WT&CG
Spreadsheet Manual For Excel Weight &
Center-Of-Gravity Calculations
Calculates weight distribution on each axle, weight
distribution on individual wheels, percentage of equip-
ment and payload on the front and rear axles, percentage
of vehicle curb weight on the front and rear axles and
centers-of-gravity (horizontal, lateral and vertical).
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WT&CG
S p r e a d s h e e t M a n u a l F o r Lotus 123 We i g h t & C e n t e r - O f - G r a v i t y C a l c u l a t i o n s
S p r e a d s h e e t M a n u a l F o r Excel We i g h t & C e n t e r - O f - G r a v i t y C a l c u l a t i o n s
WEIGHT & CENTER-OF-GRAVITY On the copy, enter the date in cell E2 by writing over
the 7/16/89 date with a label. The “edit” function can
SPREADSHEET (EXCEL) be used to enter the vehicle description in cell A5 after
The Weight & Center-of-Gravity Spreadsheet (saved on the word “VEHICLE.”
the disk as WTCG) can be used to calculate the weight Print cells A2 through 53. Intermediate calculations
and center-of-gravity, the axle loadings, the individual are performed in columns G through H. They are
wheel loadings, the percentage of equipment and necessary for the calculation process but do not
payload on each axle and the percentage of total vehicle contain output information.
weight on each axle for any combination of chassis and Data for each parameter must be consistent in the
components. The horizontal and vertical centers-of- choice of a reference point. Horizontal center-of-
gravity are used for a variety of compliance and weight gravity location can be measured from any point as
distribution calculations. Finding the individual wheel long as all horizontal measurements are taken from
loadings and some compliance calculations will require that point. Usually, the horizontal center-of gravity
the lateral center-of-gravity as measured from the measurements are referenced from the center of the
centerline of the truck to the side. front axle. Toward the rear is positive and toward the
Any one of the parameters can be calculated. For front is negative. Similarly, the vertical center-of-gravity
example, the center-of-gravity of the components is usually referenced to the top of the frame rail at the
without the chassis can be calculated by not entering a back of the cab or to the ground. Lateral center-of-
value for the front and rear weights of the chassis. gravity location is measured from the centerline of the
Similarly, the horizontal center-of-gravity can be calcu- vehicle toward the right (curb) side and is positive.
lated by entering horizontal center-of-gravity data for
each component. VEHICLE DATA Section
By including the front and rear axle treads, the Enter the WHEELBASE in cell B7 and the CAB-TO-
individual wheel loadings are calculated. This feature is
AXLE in cell B8. The TREAD dimensions are entered
very helpful when making an “off-center” installation
in cells E8 and E9 if the individual wheel loadings are
such as a digger derrick. When the axle tread dimen- desired for those trucks with off-center loading. If the
sions are not included, the spreadsheet will calculate the
TREADs are not entered, the total axle-loadings will be
total axle loading.
calculated, not the individual wheels. The axle TREAD
Copies of WTCG are available in the following dimension is the distance between the centers of the
formats with the listed file names and file extensions.
tire to the ground contact-points for the tires on an
Before using WTCG, insert the sample data in Figure 4
axle. For axles with dual tires, the TREAD is the
into a test copy to insure that your results agree with the distance between the midpoint of the dual tires on one
example. If other formats are needed, this spreadsheet is
side to the midpoint of the dual tires on the other side.
supplied in printed form with all formulas listed:
The WHEELBASE dimension must be entered to
calculate the axle weights. CAB-TO-AXLE is listed for
LOTUS 1-2-3 Release 1A ............................... WTCG.WKS
reference and is not needed.
LOTUS 1-2-3 Release 2 ................................... WTCG.WKI
MICROSOFT EXCEL ..................................... WTCG.XLS CHASSIS COMPONENTS Section
Enter the front weight and rear weight for the base
First, make a copy of WTCG under another name for chassis in cells B12 and C12.
data entry. WTCG should remain as the master without Descriptions of options are entered in cells A13
being used to make calculations. As an example, WTCG through 16, with the corresponding front and rear
could be saved in a customer’s name to perform the weights in cells B13 through 16 and C13 through 16.
calculation. The resulting front, rear and total weights are calcu-
Before data is entered, some of the cells will contain lated and shown in cells B17 through D17. The hori-
the message “ERR” or “0.00.” That indicates that the cell zontal center-of-gravity for the chassis with options is
is a formula that depends on data from other cells that calculated and shown in cell C18, labeled HOR CG.
have not been entered. As the information is entered into
the other cells, numbers will appear in these cells.
