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1. Hull Design

The function of the hull design is to provide adequate bouncy and stability for the minimum drag in all conditions of sailing. The craft’s total drag can be split up into these resistance components.

Canoe body :

Skin friction
Viscous pressure
Wave drag

Keel and rudder :

Foil profile drag
Induced drag

Rig :

Induced drag
Windage

The hull design will be concerned with canoe body resistance, each of it’s three resistance components must be considered at a variety of speeds. The best way to minimise skin frictional resistance at all speeds is to minimise wetted area. Viscous pressure drag is mainly caused by the flow of water separating around bilge and transom corners and any bluff part of the hull’s body. Wave drag is a complex function of the hull’s shape but in general slender and sleek hull forms tend to have a low value of wave drag.

 

 

1.1 The effect of hull speed on the design

Froude number (Fn) is used to scale various speeds for craft of different length and is calculated as follows.

Fn = V / ( g L )

where
L = length = 3.355 m
g = gravitational constant = 9.81 m/s2
v = speed m/s
(Note 1 knot = 0.5144 m/s )

 

Table 1.1
Comparison of speeds from different scales

Fn v (m/s) V (knots)
0 0 0
0.25 1.43 2.8
0.5 2.87 5.6
0.8 4.59 8.9
1 5.7 11.1
1.5 8.61 16.7

To simplify the analysis the speed of the craft shall be split into these three ranges :

FN < 0.5 Displacement mode
0.5 < Fn <1 Midrange
1< Fn High speed

 

Displacement mode (0 to 5.6 knots).

In this range any hydrodynamic forces act downwards. A craft with a transom would be sailed with bow down trim so that it’s transom will not be immersed, minimising viscous pressure resistance. Chines below the waterline will cause drag by creating bilge vortices. A good design for this speed range would be a round bilge cruiser sterned hull with the minimum wetted surface area possible. It is the Authors opinion that a Moth will sail in this speed range for the majority of the time.

 

Midrange (5.6 11.1 knots).

This is the speed range that is hardest to design for as the hull is neither in a displacement or planing state. Interestingly the Australian Moths tend to be hard chined transom forms, sailed by eleven and a half stone helmsmen, whilst the European designs are mainly round bilge displacement forms with ten stone sailors. This may be no surprise when we consider that Australians tend to sail in strong winds where their boats will sail mainly at speeds in this range, where as Europeans sail in lighter winds associated with the lower speed range. Clearly a good design will have to be a compromise between a displacement and semi-planing hull form.

 

High speed (>11.1 knots).

Hydrodynamic lift is likely to be as large in magnitude as the bouncy in this speed range. Most craft are said to start planing at a Froude number of about 0.8. However due to the slenderness of modern narrow Moth designs they will not plain until higher speeds are attained. At a Froude number of 1.5 it is safe to say that the craft has the potential to plain. A transom will run dry, and a trim angle of two or three degrees is realistic. Correctly placed chines will reduce wetted area by expelling green water into a spray sheet. A realistic upper limit of this range could only be found from strong wind speed trials, however I would expect it to be approaching twenty knots (Fn 1.8 ).

 

 

1.2 Aussie Axeman hull form

An Aussie Axeman is the 1995 World Championship winning design. Measurements of an Aussie Axeman for four sections (Fig 1.1 ) were taken so that a lines plan could be generated in the software Ship Shape. ( See appendix 4.) This will provide a competitive hull form with good stability characteristics which can be used to compare against the author's WSH design.

For comparison purposes I shall define the following specification for a modern Moth design. These assumptions are based on empirical data from existing boats, and will enable me to compare the Axeman against the WSH design.

Sailors weight = 70 kg
Craft weight = 30 kg
Displacement = 100 kg = 0.1 tonnes
Vertical centre of gravity = 0.75 m above LWL

The longitudinal centre of gravity is governed by sailor's position and is therefore very variable.

 

Aussie Axeman hydrostatic data

Length 3.355 Metres
CP and CM referred to section at 0.0 Metres
Vertical centre of gravity 0.0 Metres
Specific gravity of water 1.025
longitudinal datum amidships
Vertical datum waterline
Trim 0.0 Metres

 

Table 1.2
Aussie Axeman hydrostatic data.

Draught

m

Displacement

kg

VCB

m

LCF

m

LCB

m

WSA

m2

-0.02 70 -0.063 -0.213 0.060 1.34
-0.01 80 -0.057 -0.221 0.025 1.42
0.00 90 -0.051 -0.222 -0.002 1.49
0.01 100 -0.046 -0.223 -0.025 1.55
0.02 110 -0.040 -0.224 -0.043 1.62
Draught

m

KMT

m

KML

m

CB CP CM CW
-0.02 0.065 9.274 0.116 0.594 0.195 0.291
-0.01 0.061 8.437 0.125 0.611 0.205 0.297
0.00 0.058 7.655 0.134 0.626 0.214 0.301
0.01 0.056 7.020 0.142 0.639 0.223 0.306
0.02 0.056 6.494 0.150 0.650 0.230 0.310

 

 

1.3 WSH design

The WSH design is a round bilge form, similar to a ship’s lines. The features of this design, shown in appendix 4, are as follows.

