Preliminary Design of a Sloop Rigged Yacht

13.734 - Sailing Yacht Design Fall 2003 Problem Set 1 Addendum - Solutions Preliminary Design of a Sloop Rigged Yacht The solutions are computed using the same Matlab program developed for Problem Set 1 with few modifications for part 0. Numerical Results 11. Again a high accuracy and a low accuracy set of results are given. These results are for the new, smaller keel, while the mast still has the original height. The amount of ballast in this case exceeds the 5% of the total lead, being around 6.5%. The Dellembaugh angle is still well below 20 degrees. High Accuracy Results Maximum Beam Maximum Draft Canoe body displacement Canoe body LCB Canoe body VCB Keel displacement Keel root chord Keel LCB Keel VCB Keel VCG Rudder displacement Rudder LCB Rudder VCB Yacht displacement Mass of lead Mass of keel, incl. structure Empty volume in keel Internal ballast Yacht VCG Yacht VCB Yacht LCB Sectional area coefficient Metacentric height GM Yacht BM Yacht KB Yacht KG Waterplane area LCF 3 m at x = -1.6667 0.5 m at x = 0 6 m^3 0.43106 m aft of amidship 0.15916 m below DWL 0.27563 m^3 1.5 m 0.033482 m forward of amidship 1.2857 m below DWL 1.2857 m below DWL 0.017472 m^3 4.74 m aft of amidship 0.6392 m below DWL 6.2931 m^3 or 6450.4244 Kg. 3030.4244 Kg 3020.2813 Kg 0 m^3 150.1432 Kg 0.087944 m below WL 0.20983 m below WL 0.42267 m aft of amidship 0.72 1.6053 m 1.7271 m 0.29017 m 0.41206 m 20.7438 m^2 0.71412 m aft of amidship Mast height Main area Main CE Jib Area Jib CE Total Area 15 m 34.5 m^2 6.8 m above WL 27.95 m^2 5.5333 m above WL 62.45 m^2 Sailplan CE Vertical CLR Dellenbaugh angle Dellenbaugh angle (actual SA) 6.2331 m above WL 1.1667 m below WL 12.4857 deg 14.7331 deg Low Accuracy Results Maximum Beam Maximum Draft Canoe body displacement Canoe body LCB Canoe body VCB Keel displacement Keel root chord Keel LCB Keel VCB Keel VCG Rudder displacement Rudder LCB Rudder VCB Yacht displacement Mass of lead Mass of keel, incl. structure Empty volume in keel Internal ballast Yacht VCG Yacht VCB Yacht LCB Sectional area coefficient Metacentric height GM Yacht BM Yacht KB Yacht KG Waterplane area LCF 3 m at x = -1.6667 0.5 m at x = 0 6 m^3 0.43615 m aft of amidship 0.15906 m below DWL 0.27563 m^3 1.5 m 0.033482 m forward of amidship 1.2857 m below DWL 1.2857 m below DWL 0.017472 m^3 4.74 m aft of amidship 0.6392 m below DWL 6.2931 m^3 or 6450.4244 Kg. 3030.4244 Kg 3020.2813 Kg 0 m^3 150.1432 Kg 0.087944 m below WL 0.20974 m below WL 0.42753 m aft of amidship 0.72 1.609 m 1.7308 m 0.29026 m 0.41206 m 20.5414 m^2 0.67002 m aft of amidship Mast height Main area Main CE Jib Area Jib CE Total Area Sailplan CE Vertical CLR Dellenbaugh angle Dellenbaugh angle (actual SA) 15 m 34.5 m^2 6.8 m above WL 27.95 m^2 5.5333 m above WL 62.45 m^2 6.2331 m above WL 1.1667 m below WL 12.4568 deg 14.6991 deg 12. As shown in 11, the Dellembaugh angle is still too small. To find the correct mast height, the main Matlab program has been modified so that it keeps changing the mast height and performs the entire calculation until the Dellembaugh angle falls within desired interval. The results show that a mast height of either 18 m or 18.25 m satisfies the stability criteria, with the second one being closest to the desired value. And the amount of ballast is below the desired 5% limit at 2.7%. High Accuracy Results Maximum Beam Maximum Draft 3 m at x = -1.6667 0.5 m at x = 0 Canoe body displacement Canoe body LCB Canoe body VCB Keel displacement Keel root chord Keel LCB Keel VCB Keel VCG Rudder displacement Rudder LCB Rudder VCB Yacht displacement Mass of lead Mass of keel, incl. structure Empty volume in keel Internal ballast Yacht VCG Yacht VCB Yacht LCB Sectional area coefficient Metacentric height GM Yacht BM Yacht KB Yacht KG Waterplane area LCF 6 m^3 0.43106 m aft of amidship 0.15916 m below DWL 0.27563 m^3 1.5 m 0.033482 m forward of amidship 1.2857 m below DWL 1.2857 m below DWL 0.017472 m^3 4.74 m aft of amidship 0.6392 m below DWL 6.2931 m^3 or 6450.4244 Kg. 2910.355 Kg 3020.2813 Kg 0 m^3 30.0737 Kg 0.12811 m above WL 0.20983 m below WL 0.42267 m aft of amidship 0.72 1.3892 m 1.7271 m 0.29017 m 0.62811 m 20.7438 m^2 0.71412 m aft of amidship Mast height Main area Main CE Jib Area Jib CE Total Area Sailplan CE Vertical CLR Dellenbaugh angle Dellenbaugh angle (actual SA) 18.25 m 42.625 m^2 7.8833 m above 34.0058 m^2 6.6167 m above 76.6308 m^2 7.3212 m above 1.1667 m below 20.307 deg 23.9622 deg WL WL WL WL Low Accuracy Results Maximum Beam Maximum Draft Canoe body displacement Canoe body LCB Canoe body VCB Keel displacement Keel root chord Keel LCB Keel VCB Keel VCG Rudder displacement Rudder LCB Rudder VCB Yacht displacement Mass of lead Mass of keel, incl. structure Empty volume in keel Internal ballast Yacht VCG 3 m at x = -1.6667 0.5 m at x = 0 6 m^3 0.43615 m aft of amidship 0.15906 m below DWL 0.27563 m^3 1.5 m 0.033482 m forward of amidship 1.2857 m below DWL 1.2857 m below DWL 0.017472 m^3 4.74 m aft of amidship 0.6392 m below DWL 6.2931 m^3 or 6450.4244 Kg. 2910.355 Kg 3020.2813 Kg 0 m^3 30.0737 Kg 0.12811 m above WL Yacht VCB Yacht LCB Sectional area coefficient Metacentric height GM Yacht BM Yacht KB Yacht KG Waterplane area LCF 0.20974 m below WL 0.42753 m aft of amidship 0.72 1.3929 m 1.7308 m 0.29026 m 0.62811 m 20.5414 m^2 0.67002 m aft of amidship Mast height Main area Main CE Jib Area Jib CE Total Area Sailplan CE Vertical CLR Dellenbaugh angle Dellenbaugh angle (actual SA) 18.25 m 42.625 m^2 7.8833 m above 34.0058 m^2 6.6167 m above 76.6308 m^2 7.3212 m above 1.1667 m below 20.2527 deg 23.8982 deg WL WL WL WL