Trans RINA, Vol 152, Part A4, Intl J Maritime Eng, Oct-Dec 2010
Table 2: Summary of Theory’s Performance to Predict Motion RAOs Condition Heave
Roll
Supply Tanker
1 Good 2 Good 3 Frigate Good 1 Satisfactory* 2 Satisfactory* 3 Satisfactory*
Overpredicted by 300%
Overpredicted by 200%
Good
Underpredicted by 50%
Underpredicted by 50%
Underpredicted by 40%
Pitch Good
Good Good Satisfactory* Satisfactory* Satisfactory* * denotes that the RAO numerical results exhibited additional oscillations not present in experimental results
displacement. With a heavier displacement the vessel experienced larger heave motions around the resonant frequency, while either side of this the motions were largely unchanged.
The roll magnitude is very small,
thus little can be deduced from these results. Comparing the two pitch RAOs no notable change in motion is apparent for an increase in displacement.
The effect of a change in displacement is visible in the motions of the frigate. There is a small increase in the heave primary peak magnitude with an increase in the displacement of the tanker; but no discernable increase in the frigate pitch motion. As mentioned above there is a significant increase in the frigate’s roll RAO with an increase of the supply ship displacement. This again suggests that the heave motion of the tanker is the key factor influencing the roll motion of the frigate, especially with the coincidence of the tanker heave resonant peak with the roll resonant peak of the frigate.
For Condition 3 the longitudinal separation between the vessels was increased, see Figure 7. As expected, the motions of the tanker changed little from the smaller longitudinal contrast
separation condition (Condition the motions of the frigate
good; this suggests that for the other conditions tested the theory is indeed predicting the effect of interference between the vessels on the tanker roll which is not observed experimentally.
The frigate motions are generally poorly predicted. The heave response is significantly over predicted and the double peak nature of the RAO is not clearly defined by the theory. The theory also predicts an increase in heave motions whereas the experimental results show a decrease. The frigate roll motions are again under predicted quite significantly with a resonant magnitude of only 3.3, compared to an experimental peak of approximately 8.0. The theory predicted the frigate pitch resonant peak magnitude quite well, but at a lower frequency than the experiments.
2). In have changed
appreciably: the frigate heave RAO has reduced from a resonant peak of 1.4 to 1.2; the roll RAO peak has reduced from a resonant peak of 9 to 8; whilst the pitch motion has remained fairly constant. This reduction in motion for the receiving vessel with an increase in longitudinal separation concurs with the results presented in Andrewartha et al. [15]. The reduction in motions is probably due to the offset position of the frigate, so that the influence of the radiated waves from the supply tanker reduced.
The correlation between the experimental results and predictions for supply tanker in Condition 3 is excellent for all three motions. It is interesting to note that the roll magnitude is relatively small, though the correlation is
Whilst the magnitude of the motions of each vessel during a RAS operation is important, of greater consequence is the relative motion between the two vessels. The relative motion between the replenishment points on the vessels, and hence the tension in the cable connection, will be critical for a successful operation. Therefore the relative motion between the two vessels, which accounts for their heave, pitch and roll motions, was investigated for the various operating conditions.
The motions at the replenishment point in the x, y and z directions can be expressed using the following set of three equations:
Δη η − − g Δη η − − z ηg ) 4 Δη η − − x ηg ) 5
x=+ −(z z ) 5 y(x=+ − x2p g ) 6 z(y=+ − y3p g ) 4
1p g
( y y )η6 ( zp ( xp
p (6)
where ηk is the displacement in the k direction for k = 1 to 6. The location of the replenishment point in each of the directions x, y and z is denoted by the subscript p whilst the subscript g denotes the vessel’s centre of
A-186 ©2010: The Royal Institution of Naval Architects
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74