Review centre of gravity calculation

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SUMMARY

The discussion centers on calculating the center of gravity (CG) for a half octagonal prism with specific dimensions: A = 0.12 m, B = 0.2 m, H2 = 0.065 m, H1 = 0.095 m, and H = 0.16 m. Participants emphasize the importance of using a consistent reference point for measuring centroids of individual shapes, particularly when combining trapezoids and rectangles. The correct formula for the overall centroid is confirmed as C_x = (∑(A*Cx))/(∑A) and C_y = (∑(A*Cy))/(∑A). The final calculation for the height of the center of gravity (KG) is established as KG = ((W1*y1)+(W*y2))/(W1+W), where W1 is the mass of the small weight and W is the mass of the entire body.

PREREQUISITES
  • Understanding of centroid calculations for composite shapes
  • Familiarity with the principles of moments and equilibrium
  • Knowledge of basic geometry, particularly trapezoids and rectangles
  • Ability to apply formulas for center of gravity in engineering contexts
NEXT STEPS
  • Study the derivation of centroid formulas for various geometric shapes
  • Learn about the impact of weight distribution on center of gravity in fluid dynamics
  • Explore the implications of center of gravity in stability analysis for vessels
  • Investigate the role of reference points in calculating moments for composite bodies
USEFUL FOR

Engineers, naval architects, and students in mechanical or civil engineering who are involved in stability analysis and design of structures or vessels.

  • #31
Wait, I think I have it figured out now. Let me correct this and get back to you
 
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  • #32
Samiha Samin said:
Wait, I think I have it figured out now. Let me correct this and get back to you

When you do your calculations of vessel KG, remember to include not only the inclining weight, but all the gear (scales, plumb bob, mast holding the plumb bob, etc.) with which the model vessel is fitted to carry out the inclining experiment. The experiment gives the KG of the vessel as inclined, and the weight and KG of the vessel by itself must be found by removing the items used to carry out the experiment, by doing a separate calculation of their weights and KGs and subtracting from the inclined condition.
 
  • #33
SteamKing said:
When you do your calculations of vessel KG, remember to include not only the inclining weight, but all the gear (scales, plumb bob, mast holding the plumb bob, etc.) with which the model vessel is fitted to carry out the inclining experiment. The experiment gives the KG of the vessel as inclined, and the weight and KG of the vessel by itself must be found by removing the items used to carry out the experiment, by doing a separate calculation of their weights and KGs and subtracting from the inclined condition.
Okay I have found the masses of each individual parts, but when I add them up it is not equal to the mass of the whole vessel that I measured on a weighing scale. In fact it sums up to a mass that is greater than the mass of the whole vessel. Does this indicate an error in my calculation?
 
  • #34
Samiha Samin said:
Okay I have found the masses of each individual parts, but when I add them up it is not equal to the mass of the whole vessel that I measured on a weighing scale. In fact it sums up to a mass that is greater than the mass of the whole vessel. Does this indicate an error in my calculation?
Yes, I'm afraid it could.

Just out of curiosity, how much did the vessel weigh on the scale, and how much is your calculated weight?

Did you weight the vessel with or without all of the inclining experiment gear attached?
 

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