1 If you have problems using this Spreadsheet, call the NTEA at 1-800-441-NTEA.
WT&CG
S p r e a d s h e e t M a n u a l F o r Lotus 123 We i g h t & C e n t e r - O f - G r a v i t y C a l c u l a t i o n s
S p r e a d s h e e t M a n u a l F o r Excel We i g h t & C e n t e r - O f - G r a v i t y C a l c u l a t i o n s
ADDED COMPONENTS Section OUTPUT DATA Section
All horizontal center-of-gravity measurements must be TOTAL WEIGHT (cell E38) is the sum of all of the
taken from the same reference point; all vertical center-of- entered weights for chassis, equipment and payload.
gravity measurements must be taken from the same
reference point; all lateral center-of-gravity measure- HORIZONTAL CENTER-OF-GRAVITY (cell C40) is the
ments must be taken from the same reference point. horizontal center-of-gravity for all of the chassis, added
Horizontal center-of-gravity information is necessary to components and payload listed in the input data sec-
calculate the weight distribution. Vertical and lateral tions.
center-of-gravity data is entered only if the resultant
lateral or vertical center-of-gravity is needed. Neither VERTICAL CENTER-OF-GRAVITY (cell C41) is the
vertical nor lateral C-G information affects the weight vertical center-of-gravity for all of the chassis, added
distribution calculations. components and payload items in the input data sec-
The data for the chassis center-of-gravity and the tions.
weight are automatically entered in cells B21 and E21
from the calculations performed above in the spread- LATERAL CENTER-OF-GRAVITY (cell C42) is the
sheet. The front axle is used as the reference point for the lateral center-of-gravity for all of the chassis, added
center-of-gravity. The vertical and lateral centers-of- components and payload items in the input data sec-
gravity data for the chassis is entered in cells C21 and tions.
D21 if the vertical and lateral centers-of-gravity calcula-
tions are made. Rows 22 through 36 are for entering the FRONT AXLE — LEFT, RIGHT and TOTAL (cells C45,
data for other components such as: body, bumper, frame D45 and E45): are the weights of the left and right wheels
sections, hoists, lift gates, snowplows and winches. on the front axle, if the tread information was included
Horizontal centers-of-gravity, measured from the and the total weight on the front axle.
centerline of the front axle, is entered in column B with
positive toward the rear and negative toward the front. REAR AXLE — LEFT, RIGHT and TOTAL (cells C46,
For example, a front-mounted winch would have a D46 and E46): are the weights of the left and right wheels
negative center-of-gravity measurement. Vertical centers- on the rear axle if the tread information was included
of-gravity, measured from either the top of the frame rail and the total weight on the rear axle.
at the back of the cab or the ground, are entered in
column C. Lateral centers-of-gravity are positive when PERCENTAGE OF EQUIPMENT AND PAYLOAD
measured from the centerline of the vehicle toward the WEIGHT FRONT AND REAR AXLES (cells D49 and
right (curb) side. These are entered in E49): is the percentage of the equipment and payload
column D. weight that are carried on the front and rear axles. If the
Row 37 is labeled for PAYLOAD data. The payload chassis weights are entered, they are not included in this
horizontal center-of-gravity is entered in cell B37, the calculation.
vertical and lateral C-Gs in cells C37 and D37 (if needed),
and the weight in cell E37. PERCENTAGE OF TOTAL VEHICLE WEIGHT—
If PAYLOAD data is entered, the weight of the FRONT AND REAR AXLE (cells D50 and E50): is the
PAYLOAD can be increased in steps to see whether the percentage of the data items entered that is carried on
front or the rear axles load to capacity first or the vehicle the front axle. Chassis weights are included in this
to GVWR. The PAYLOAD capacity of the vehicle is calculation.
determined when one of the axles is loaded to capacity
or the GVWR is reached. EXAMPLES
FIGURE 1
Shows the WTCG spreadsheet with no data. This is a
printout of the master. “0.00” indicates cells that are
dependent on the data in other cells. “ERR” means error
and is the result of dividing by zero. As data is entered,
the zeros and “ERR” output will be replaced with
numbers.
