Resistance Concepts

8/8/2019 Resistance Concepts

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Stephen Wallis - Southampton Solent

Resistance

William Froude first discovered that there are two

principle forms of resistance:-

Frictional Resistance.

Is due to the friction of the water as it slides over

the surface of the hull.

It is dependent on the speed of flow, length of

hull and the viscosity of the water.

Reynolds Number Re = V.L/R

R is the kinematic viscosity




Resistance

Reynolds Number Re = V.L/R

R is the kinematic viscosity

Kinematic viscosity of water:

TempoC Fresh x 10

-6Salt x 10

-6

16 1.1097 1.1592

18 1.0546 1.104420 1.0037 1.0537

22 0.9568 1.0068




Resistance

Wave Making.

Is due to the pressure disturbances in the flow

around the hull causing wave systems at the bow

and stern.

It is dependent on the the inverse of the square

root of length.

Froude Number Fn = V/root gL.

g is the acceleration due to gravity




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Frictional Resistance

Initially the flow is smooth, stream lines are

distinct and do not cross - Laminar Flow




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The local Reynolds Number is small - small L1




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As Re increases the flow starts to become

TURBULENT - Critical Re @ L2




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A turbulent BOUNDARY layer is created,

extending aft and thickening.




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Wave Making

A rise in pressure is initiated at the bow, creating

a bow wave system, moving at the same speed.

P

The wave length P is the distance between peaks.




Resistance

Wave Making

A fall in pressure at the stern causes a stern

wave system, moving at the same speed.

P

This has the same wave length P

P




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Wave Making

The wave length is a function of speed. The faster

the speed the longer the wave

PP




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Wave Making

The wave length is a function of speed. The faster

the speed the longer the wave, and the bigger the

wave

PP




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Wave Making

The bow and stern wave systems interact

differently with changing speed

At some speeds they tend to cancel each other -

leading to hollows in the wave resistance curve






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Wave Making



Prismatic hump is about when 1.5P = 0.9 Lwl

P

9 Lwl

Fn = 0.31




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Wave Making



Hull speed is about when 0.5P = 0.9 Lwl

P

9 Lwl

Fn = 0.535




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Wave Making



The hull will squat heavily at the stern, and cannot go

faster

P

9 Lwl




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Wave Making



The hull will squat heavily at the stern, and cannot go

faster

P




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Wave Making

These interaction

will be apparent

on a graph of

wave resistance

as:-

Wave

e¡

i¡

¢ an £ e

¤

¥

¤ ¤ ¤

2¤ ¤ ¤

¦ ¤ ¤ ¤

4¤ ¤ ¤

§ ¤ ¤ ¤

6¤ ¤ ¤

¤

̈ 2¤ ¤ ¤

̈ 2§ ¤ ¤

̈

¦ ¤ ¤ ¤

̈

¦ § ¤ ¤

̈ 4¤ ¤ ¤

̈ 4§ ¤ ¤

̈

§ ¤ ¤ ¤

̈

§ §

¤

© r

e

m er © n

W a v e

e

i

a n

e

Humps

Hollows




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Total Upright Resistance

Total resistance is:

Friction Resistance R f + Wave Resistance R w




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Frictional resistance can be calculated from Reynold¶s

number.

f f C V S R ...

2

1 2 V!

? A2

2log

075.0

!

e

f

R

C

C f = Friction coefficient

S = wetted surface area

V = Speed m/s

Y

LV R

e

.!




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Wave resistance has to be measured from models

wwC V S ...

2

1 2 V!

C w = Wave coefficient - found from model tests or

systematic series

S = wetted surface area

V = Speed m/s




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Testing scale models is the best way to find the

resistance at full size, but there is a problem.

Friction resistance depends on L, but wave resistance

depends on 1/rootL, so we cannot simply scale up model

total model resistance

Friction resistance at model scale is calculated based on

model wetted area and speed.

It is then subtracted from the Total model resistance,

leaving the model scale wave resistance.

This is scaled to full size, and calculated full size friction isadded back in, giving full scale Total resistance.




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Testing scale models is the best way to find the

resistance at full size, but there is a problem.

Since model speed and length are small the flow at model

scale is L AMIN AR.

At full size the speed and length are much greater so muchof the flow ill be TURBULENT

This will give differences in the frictional resistance unless

we correct for this.

This is done by adding TURBUL ATORS to the model tostimulate turbulent flow.




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A typical resistance

plot looks like this

Resistance

!

!

2

2

"

.2 .2 . " . " .4 .4 .

Froude # umber Fn

R e s i s t a n c e

Friction component

Wave component

TOT AL upright




Resistance



Resistance

$

% $ $

& $ $ $

& % $ $

2$ $ $

2% $ $

' $ $ $

$ .2 $ $ $ .2% $ $ . ' $ $ $ . ' % $ $ .4 $ $ $ .4 % $ $ . % $ $

Froude ( umber Fn

R e s i s t a n c e

At low speeds the

friction component

makes up the majority

of the Total drag.




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Resistance

)

0 ) )

1 ) ) )

1 0 ) )

2) ) )

20 ) )

2 ) ) )

) .2 ) ) ) .20 ) ) . 2 ) ) ) . 2 0 ) ) .4 ) ) ) .4 0 ) ) . 0 ) )

Froude 3 umber Fn

R e s i s t a n c e

As hull speed is

approached the wave

component increases

rapidly, until it is 7 -

8 % of the total




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4

5 4 4

6 4 4 4

6 5 4 4

24 4 4

25 4 4

7 4 4 4

4 .2 4 4 4 .25 4 4 . 7 4 4 4 . 7 5 4 4 .4 4 4 4 .4 5 4 4 . 5 4 4

Froude 8 umber Fn

R e s i s t a n c e

At typical windward

sailing speeds Wave

resistance is less than

half the total

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Resistance Concepts