32 gun frigate - richards model boats - homerichardsmodelboats.webs.com/pdf/southampton velocity...

32 GUN FRIGATE

HMS SOUTHAMPTON

VELOCITY PREDICTION

R. Braithwaite

Issue 02

Nov 2009

HMS Southampton Velocity Prediction

R.Braithwaite Page 1 Issue 02

CONTENTS 1 Introduction ....................................................................................................... 2 2 Spreadsheet Guide ............................................................................................. 4

2.1 Force and Moment Balance ......................................................................... 4 2.2 Aerodynamic Forces ................................................................................... 8

2.3 Hydrodynamic Forces ................................................................................. 9 2.3.1 Hydrodynamic Drag: ............................................................................ 9

2.3.2 Induced Drag...................................................................................... 11 2.3.3 Hydrodynamic Lift: ............................................................................ 12

2.4 Operation of Spreadsheet........................................................................... 13 3 Results ............................................................................................................. 15

4 Discussion ....................................................................................................... 17 5 Scale Effects .................................................................................................... 18

6 References. ...................................................................................................... 21



1 Introduction

This report describes a spreadsheet created to model the performance of the 32 gun

frigate HMS Southampton . The ship design data used for this analysis were taken

from Refs 3 and 5. The loading condition assessed is based on the design condition

(Ref. 3).

The engineering assumptions made are described together with instructions in the use

of the spreadsheet. I have not been able to find any tank test data for 18th century

frigate hull forms and have uded the Delft model series data for upright wavemaking

resistance (Ref.2) and simple aerofoil theory for lift and induced drag characteristics.

Lift/drag properties of square sail rigs have been based on a graph in Marchaj’s book

(Ref. 1).

Despite all this the resulting spreadsheet does predict performance that is not too

dissimilar from contemporary sailing reports.

The report also presents the performance predicted for this vessel in a number of

conditions (full plain sail, deep reefed topsails, storm canvas and bare poles) and

makes some comparisons with contemporary sea trial results.

Revision 2 of this report covers Revision 2 of the spreadsheet which includes a

facility for evaluating scale models. A discussion of scale effects is included in the

report.



Figure 1 HMS Southampton Body Plan

Figure 2 HMS Southampton Sail Plan



2 Spreadsheet Guide

2.1 Force and Moment Balance

The model derives Speed, Leeway and Heel angle by iteratively varying these three

parameters until the calculated aerodynamic and hydrodynamic forces and moments

are balanced for these three degrees of freedom. A fourth degree of freedom (Yaw) is

balanced by varying sheeting angles and/or rudder angle to bring the center of lateral

resistance (CLR) of the underwater hull in line with the center of effort (CE) of the

sail plan.

Figure 3 shows the forces involved in the x,y plane for the vessel with zero degrees of

heel, and in yaw equilibrium. The axis system is parallel to the track of the vessel (i.e

the vessel heading differs from the x axis by the calculated Leeway angle).

Figure 3 Balance of forces

Vtw = True wind vector

Vaw = Apparent wind vector

Vs = Ship velocity vector

AWA = Apparent wind angle

AOA = Sail angle of attack

BA = Bracing angle

Lee = Leeway angle



The vessel is in equilibrium when the sum of the forces in the x and y direction are

equal to zero i.e.:

0icDragHydrodynamcThrustAerodynamiFx 1

0eicSideForcHydrodynamcSideForceAerodynamiFy 2

Where:

)cos(.)sin(. AWAcDragAerodynamiAWAcLiftAerodynamicThrustAerodynami

)sin(.)cos(. AWAcDragAerodynamiAWAcLiftAerodynamicSideForceAerodynami

at zero heel

Hydrodynamic SideForce = HydrodynamicLift at zero heel

The apparent wind vector (Vaw) is calculated as the true wind vector (Vtw) minus the

ship speed vector (Vs).

The angle of attack of the sails is calculated as:

AOA = AWA – BA – Lee

The situation as the vessel heels is shown in Figure 4

Figure 4 Heel equilibrium

The variation in wind as the vessel heels is dealt with by calculating an “Effective

Apparent Wind” in the plane of the rig.

The x component of the apparent wind is unchanged and the y component is

multiplied by the cosine of the Heel Angle.



The aerodynamic force acting on the rig due to this wind is then calculated for each

component of the rig, topsides etc. as the Aerodynamic Heel Force.

