Stability and hull shape - KTH · Equal heeling moment 22 deg 11 deg G B GZ G ... Homework 2- Hull and Stability and hull shapes-Digitize the hull sections view into numerical model

Sailing for PerformanceStability and hull shape

SD2706

Maximize stability to keep boat upright

Wide hull& low CG

Movable ballast to windward

Wide hull

Keel to windward

To maximize engine size (sail area)

GZ - The rightening arm

B

G

B

GGZ

Rightening arm

Rightening moment = displacement*rightening arm = mg*GZ

Influence of Hull Shape

B

GZ

Equal displacementEqual heeling moment

11 deg22 deg

G

B

GZ G

Same GZ at different heels since B moves differently depending on hull shape

Stability characteristics set by beam and centre of gravity

Form stability

Righting Arm - GZ curve

-0.5

-0.2

0

0.2

0.5

0.7

0.9

0 45 90 135 180

0.8

0.6

0.4

0.2

0

-0.2

-0.4

Text

GZ (m)

0° 45° 90° 135° 180°

Angle of Heel (degrees)

Stability range

Max GZ:0.8m @60°

The moment equilibrium eq.

CE

CLR

G B

GZ

CEz-CGz

Moment equilibrium: MH + MR = 0

Heeling moment: MH = FAY /cos(heel)*(CEz+CGz) Rightening moment: MR = GZ*mg

FHY /cos(heel)

FAY /cos(heel)

The ability to effectively build rightening moment dictates the performance

At low drag cost

mg

Maximize GZ to keep boat upright

Beautiful picture of wide hull of TP52 boat RAN

Note position of movable ballast

Differences between boat types

Monohull

CatamaranTrimaran

Same rig => same heeling moment

Small GZ requires large forces, i.e. monohull must be heavier than cats/trimarans !

GZ

90° 180°

Catamaran TrimaranKeelboat

0°

heel heel heel

90° 180°0° 90° 180°0°

GZ GZ

GZ - for different hulls

Different Hulls Narrow hulllow G

Wide hulllow G

Wide hullhigh G

Effects on GZ

GZ ok

GZ ok GZ large

GZ ok

GZ okGZ ok

GZ<0

GZ<0

GZ<0

GZ≈0

Wide hulls superior at low heel angles

GZ large

Multihulls (high G) small stability range

Wide hull looses GZ...

Narrow hull large stability range

Water Ballast

-1.200

-0.960

-0.720

-0.480

-0.240

0

0.240

0.480

0.720

0.960

1.200

0 36 72 108 144 180

Rig

htin

g ar

m, G

Z (m

)

Angle of Heel (degrees)

no water ballastwater ballast added to windward side

Canting keel - to increase GZ

xxx

B

GZ

GZ

Avoiding the Heeling Moment

Wind

FA

FH

No heeling moment :-)

Avoiding the Heeling Moment

Homework 2- Hull and Stability

Digitize a hull from a lines drawing and examine the flotation and stability

Moro di Venezia hulls Fossati, Appendix A

digitize using digi.mJust a tool for finding coordinates in a picture

Britfair... and digitizing...

msy_hydrostatics Numerical tool for basic calculations

- Reads geometry files from text files (britfair)

- Hull discretized in sections (like loaf of bread)

- Hull loaded with mass and KG, LCG, TCG

- Calculates draft, equilibrium flotation, wet area, CB, GZ-curve etc

- Functionality for hull modification

Download from course web site

Britfair Just one of many geometry file formats

Homework 2- Hull and Stabilityand hull shapes

- Digitize the hull sections view into numerical model via Britfair file.

- How to find the scale? :-)

- Calculate GZ-curves

- Modify the hull and investigate effects

- Design waterline: Kwl

- Z-waterline position: Zwl

sections view

Stern Bow

Kwl=Zwl

B

D