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3DFoil: Sailboat Keel Analysis
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Tapered keels and rudders can be readily analyzed in 3DFoil and MultiSurface Aerodynamics. In the following article, we will analyze the tapered keel shown below in Figure 1. For this article, we will use the 3DFoil software although the steps are identical for MultiSurface Aerodynamics. We will use 3DFoil to investigate how two different sweep angles affect the lift, drag and the location of the center of lateral resistance for a new keel design.

Figure 1: Tapered Keel

Keel Planform Setup
We start the tutorial by entering the keel dimensions into 3DFoil. To do this, click on the Design menu followed by the Top Elevation option. This will invoke the Surface Editor screen shown below in Figure 2. The surface editor shows the default wing which is a 1m X 1m square surface.

Figure 2: The SurfaceEditor

The next step is to change the default surface into the keel of interest. To do this, double-click within the boundary of surface no. 1 on the SurfaceEditor screen to invoke the Edit Surface window show below in Figure 3.

Figure 3: Edit Surface Dialog Box

In the edit surface window, change the Span value to 100 and the span unit of dimension from meters (m) to inches (in). We choose to make the right chord the root of the keel and the left chord the tip. In the dialog box, change the Right Chord value to 100 and the unit of dimension from meters (m) to inches (in). Next, change the Left Chord dimension and unit to 70 and inches respectively.

For this tutorial, we wish to analyze sweep angles of 30 and 45 degrees. For the first investigation, set the sweep angle to 30 degrees in the Sweep Angle box. The sweep is about the 25% chord line so you must set the About Angle box to 25 % of chord. 3DFoil allows you the option of setting the sweep about the left or right tips of the keel. Here, choose the right tip and click on the right tip option in the Edit Surface dialog box. Figure 4 shows the new setting as they now appear in the Edit Surface dialog box.

Figure 4: Edit Surface Size/Shape Settings

Airfoil Settings
The keel (see Figure 1) has an 18% thick airfoil at the root chord and a 12% thick airfoils at the root chord. To set the airfoil at the root chord, select the Right Airfoil tab on the Edit Surface dialog box as shown in Figure 5. To change the default airfoil from the NACA 0012 to NACA 0018, I click on the right airfoil Select button. The select button invokes the Airfoil Data dialog box shown in Figure 6. To set the NACA 0018 airfoil, click on the NACA 4-Digit Airfoil button to invoke the NACA 4-Digit Airfoils dialog box. Figure 7 shows the NACA 4-Digit airfoil dialog box. Use the list boxes to choose the desired airfoil number. In this case it is the NACA 0018.

Figure 5: Right Airfoil Tab

Figure 6: Airfoil Data Dialog Box

Figure 7: NACA 4-Digit Airfoils Dialog Box

After setting the airfoil for the root, click on the Left Airfoil Tab of the Edit Surface dialog box and repeat the airfoil selection procedure for the airfoil at the tip of the keel. In the NACA 4-Digit Airfoils dialog box (see figure 7), select the NACA 0012 airfoil for the tip instead of the NACA 0018.

Figure 8 shows the plan view of the keel as seen in the SurfaceEditor window.

Figure 8: Planform view of the keel.

Flow Field Settings
We now wish to choose the fluid type (water) and set the speed of the boat. To do this, click on the Flow Field menu and select the Flow Field Conditions option. This invokes the Flow Field Conditions dialog box shown below in Figure 9.

To set an angle of attack of 5 degrees, enter 5 in the Angle of Attack box. To set a speed of 10 knots, enter 10 in the Speed box and select units of knots.

Figure 9: Flow Field Condition Dialog Box

To set water as the fluid, select the Fluid Type: Other button and then select properties of Sea Water 60 Degrees F. The user can select a variety of fluid properties and has the choice of entering a table of water densities, viscosities and vapor pressures.

We then click on the Forces/Moments tab to set the results units as shown below in Figure 10. First, set the moment Reference length to 1 meter. The reference length is used in all moment coefficient calculations. Since we wish to display force results in pounds, set the Force Units to Pounds. Set the Length Unit to inches to display the length results in inches. The speed results are displayed in the speed units selected under the Flow tab.

Figure 10: The Force/Moments Tab is used to set the Display Units.

Center of Gravity Settings
The center of gravity location is used a reference point and datum for moment calculations and center of pressure measurements. To use the origin as the center of gravity, click on the Weight/CG tab as shown below in Figure 11. Set the X-Distance, Y-Distance and Z-Distance boxes to zero. This (0,0,0) setting will place the reference point at the leading edge of the root chord of our keel.

Figure 11: The CG Locations is used as a reference point.

Modeling the Hull
Since the root chord of the keel is attached directly to the hull, it must be modeled as a reflective plane. Click on the Mirror/Ground Effect tab of the Flow Conditions dialog box as shown below in Figure 12. Next, click on the Mirror Image in X-Z Plane setting to select the radio button. Figure 8 shows the line of symmetry (labeled mirror) that models the hull.

Results and Graphs
The lift coefficient versus angle of attack graph shows the lift (lateral resistance) developed by the keel as the angle of attack (leeway angle) increases. With the sweep back setting of 30 degrees, click on the Surface Analysis menu and Cl vs AOA option. Next, set the sweep back angle to 45 degrees and again click on the Surface Analysis menu and the Cl vs AOA option. This will produce the graph of Cl vs AOA as shown below in Figure 13. The graph shows that the lift with 30 degrees angle of sweep is higher than with 45 degrees angle of sweep for corresponding angles of attack. Click on the Surface Analysis menu and the Cl vs Cd option to obtain the lift-drag polar for the keel as shown below in Figure 14.

Figure 12: Modeling the hull with the mirror image setting

Figure 13: Lift Coefficient vs Angle of Attack

Figure 14: Lift Coefficient vs Drag Coefficient

We can use the Reports menu and the Results Summary Table option to create a comparison chart of the keel's performance at a desired set of angles of attack. Figure 15 shows the results for the 30 degrees sweep back angle at the speed of 10 knots. 3DFoil computes lift, drag and moments about the reference location (CG). The program computes the center of lateral resistance for the keel as well. The x-component (horizontal value) is obtained by dividing the pitching moment by the lift. The y-component (depth) is obtained by dividing the roll moment by the lift. The results place the center of lateral resistance a distance of about 49 inches from the keel root leading edge and 44 inches in depth.

Figure 15: Results for 30 degrees sweep angle.

Figure 16: Results for 45 degrees sweep angle.

The results for 45 degrees sweep angle places the center of lateral resistance at 69 inches from the root leading edge and 44 inches in depth as shown in Figure 16.

For more information about 3DFoil, please visit http://www.hanleyinnovations.com. For availability and price, please call us at (352) 240-3658.

More Resources: MultiSurface Aerodynamics