Making an Fast Sailboat Body by Minimizing the Volume of Hydrodynamic and Aerodynamic Boat Elements Tom Augenstein, Mechanical Engineering Class of 2017 Sara Gregg, Mechanical Engineering Class of 2016 Jacob Langenbacher, Mechanical Engineering Class 2016 Biorobotics and Locomotion Laboratory Cornell University United States May 14, 2016 Abstract Our research is to design and manufacture a small, cheap, and mass-producible autonomous robotic sailboat that can intelligently navigate the ocean and collect data. The project is meant to decrease the cost of environmental research by designing a research vessel that can cheaply collect data such as salinity, turbidity, fluorescence, or acoustic patterns. Our boat has a symmetrical airfoil sail, a thin, bulbed keel, and a new and unique control surface: a controlled tail fixed to the trailing edge of a controlled sail. Our simulations suggest that this set-up has directional stability. Directional stability is a boat's ability to maintain any stable heading without electrical or mechanical actuation. Directional stability will help our smaller sailboat intelligently navigate high water current environments such as the ocean. This is important because smaller sailboats like ours are slow and more susceptible to motion dominated by these currents. This report documents the design and fabrication processes of the "body" of sailboat, addresses the discovered shortcomings of our designs, and discusses our plans to improve. The body of the boat is everything that keeps the boat afloat and upright, like the hull, deck, and keel. The body also includes elements inside the body such as the mast controlling system. The primary objective of our designs was to reduce drag on each body element while preserving each components role. For the hull and deck, this means eliminating as much volume above and below the waterline as possible to reduce aerodynamic and hydrodynamic drag, respectively. We accomplished this by scaling an existing racing yacht hull shape to a one-meter waterline length. With the new, small shape, we eliminated the majority of the hull's volume above the waterline, leaving us with a very thin and narrow hull with very little exposed volume above or below the waterline. The keel is very thin and deep to reduce drag with a heavy ballast at its deepest point to maximize its righting moment. The keel tapers as it moves towards the ballast, with a longest chord near the hull, to keep the side force close to the hull and reduce unwanted heeling moments. Preliminary testing indicates that our designs should be improved to increase the pitching and heeling stability of our sailboat in high winds. During testing, we found that higher winds sometimes result in unwanted sailing behavior such as oscillatory motion and the boat finding a stable equilibrium position with the tail upwind to the sail. We plan to improve our sailboat's high wind behavior by implementing one or more of the following elements: Heavier ballast, outer rigging, active keel to increase righting moments, and an active mast to keep the sail's driving force above the keel's center of pressure during heeling. In addition, in high wind situations, the sailboat will nosedive while sailing downwind. This will likely be remedied by elongating and sharpening the prow (the above-water part of the bow), similar to a viking longship, to more effectively cut through the water and stay afloat. Contents 1 Introduction 2 2 Selecting the Shape of Our Boat Components 2 2.1 Selecting our Hull Shape . 2 2.2 Designing with our Hull Shape . 4 2.3 Mast Control Design . 7 2.4 The Deck . 10 2.5 Mass Projection . 11 2.6 Designing the Keel Shape . 11 2.6.1 Theory . 11 2.6.2 Design Specifics . 13 3 Fabrication of Our Boat Components 17 3.1 Fabrication of Our Sailboat Hull/Deck . 17 3.2 Fabrication of Our Keel . 20 3.3 Fabrication of Our Mast Control . 21 4 Analysis 22 5 Future Work 24 6 Conclusions 25 7 Appendices 26 7.1 Appendix I: Detailed Hull Fabrication Process . 26 7.2 Appendix II: Detailed Keel Fabrication Process . 30 7.3 Appendix III: Epoxying Procedure . 31 7.4 Appendix IV: Vacuum Bagging . 31 7.5 Appendix V: Wind Vane . 