The distance between a helicopters main wheels and nose wheel is 6 meters. The single nose wheel load is 500 kg and a single main wheel load is 4 000 kg. How far is the centre of gravity in front of the main wheels?
Refer to figure.
The manufacturer measures the weight of the helicopter after it has been fully assembled, the measured weight is known as the Basic Empty Mass (BEM). This weight is measured from a minimum of 3 supporting points, giving the data needed to determine the helicopter's Centre of Gravity (CG) position at BEM.
The question doesn't give the datum. Therefore, we can choose a point as the datum. In the example, the main wheels have been chosen as the datum position.
Therefore:
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Nose wheel arm = 6 m.
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Main wheel arm (datum) = 0 m.
Now that the arms are established, the Moments can be calculated by using the formula:
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Moment = Mass x Arm
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Nose wheel moment = 500 kg x (- 6 m) = - 3 000 kg.m
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Main wheel moment = (2 x 4 000 kg) x 0 m = 0
Now that each position’s moment has been calculated, we can find the arm for the CG of the helicopter by taking the total moment and dividing it by total mass:
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Total moment = - 3 000 kg m + 0 kg m = - 3 000 kg.m
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Total mass = 500 kg + 4 000 kg + 4 000 kg = 8 500 kg
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CG = Total Moment / Total Mass
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CG = -3 000 kg.m / 8 500 kg = - 0.35 m = - 35 cm
The CG of the helicopter is given as -35 cm, which means that it is at a distance of 35 cm forward of the main wheel, since the main wheels were chosen as the datum point.
NOTE:
The phrasing of this question is tricky, the part stating “a single main wheel load is 4 000 kg” means each main wheel has a load of 4 000 kg giving us the load of the main wheel as 8 000 kg.
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