Capt. Pham Thanh Tuyen
Prior to this, all bulk cargo ships across the world, when the Draft Survey be conducted to determine the weight of goods, the method “Quarter Mean Draft” has been used. Over time, with the continuous development of science and technology, today’s ships have a deadweight of up to ten thousand tons, a length of several hundred meters. Through research, I found that traditional methods of “Quarter Mean Draft” is ineffective, generating errors up to several hundred tons. This manuscript refers to the error of traditional methods, and propose new methods of consistent and accuracy, to contribute a scientific measures in the global shipping industry.
A. Method “Quarter Mean Draft”
1) Definition:
2) Quarter Mean Draft
In this method, the Final Mean Draft is calculated as follows:
From the formula (A.1) (A.2), (A.3), inferred
Since the average twice in the formula (A.2), (A.3), so dFinalMean is different d¤ a quarter of the (d¤ – dm), so it is called the Quarter Mean Draft .
“Figure 2” below will illustrate this more clearly
3) Proof of method error
Figure 2
Region ABCKD denotes the ship below the waterline. Because the ship is curved along, the midpoint M of the ship’s bottom was sagging down into the K. The problem now becomes flat geometry problem. MK segment called deflection(sagging) Δd of ship.
Thus the MK (is also the deflection Δd) is divided into four equal parts, where NK is a quarter of Δd. Can be said that the draft dFinalMean is determined by one-quarter decrease deflection Δd, so dFinalMean called Quarter Mean Draft .
In “Figure 2”, dQuarterMean to be used as a Equivalent Draft to assume that the ship is not bent along. Thus, the assumed ship’s bottom is line EF passes through point N, we have the equivalent trapezoidal ABEF. At symmetrical half of the ship forward, it is easy to see that measures of equivalent assumption can only be acceptable when the NKP area equals the area of the DPF.
By visually, can immediately see the NKP area smaller than the area of DPF a lot. So error of method has been proven.
2. Second way, proved by calculation:
Figure 3
Call the ABCKD area is S1. Divide the length of Lpp into three equal parts by the points P, Q as “Figure 3”
According to the formula (A.8), (A.9), the area S1 and area S2 are equal only when d¤= d¤1.
“Figure 3” shows that the T is always above the point K, that means LT always less than LK. In other words, d¤1 is always smaller d¤.
Thus, the error of the method has been shown.
B. The new methods, fix errors
1) Method to add the draft measures
Let us install additional draft measures at the positions of third of her hull length from the bow and from the stern to be able to read and obtain the drafts df1 and da1 as “Figure 3” shown.
The formula (A.6) is the formula for calculating the original area exactly. Get this area divided by the length of the LPP will be dFinalMean as follows:
*Features: This method requires additional design of ship, but the advantage is simple to calculate.
2) Method of Bending Moment
Figure 4
Currently there have been software calculated Shearing Force and Bending Moment onboard.
Green curve in “Figure 4” denotes bending moment M along the longitudinal axis (horizontal axis l ) from the After perpendicular to the Fore perpendicular. The table to the left of the graph contains bending moment data have been calculated in the key frames numbered from zero starting at the After perpendicular. The adjacent frames coordinate with the horizontal axis and the moment curve to form the small trapezoids. By composite trapezoidal method, it is easy to calculate definite integrals of the moment M on the length of Lpp. In this example, Lpp = 132 (m), I calculated the results of integrals are:
* Features: This method requires Bending Moment data, but owns high precision and no need to add any draft measure.
* “Figure 4” is copied from a software named Loading Wizard 2011 which I’ve written.
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