MAE142_L10_Mass.pdf

# MAE142_L10_Mass.pdf - Mass and Buoyancy Center of Gravity...

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Mass and Buoyancy Center of Gravity Center of Mass Center of Buoyancy Moments of Inertia Composite Bodies Swing Balances MAE 142 Macon Dirigible (NASA Image)

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2 MAE 142 Center of Gravity The vehicle center-of-gravity is the point where the entire body can be balanced in a static equilibrium. 0 = F cg = R i w i 0 = M cg = i  r i − r cg × w i R = i w i i r cg × w i = i r i × w i resultant force center-of-gravity location x B z B y B w i r i R r cg center-of-gravity w i = weight vector element i
3 MAE 142 Center of Mass The center of mass assumes all weight vectors act in the same direction. i r cg × m i g = i r i × m i g R = i w i = i m i g w i = m i g i r cg × w i = i r i × w i [ i r cg m i ] × g = [ i r i m i ] × g r cg = r cm = 1 M i m i r i R = M g M = i m i

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4 MAE 142 Center of Buoyancy
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