By: Louie Kleinstiver
Center of gravity (CG) is the point at which the weight of
the chassis, body/equipment and payload (if collectively or individually
supported) would balance vertically, horizontally and laterally. This
engineering concept finds the center of the mass of an object.
The weight of the body and attached equipment and their
center of gravity locations (horizontal and vertical), as well as the
positioning of the cargo load, are important to the stability, handling and
braking of the vehicle.
Adhering to the CG recommendations provided by the chassis
manufacturer and the second unit body weight limitations for compliance with
Federal Motor Vehicle Safety Standards (FMVSS) is only part of the task of
producing a completed or altered vehicle that performs well in service. The
allowable CG limits (vertical and horizontal) for truck chassis are contained
in the incomplete vehicle document (IVD) or manual and the body builder’s
book.
Check your math
Normal truck body installations require the calculation of
the horizontal and vertical centers of gravity. In a few instances the lateral
or side-to-side CG will need to be calculated. When calculating the CG for a
complicated piece of equipment, the CG for component pieces can be computed and
then combined.
The first step in calculating the CG is to establish the
reference points for the horizontal, vertical and lateral center of gravity
measurements. For compliance calculations, the horizontal CG measurements from
the centerline of the front axle can be used. If the CG of a body is being
calculated, any point such as the outside surface of the front wall can be
used. Measurements forward of the reference point are negative.
The vertical CG for a chassis can be measured either from
the ground or the top of the frame rail at the back of the cab for compliance
calculations, depending on the requirements outlined in the IVD. If the CG of a
body is being calculated, any point such as the bottom of the long sills can be
used.
Any point can be used to locate the center of gravity. For
example, if you need to determine the vertical CG of a truck body using the
ground as a reference point, but only know the CG of the body as measured from
the top of the frame rail at the back of the cab, simply add the vertical CG of
the body and the distance from the top of the frame rail to the ground.
Remember, component CGs below the vertical reference point
and forward of the horizontal reference point are negative.
In order to calculate the horizontal and vertical center of
gravity for a truck or truck body, the weight and CG for each component must be
identified and then combined to find the total CG for the truck or body.
The basic formula for center of gravity is the sum of the
weight times the distance from the reference point for each component divided
by the total weight of all components. The basic formula is as follows:
CG = (W1 x D1) + (W2 x D2) + (W3 x D3) + (Wn x Dn)
W1 + W2 + W3 + Wn
CG = Center of gravity
W = Weight of component
D = Distance from reference point
n = Last item
The NTEA recently released a new software program called
UltraMod that is designed to assist with what can be tedious center of gravity
and weight distribution calculations. UltraMod is an Excel-based spreadsheet
program that allows users to quickly determine the weight distribution of a
truck, including wheelbase changes and additional axles. The program allows
users to configure the vehicle for optimal payload while assuring the vehicle
and/or individual axles are not overloaded.
A “WTCG” program also is available that allows
you to calculate axle loads; percentage of body/equipment payload on each axle;
horizontal, vertical and lateral centers of gravity (depending on input); and
individual wheel loads. A “TRKTLR” program enables you to calculate
axle loads and horizontal and vertical centers of gravity for a straight truck
and trailer combination; and wheelbase modifications and adding axles.
Programs are available separately on a CD-ROM or 3.5-in.
diskette by calling the NTEA at 800/441-NTEA (6832).
About The Author: Kleinstiver is director of Technical Services for the NTEA, Farmington Hills, Mich.