The Heeling moment is then calculated as the Aerodynamic Heel Force multiplied by

the lever between the center of lateral resistance of the Hydrodynamic Heel force and

the center of effect of the Aerodynamic Heel force. This Heeling Moment is opposed

by the righting moment derived from the Buoyancy/Weight couple. The third

equilibrium equation is therefore:

Aerodynamic Heel Force. Lever= 9.81. Displacement.GZ 3

Where:

Lever = Distance between the Centre of Lateral Resistance of the underwater

hull and the centre of action of the Aerodynamic Heel Force

GZ= The lever between the line of action of the weight of the vessel acting

through the center of gravity (CG)and the line of action of the

buoyancy force acting through the center of buoyancy (CB) (Figure 4)

Changes in sail setting and bracing angle will move the Center of Effort (CE) of the

sail plan so that it moves away from the Center of Lateral Resistance (CLR) of the

underwater hull in the longitudinal direction . Similarly changes in heel angle will

move the CE and CLR out of line laterally. Both of these effects will introduce yaw

moments which need to be corrected by adjustments to the sail or rudder to keep the

vessel sailing in a straight line. These adjustments will have an effect on the speed

achievable in different conditions (e.g. additional lift and drag created by the rudder)

The spreadsheet uses the following approach to account for yaw. Figure 5 shows the

forces and levers considered.

Figure 5 Yawing levers



Levers and moments calculated as follows:

Hydrodynamic Levers and Moments

L1= HCLR.cos(Lee)+VCLR.sin(Heel).sin(Lee)

L2= HCLR.sin(Lee)-VCLR.sin(Heel).cos(Lee)

Where:

HCLR = horizontal distance to center of lateral resistance of hull from aft perp in ship

axes (assumed constant at a given “lead” to the center of area of the underwater

profile)

VCLR = vertical distance to center of lateral resistance of hull from base line in ship

axes (assumed constant at the center of area of the underwater profile)

The Yaw moment due to the hydrodynamic forces acting on the hull is then calculated

as follows:

HydrodynamicYaw Moment=L1.HydrodynamicSideForce+L2.HydrodynamicDrag

The yaw moment due to the rudder is calculated similarly and a combined total

hydrodynamic yaw moment calculated.

The Total Hydrodynamic Force is calculated as:

22 icDragHydrodynameicSideForcHydrodynamcedynamicForTotalHydro

The Effective Lever to the CLR is then calculated as:

cedynsmicForTotalHydro

MomentdynamicYawTotalHydroLREffectiveC

Aerodynamic forces and Moments.

L3= HCE.cos(Lee)+VCE.sin(Heel.)sin(Lee)

L4=- HCE.sin(Lee)+VCE.sin(Heel.)cos(Lee)

HCE = horizontal distance to combined center of effort of sails etc. from aft perp in

ship axes.

(calculated by dividing total moment of the side force, on all sails, spars etc., about

the aft perp by the total aerodynamic side force). This will vary with sails set, wind

strength etc.

VCE= vertical distance to combined center of effort of sails etc from base line in ship

axes (calculated by dividing total moment of the side force about base line by the total

aerodynamic side force).Again, this will vary with sails set, wind strength etc.



The Total Aerodynamic Yaw Moment is then calculated as:

AerodynamicYaw Moment= -L3.AerodynamicSideForce+L4.AerodynamicThrust

The Total Aerodynamic Force and Effective CE Lever are then calculated in the same

way as the Hydrodynamic Force/Lever above.

The balancing of these yaw moment is accomplished in the program manually by

adjusting rudder angle and sail set.

NOTE: the center of lateral resistance of a long keel vessel of this kind is generally

regarded as being well forward of the center of area of the center of area of the

underwater profile (typically around 75% of LWL from the AP – Ref. 4). In this case

the “lead” was derived by setting a “full” set of sails at a 40degree bracing angle in a

10 knot beam wind (true) and assuming yaw balance with 5 degrees of weather helm.

The effectiveness of the rudder was adjusted by varying the effective aspect ratio so

that a 5 degree rudder angle moves the effective CLR by 5% of LWL.

2.2 Aerodynamic Forces

All Aerodynamic forces and moments are calculated on the “AERO” sheet of the

spreadsheet.

The forces acting on each sail are calculated as follows:

The plan area, centroid (above underside of keel and longitudinally), width and depth

were taken from the sail plan. The area is then converted to an effective area taking

account of one sail blanking another given the direction of the effective apparent wind

angle.

The Aspect Ratio is calculated for a “stack” of sails as:

Aspect Ratio= Depth2/Area

Where the depth and area correspond to the sum for the stack concerned (a stack

being taken as the square sails set on one mast)

The lift and drag coefficients for each sale is based on the angle of attack and the

aspect ratio taken from Ref. 1.

