Theory Design Air Cushion Craft 2009 Part 4 doc

Method used in Japan [28] Reference 28 introduces the measurement of the inner/outer wetted surface area of a plate-like sidewall of an SES with cushion length beam ratio IJB C of about

106 Steady drag forces

inner wetted surface outer wetted surface

Fig 3.20 Sketch of wetted surface of SES.

f ^iO ' ^outO -*^out \J.£J) where K out can be obtained from Fig 3.21, which has been obtained by statisticalanalysis of photographs on model no 4 by MARIC It is found that there are twohollows on the curve of the outer wetted surface area, the first is due to the humpspeed, which leads to a large amount of air leakage amidships, and the second iscaused by small trim angle at higher craft speed

Method used in Japan [28]

Reference 28 introduces the measurement of the inner/outer wetted surface area of a

plate-like sidewall of an SES with cushion length beam ratio (IJB C ) of about 2 on the

cushion and represented as follows (Fig 3.22):

where Sf is the area of the wetted surface of sidewalls (m ), Sf30 the area of the wettedsurface of sidewalls at high speed (m2) and/s the correction coefficient for the area ofthe wetted surface, which can be related to Fr,, as shown in Fig 3.23 and which isobtained by model test results

In the case of craft at very high speed (higher than twice hump speed), the watersurface is almost flat at the inner/outer wave surface and also equal to each other.With respect to the rectangular transverse section of the sidewalls, the wetted area can

be written as

S* = [4(A2 - Aeq) + 2 B,] /,

S m is the wetted surface area of the sidewalls of craft hovering statically (m ),

(3.27)

Sidewall water friction drag 107

Using flexible bow/stern seals

where 5S is the width of the sidewalls with rectangular transverse section (m), /s the

length of sidewalls (m), /zc the depth of cushion air water depression, hovering static

(m), /z, the vertical distance between the lower tip of skirts and inner water surface, i.e

//! = h 2 ~ T } , as shown in Fig 3.24, hovering static (m), H 2 the vertical distance

between the lower skirt tip and craft baseline (i.e zb, zs, in Chapter 5) (m), T { the inner

sidewall draft, hovering static, and /zeq the equivalent air gap,

where Q is the cushion flow rate (m'Vs), p 2 the cushion pressure (N/m), p a the air

density (Ns2/m4), l } the total length of air leakage at the bow/stern seal (m) and B c the

cushion beam (m)

108 Steady drag forces

Fig 3.24 Correction coefficient for sidewall wetted surface area.

From equations (3.27) and (3.28) the area of wetted surface at any given Fr\, can be

interpolated from

at Fr{ = 0, S( = S m (max area of wetted surface)

at Fr{ = °° S f = S fx (min area of wetted surface)

and

Sidewall water friction drag 109

Based on model tests in their towing tank, the following method was obtained by

NPL:

S t = (S a + ASf) (1 + 5 5smax//s) (3.29)where 5smax is the max width of sidewalls at design water line (m), ASf the area cor-

rection to the wetted surface due to the speed change (m") and S m the area of wetted

surface of sidewalls during static hovering (m )

This expression is suitable for the following conditions:

8 < / 7c/ /c< 1 6 and Fr\ > 1.2

Figure 3.25 shows a plot enabling A5"f to be determined within these conditions

B A Kolezaev method (USSR) [19]

B A Kolezaev derived the following expression for sidewall drag:

Sf = Kf S m

where S f is the area of wetted surface, hovering static (Fig 3.26), K f the correction

coefficient for the wetted surface, related to Fr (Fig 3.27) S m can also be written as

below (see Fig 3.26):

110 Steady drag forces

Fig 3.26 Typical dimensions for wetted surface of sidewalls.