 

Midbody U Sections

The midbody U sections are approximately as wide as they are deep below the waterline. This is to provide underwater volume for a minimum of wetted surface area.

 

Topsides

The topsides flair out to provide a suitable deck width and extra buoyancy. A degree of tumble home on the topsides is employed on similar designs. However this will only increase wetted area, and the reduction of waterplane area will also make the boat more unstable. The proposed reduction in wave making will be very small as the volume of the boat is not deep enough below the free surface.

 

Transom

The transom below the waterline is similar to the stem. It mimics the trailing edge on a foil, so that the viscous pressure losses are minimal. The transom’s topsides are then flared out quite aggressively so that, hopefully, there will be adequate bouncy at the back of the boat to enable the rudder to be raised or lowered without the boat standing up on its stern.

 

Freeboard

This design has slightly more freeboard than the Axeman, because I have noticed that the stem height on an Axeman is not quite large enough when sailing in waves.

 

Flares at the Shear Line

The flares at the shear line are there to increase deck area, and they also help shed water that rises up the hull. The flares on the WSH design are slightly smaller than those on the Axeman. This is so that a small weight saving is made. The smaller flares will also not have to be as strong as larger ones to achieve the same deflections and hence perceived strength.

 

Rocker Curve

There is a slight rocker curve to reduce wetted area at the ends as these corners do not have much volume but have large wetted area.

 

Bilge Corners

The bilge corners are rounded so that no bilge vortices are induced. Chines and spray rails below the waterline would only be of benefit when the transverse component of flow is great enough. The deeper the chine or rail the greater the component of transverse flow would have to be for these features to run dry and reduce the hulls overall resistance.

 

Spray Rails

There may be a case for spray rails to be fitted some height above the waterline: these would not interfere with the flow in displacement mode but would reduce wetted area by shedding green water into a spray sheet. The position of these rails could be determined after a visual analysis of a model towed at various speeds with different spray rail configurations.

 

Hull

The bottom of the hull is flat so that it will generate good lift in a planing state. I think that the loss of planing area aft, associated with the canoe transom, is nothing to worry about as dynamic pressure is small in this region. Hopefully the overall lift will not be much less than the Axeman design.

 

 

WSH hydrostatic data

Length 3.355 Metres
CP and CM referred to section at 0.0 Metres
Vertical centre of gravity 0.0 Metres
Specific gravity of water 1.025
longitudinal datum amidships
Vertical datum waterline
Trim 0.0 Metres

 

Table 1.3
WSH hydrostatic data.

Draught

m

Displacement

kg

VCB

m

LCF

m

LCB

m

WSA

m2

-0.02 90 -0.088 -0.034 -0.049 1.37
-0.01 90 -0.083 -0.034 -0.048 1.44
0.00 100 -0.078 -0.034 -0.047 1.51
0.01 110 -0.072 -0.039 -0.046 1.57
0.02 120 -0.067 -0.048 -0.046 1.64
Draught

m

KMT

m

KML

m

CB CP CM CW
-0.02 -0.045 4.124 0.140 0.582 0.241 0.200
-0.01 -0.041 3.907 0.144 0.587 0.245 0.203
0.00 -0.038 3.716 0.147 0.592 0.248 0.206
0.01 -0.033 3.567 0.149 0.596 0.251 0.209
0.02 -0.028 3.478 0.152 0.601 0.253 0.214

 

 

1.4 Comparison of the two designs

The hydrostatic data reveals that both designs have approximately the same wetted area and longitudinal centre of buoyancy position. This is encouraging as it means the WSH design is not too radically different from the Axeman.

I suspect that the WSH design would be superior in light winds and that the Axeman may have the upper hand downwind in strong winds, where high planing speeds are achieved. The only way to quantify this would be with towing tank data. Models would be about 13 cm long to reach the corresponding Froude number of a craft at 15 knots, assuming a maximum reliable speed of the towing tank car of 2 metres per second. This size of model may be too small for measuring accurate resistance data so, as the time for extensive testing is not available, I shall not pursue this option.

 

One important factor in hull design is ease of construction. The Axeman will be a lot easier to build than the WSH design. The complicated curves of the WSH design could be achieved but would offer a formidable challenge to the builder. Production time is not a dominant priority in high performance racing boat design so, as long as it is possible to build, as the Author believe it is, its complex shape is not too much of a problem.