After reviewing some comments on the posts, I decided to write this post. Flash back, this post is explains several basic calculation that usually use by marine cargo ship surveyor to complete their jobs. I think this will be usable for beginner.
Vessel Trim Calculation
Trim is different between aft draft and forward draft of the vessel.
Trim = Draft Aft (DA) – Draft Fore (DF)
Example : DF: 5.40 M, and DA: 7.25 M
Trim = 7.45 – 5.40
Trim = 2.05 M (Apparent Trim / AT)
Draft Corrected to Perpendicular
The After Perpendicular is a right angle line to the keel passing through the rudder post; it is also the first frame marked «0» on the vessels drawings.
The Forward Perpendicular is a right angle line to the keel cutting the vessel’s Summer waterline at the stem. The vessels stability information is calculated on the drafts measured at the perpendiculars; as the draft marks rarely coincide with these lines, a draft as read must be corrected. If the marks are not on the perpendiculars, the vessel usually has a tabulated plan in her hydrostatic books.
However, some of the older vessels do not have their tabulation and it is therefore necessary to work out the correction to be applied by referring to the vessels capacity plan and measuring the horizontal distance between the draft marks and the perpendiculars of the waterline.
Forward Correction = (AT x Fd)/(LBM)
Aft Correction = (AT x Ad)/(LBM)
Midships Correction = (AT x Md)/(LBM)
Fd: distance Draft Forward to Forward Perpendiculars
Md: distance Draft midship to midship
Ad: distance Draft Aft to Forward Perpendiculars
LBM: distance from Da to Df or LBM: LBP – (Ad + Fd)
DF: 5.40, DM: 6.30, DA: 7.25
AT: 2.05
Fd: 0.80, Md: 0.50, Ad: 4.50
LBP: 150.00
LBM: 150.00 – 0.80 – 4.50 = 144.70
Forward Correction: AT x Fd / LBM = 2.05 x (-0.80) / 144.70 = -0.0113 (Fc)
Forward Corrected Draft : DF + Fc = 5.40 + (-0.0113) = 5.3887
Mid Correction: AT x Md / LBM = 2.05 x (-0.50) / 144.70 = – 0.0071 (Mc)
Mid Corrected Draft : DM + Mc = 6.30 + (-0.0071) = 6.2929
Aft Correction: AT x Ad / LBM = 2.05 x 4.50 / 144.70 = 0.0638 (Ac)
Aft Corrected Draft : DA + Ac = 7.25 + 0.0638 = 7.3138
1. The rule to apply the correction:
Trimmed by the STERN : Forward Correction = MINUS (-) After Correction = PLUS (+)
Trimmed by the HEAD : Forward Correction = PLUS (+) After Correction = MINUS (-)
2. Each of these corrections is applied according to the following rule:
If the direction of the displacement of the draught marks from the relevant perpendicular is the same as the direction of the trim, then the correction applied to the observed draught is negative, otherwise it is positive.
Interpolation
Interpolation is a method of constructing new data points within the range of a discrete set of known data points.
Example : Sounding : 1.15 (S) Trim : 2.50 (T)
S 1.00 (1), T 2.00 (5) : 300 m3 (A)
S 1.50 (2), T 2.00 (6) : 340 m3 (B)
S 1.00 (3), T 3.00 (7) : 290 m3 (C)
S 1.50 (4), T 3.00 (8) : 330 m3 (D)
Step One
S 1.15, T 2.00 :
= A+((B-A)x(S-1)/(2-1))
= 300 + ((340-300)x(1.15-1.00)/(1.50-1.00))
= 300 + (40 x 0.15/0.50)
= 300 + 12
= 312 (X)
Step Two
S 1.15, T 3.00 :
= C+((D-C)x(S-3)/(4-3))
= 290 + ((330-290)x(1.15-1.00)/(1.50-1.00))
= 290 + (40 x 0.15/0.50) = 290 + 12
= 292 (Y)
Step Three
S 1.15, T 2.5 :
= X+((Y-X)x(T-5)/(8-6))
= 312 + ((292-312)x(2.50-2.00)/(3.00-2.00))
= 312 + (-10 x 0.50/1.00)
= 312 + (-5)
= 307 (Z)
Quarter Mean or MMM Draft Calculation
Quartermean is the mean of the drafts at the bow and the stern; for a vessel with a straight keel, the draft at the midpoint of the waterline length.
Example :
Fore Draft (FD) : 5.40 M
Mid Draft (MD) : 6.30 M
Aft Draft (AD): 7.25 M
The above sample of FD, MD and AD are using Draft after corrections to Perpendiculars.
MMM = ((6 x MD) + (1 x FD) + (1 x AD)) / 8
MMM = ((6 x 6.30) + (1 x 5.40) + (1 x 7.25)) / 8
MMM = (37.80 + 5.40 + 7.25) / 8 MMM = 50.45 / 8
MMM = 6.30625
Trim factors
Some stability information books tabulate trim factors, forward and aft, but no position for the longitudinal center of flotation (LCF) forward of the aft perpendicular(AP).
The LCF can be found from the trim factors by the following formula:
LCF from AP = (length between perpendiculars x aft trim factor)/ (forward trim factor + aft trim factor)
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Regards,
Surveyors