Fig 3.27 Correction coefficient of wetted surface area of sidewalls vs Froude Number.

where Tj, T 0 are the inner/outer drafts, hovering static (m), b s the width of the base

plate of the sidewalls (m), B s the width of sidewalls at designed outer draft (m) and /?the deadrise angle of sidewalls (°)

A number of methods used for predicting the area of the wetted surface have beenillustrated in this section It is important to note that one has to use these expressionsconsistently with expressions by the same authors to predict the other drag compo-nents, such as skirt drag, residual drag, etc., otherwise errors may result

As a general rule, the methods derived from model tests and particularly photorecords from the actual design or a very similar one will be the most accurate The dif-ferent expressions may also be used to give an idea of the likely spread of values forthe various drag components during the early design stage

Sidewall wave-making drag 1 1 1

1,9 SWewall

Equivalent cushion beam method

SES with thin sidewalls create very little wave-making drag, owing to their high

length/beam ratio, which may be up to 3CMO To simplify calculations this drag may

be included in the wave-making drag due to the air cushion and calculated altogether,

i.e take a equivalent cushion beam B c to replace the cushion beam B c for calculating

the total wave drag Thus equation (3.1) may be rewritten as

where R w is the sum of wave-making drag due to the cushion and sidewalls, Cw the

coefficient of wave-making drag, Cw = f(Fr b \JB C ) and B c the equivalent beam of air

cushion including the wave-making due to the sidewalls

The concept of equivalent cushion beam can be explained as the buoyancy of

side-walls made equivalent to the lift by an added cushion area with an added cushion

beam The cushion pressure can be written as

where W s is the buoyancy provided by sidewalls and W the craft weight Then the

equivalent cushion beam can be written as

W W B

The method mentioned above has been applied widely in China by MARIC to design

SES with thinner sidewalls and high craft speed and has proven accurate Following

the trend to wider sidewalls, some discrepancies were obtained between the

calcula-tion and experimental results For this reason, [29] gave some discussion of alternative

without the consideration of wave-making drag caus_ed by sidewalls, Cw the coefficient

due to the wave-making drag with respect to Fr, IJB C

12 Steady drag forces

greater the WJW, the more the wave-making drag of the sidewalls.

Figure 3.28 also shows that wave-making drag decreases as the WJW exceeds 0.5.

This seems unreasonable The calculation results of [30] and [31] showed that

wave-making drag will increase significantly as WJW increases Reference 32 also showed that the wave-making drag of sidewalls could be neglected in the case of WJW <

15%

The equivalent cushion beam method is therefore only suitable to apply to SES withthinner sidewalls It is unreasonable to use this method for SES with thick sidewalls

or for air cushion catamarans (e.g WJW ~ 0.3-0.4) and for these craft the

wave-making drag of sidewalls has then to be considered separately

Sidewall wave-making drag 113

Yim [30] calculated the wave-making drag due to sidewalls by means of an even

simpler method He considered that the total wave-making of an SES would be equal

to that of an ACV with the same cushion length and beam, i.e it was considered that

the sidewalls did not provide any buoyancy, and the total craft weight would be

sup-ported only by an air cushion as to lead the same wave-making due to this equivalent

air cushion The effective wave-making drag coefficient of the sidewalls calculated by

this method is similar to that for WJW > 0.5 above (see Fig 3.28).

Hiroomi Ozawa method [31]

The theoretical calculation and test results of the wave-making drag of air cushion

catamarans have been carried out by Hiroomi Ozawa [31] Based on rewriting his

equations found in [29], the final equation for predicting total wave-making drag may

be written as (when Fr = 0.8)

V = [1 - 0.96 WJW + 0.48 (WJW) 2 } [Cw B c /(p v gj\ [Wl(l c B c )] :

A comparison between the equivalent cushion beam method, the Ozawa method and

the Yim method is shown in Fig 3.28 It can be seen that satisfactory accuracy can be

114 Steady drag forces

obtained by the equivalent method in the case of WJW < 0.2, but the wave-making

drag of sidewalls and its interference drag with the air cushion have to be taken into

account as WJW increases.