Lift and Drag for each sails are then calculated and converted to thrust and heeling

force in the track axes as follows:

)cos(.)sin(. EAWADragEAWALiftThrust

)sin(.)cos(. EAWADragEAWALiftHeelForce

AerodynamicSide Force = HeelForce.cos(Heel)



Heeling Moment = HeelForce. Lever to BaseLine

Where EAWA = Effective Apparent Wind Angle

Similarly Thrust and Drag are calculated for each mast and spar and the topsides.

The area in the case of spars is taken as the length multiplied by the maximum

thickness and for the topsides the area is based on the area presented to the effective

apparent wind considering the topsides as a rectangular box with length breadth and

height equal to waterline length, max beam and freeboard respectively.

The drag coefficients were taken as 0.8 for the spars and 1.13 for the topsides and the

Thrust, Heel Force, Side Force and Heeling moment calculated as above (with no lift

force calculated)

The Thrust, Side Force and Heeling moments are then summed for all elements for

input into the balancing equations (1,2, and 3).

The center of effort of the sail plan is calculated by dividing the longitudinal moment

of the heeling forces due to each sail, spar etc and dividing by the total heeling force.

2.3 Hydrodynamic Forces

All Hydrodynamic Forces/Moments are calculated on the “HYDRO” sheet of the

spreadsheet.

2.3.1 Hydrodynamic Drag:

Hydrodynamic Drag is calculated as the sum of:

Upright resistance

Additional allowance due to heel

Induced Resistance

Upright resistance of the vessel is calculated as the sum of skin friction resistance and

wavemaking resistance:

RT=RF+RW

FF CSVR 2

21

Where:

RF= Skin Friction resistance in Newtons

ρ= density of water (kg/m3)

S=wetted surface area (m2)

V= speed (m/s)

CF= skin resistance coefficient



2

10 2log

075.0

RnCF

ITTC 1957 formulation

Where:

Rn = Reynolds number based on waterline length

Wave making resistance is derived from model tests conducted by Delft University

for yacht type hulls (Ref. 2)

This calculates wavemaking resistance from a polynomial fit of model data to the

following parameters:

Displacement

Prismatic Coefficient

Longitudinal Center of Buoyancy

Beam/Draught ratio

Length/Displacement1/3

ratio

These parameters were calculated from the Maxsurf Model described in Ref. 3

It should be noted that some of the form parameters are slightly outside the range of

models tested:

Parameter Minimum Maximum HMS Southampton

LWL/BWL 2.76 5.00 3.85

BWL/Tc 2.46 19.32 2.22

LWL/Disp 1/3

4.34 8.50 4.13

LCB 0.00 -6.00% +1.99%

Cp 0.52 0.60 0.63

Table 1 Delft Series Form Parameter Range

However, previous studies have shown good agreement between model testing of an

80m 3 mast topsail schooner and the Delft polynomial prediction, despite the model

hull being outside the parameters of the Delft models (Ref. 7)

The calculated resistance curve is shown in Figure 6. It can be seen that skin friction

resistance predominates up to about 7 knots.



Resistance Curve

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0 2 4 6 8 10 12 14

Speed (kts)

Re

sis

tan

ce

(N

)

Frictional

Total Heeled

Total Upright

Figure 6 Calculated Resistance Curve at 10 degrees heel (excluding induced resistance)

2.3.2 Induced Drag

The presence of Leeway generates induced resistance. This is calculated by the

spreadsheet as follows:

DICSVgInducedDra 2

21

Where:

S = Plan Area of Underwater Hull

CDI= Induced Drag Coefficient

AR

CC L

DI.

2

Where:

AR= Aspect ratio of underwater hull

CL= 3D Lift Coefficient

AR

LeeCL

21

.1.0

Where:

Lee = Leeway Angle



2.3.3 Hydrodynamic Lift:

LCSVicLiftHydrodynam 2

21

And:

Hydrodynamic Side Force= Hydrodynamic Lift. cos(Heel)

This calculation is repeated for the rudder where the angle of attack is taken as the

Leeway angle + the rudder angle. Since the rudder is hinged on the sternpost the

aspect ratio is taken as that of the whole underwater hull. This is multiplied by a

factor to give the required rudder effectiveness (see section 2.1)

The Hydrodynamic lift and side force taken forward is the sum of that due to the

rudder and underwater hull.



