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GTS250ie : Weight, Balance, and Center of Gravity
The purpose of this exercise was twofold:
1) to determine the wheel loading and center of gravity of a 2007 GTS250 (unloaded, and with rider and
luggage rack loads), and
2) to determine how center of gravity and wheel loading are affected by luggage rack loading. Luggage rack
loading is known to aggravate the GTS's characteristic front wheel headshake.

The first step was to measure the positions of the loading stations on the bike's moment (lever) arm. The bike's
moment arm can be visualized as the centerline of the bike, projected onto the ground directly underneath the
bike. The loading stations would be, working rearward: the front wheel contact point, the midpoint of the saddle,
the rear wheel contact point, and the midpoint of the luggage rack. Taking the front wheel contact point as the
datum (reference), these positions are:
STATION INCHES MM
Front wheel contact point 0 0
Saddle midpoint 42 1067
Rear wheel contact point 55 1397
Luggage rack midpoint 64 1626

The second step was to measure the force (weight) with which each wheel bears down on the ground. For these
measurements, all fluid reservoirs were full to published capacity, and the glovebox and pet carrier were empty.
Also, my bike had the following accessories installed, which I did not remove for the sake of this exercise:
front fender crashbar, flyscreen, floormat, and rear crashbars (all Piaggio). I used a Healthometer model 155ND
bathroom scale (analog, 300 lb capacity) to take these measurements.

The procedure I followed was:
1) Place the scale on the pavement at the position from which it will be read,
2) Tare (zero) the scale,
3) Place a wooden block on the pavement 55 inches from the scale so as to raise the opposite wheel (and keep the
bike level) while measuring,
4) Roll the bike up onto the scale and block,
5) Position myself to read the scale with as little parallax as possible,
6) Steady the bike with as light a hand as possible,
7) Read the scale,
8 ) Roll the bike off the scale and block, put the bike on its centerstand, and
9) Record the reading.
10) Repeat for the opposite wheel.

I obtained the following:
WHEEL POUNDSKG
Front 139.5 63.3
Rear 228.0 103.4
CURB WEIGHT 367.5 166.7

Before proceeding, I did a "reality check" to determine if these measured weights are credible:
The published dry weight of the bike is 326 lb, which puts the measured curb weight
367.5 lb - 326 lb = 41.5 lb
over the dry weight. This would be the combined weights of the fluids and accessories.

The weights of the fluids are:
FLUIDCAPACITY
(gal)
SPEC. WEIGHT
(lb / gal)
FLUID
WEIGHT (lb)

Gasoline 2.43 6.17 15.0
Coolant 0.56 9.17 5.1
Engine oil 0.35 7.50 2.6
Hub oil 0.0664 7.50 0.5
TOTAL 23.2

To repeat, the measured curb weight of my bike is 41.5 lb over the published dry weight.
Subtracting the total fluid weight, I obtain
41.5 lb - 23.2 lb = 18.3 lb
which would be the combined weight of my accessories (front fender crashbar, flyscreen, floormat, and rear crashbars).
I do not have these weights, but 18.3 lb certainly sounds credible. I called my measurements good, and proceeded.

A free-body diagram of the loaded scooter, represented as a simply-supported beam, is shown below. Moment arm
lengths are taken to be the distance from an arbitrary datum (or zero reference point) to the lettered loading stations
on the axis shown below the beam. Also shown are the expressions giving the reaction forces at the wheels (wheel
loading), and the center of gravity. Reaction force is the force acting upward on the wheel by the ground, and is
equal and opposite to that wheel's share of the bike's curb weight, the rider's weight, and the luggage rack load. Center
of gravity is that point along the bike's axis about which the moments due to the reaction forces at the wheels are balanced
(equal and opposite). The expressions are shown both for the general case (arbitrary datum), and for the special case in
which the datum is taken to be the contact point of the front wheel. This special case simplifies the calculations, and is the
case I used in working up the results. It bears mentioning that choice of datum does not affect the results of the calculations.
It also bears mentioning that this model represents only the horizontal component of center of gravity. My primary reference
was Engineering Mechanics, Irwin H. Shames, 3rd ed., 1980, Prentice-Hall. Another good reference is the Aircraft Weight
and Balance Handbook
, FAA-H-8083-1A, available for free download at http://www.faa.gov/library/manuals/aircraft/


The following tables show results for a range of rider weights; with zero load, max rated (6 Kg) load, and an overload on the
luggage rack at each rider weight.
RIDER WEIGHT
(lb)
RACK LOAD
(lb)
FRONT WHEEL
LOADING (lb)
REAR WHEEL
LOADING (lb)
GROSS WEIGHT
(lb)
C.G. (in)
0 0 139.5 228.0 367.5 34.1
100 0 163.1 304.4 467.5 35.8
100 13.2 161.2 319.7 480.7 36.6
100 30 158.2 339.3 497.5 37.5
150 0 175.0 342.5 517.5 36.4
150 13.2 172.8 357.9 530.7 37.1
150 30 170.0 377.5 547.5 37.9
200 0 186.8 380.7 567.5 36.9
200 13.2 184.6 396.1 580.7 37.5
200 30 181.9 415.6 597.5 38.3
250 0 198.6 418.9 617.5 37.3
250 13.2 196.4 434.3 630.7 37.9
250 30 193.7 453.8 647.5 38.5
300 0 210.4 457.1 667.5 37.7
300 13.2 208.2 472.5 680.7 38.2
300 30 205.5 492.0 697.5 38.8

With loads given in SI mass units (Kg):
RIDER WEIGHT
(Kg)
RACK LOAD
(Kg)
FRONT WHEEL
LOADING (Kg)
REAR WHEEL
LOADING (Kg)
GROSS WEIGHT
(Kg)
C.G. (mm)
0 0 63.3 103.4 166.7 867
45 0 73.9 137.8 211.7 909
45 6 72.9 144.8 217.7 929
45 15 71.5 155.2 226.7 957
65 0 78.6 153.1 231.7 923
65 6 77.7 160.0 237.7 941
65 15 76.2 170.5 246.7 966
85 0 83.4 168.3 251.7 934
85 6 82.4 175.3 257.7 950
85 15 80.9 185.8 266.7 973
105 0 88.1 183.6 271.7 944
105 6 87.1 190.6 277.7 959
105 15 85.6 201.1 286.7 980
125 0 92.8 198.9 291.7 952
125 6 91.8 205.8 297.7 966
125 15 90.4 216.3 306.7 985

Observe that for a given rider weight, two things change as luggage rack load increases:
1) The heavier the luggage rack load, the further the C.G. moves to the rear.
2) For every increment of luggage rack increase, front wheel loading decreases, and rear wheel loading increases by
the increment of the load plus the decrease at the front wheel. This is because the luggage rack is behind the rear wheel.

These effects play into the decrease in front-end stability with increase in luggage rack load. The above exercise is only a
piece of the much larger task of building a representative dynamic model of the GTS's front end.
Last Updated Fri May 14, 2010 5:07 pm
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