In conclusion, the methods for estimating sidewall drag introduced here are suitablefor SES with sidewall displacement up to about 30% of craft total weight Where alarger proportion of craft weight is borne by the sidewalls, the sidehull wave-makingshould be considered directly, rather than as a 'correction' to the cushion wave-making Below 70% contribution to support from the air cushion, the beneficial effect

of the cushion itself rapidly dies away, and so it is more likely that optimizing maran hulls will achieve the designer's requirements in the speed range to 40 knots.Above this speed, an air cushion supporting most of the craft weight is most likely togive the optimum design with minimum powering

cata-Calculation method for parabola-shaped sidewalls [33]

In the case where the sidewall water lines are slender and close to parabolic shape,then the wave-making drag of sidewalls can be written as

(8 Av gin) (B s T 0 //s) (3.43)

where R^ is the wave-making drag of the sidewall (N), Csww the wave-making drag

coefficient (Fig 3.29), p w the density of water (Ns"/m ), B s the max width of sidewalls

(m) and T 0 the outer draft of sidewalls (m)

B A Kolezaev method [19]

Kolezaev defined the residual drag of sidewalls as a function of craft weight:

where R^ is the residual drag of sidewalls (N), K fr the coefficient of sidewall residual

drag, obtained from Fig 3.30, and IV the craft weight (N).

1.6

10 12 14 l/2Fr2=g/s/2v2

Fig 3.29 Wave-making drag coefficient of slender sidewalls with the parabolic water planes [39]

Underwater appendage drag 115

Fig 3.30 Residual drag coefficient of sidewall as a function of LJB^ and Froude number.

3.10 Hydrodynamic momentum drag due to engine

cooling water

In general, the main engines mounted on SES have to be cooled by sea water which

is ingested from Kingston valves or sea water scoops mounted at propeller brackets,via the cooling water system, then pumped out from sidewalls in a transverse direc-tion The hydrodynamic momentum drag due to the cooling water can be written as

the flow rate of cooling water (m/s)

3,11 Underwater appendage drag

Drag due to rudders, etc.

Drag due to rudders and other foil-shaped appendages, such as plates preventing airingestion, propeller and shafts brackets, etc can be written as [34]:

rudder surface In this case Re = (vc/u) where c is the chord length of rudders or other foil-like appendages (m), dvlv is the factor considering the influence of propeller wake:

116 Steady drag forces

dvlv = 0.1 in general, or Svlv = 0 if no effect of propeller wake on this drag;

v is craft speed (m/s), r the empirical factor considering the effect of shape, r = 5 tic,

This equation is suitable for rudders or other foil-shaped appendages totallyimmersed in the water

Drag of shafts (or quill shafts) and propeller boss [35]

This drag can be written as :

shaft (quill shaft) and boss For a perfectly immersed shaft (quill shaft) and boss and5.5 X 105 > RCm > 103, then it can be written:

Rem = v(ll+l2)/D

Drag of strut palms

According to ref 34, the drag of strut palms can be written as

thickness of the boundary layer at the strut palms:

6 = 0.0l6x p (m)

Drag of non-flush sea-water strainers

According to ref 34, the drag of non-flush sea-water strainers can be written as

Total ACV and SES drag over water 117

area of the sea-water inlet (m), C0 the drag coefficient due to sea-water strainers, and

v the craft speed (m/s)

There are a number of methods for predicting the appendage drag In this respect,

there is no difference between the appendages of SES and planing hulls, or

displace-ment ships: the data from these can therefore be used for reference

3,12 Total ACV and SB drag over water

Different methodologies to calculate the total drag of ACV/SES have been compiled

and compared at MARIC [27] Three methods for ACVs and five methods for SES

may be recommended, as summarized below

ACV

The calculation methods are shown in Table 3.2 Notes and commentary are as

follows:

• It is suggested that method 1 can be used at design estimate or initial design stage

