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Hydrodynamics: Wave Generating Drag

Issue No 62, 20 May 2024

By: Anthony O. Ives

In a previous article, buoyancy [1] was looked at when sizing helicopter floats [2] but the same princple applies to anything including boat hulls. However, when a boat or float starts moving through the water it generates a resistance force similar to an aircraft which can also be called drag generally referred to as hydrodynamic drag. There are two main types of hydrodynamic drag, skin friction drag and wave generating drag.

Aircraft such as flying boats, float planes and amphibian aircraft which take off in water will also generate hydrodynamic drag until they get airborne. These type of aircraft need floats or a hull that generate the minmum of hydrodynamic drag. This could also apply to helicopter floats or hulls as in certain circumstances a helicopter may need to do a running landing.

As explained earlier in the article there are two types of hydrodynamic drag. The first type of hydrodynamic drag; friction drag can be calculated in the same way as aircraft aerodynamic drag [3] except using the values of water for density, ρ_water=997.0kgs^-1 and vicosity, μ_water=1.0016×10^-3Pas.

Wave generating drag is the other type of hydrodynamic drag which is specfic to boats or other surface vessels which move on top of the water. Submarines when submerged do not make waves so therefore do not produce wave generating hydrodynamic drag however, when surfaced submarines do make waves and have to overcome wave generating hydrodynamic drag as well. Submarines generally can achieve a higher maximum speed when submerged as they are usually designed to be submerged under water. Hydrodynamic drag is generally the dominating hydrodynamic drag of surface watercraft hence surface watercraft hulls are usually designed to minmise this type of drag.

There are two types hulls that surface watetcraft can have that is displacement and planning hulls. Most watercraft such canoes, kayaks, rowboats, sailboats, etc have displacement hulls. Some motor boats can have displacement hulls as well however, these are generally larger boats or boats not designed for speed. Nearly all small speed boats or fast boats such as RIBs (Rigid Inflatable Boats) need a planning hull in order to achieve high speeds.

A displacement hull is always partially submerged in the water as required for bouyancy [1] and hence has to make waves in order to move through the water. Therefore, a displacement hull typically has a limited maximum speed related to the length of the hull.

Hull speed of the a displacement hull is the speed at which the wavelength of the bow wave of the vessel is equal to the waterline length of the vessel. The approximate hull speed can be determined by the following equation:

\[u_{hull} \approx 1.34 \sqrt{L_{WL}}\]

Therefore u_hull is the hull speed in knots and L_WL is the length of waterline in feet. Converting the hull speed to metres per second, ms^-1 and the waterline length in metres the equation becomes:

\[u_{hull} \approx 0.514 \times 1.34 \times \sqrt{3.281} \times \sqrt{L_{WL}}\] \[ \approx 1.248 \sqrt{L_{WL}}\]

The hull speed of the vessel is generally considered the maximum practical speed the vessel is capable of as trying to exceed it requires extremely high power which could not be practically possible. Froude number is a non dimensional number which can be used to define a vessel's speed defined as below:

\[Fr=\frac{u_0}{\sqrt{gL_{WL}}} \]

Where Fr is Froude number, u₀ is the vessel's speed and g is gravity or accerelation of freefall which as usual is assumed to be 9.81 ms^-2. Therefore the equivalent Froude number for hull speed is defined below:

\[Fr_{hull} \approx \frac{1.248 \sqrt{L_{WL}}}{\sqrt{gL_{WL}}}\] \[ \approx \frac{1.248}{\sqrt{g}} \] \[ \approx 0.398 \]

Displacement hull design theory has been used by Terry Laughlin in his series of books on the swimmmimg technique 'Total Immersion' [4]. The 'Total Immersion' swimming technique uses the principle of reducing a swimmer's Froude number by increasing their length by always holding one arm out in the water and swimming on their side to reduce their surface area, etc.

Calculating wave generating drag [5] for a displacement hull can be done by using a complicated equation requiring numerical integration [6]. Wave generated drag calculations will be looked at in a future article.

Planning Hulls overcome hydrodynamic drag due to wave generation by having a hull that is designed to produce hydrodynamic lift which does not require the hull to be as partially submerged as a displacment hull when moving at high speed. For a planning hull therefore the hull sits on the bow wave hence is not restricted and can exceed its hull speed for its small size. Hydrodynamic lift, etc required for planning hull can be calculated [7]. However a future article will look in more detail at the calculations required to design a planning hull. Sailboats generally have a displacement hull but some small high performance sailboats can be made to plane briefly if they are lightly loaded, their centre of gravity is kept at the aft and winds, sea conditions are favorable.

A hydrofoil is a type of submerged wing fitted to the underneath of the front of the watercraft's hull which produces a form of hydrodynamic lift simliar to aerodynamic lift [8] produced by an aircraft wing. At certain speed the hydrofoil lifts the front of the watercraft's hull out the water reducing both wave generating and skin friction drag. Calculations [8,9] for a hydrofoil's lift can be made in a similar way as they are for an aircraft wing only using the properties of water instead of air.

Larger vessels genetally do not need to consider wave generating hydrodynamic drag as much as smaller watercraft due to their length giving a sufficient hull speed. However, some large vessels use a bulbous bow to reduce wave making hydrodynamic drag and increase performance, etc. The bulbous bow uses the principle of cancellation by creating opposite and equal waves, etc. Another method to reduce wave generating hydrodynamic drag is a wave piercing hull which has a very fine bow which just literally pierces through the wave due to lack of bouyancy at the forward part of the hull preventing it from riding over the top of the wave. A wave piercing hull also results in a smoother ride in rough seas.

Please leave a comment on my facebook page or via email and let me know if you found this blog article useful and if you would like to see more on this topic. Most of my blog articles are on:

Mathematics
Helicopters
VTOL UAVs (RC Helicopters)
Sailing and Sailboat Design

If there is one or more of these topics that you are specifically interested in please also let me know in your comments this will help me to write blog articles that are more helpful.

References:

[1] Mechanics of Fluids, B. S. Massey, John Ward-Smith, 7th Edition, 1998, CRC Press

[2] http://www.eiteog.com/EiteogBLOG/No61EiteogBlogBoat.html

[3] http://www.eiteog.com/EiteogBLOG/No2EiteogBlogDragCD.html

[4] 'Total immersion: The revolutionary way to swim better, faster and easier', Terry Laughlin, John Delves, 2004, Fireside

[5]The Wave-Resistance of a Ship, John Henry Mitchell, Philosophical Magazine, 1898, Vol 45, Ser.5, pp. 106-123 https://www.boatdesign.net/attachments/the-wave-resistance-of-a-ship-pdf.34511/

[6] http://www.eiteog.com/EiteogBLOG/No50EiteogBlogIntegration.html

[7] Performance Prediction of Hulls with Transverse Steps, David Svahn, June 2009, MSc Thesis Royal Institute of Technology, KTH, Centre for Naval Architecture, Stockholm, Sweden

[8] http://www.eiteog.com/EiteogBLOG/No1EiteogBlogLiftCL.html

[9] http://www.eiteog.com/EiteogBLOG/No23EiteogBlogLift.html

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