Ines The outside surface of a ship is the surface of a solid with curvature in two directions. The curves which express this surface are not in general given by mathematical expressions, al though attempts have been made from time to time to express the surface mathematically. It is necessary to have some drawing which will depict in as detailed a manner as possible the outside surface of the ship. The plan which defines the ship form is known as a 'line plan. The lines plan consists of three drawings which show three sets of sections through the form obtained by the intersection of three sets of mutually orthogonal planes with the outside surface Consider first a set of planes perpendicular to the centre line of the ship. Imagine that these planes intersect the ship form at a number of different positions in the length. The sections obtained in this way are called body section and are drawn in what is called the sections as shown in Figure 1*. When drawing the body plan half-sections aft of amidships( the after body sections)are drawn on one side of the centre line and the sections forward of amidships( the fore body sections) are drawn on the other side of the center line. It is normal to divide the length between perpendiculars into a number of divisions of equal length(often ten)and to draw a section at each of these divisions. Additional sections are sometimes drawn near the ends where the changes in the form become more rapid. In merchant ship practice the sections are numbered from the after perpendicular to the forward perpendicular -thus ap is 0 and fp. is 10 if there are ten divisions. The two divisions of length at the ends of the ship would usually be subdivided so that there would be sections numbered 1/2, 11/2, 81/2, and 9172. Sometimes as many as 20 divisions of length are used, with possibly the two divisions at each end subdivided, but usually ten divisions are enough to portray the form with sufficient accuracy Suppose now that a series of planes parallel to the base and at different distances above it are considered. The sections obtained by the intersections of these planes with the surface of the ship are called" waterlines'or sometimes "level lines. the lines are shown in Figure 1. the waterlines like the body sections are drawn for one side of the ship only. They are usually spaced about, lm (3-4ft)apart, but a closer spacing is adopted near the bottom of the ship where the form is changing rapidly. Also included on the half breadth plan is the outline of the uppermost deck of the ship a third set of sections can be obtained by considering the inter-section of a series of vertical planes parallel to the centre line of the ship with the outside surface. The resulting sections are shown in a view called the sheer profile see Figure I and are calledbuttocks' in the after body and bow lines'in the fore body or often simply buttocks. The buttocks like the waterlines will be spaced Im(3-4ft)apart. On the sheer profile the outline of the ship on the centre line is shown and this can be regarded as a buttock at zero distance from the centre line The three sets of sections discussed above are obviously not independent of one another, in the sense that an alteration in one will affect the other two. Thus, if the shape of a body section is altered this will affect the shape of both the waterlines and the buttocks. It is essential when designing the form of the ship that the three sets of curves should be 'fair'and their ependence becomes important in this fairing process. What constitutes a fair curve is open to question. But formerly the fairing process was done very largely by eye. Nowadays the lines plan is often faired by some mathematical means which will almost certainly involve the use of theLesson Six Ship Lines The outside surface of a ship is the surface of a solid with curvature in two directions. The curves which express this surface are not in general given by mathematical expressions, although attempts have been made from time to time to express the surface mathematically. It is necessary to have some drawing which will depict in as detailed a manner as possible the outside surface of the ship. The plan which defines the ship form is known as a ‘line plan’. The lines plan consists of three drawings which show three sets of sections through the form obtained by the intersection of three sets of mutually orthogonal planes with the outside surface. Consider first a set of planes perpendicular to the centre line of the ship. Imagine that these planes intersect the ship form at a number of different positions in the length. The sections obtained in this way are called ‘body section’ and are drawn in what is called the ‘body sections’ as shown in Figure 1*. When drawing the body plan half-sections aft of amidships（the after body sections）are drawn on one side of the centre line and the sections forward of amidships (the fore body sections) are drawn on the other side of the center line. It is normal to divide the length between perpendiculars into a number of divisions of equal length (often ten) and to draw a section at each of these divisions. Additional sections are sometimes drawn near the ends where the changes in the form become more rapid. In merchant ship practice the sections are numbered from the after perpendicular to the forward perpendicular —thus a.p. is 0 and f.p. is 10 if there are ten divisions. The two divisions of length at the ends of the ship would usually be subdivided so that there would be sections numbered 1/2, 11/2, 81/2, and 91/2. Sometimes as many as 20 divisions of length are used, with possibly the two divisions at each end subdivided, but usually ten divisions are enough to portray the form with sufficient accuracy. Suppose now that a series of planes parallel to the base and at different distances above it are considered. The sections obtained by the intersections of these planes with the surface of the ship are called ‘waterlines’ or sometimes ‘level lines’. The lines are shown in Figure 1. The waterlines like the body sections are drawn for one side of the ship only. They are usually spaced about, 1m (3-4ft) apart, but a closer spacing is adopted near the bottom of the ship where the form is changing rapidly. Also included on the half breadth plan is the outline of the uppermost deck of the ship. A third set of sections can be obtained by considering the inter-section of a series of vertical planes parallel to the centre line of the ship with the outside surface. The resulting sections are shown in a view called the ‘sheer profile’ see Figure 1 and are called ‘buttocks’ in the after body and ‘bow lines’ in the fore body or often simply ‘buttocks’. The buttocks like the waterlines will be spaced 1m (3-4ft) apart. On the sheer profile the outline of the ship on the centre line is shown and this can be regarded as a buttock at zero distance from the centre line. The three sets of sections discussed above are obviously not independent of one another, in the sense that an alteration in one will affect the other two. Thus, if the shape of a body section is altered this will affect the shape of both the waterlines and the buttocks. It is essential when designing the form of the ship that the three sets of curves should be ‘fair’ and their interdependence becomes important in this fairing process. What constitutes a fair curve is open to question. But formerly the fairing process was done very largely by eye. Nowadays the lines plan is often faired by some mathematical means which will almost certainly involve the use of the