Since many factors cannot be taken into account at this stage, the method is

approximate, taking a wide range of coefficients for residual drag Method 3 is still

approximate, although more accurate than method 1 For this reason it can be

applied at preliminary design stage With respect to method 2, it is suggested using

this at detail design or the final period in preliminary design, because the

dimen-sions in detail and the design of subsystems as well as the experimental results in

the towing tank and wind tunnel should have been obtained

• The drag for above-water appendages (air rudders, vertical and horizontal fins,

Table 3.2 Methods for calculating ACV over water drag

Drag components Method 1

Estimation

Method 2 Conversion from model tests

Method 3 Interpretative

Aerodynamic profile drag

Aerodynamic momentum

drag

Momentum drag due to

differential leakage from

bow and stern skirts

Cw can be obtained from Figs 3.2 and 3.3 Wave-making drag

Skirt drag or residual

See Note 2

X 10" 6 (/i {[2.8167 + 0.112

^ + R m R', k )

//,) °' 34

PJl c

+

Note 1: In methods 1 and 3 a" denotes the angle between the inner water surface and the line linking the lower tips of bow

and stern skirts.

Note 2: In method 3, normally Kj = 1.15-1.25, but where a large amount of references and experimental data are

avail-118 Steady drag forces

300z

Total ACV and SES drag over water 119

X9.8N

16000140001200010000800060004000

20 40 60 80 100 120 140 v(km/h)

2000

20 40 60 80 v(kn)

Fig 3.33 The drag and thrust curves of SR.N4.

etc.) is included in the air profile drag, because in general the air profile drag

co-efficient Ca, which can be obtained either by model experimental data or by the

data from prototype craft or statistical data, implicitly includes appendage drag in

the coefficient

• Similarly to conventional ships, model drag can be converted to drag of full scale

craft according to the Froude scaling laws (see Chapter 9)

• Taking the Chinese ACV model 7202 and 711-11A as examples, we calculate the

drag components for these craft as shown in Figs 3.31 and 3.32 The propeller

thrust in the figure was calculated according to the standard method for predicting

the air propeller performance published by the British Royal Aeronautical Society

If K T is assumed equal to 1.23 and 1.1 for craft 7202 and 711-IIA respectively and

method 3 is used, then the calculated results agree well with the trial result

When MARIC used method No 1, taking K 7 as 1.65 for craft 7202 and 1.5 for

craft 711-IIA, then the calculations agreed with test results It can be seen that

method 1 is approximate, because of the large K^ value.

• A typical resistance curve for the British SR.N4 can be seen in Fig 3.33

SES

There are many methods for calculating the drag components of an SES as are

men-tioned above, though one has to use these methods carefully and not mix them with

Table 3.3 Methods for calculating the drag of SES over calm water

Method Method 1 Method 2 Method 3

Estimation Conversion from NPL Method

model tests Drag items

Aerodynamic profile /? a = 0.5p Ca S A v

drag

Wave-making drag due R m = p A Q v

to air cushion

Friction drag of the /? w = C w pi BJ(p w g) Cw can be obtained

sidewalls from Fig 3.2 and 3.3

Wetted surface area of R^f = (C { + ACf) S t q w

sidewalls

Residual drag of R w = 0.05 Cw (pi 5C)/ R^ is included in R,

sidewalls (p v g) where Cw is from

Skirt drag or residual

R dp can be obtained by the same methods

as for high-speed boats

Remarks If the craft is at optimum

trim angle then use C sk as shown in Fig 3.17, otherwise increment.

Skirt/terrain interaction drag 121

Fig 3.34 The drag and thrust curves of 717C.

each other, otherwise errors may be made We introduce five methods for SES total

drag reference, outlined in Table 3.3 and add some commentary as follows:

1 It is suggested that method 1 can be used at the preliminary design stage and by

comparison with methods 3, 4 and 5 With respect to method 2, this can be used at

the final period of preliminary design or the detailed design stage

2 The key problems for predicting the friction resistance of sidewalls are to

deter-mine accurately the wetted surface area Of course it can be obtained by model

tests in a towing tank However, it can also be estimated by Figs 3.24, 3.25 and

3.27

3 The sidewall residual drag (or sidewall wave-making drag) can be calculated

according to Table 3.3, i.e one can use the Newman method to calculate the

wave-making drag (use Fig 3.2 and 3.3) due to the air cushion, then take 5% of this as

the sidewall residual drag In the case of small buoyancy provided by the sidewalls

