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Boat Resistance

QUESTION: What makes up the resistance of a boat and how might it be calculated?

Total boat resistance is typically made up of several factors:

Frictional Resistance

Although both frictional and wave-making resistance vary with Length and Speed, they do not vary in the same way.
For over 100 years, it was realized that FRICTION varied with the wetted surface and the square of speed (SV²) and mildly affected by length.
Since that time, a formula by Englishman William Froude was used, namely:

R = ƒSV1.83    with values for ƒ being as follows:
[Where R = resistance in lbs, S = surface in ft², L = length in feet, and V = speed in knots]

Although Froude did notice some irregularities in the results, the formula was used for over 50 years without much challenge and in fact, is still surprisingly good for boats under 50 ft.

During the last 50 years or so, it has been realized that frictional resistance also varies with the ratio of: Viscosity (v) to surface length and speed. (Viscosity can be considered as the resistance to flow or to shear within the fluid.)

In the 1860–70s, British Professor Osborne Reynolds conducted tests of liquids flowing through pipes of various diameters and lengths, at varying velocities and discovered that for each specific value of Viscosity, ν ÷ L × V, the dynamic conditions were comparable. Since then, the reciprocal flow value LV/ν has become known as the Reynolds Number (Re) and more recent calculations of friction, take this into account. (This dimensionless Reynolds Number is, in effect, a ratio of the inertial force to its viscous resistance.)

The basic formula for frictional resistance is similar though; namely, R = Cf × S × V² with a new coefficient of friction (Cf) now varying with the Reynolds Number, according to charts by various researchers. The graph most commonly accepted and followed today by research facilities worldwide, is one by Schoenherr, though as I mentioned, the resistance figures given by the much earlier Froude formula are still quite acceptable for smaller boats.

The reason we need to separate Frictional resistance from Wave-making resistance, when evaluating model test results, is that they vary very differently for the much smaller test model as compared to the full-size boat or ship. (A typical model might be anywhere from 15 to 150 of the full size boat or ship, depending mainly on the size of the test tank and speed of the carriage that runs the model through the tank.)

Frictional resistance is actually more complicated than it may first appear. Research has shown that there is a thin boundary layer of water that is pulled along by the surface and the thickness of this layer increases as one moves aft. Within this layer, the water particles shear on one another so that the layer closest to the hull is 'pulled along' with hull speed, while the outside layer of this boundary does not move at all relative to the water adjacent to and outside of it. About 50% of this variation in water speed, takes place in a very thin film (about 1500" thick) close to the hull, while the remaining 50% takes place in the thicker turbulent outer area of the boundary layer.

Laminar Flow

If the surface is super smooth and the water flow slow, then something called laminar flow can take place. Such flow is linear and non turbulent and as the water particles shear far more easily on each other within that laminar-flow area, frictional resistance can be lowered very significantly (say 30-60%) but only IF in fact, laminar flow can indeed be achieved.

Whether any particular boat can have laminar flow is a subject for much debate—somewhat similar to 'can a multihull plane?'—but even harder to answer. As always, there are many ifs and buts and it's only likely over a small area of the bow, at very low speeds and with a surface prepared to be 'the least likely to provoke turbulent flow'. Actually, there is some talk that porpoises may develop laminar flow over a fair extent of their bodies as experts look for some plausible explanation of why they can travel much faster than their muscle weight would indicate.

Interestingly, they apparently have a skin surface just behind the head, that has microscopically fine ribs that are located not with the flow, but at 90° to it, that are perhaps the secret of how it's achieved. So perhaps we need to paint our underwater bow sections with vertical brush strokes, rather than painting with the flow! :-) I personally think that at speeds under 1.5 knots, a small area of laminar flow 'might' be possible and if so, it would certainly lower resistance at low speed.

For ship models that sometimes go to 20' in length, laminar flow is nearly always apparent in the bow area and in such cases, it so upsets the required calculation of resistance that small pins (or the equivalent) are added to the model in the bow area to actually provoke turbulent flow in order to achieve a more realistic resistance prediction for the full size boat or ship.