2.4 Operation of Spreadsheet

The only sheets requiring input are the “Design” and “Interface” sheets. Input cells

contain red text.

All the Inputs that define the design are entered into the “Design” worksheet as shown

in Figure 7. This shows the data for HMS Southampton. The spreadsheet could also be

used to assess the performance of other ship rigged vessels. Revision 2 of the

spreadsheet includes evaluation of scale models. This is achieved by altering the scale

factor from 1 to the desired scale. The input data in the design sheet is then scaled in

the Model sheet, and it is this scaled data that is used in the analysis.

Figure 7 Design Definition Sheet

Once this data has been entered the spreadsheet is operated through the “Interface”

sheet (Figure 8)

The basic process is as follows:

1. Input the True Windspeed and direction.

2. Input Y/N for each available sail together with the bracing angle. An

additional option (R) is available to reef some sails.

3. Click on the Balance Button repeatedly until equations 1,2 and 3 are balanced

within the required tolerance.



NOTE: the reset button is used if speed, heel or leeway start to diverge wildly, in

order to set them to reasonable levels so as to make rebalancing possible. Balancing

can also be achieved on the “Balance” sheet either by manually adjusting the speed

heel and leeway, or clicking the balance buttons to balance these parameters

separately.

The outputs calculated are:

Speed

Heel Angle

Leeway

Velocity made good to windward (VMG)

If a significant yaw imbalance results, this can be corrected by either adjusting the

rudder angle or individual sail bracing angles. This is followed by rebalancing in the

other 3 degrees of freedom (by clicking the “balance” button).

Figure 8 Interface Sheet

The spreadsheet does include Delft University data for calculating added resistance in

waves. However, the ship speeds relevant to this study are too low and out of range

for the data. Accordingly the significant wave height has been set to zero.



3 Results The spreadsheet described above was used to generate the polar diagrams, presented

in Figure 9. and the tabular results presented in Table 3 to Table 6 For each condition

the vessel was balanced as described above (yaw balance achieved to align CLR and

CE within 1% of LWL). The bracing angle was adjusted to give maximum thrust (a

minimum bracing angle of 40 degrees was assumed).

The sail combinations considered are listed in Table 2

Plain Sail Reefed Topsails Storm Canvas Bare Poles

Main Course Main Topsail (deep

reefed)

Main Staysail

Main Topsail Fore Course Fore Staysail

Main Topgallant Fore Topsail (deep

reefed)

Mizzen Staysail

Fore Course Fore Staysail

Fore Topsail

Fore Topgallant

Mizzen Topsail

Mzizen Course

Fore Staysail

Fore Topmast Staysail

Jib

Table 2 Sail Combinations

70 80 90 100 110 120 140 160 180

Speed (Knots) 4.2 6.3 7.3 7.7 7.8 7.8 7.3 6.4 4.3

Heel Angle 1.3 1.9 2.5 2.8 2.8 2.3 1.0 0.1 0.0

Leeway 5.4 3.2 3.0 2.9 2.8 2.2 1.0 0.2 0.0

VMG to windward 1.4 1.1 0.0 -1.3 -2.7 -3.9 -5.6 -6.0 -4.3

Speed (Knots) 6.5 8.5 9.4 9.7 9.9 9.9 9.5 8.3 6.7

Heel Angle 2.9 4.6 5.8 6.3 6.1 4.7 2.1 0.1 0.0

Leeway 4.8 4.2 4.2 4.1 3.6 2.8 1.3 0.1 0.0

VMG to windward 2.2 1.5 0.0 -1.7 -3.4 -4.9 -7.3 -7.8 -6.7

Speed (Knots) 8.0 10.0 10.7 10.9 11.1 11.3 11.0 9.7 8.1

Heel Angle 5.3 8.6 10.2 11.4 10.3 7.3 3.3 0.1 0.0

Leeway 5.8 5.4 5.4 5.4 4.4 3.0 1.5 0.1 0.0

VMG to windward 2.7 1.7 0.0 -1.9 -3.8 -5.6 -8.4 -9.1 -8.1

Speed (Knots) 9.0 10.9 11.4 11.6 11.9 12.4 12.3 10.8 9.4

Heel Angle 8.1 12.9 15.6 17.4 14.7 10.3 4.2 0.2 0.0

Leeway 6.9 6.7 6.8 6.6 5.0 3.4 1.4 0.2 0.0

VMG to windward 3.1 1.9 0.0 -2.0 -4.1 -6.2 -9.4 -10.1 -9.4

25

True Wind Direction (degrees)