If you have problems using this Spreadsheet, call the NTEA at 1-800-441-NTEA. 2
WT&CG
S p r e a d s h e e t M a n u a l F o r Lotus 123 We i g h t & C e n t e r - O f - G r a v i t y C a l c u l a t i o n s
S p r e a d s h e e t M a n u a l F o r Excel We i g h t & C e n t e r - O f - G r a v i t y C a l c u l a t i o n s
FIGURE 2 FIGURE 4
Shows the analysis of the equipment that is added to the Shows a different GMC Brigadier with a single rear axle, a
chassis with no data entered for the chassis except for service body, high roof and a digger derrick. Because the
the wheelbase. When the wheelbase is entered, the front digger derrick is relatively heavy and mounted off-center,
and rear axle weights and the percentages of weights on the lateral center-of-gravity and the individual wheel
each axle are calculated. Without the wheelbase, the loadings become significant. With off-center loading, the
centers-of-gravity will be calculated but the axle load- axle weights will not divide equally between the left and
ings and percentages will not. This calculation shows right wheels. The PAYLOAD was not included in this
the effect of the added equipment on the front and rear example. The horizontal center-of-gravity reference point
axle weights and the centers-of-gravity. In this example, is the center of the front axle. The vertical center-of-gravity
the horizontal center-of-gravity reference point is the is measured from the ground. The lateral center-of-gravity
center of the front axle. The vertical center-of-gravity is is measured from the centerline of the chassis, with the
measured from the ground. The lateral center-of-gravity curbside being positive. The results show the three
is measured from the centerline of the chassis, with the centers-of-gravity (horizontal, vertical and lateral),
curbside being positive. Notice that all of the center-of- individual wheel loadings, axle weights and the percent-
gravity measurements are positive. age of weight on each axle for the chassis and equipment.
The results show the three centers-of-gravity (hori- Because the digger derrick is heavy and is mounted
zontal, lateral and vertical), the front and rear axle behind the rear axle, the front axle weight of 5,160 lbs.
weights and the percentages of weight on the axles for with all of the equipment mounted is less than the base
the body and hoist and related equipment. Because the chassis weight of 5,800 lbs. The percentage of EQUIP-
chassis data was not entered, the percentage of EQUIP- MENT and PAY LOAD WEIGHTS show that the FRONT
MENT and PAYLOAD WEIGHTS and the percentage AXLE percentage is –7.62% and the REAR AXLE percent-
of the TOTAL VEHICLE WEIGHTS are the same. age is 107.62%. 7.62% of the equipment weight is removed
from the front axle and transferred to the rear axle.
FIGURE 3
Shows the same truck as in Figure 2, except with data
entered for the front and rear chassis weights, the cab-
to-axle and the payload. Maximum payload can be
determined by increasing the payload weight until
either the front or rear axles reach their capacity, or the
legal load limit of 48,500 lbs. is reached. However, since
the tread information is missing, the right and left
wheel weights were not calculated. In this example, the
horizontal center-of-gravity reference point is the
center of the front axle. The vertical center-of-gravity is
measured from the ground. The lateral center-of-
gravity is measured from the centerline of the chassis,
with the curbside being positive.
The results show the three centers-of-gravity (hori-
zontal, vertical and lateral) for the chassis and all of the
equipment, the front and rear axle weights and the
percentages of weight on each axle with the truck fully
loaded. The PAYLOAD was adjusted to 26,872 lbs. to
achieve a gross vehicle weight of 48,500 lbs., which is
the legal limit.
3 If you have problems using this Spreadsheet, call the NTEA at 1-800-441-NTEA.
Figure 1
WT&CG
S p r e a d s h e e t M a n u a l F o r Lotus 123 We i g h t & C e n t e r - O f - G r a v i t y C a l c u l a t i o n s
If you have problems using this Spreadsheet, call the NTEA at 1-800-441-NTEA.
Figure 2
Figure 3
Figure 4