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How do I calculate a boat's keel or daggerboard (area and lift of the fin)?
A daggerboard (keel, fin, rudder) is a hydrodynamic aerofoil whose lift opposes the side force of the sails. Sizing it means finding the area S and the leeway angle (angle of attack of the fin relative to the course) such that the lift balances that side force with the least drag. Lift is ½ ρ V² S CL: water density (1,000 kg/m³), boat speed squared, fin area and lift coefficient of the aerofoil at the leeway angle. Example: at 6 knots (3.09 m/s), to balance 1,000 N with a symmetrical NACA 0009 section at 3° of incidence (CL ≈ 0.25), 0.84 m² of fin is needed.
Lift formula for a daggerboard
- FL: lift of the fin, in N; it must balance the side force of the sails
- ρ: density of water, 1,000 kg/m³ (1,025 kg/m³ at sea)
- V: boat speed through the water, in m/s (1 knot = 0.514 m/s)
- S: fin area, in m² (chord × immersed span)
- CL: lift coefficient of the aerofoil at the leeway angle, read on its polar: about 0.08 per degree for a symmetrical section, up to the stall at 12 to 15°
Fin area required against boat speed
| Boat speed | Speed in m/s | Dynamic pressure ½ ρ V² | Fin area S |
|---|---|---|---|
| 3 knots | 1.54 | 1,190 Pa | 3.36 m² |
| 4 knots | 2.06 | 2,117 Pa | 1.89 m² |
| 6 knots | 3.09 | 4,764 Pa | 0.84 m² |
| 8 knots | 4.12 | 8,470 Pa | 0.47 m² |
| 10 knots | 5.14 | 13,230 Pa | 0.30 m² |
Lift of a 1.5 m² fin against leeway angle
| Leeway angle | CL (NACA 0009) | Lift FL |
|---|---|---|
| 1.5° | 0.13 | 929 N |
| 3° | 0.25 | 1,786 N |
| 6° | 0.50 | 3,573 N |
| 10.5° | 0.78 | 5,574 N |
Detailed explanations and calculation in Mecaflux
Example of calculating a boat keel dagger board rudder profile, with software mecaflux:
What are the forces?
The wind in the sails (sail example calculation), generates a propulsive component (this is the one that moves the boat) and a drift component. (This is the one that push the boat on the side). We will assume for this calculation that the drift component is 1000 Newtons and applies a profile that we call: dagger board .
The role of this dagger board is to create a force drift control balancing 1000N with the Lift force generated by its profile.
Fluid velocity is the speed of the boat.
The incidence (or attack) of profile, relative to the direction of the fluid, is the slip angle of the boat or drift. You have, in the converter mecaflux, a trigonometric triangle, which will give you the angle of incidence quickly if you enter the distance as adjacent side and drift as opposite side.
In reality, the lift is perpendicular to the movement of fluid but slightly simplify our example.
-We seek a lift force that balances 1000 Newtons
To realize this we can playing on:
-boat speed (average speed for a boat: 6 knots) (use convertor)
-the slip angle of the boat (that is the angle formed by the axis of the vessel with its actual trajectory)
-the length of the dagger board
-the width or chord of the dagger board:
calculating dagger board with mecaflux software
- Select a profile with drag and lift for your dagger board, if it is a drift windsurfing or boat he'd better be symmetrical (when you enter the profile chord its camber appears, if it remains null, is that it is a symmetrical profile).
Two symmetrical profiles tested in the wind tunnel are usable: NACA0009 and J5012 (polar patterns are already set in MECAFLUX but you can change the Cd and CL , Here we chose NACA0009 .
- Enter the parameters of the fluid (speed : 6 knotes, temperature:20°C, density:1000Kg/m3)
- Enter the profile chord (the width of the dagger board, take 1 meter)
- Enter the length of the dagger board (say 1.5 meters)
- Enter incidence profile (attack angle betwen the flow direction and the profile chord) let's try 10.5°. The proposed impact values are those studied in wind tunnels, they are limited to the interesting angles, beyond the profiles are stalling)
-Click to calculate
The result sheet is convenient to print or save the calculations, but for our case rather look at the diagram, close the result sheet:
The diagram of the profile indicates the value of the lift and drag ...
We see that the lift is 5588 Newtons ( 570 Kg.f ) this is far more than we need, we can say that our daggerboard, when the boat drifting 10.5°,more than makes up slippage. We can assume, at this speed (6 knots) it will never reach this drift angle.. Then adjust the angle of drift until it generates a lift balancing 1000 Newtons...
-With 3° incidence :Lift=1748 Newtons ( 178 Kg.f ) Drag: 5,1 Newtons
-With 1.5° incidence : Lift=911 Newtons ( 92 Kg.f ) Drag:4,4 Newtons
We can say that our greaSupert-Daggerboard give us a super-boat that derive only 1.5° à 2°. Which will be the envy of América-cup competitors. Unfortunately the drag of our super-Profile is a super drag and super-slowing down our boat (it will take about 1m ² of additional sail at force 5 to compensate for its drag ......)
Seek a lower drag by reducing the friction surface of the profile::
- With an incidence 6° , a chord 0.5 and a length 1 meter (surface: 0.5m²) wee obtain:
Lift force of naca0009 is 104 Newtons ( 106,5 Kg.f )
Drag force for naca0009 is 4,2 Newtons
it is up to you to look for the best compromise between speed, incidence, drag, lift, size, strength ... of your future boat ...
MECAFLUX gives the results of a sufficient finesse to think and approach a good compromise , to refine the calculations of wings or daggerboards of more complex shapes by integrating losses tips, you can also use Heliciel .. See calculation daggerboards and wings with Heliciel:
Back to External flow exemples
Frequently asked questions
Why does a daggerboard have a symmetrical section?
Because it must lift equally on port and starboard tack: a cambered section would favour one tack. The symmetrical NACA 0009 and NACA 0012 sections are the most common; the 0009, being thinner, has less drag, while the 0012 is stronger and stalls a little later. The rudder follows the same logic.
What is the normal leeway angle of a sailing boat?
From 3 to 6° close-hauled for a cruising boat, 2 to 4° for a racing yacht with an efficient keel. At these angles the lift coefficient is 0.2 to 0.5. Beyond 12 to 15° the section stalls: lift collapses and the boat slides sideways, which happens at low speed, for instance just after tacking.
How can the drag of the fin be reduced?
By keeping the area to what is strictly needed, by increasing the aspect ratio (a deep, narrow fin rather than a short, wide one, to reduce tip losses) and by keeping the surface smooth. Drag is made of skin friction, proportional to the wetted area, and induced drag, proportional to CL² and inversely to the aspect ratio: a fin of aspect ratio 3 has three times less induced drag than a square fin.
How do I size the keel or daggerboard of my own boat?
In the drag and lift tab of Mecaflux Standard you choose a section (NACA 0009, 0012 or your own), water and its temperature, the speed, the chord, the span and the incidence: the software displays the lift, the drag and the diagram of the section for each setting. Heliciel goes further for a fin or foil of varying shape: chord distribution, twist, tip losses and 3D export to CAD. For a boat to design or improve, Mecaflux carries out the study of your project, or offers training on the software applied to your own project.