10

Wind speed

(knots)Parameter

20

15

6

Beaufort

3

4

5

Table 3 Plain Sail



77 80 90 100 110 120 140 160 180

Speed (Knots) 8.4 9.6 11.0 11.8 12.6 12.9 13.2 11.7 11.0

Heel Angle 10.3 12.0 15.2 16.4 13.4 10.8 3.6 0.7 0.0

Leeway 13.4 11.4 10.0 8.8 6.4 4.8 1.6 0.4 0.0

VMG to windward 1.9 1.7 0.0 -2.1 -4.3 -6.5 -10.1 -11.0 -11.0

True Wind Direction (degrees)

45

Wind speed

(knots)ParameterBeaufort

9

Table 4 Reefed Topsails

70 80 97 100 110 120 140 160 180

Speed (Knots) 9.7 10.9 12.4 13.1 14.0 13.0 12.4

Heel Angle 12.8 12.9 12.3 10.0 4.3 1.8 0.0

Leeway 16.0 12.4 8.6 5.8 2.1 0.8 0.0

VMG to windward -1.2 -1.9 -4.2 -6.6 -10.7 -12.2 -12.4

ParameterWind speed

(knots)

65

True Wind Direction (degrees)Beaufort

12

Table 5 Storm Canvas

70 80 90 100 110 120 140 160 180

Speed (Knots) 9.4 11.1 10.8 8.9

Heel Angle 6.1 3.9 1.7 0.0

Leeway 8.3 3.3 1.2 0.0

VMG to windward -4.7 -8.5 -10.2 -8.9

65 12

Wind speed

(knots)Parameter

True Wind Direction (degrees)Beaufort

Table 6 Bare Poles

Figure 9 Polar Diagrams for HMS Southampton



4 Discussion

The stability analysis of HMS Southampton (Ref.3) suggested that a maximum heel

angle of 15 degrees would be prudent to minimise the risk of immersing gunports in

gusts. The results presented in Table 3 would therefore indicate taking in of topgallant

sails between 20 and 25 knots of wind. This aligns with the guidance given in Ref.8

that topgallant sails were generally carried up to force 5 or 6.

With full plain sail set the spreadsheet was not able to converge to a balanced solution

with a true wind of less than 70 degrees. This agrees with the statement in Ref.8 that

traditional square rigged ships could not make good a course closer than 6 points

(67.5 degrees) to the wind.

Contemporary sailing trials of HMS Southampton (Ref. 6) state that she could make 7-

8 knots close hauled in a “topgallant gale” and 12 knots before the wind. A topgallant

gale was taken as the maximum wind strength that topgallant sails would be set, in

this case assumed to be around 20 knots. The spreadsheet predicts a speed of 8 knots

close hauled , making good a course of 70 degrees to the wind(Table 3 ) in 20 knots

of wind with a maximum speed of 11.3 knots on a broad reach (wind 120 degrees

true).

Sailing trials for the Niger class (Ref.6) stated that leeway of ¼ point was achievable

(approx 3 degrees) close hauled. The Niger class was the next class of 32 gun frigate

designed by Thomas Slade. It was generally considered to have remarkably good

sailing characteristics, particularly windward ability, and so would have probably

outperformed HMS Southampton in this respect. Accordingly the leeway prediction

from the spreadsheet of 5.8 degrees close hauled in 20 knots wind does not seem

unreasonable.

Ref 8. suggests that traditional ship rigged vessels would typically reduce sail to deep

reefed topsails and fore course in Force 9 conditions. Table 4 shows the spreadsheets

predictions for this condition. Heel angles are a little high which means that operating

the main deck guns might have been difficult (particularly with a large sea running).

Making progress to windward would also be difficult. The spreadsheet failed to find a

solution for a true wind angle less than 77 degrees and predicted a velocity made good

to windward of 1.9 knots. However, the effect of wave resistance is not included and

this would have been significant in gale conditions for a ship with bluff bows like

HMS Southampton.

Table 4 and Table 6 present the spreadsheet predictions for extreme (hurricane)

conditions (again it should be noted that the effects of waves is excluded), both under

storm canvas and under bare poles. Progress to windward is impossible under these

conditions. Under sail the closest the spreadsheet can get is 97 degrees and is losing

ground at 1.2 knots to leeward. Under bare poles the spreadsheet can only make good

a course of 120 degrees to the wind, when the speed made to leeward is 4.7 knots.

Clearly not a good situation on a lee shore.