(WJW< 0.2) the total wave-making drag can be calculated by the equivalent

cush-ion method The sidewall resistance can also be estimated by equatcush-ion (3.43) or the

Kolezaev method

4 Seal drag R^ can be calculated by the statistical method (MARIC method) or by

taking 25-40% of total resistance (except R sk itself) as the seal drag

5 Taking Chinese SES model 717 as an example measurements and calculations are

as shown in Fig 3.34 It is found that the calculation results agree quite well with

the test results, The typical SES resistance curve can be seen in Fig 3.1

'3.13 ACV skirt/terrain interaction drag : ; ; ; ' ; 'ih/rh^l

For an ACV which operates mainly over land, such as self-propelled air cushion

plat-forms, it is important to accurately determine the skirt/terrain interaction drag, as it

122 Steady drag forces

is a high percentage of the total drag The total overland drag of ACV can be written

as follows:

^gacv = ^a + ^m + ^sp + ^si + ^sk (3.50)

where R gacv is the total overland drag of ACV (N), R a the aerodynamic profile drag

(N), R m the aerodynamic momentum drag (N), R sp the spray (debris) momentum drag

(N), R si the slope drag (N) and R sk the skirt/terrain interaction drag (N)

R a , R m can be calculated by the methods outlined above R sp can usually beneglected due to the craft's low speed The slope drag can be calculated according tothe geography of the terrain The skirt/terrain interaction drag is very strongly sensi-tive to lift air flow and is a function of craft speed and terrain condition It is difficult

to determine analytically and is usually determined from experimental data

The overland drag curve of an ACV can be divided in three modes controlled bycushion flow rate as shown in Fig 3.35:

1 Mode A, ACV profiles the terrain perfectly (i.e a clear air gap between ACV andterrain);

2 Mode B, ACV experiences strong skirt/terrain interaction effects;

3 Mode C, ACV operates in 'ski' mode

In mode A, at high flow rates, drag is relatively low Normally in this flow region there

is an air gap under most of the skirt periphery In mode B, segment tips drag on thesurface, but the delta regions between skirt tips still exist In mode C, segment tips arepressed against the surface and the air flow acts more as a lubricant

Figure 3.35 shows that the skirt/terrain interaction drag is closely related to skirt tip

air gap According to Chapter 2, the lift air flow Q can be written as

Drag

Fig 3.35 Three operation modes of an ACV over ground terrain.

Skirt/terrain interaction drag 123

where Q is the lift air flow (m ), /_, the peripheral length of the skirts (m), h the skirt

clearance, including the equivalent clearance regarding the air leakage from the delta

area of fingers, </> the air flow discharge coefficient and/?c the cushion pressure (N/m~)

Different terrain conditions can radically change the effective discharge coefficient,

(see Table 3.5) Grass or rock have the greatest effect It is inappropriate therefore to

characterize the air gap by h alone, since rough terrain and stiff grasses or reeds will

reduce the skirt clearance significantly at the same air flow

Fowler [36] defined h { K as the gap height instead of using h alone (i.e h f K = h),

where K is referred directly to the terrain condition This gap height for various craft

is shown in Table 3.4 Then it can be seen that a high gap height h { K is normal for a

high-speed ACV and low h f K for hover platforms.