Wave-making Resistance

Although some attempts have been made to predict this 'form resistance' though formulae, this can only hope to work for designs that also follow very set rules of form—something rarely done.
Accurately estimating this important part of the total resistance, is the main reason that model tests are conducted in the first place and without them, there really is no other way to accurately predict performance other than relating one design with another one that is very close. In such a case, one can compare the hulls at similar Speed-Length Ratios (V/√L) using the numerous ratios that have been shown to have much importance, of which the following are the most common:

Prismatic Coefficient = Volume of Displacement ÷ (Midship Area × L)
      (a low figure, like 0.50, defines a boat with very fine ends)

Displacement-Length Ratio = Displacement in tons ÷ (L/100)³
      (a low figure, <100, defines a boat with long slim form)

Beam-Draft Ratio = Beam ÷ Draft
      (a low figure, like 2.0, defines a boat with low stability but low wetted surface, but also unsuitable for planing)

Length-Beam Ratio Length ÷ Beam
      (a low figure, like 3.0, defines a very beamy boat of possible planing form)

Corresponding model speed for similar wave making resistance will be the speed of the fullsize boat, divided by the square root of how many times smaller is the scale model. (So if a boat with 64' length on the waterline is to go 16 kt, then a 110-scale model will need to be run at 16/√10 or 5.06 kt, so that both boat and model will be running with a SLR of 2.)

Form resistance can increase with heeling though this is far less so with a multihull than for a monohull. In fact, overall resistance generally drops when a multihull heels enough to lift a hull completely out as the added resistance of the leeward hull is more than offset by the lifting of the windward one, so overall, this is of minor concern. By comparison, a monohull heeling to 30° might show a 20-25% increase in form resistance.

Drift Resistance

This is the added resistance of a boat's form due to slippage in the water at an angle from the boat's centerline, generally due to wind forces when sailing to windward and often referred to as 'leeway'. This resistance can again be assessed by towing a model at a given drift angle and comparing the total drag with that when going straight. Typically, such drift is about 2–4° for a high performing multihull but might well be double that angle for a cruising boat. Test figures have shown this added resistance can be quite high—perhaps adding 10-30% to the straight line form resistance. Naturally, this drag can be reduced with adequate underwater foil surfaces and low wind resistance. Veed hulls are likely to reduce the actual drag angle while rounded hulls are likely to allow somewhat higher drag angles, though with proportionally lower percentage drag increase. Who said it was easy?

Air Resistance

This becomes important and significant in high winds and high boat speeds. High freeboard adds to this, as does a non-rotating mast, rigging and various appendages on deck such as hatches, coamings, winches, rails etc.
Because trimaran amas are usually low and often rounded, catamarans tend to have higher air resistance than trimarans and both generally have more than the typical monohull. This is most noticeable when approaching a dock or mooring at low forward speed—particularly as the multihull generally has far less underwater area to resist the resulting wind drift.
Air resistance alone can be as much as 30% of the total resistance and take off as much as 20% of a boat's speed, so it's certainly something significant. Air resistance of mast and all its rigging will often come close to the air resistance of the hulls, though for accuracy, calculations will be needed for each case.
Such air resistance Ra can be expressed like this :

Ra = Cs × 0.0012 × v² × Sp (based on Newton's classic formula)

Where Ra = air resistance in lbs; Cs = coefficient for shape; v = speed in ft/s;
and Sp = projected surface area in ft²

While the resistance of a boat is based on hull speed though the water, the air resistance is based on the apparent wind that hits the above-water parts and that could be either much higher (as when going upwind), or much lower (as when sailing downwind). The coefficient Cs will depend on the shape of the form or section that the wind has to blow around and will typically vary from about 1.2 for a mast or wire cable to say 0.5 for a reasonably streamlined hull, down to 110 of that (0.05) for a highly streamlined foil shape.

For fast boats, every effort should be made to keep decks free of unused sails and other clutter. The same applies while at a mooring in very strong winds as boats with all sails and loose deck gear stowed below during a hurricane, always suffer less damage.

Appendage Resistance

Because above-deck appendages are generally considered along with air resistance, this resistance generally relates to underwater items such as skegs, fins, foils, keels, propellers and shafts, plus any small 'bubbles or bulges' built-in to house some component such as a depth sounder, speed log etc.. Because these items are running through the relatively dense medium of water, more attention needs to be paid to their resistance and form, eliminating or making smaller, as many of them as possible. For example, while foils are needed in order to steer and control a sailboat drift, they should not be lowered more than is really needed, though it's often a case of trading lowered appendage resistance against increased drift resistance.
The same Newton formula as used for air resistance will apply, although needing adjustment for the density of water compared to air—i.e. 810 times more. So the factor 0.0012 will become about 1.0, though of course, the value of 'v' will be much lower— being now relative water flow rather than air flow.

Closing Comment

Although most model test work is conducted to calculate the 'difficult to assess' Form or Wave-making resistance of a boat, resistance due to the underwater surface friction and above-surface air is actually likely to exceed that of the wave resistance by a fair amount. And finally, just to put some perspective on things, the typical total resistance of a multihull of say 25'–30' will likely range from 10 to 500 lbs, depending greatly on the speed it's driven.

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