5 Scale Effects

The following discussion relates to the evaluation of a scale model in which the

weight distribution (and therefore the vcg as a proportion of ship length) is the same

as the original.

The equivalent wind strength that would cause a scale model to heel by the same

amount as the full size ship can be calculated as follows:

For geometrically scaled vessels, the vertical height of the center of effort of the sail

plan etc (above the CLR) is equal to a constant times the waterline length:

CE = K1.L

Similarly the area of the sails is equal to a constant times the square of the waterline

length:

Sail Area = K2.L2

The force acting on the sails is proportional to the square of the wind velocity

multiplied by the sail area (for similar heading, sail bracing angles):

Force on sails = K3.K2.L2.Vwind

2

The heeling moment is therefore:

Heeling moment = CE. Force on sails = K1.L. K3.K2.L2.Vwind

2 = K4.L

3 .Vwind

2

Assuming similar weight distributions (i.e scale vcg) the GZ lever is:

GZ= K4.L

The displacement will scale with the cube of the length:

Displacement = K5.L3

Therefore:

Righting Lever = GZ.Displacement = K4.L. K5.L3 = K6.L

4

At the equilibrium heel angle:

Heeling moment = Righting Moment

Hence:

K4.L3 .Vwind

2 = K6.L

4

OR



Vwind2 /L= K OR

'KL

Vwind

Let:

L1 is the waterline length of the original vessel

Vwind1 is the wind strength to heel the original vessel to θ degrees.

L2 is the waterline length of the scale model

Vwind2 is the wind strength to heel the scale model to θ degrees.

Then:

2

2

1

1

L

V

L

V windwind

And:

12.12 LLVV windwind

What this means is that the “scale wind” for a geometric scale model varies with the

square root of the linear scale factor.

For example the scale wind for a 1/16th scale model of HMS Southampton would be ¼

of the equivalent wind acting on the full size ship.

Results from the spreadsheet for HMS Southampton at full size and 1:16 scale with a

20 knot (full scale) and 5 knot wind (scale equivalent) are shown in Table 7.

Scale 1:1 1:16

Wind Speed (knots) 20.0 5.0

True Wind Angle (degrees) 100 100

Boat Speed (Knots) 10.9 2.6

Heel Angle (degrees) 11.4 11.3

Leeway (degrees) 5.4 6.1

VMG to windward (knots) -1.9 -0.4

Froude Number 0.283 0.267 Table 7 Results for 1:16 Scale Model

It can be seen that the heel angle is virtually identical. The Froude number is also very

similar. Froude number is a non dimensional parameter based on speed and length, it

is defined as:

gL

VFn

Where:

V is the speed of the ship (m/s)



G is acceleration due to gravity (m/s2)

L is the waterline length in (m)

The significance of Froude number is that geometrically similar models travelling at

speeds with the same Froude numbers will have the same wavemaking resistance

coefficient. They will also generate a similar pattern of waves in their wake. This

relationship is the basis for using model tests for predicting the full size resistance and

wake characteristics during the design of ships.

It can be seen that the “scale” wind strength that will heel a model sailing ship to the

same extent as full size should also drive it at a speed corresponding to the same

Froude number. i.e. the wake characteristics will be very similar.

It should also be noted that at full scale wind strength of 65 knots the full size ship is

forced to reduce sail to storm staysails and can no longer make any progress to

windward. This would correspond to a wind speed of only 16.3 knots even for a

relatively large (1:16th scale model weighing 226 kg).



6 References.

1. Marchaj, .AeroHydrodynamics of Sailing

2. J.Gerritsma, J.A.Keuning and R.Onnink, Sailing yacht performance in calm

water and in waves, Report No. 925-P, 12th International Symposium on Yacht

Design and Construction, HISWA, November 1992.

3. R.Braithwaite, 32 Gun Frigate, HMS Southampton Stability Analysis,

http://richardsmodelboats.webs.com/

4. S.Wallis, The Design of a Brigantine Rigged Sailing School Research Vessel

for the Sea Education Association, Transactions of the Royal Institution of

Naval Architects, 2003

5. R.Braithwaite, Notes to accompany Reconstructed Drawings of HMS

Southampton , http://richardsmodelboats.webs.com/

6. Robert Gardiner, The First Frigates, Conway 1992

7. G.J.C. Nijsten, J,de Vos, Propulsion Aspects of Large Sailing Yachts, 17th

International Symposium on Yacht Design and Yacht Construction (HISWA)

2002

8. J. Harland, Seamanship in the Age of Sail, Conway Maritime Press, 1985.



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