (4,500 *100) (4,500 * 20) CoGx 100 20 450,000 90,000 CoGx 4,500mm 120
Definition of the Center of Gravity; The Center of Gravity (CoG) is the point at which an object’s entire mass can be assumed. While transporting heavy loads, more often than not, we make use of the “combined Center of Gravity”. This means that of two individual items with each its own CoG, a combined CoG is calculated. For engineering purposes this newly established combined CoG is then used as the only CoG of both items. The combined CoG of a transporter and a load is the most common example of such an application. There are a few specific reasons for using the combined CoG as opposed to using individual CoG’s.
Once the combined CoG has been established (calculated) the engineering on a heavy transport becomes easier as there is only one CoG coordinate to deal with.
For CoGy;
For CoG z;
Establishing a combined CoG results in a lower, measured from grade, z-coordinate. This in turns results in an increased stability and safety during the transport.
The location of a CoG is expressed as a coordinate, in mathematical notation CoGLOAD(x,y,z). This means that the CoG of the load can be found at location (x,y,z). The distances are measured from a reference point called the Origin, the Origin is found at coordinates (0,0,0). The following figure illustrates this.
Dx * W W ( Dload *Wload ) ( Dtransporter *Wtransporter ) CoGx
For CoGx;
CoG y
D y *W
W (1,500 *100) (1,500 * 20) CoG y 100 20 150,000 30,000 CoG y 1,500mm 120
Dz *W W (3,500 *100) (900 * 20) CoGz 100 20 350,000 18,000 CoGz 3,067mm 120 CoG z
The coordinates of the combined CoG are; CoGcombined (4,500; 1,500; 3,067) mm or (14’-9.2”; 4’-11”; 10’-0.7”) ft-inch The use of a combined CoG has a positive effect on the z-coordinate. Compare the z-coordinate of the load with the z-coordinate of the combined CoG. z-coordinate load = 3,500 mm or 11’-6”. z-coordinate combined CoG = 3,067 mm or 10’-0.7”. A significant reduction of 433 mm or 1’-5” in the height (elevation) of the CoG that positively influences the stability of the transport. Taking advantage of the combined CoG makes it possible to execute transports of loads with extreme high CoG’s.
Figure 1, Center of Gravity location
Exercise:
The above figure shows a 6-axle line transporter with a load positioned on its deck. Both the CoG of the load and the CoG of the transporter is identified. Further the Origin of the coordinate system and the directions of the X-, Yand Z- axis are shown. The weight of the transporter (W t) is 20 ton and the weight of the load (W L) is 100 ton. For this example it is assumed that; CoGtransporter (4,500; 1,500; 900) mm or (14’-9.2”; 4’-11”; 2’-11”) ft-inch. CoGload (4,500; 1,500; 3,500) mm or (14’-9.2”; 4’-11”; 11’-6”) ft-inch. The combined CoG can be determined with the equation;
CoG
D * W W
Equation 1, determination of Center of Gravity (CoG) This equation states that the CoG can be determined by summing (Σ) all the multiplications of distance (D) from Origin and individual weight (W) and dividing this by the sum (Σ) of all the individual weights (W). This generic formula needs to be split in separate formulas for each of the axis, x, y and z.
CoGx
Dy * W Dx * W CoG y W W
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Assume that the transporter in Figure 1 carries another two items. In front of the load and behind the load two counterweights (CW) have been placed of 25 ton each. The CoG of each counterweight is; Figure 2, load with high Center of Gravity CoGCW1 CoGCW2
(1,500; 1,500; 1,500) mm or (4’-11”; 4’-11”; 4’-11”) ft-inch. (7,500; 1,500; 1,500) mm or (24’-7.3”; 4’-11”; 4’-11”) ft-inch.
Calculate the combined CoG of transporter, load, CW1 and CW2. Answers will be provided in the next Transport Treasure. Every effort is made to ensure accuracy and correctness of the contents of this news letter. However, if you find any mistakes, we would appreciate it if you make us aware of it.
Marco J. van Daal has been in the heavy transport industry since 1993 starting with Mammoet Transport from the Netherlands and later with Fagioli PSC from Italy, both esteemed companies and leading authorities Dz * W CoGz in the industry. He currently resides in Aruba, Dutch Caribbean, with his W wife and two daughters. website: www.the-works-int.com HAVE A SAFE AND STABLE DAY ! Page 1 of 1