Background:
Hydrostatic stability is the ability of a floating body to remain upright or correct its
orientation after being inclined by external forces. There are three key points that help
determine a bodies stability: The centre of gravity (G) is where the bodies weight acts, it is
the sum of each parts weight multiplied by its distance from a reference datum, divided by
the sum of each parts weight.
∑(𝑤𝑖 ∙ 𝑥𝑖 )
𝐶𝐺 =
∑𝑤𝑖
The centre of buoyancy (B) is where the resultant buoyancy force acts, and always exists at
the geometric centre of the submerged portion of the body.
The metacentre of a body (M) is the point defined as the intersection of two vertical lines
drawn through the centre of buoyancy at different tilt angles, it’s a key indicator to a body’s
ability to right itself. When the metacentric height (distance between M and G) is positive
that means the body is stable, if the distance is zero the body is neutrally stable, and if the
distance is negative the body is unstable.
The stability of bodies with positive and negative metacentric heights is demonstrated in
figure 1.1. In Case A, when the body is tilted the moment created by the opposing forces
(Buoyancy and Gravity) is clockwise, opposing the direction of tilt. Whereas in case B the
resultant moment is counter clockwise, complementary to the direction of tilt. In case A the
moment will counteract the tilting motion and correct the body’s orientation, and in case B
any tilting motion will cause the body to capsize.
The magnitude of the distance between the centre of gravity and the metacentre is also
useful in determining stability, as a high positive value indicates the body can be tilted quite
significantly and still be able to correct itself.
Intro:
In our experiment we will use two different methods to measure a body’s metacentric
height, and thus interpret their stability. In the first method we will utilise a control jockey
weight and measure the incurred angle of tilt, using trigonometry we are then able to derive
the theoretical metacentric height. The second method involves raising the body’s centre of
gravity higher until we reach the point of instability, indicating that we have reversed the
metacentric height from positive to negative.
Results:
Draft 3cm
Freeboard 7.5cm
Initial weight height from base
Mast height(from ruler) 63.5cm
Below/including ruler 14cm
Right side weighted
𝑤𝑗
Test
W
dx
1
951 g 6760g
2cm
2
951 g 6760g
4cm
3
951 g 6760g
6cm
4
951 g 6760g
8cm
5
951 g 6760g
10cm
6
951 g 6760g
12cm
d
2.2
3.8
4.7
6
7.2
8.4
d in radians
0.038
0.066
0.082
0.105
0.126
0.147
GM
0.073
0.085
0.103
0.107
0.112
0.115
Left side weighted
𝑤𝑗
Test
1
951 g
2
951 g
3
951 g
4
951 g
5
951 g
6
951 g
d
1.7
1.9
4.2
5.5
6.8
7.9
d in radians
0.030
0.033
0.073
0.096
0.119
0.138
GM
0.095
0.170
0.115
0.117
0.119
0.122
W
6760g
6760g
6760g
6760g
6760g
6760g
dx
2cm
4cm
6cm
8cm
10cm
12cm
Mast weight raised tests
(mast weight 1822g)
Test
1
2
3
4
5
Mast height (centre of Gravity)
56cm
56cm
54cm
56.5cm
56.5cm