Safe Loading - Subpart C
Calculation of Maximum Displacement
Simpson’s Rule: This is a method used to calculate the volume of odd-shaped objects. It is based on dividing the object into stations, finding some specific dimensions, and then applying a series of multiplier factors to come up with the volume of the object. Later in this section we will discuss this system and include blank forms for the calculations, as well as including an example.
The actual dimensions used in this formula can be obtained from either:
- Hull lines drawings;
- Measuring a hull mold; or
- Measuring a boat.
Hull Lines Drawings: You can establish the static float-plane and all the sections as required by Simpson’s Rule on the hull lines drawings, and then figure the section areas with a planimeter; or you can measure the vertical dimensions at the proper stations directly from the drawings, and compute the volume as per the worksheet below.
Measuring a Hull Mold: You can also measure a hull mold by establishing the float-plane. Install a string along the centerline, establish all the sections, and enter all measurements on the work sheet. This is the easiest method if you do not have boat drawings or a CAD system. Measurements must be taken to the inside of the mold surface (outside of the boat’s surface). Do not consider rub-rails or any hardware when establishing beam and length dimensions.
Measuring the Boat: There may be cases in which it is impractical to measure a mold, so an alternative method is to measure an existing boat. The figures needed for using Simpson’s Rule are the same as in Figure 3 below, except that the method used is the reverse of measuring the mold. In other words, after establishing a float-plane, establishing the calculation length, and establishing the stations (or sections), the measurements are taken by drawing a line on the floor as the projection of each station, from the centerline to the projected calculation beam at each station location. Then divide the half-beam line into five equal spaces and measure from the floor to the projected points a, b, c, d, e, and f, where these intersect with the bottom of the boat. Subtract these measurements from the calculated distance between the float-plane and the floor. This will result in the values to be entered on the work sheet.
The method to calculate the displacement by measuring the mold is adapted so the same procedure may be used with all three categories of boats. The specific differences will be clearly noted for the technician to include in the calculations. For example, in the case of an outboard boat, the volume of the engine-well below the float-plane must be deducted, while an inboard boat does not have this feature. This method simplifies the calculation by making the displacement calculations equal for all boat categories.
FIGURE 3 - Determination of Boat Displacement
Mold Preparation: Set the hull mold on the floor so that the keel line is level as described under the definition of "Horizontal Boat" in section 2.0.
Determine where the float-plane will intersect the transom. Look for the lowest point of water ingress on the boat (possibly the external engine vents on an inboard or the coaming of the engine well on an outboard). If the boat does not need to be rated for the largest capacity possible, ignore the deck or other superstructure. Remember that drains, scuppers, bilge-pump discharge fittings, deck-to-hull joint, and other sources of minor leaks may be below the float-plane.
Attach a string to the bow of the mold on the centerline, and to the point on the transom or transom plane where all points of major leaks are now above the string. This is the static float-plane.
Look at Figure 3 and notice that the calculation length (L) dimension we will use for Simpson’s Rule is not the same as the LOA, or length-over-all, of the boat. Rather, it is the dimension taken from the most forward point of the interior of the mold below the static float-plane to a point on the transom (or transom plane for those boats with odd-shaped sterns) which is the mid-point between the static float-plane and the keel line or its projection. Mark, with a piece of tape on the string, the vertical projection of this mid-point on the transom. The calculation length (L) will be the horizontal distance from this tape to the most forward point on the interior of the mold.
Divide the length of the string into four equal spaces, and then divide the most forward of these into two equal spaces. Look again at the hull in Figure 3. You now have established Sections: AA, A, B, C, and D.
The next step is to mark, on the topside flange of the mold, the places where the beam of each section will intersect the hull sheer or perimeter of the mold. The easiest method is to attach a piece of masking tape to the top of the mold approximately in the area where this intersection will be, and then, with a straight edge across the top of the mold, mark the outboard point of intersection when both ends of the straight edge are equidistant from the transom (or perpendicular to the centerline string). Now you have marked the place where the calculation beam used in the formula will be measured. The float-plane may very well be below the top flange of the mold where the straight edge has been placed, so if you measure the distance between the straight edge and the string marking the float-plane and call it dimension x (see figure 3A), this number must be subtracted from the measurements in the next step.
Divide the half-beam distance on each station (or section) into five equal spaces. Measure the vertical distance from the straight edge to the bottom of the mold at each of the points marked a, b, c, etc. Then subtract dimension x from these measurements to arrive at the net dimension between the static float-plane and the mold bottom (outside skin of the boat), to be entered on the blank spaces provided in Figure 4, for a, b, c, etc.
Look carefully at Figure 3-A. You have measured the net dimension between the float-plane and the boat on each of the vertical lines at each station; now enter them in the blank form located in section 4.1. Then enter the beam at each station. Remember this is the full calculation beam and not the half-beam. Enter the calculation length (L). Figure 4 shows a detailed look at the manner in which the stations A-A, A, B, C and D are laid out and measured.
FIGURE 3 A - Determination of Boat Displacement - Detailed
We are now ready to calculate the displacement in pounds. In Figure 4 we have a worksheet to compute the Simpson’s Rule formula and arrive at the cubic capacity which, when multiplied by the weight of a cubic foot of water, will give us the boat’s displacement below the float-plane. It’s a good idea to make extra copies of these blank forms. Fill in the values measured and run the equations to get cubic capacity.
When you finish the calculations on these forms, the displacement of the boat measured inside a mold has been determined. This figure, known as the maximum displacement, is used to calculate the maximum weight capacity.
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