32 1 1 Introduction It is logical to think of a sailboat as a sideways airplane moving in two different fluids. Both vehicles are governed by the same by physical laws, harness similar lift forces, and fight similar drag forces. This thought experiment allows us to imagine a \physically-optimized" sailboat, or a sailboat with only lift forces and no drag forces. A truly optimized sailboat has a thin, near-infinitely deep keel with small point mass at its end. The sail is the same, very thin and reaching very high. The last source of drag on our perfect sailboat to eliminate is that on the hull moving through the water. Because a hull does not provide a lift force, our perfect boat's hull is nonexistent (assuming that the sail and keel are massless). A non-existent hull is not feasible, but a long, narrow, and thin hull is feasible and a reasonable substitute because it minimizes the drag forces from both the air and water. Our hull is one meter long, narrow, and very flat, with only three-quarters of an inch vertically above the waterline. The shape is meant to be fast and minimize both air and water drag while maintaining rolling and pitching stability, supporting our mass budget, and providing space for an effective mast motor control system. The keel is very thin, starting with a long chord near the hull and tapering to a very small chord at its end. There is a torpedo shaped ballast fixed to the bottom. Both the hull and the keel were manufactured using a smoothed foam surface shaped into our desired shape. For the hull, the smooth surface was used to take both negative and positive molds with fiberglass. 2 Selecting the Shape of Our Boat Components 2.1 Selecting our Hull Shape Before choosing the curvature of our sailboat, we first had to define what we considered to be a \good" shape. We define a good hull as fast, stable, and supportive of our mass budget. We chose an existing hull shape and scaled the shape down to one meter long instead of designing our own due to time constraints. A fast boat hull is typically long and very narrow. Also, fast hulls typically have very little volume below the waterline to further decrease drag. A stable hull has a low draft to beam ratio i.e. small depth compared to width. Seeking a narrow and shallow hull barely filtered our pool of potential hulls because there are an uncountable number of existing monohulls, catamarans, and trimarans that satisfy our criteria. Our mass budget drastically reduced the number of useful hulls. We expected that our sailboat would weigh approximately five kilograms, so we chose a hull with a long, narrow shape that, when scaled to our sizes, could support our mass budget. It is important to note that \supporting" a mass budget is different than floating with a given mass. Professionally made sailboats have a \Displacement" characteristic, measured in units of mass. This displacement value is the mass of the water that the hull displaces when it is sailing under normal circumstances (expected number of passengers, constant velocity, no tipping, etc.). In other words, it is the mass that the boat was designed to sail with. However, when scaling a hull's length by some factor, according to Archimedes' Principle, the displacement scales by the cube of the same factor. This relationship is shown mathematically below. In the following equations, we assume a boat hull is a perfectly submerged rectangle, with its top surface flush with the waterline. In addition, L is the length of the rectangle, W is width, H is height, 2 and C is an arbitrary scale factor. ρwater is the density of water, g is the gravitational acceleration, and V is the hull's volume. Lnew = C ∗ L (1) Wnew = C ∗ W (2) Hnew = C ∗ H (3) Displacement = ρwater ∗ g ∗ V = ρwater ∗ g ∗ (L ∗ W ∗ H) (4) Displacementnew = ρwater ∗ g ∗ (Lnew ∗ Wnew ∗ Hnew) = ρwater ∗ g ∗ (C ∗ L ∗ C ∗ W ∗ C ∗ H) (5) 3 Displacementnew = Displacement ∗ C (6) Many modern racing sailboats, when scaled down, have mass budgets too small to fit our needs. For example, The Comanche, one of the fastest racing yachts in the world, can reach up to 40 knots (46 mph). The Comanche has an overall length of 100 ft and displacement of 35 metric tons [1]. When scaled down to a meter length, the Comanche has a resulting displacement of only 1.23 kilograms. This drastic drop in mass budget compared to size removed all racing trimarans and catamarans, or at least the ones we could find. It also eliminated most modern racing yacht hulls, typically possessing a scaled displacement between one and two kilograms. The small displacement of these hulls arises from their narrow, flat shape, which displaces very little water compared to passenger yachts of comparable sizes. We decided that the Luja, a modern racing yacht by Sparkman & Stephens, is a suitable fit. An image of Luja's hull line plans are shown below. Figure 1: Line Plans of the Luja 3 The hull is long, narrow, and has flatter curvature below the waterline. This hull design is notably older than the other hulls we initially looked at (The Luja debuted in 1929 while the the Comanche was debuted in 2015). Older racing yacht hulls are better for our needs because they are typically much wider than more modern models.