Test results demonstrating the relation between skirt/terrain interaction drag and

h f K as well as the terrain conditions are shown in Fig 3.36 [36] It is clear that the

skirt/terrain interaction drag is very strongly sensitive to lift air flow

Skirt/terrain interaction drag will increase at a higher rate as the skirt air gap is

reduced below a critical value For this reason, an optimum skirt air gap has to be

selected as shown in Table 3.5 [37], recommended by Fowler

Figure 3.37 shows the relation between the skirt/terrain interaction drag and craft

speed Figure 3.38 shows the drag for craft running on an ice surface in relation to the

Froude number These test results are provided for reference

Table 3.4 Gap height h ( K of various ACV

Item 1 2 3 4 5 6 7 8 9 10 11 12

Craft SR.N5 SR.N6 SR.N4 SR.N4 Mk2

Voyageur Viking

LACV-30 ACT 100

Sea Pearl Yukon Princess

Hex-55 Hex- IB

Type ACV ACV ACV ACV ACV ACV ACV ACP ACP ACP ACP ACP

h f K

0.08 0.07 0.084 0.073 0.08 0.068 0.062 0.019 0.018 0.012 0.018 0.015

Table 3.5 The suggested gap height h { K for various ACV terrain conditions [36]

Smooth concrete, slow speed

Firm snow

Short grass

Moderate grass

Long reedy grass (1st pass)

Long reedy grass (10th pass)

Crushed rock

Mudflats

Concrete, high speed

0.0035 0.0055 0.02 0.02 0.022 0.022 0.02 0.016 0.013

1.0 1.5 6 6 6 6 6 5 4

2 2.5 2 2 40 5 15-30 2-5 2

124 Steady drag forces

Firm snow

10 15 20 Skirt drag/Craft weight x 100(%)

2

-Test on concrete surface

2 4 6 8 10

vs (m/s)

Fig 3.37 Skirt ground interference drag as a function of /?f /f and craft speed.

3.14 Problems concerning ACV/SES take-off

The acceleration capability of ACV/SES through hump speed is a very importantdesign feature Designers and users are therefore often concerned about the 'take-off'capabilities of ACV/SES running over water, because the hump speed is only one-

Problems concerning ACV/SES take-off 125

Fig 3.38 Skirt drag of ACV running on ice as a function of Fr.

third to one-fifth of normal design speed The physical phenomenon of take-off is

therefore considered here and some comments on craft optimization presented

When craft speed increases, at Fr of about 0.38 the craft begins to ride between two

wave peaks located at the bow and stern respectively The midship portion of the craft

is then located at a wave hollow and a large outflow of cushion air blowing up water

spray is clearly observed in this region, as shown in Figs 3.18(c) and 3.39 This in turn

reduces the air gap below the bow and stern, which in the present case with wave

peaks located at the bow and stern seals, would result in contact of water with the

planing surface of the seals and present a new source of drag acting on the craft

This condition was investigated by MARIC by towing tank model experiments The

surface profile was obtained with aid of a periscope and photography [28]

Seal drag consists of two parts One part is the induced wave drag of the seals and

the other is frictional drag acting on the planing surfaces A large amount of induced

wave drag can be built up when the seals are deeply immersed in water and the

plan-ing surfaces contact at large angles of attack

The skirt-induced wave is also superimposed on the wave system induced by internal

cushion pressure and constitutes secondary drag In the case of poorly designed seals

or skirts, the peak drag at Fr = 0.38 may be larger than that at Fr = 0.56 (main resistance

hump speed) Meanwhile, transverse stability will most probably also decrease

A craft will tend to pitch bow down when the craft has a rigid stern seal (such as

fixed planing plate with a large angle of attack or a balanced rigid stern seal) and a

relatively flexible bow seal The craft will most probably be running at a large yawing

angle as well, due to poor course stability The operator of the ACV or SES will be

obliged to use the rudder more frequently

The forces arising from these situations are complicated and quite large in

magni-tude Meanwhile the ship may be difficult to control, the propulsion engines are

over-loaded and a lot of water spray is blown off from the air cushion and flies around the

craft, interfering with the driver's vision, making handling of the craft even more

dif-ficult Operation would probably become very complicated if the sea were rough

rather than the calm conditions considered in this chapter Such phenomena are the

features of a craft failing to accelerate successfully through secondary hump speed

Meanwhile, if the thrust of the propellers is larger than the resistance of the craft,