Wind tunnel tests of a 1/3rd scale model of an X-one design yacht's sails

(1)

ARCHIEF

ADVISORY COMMITTEE FOR YACHT RESEARCH

1 'II Id 0 I'.

Lab. v.

Scheepsbouwwunae

Technische

Hageschool

R EEP:r.;

Delft

6 _{WIND TUNNEL TESTS}

.OF A 1 3rd SCALE MODEL OF AN X-ONE DESIGN YACHT'S SAILS

by

Marchaj

-4.

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- 7.19' kev

'DEPARTMERT OF AERONAUTICS & ASTRONALMICS

ii J I'' 'October 1962. a

University of Southampton

4 a ' -C .A .

(2)

CONT2_NTS

Page No.

List of Symbols ₁

2. Introduction . _{,0000,oe.000000oeVo0000r000,,00.Orarrra} _2.

Results

4. Discussion

_{00i0000000000f0.0000000 000e0400eve}

₄

ConclusionsV7'in .7'7 .7.-On Fe; r:e- 0 0 q0. 0 0 .0re .0 a Ur or o 00

a

References ti pc .0 0 wor oro ohs 0 010.00,0,0.0 e o 0+0 _{000 oa.otole}

Figures 1 , 12 Tables 1 Ll 7 00100000/0000000000000o0000000 2 Conclusions 14

(3)

-1. LIST OF SYMBOLS (see Figs. 3 4 &

cross-wind force in lb. crosswind force coeff

-q x S A

Y x

dynamic pressure - 2g v2 - 000119 x v'

wind velocity in ft/sec.

SA - sail area in sq. ft.

D Aerodyn, drag in lb.

- Drag Coeff =

---q x SA

F - _{driving force in lb.}

CR - driving force coeff - _{q x SA}

FH - heeling force in lb.

H

CH heeling force coeff - _{q x SA}

Mom - _{heeling moment in lb. ft.}

Mom

Cm _{heeling moment coeff =}

q x

mainsail setting angle relative to _{hull centreline}

oM

F foresail setting angle relative to hull centreline

heading; _{angle between hull centreline and wind}

direction

X _leeway,

angle between hull centrel,Ine and course sailed

1

-9)

-D

(4)

N.B. Attention is particularly invited to the definitions

of the symbols FR, CR, FH and CH since in this report they

represent horizontal force components or coefficients

measured parallel or perpendicular to the plane of symmetry of the hull when unheeled and therefore differ from those frequently used to represent the hydrodynamic forces on

the hull. In this latter connection it is common practice

to quote force components and coefficients measured parallel and perpendicular to the direction of motion of the hull through the water.

(5)

2. Introduction

Some wind tunnel tests have been carried out at Southampton University on an accurate 1/3rd scale model of soft sails of the XONE DESIGN CLASS yacht.

Details cf the model tested are shown in Figure 1 and photographs.

Terylene sails (mainsail and foresail) of total area 20°5 sq0 ft,

were kindly supplied by Col. C,E. 3owden who used them on a large radio controlled free sailing model.

Experiments on radiocontrolled models in connection with wind tunnel testing were made in order to obtain correlation data between

fullscale and the model behaviour.

-And tunnel tests were performed over ranges of heading angles

X) = 15°

421°

to cover closehauled conditions.

2

The primary purpose of the research programme was to evaluate:

Driving force, FR

Heeling force, FE_

Heeling moment and vertical C.E. position at various

wind speeds; 18, 12 and 10 knots (30, 20, 17°1 ft/sec).

Significance of the sheeting base on sail efficiency

(1 i) Influence of 200 heel on aerodynamic characteristics of _sails.

3. Results

Figures 2, 3 and 4 represent the results obtained _{on sails in the}

upright position at a wind speed of V = 20ft/sec (12 knots). Sketches

in Figures 3 and 4 define the angles and forces used in the analysis.

Crosswind force L, drag D _{and heeling moment were measured}

directly. Driving force FR was calculated by resolving L

and D

along and across an axis formed by the hull centreline _{according tq the}

formula

FR = L sin (IJ x) D cos X)

(6)

6 =

50,

Ivi

was constant and measurements were taken for different

sheeting angles of the foresail (OF) in the range from 71° to 200

1 in steps of 2°

Figures 5 and 6 represent some data obtained in similar conditions to that of Figures 2, 3 and 4 but during the tests the

1

foresail was fixed = 177, and the sheeting angle of the

main-sail was varied in the range 6 = 5° 15° every 5 degrees.

The vertical C.E. position was calculated from the formula

C.E. (ft)

where FH = L cos (V, X) + D sin

The results of the experiments shown in Figures 7, 8 and 9 were obtained at wind speeds

V = 30, 20, 17°1 ft/sec,,

for constant sails configurations

b = 50

= 20°

In order to compare the characteristics of the sails at various wind speeds, the results are shown in the form of nondimensional co

efficients' C

0D' and C

9 L' D' R M

Figures 10 and 11 show the aerodynamic characteristics of the sails

in both the upright position and at 20° of heel. Measurements were

taken at a wind speed of 20 ft/sec0 and the sails were set so that

1

6m = 10°, 6F = 17-f in both cases.

Heeling moment Mom

Heeling force

FH

(7)

f

4, Discussion

From Figures 2, 3 and 4 it can clearly be _{seen that the' aerodynamic}

Characteristics of the sails and attainable v.)lue of driving force Fa

depends very much on mutual positions of two interfering sails, main and foresail.

The sheeting angle of the foresail

(op)

_{whidh determines the}

',interaction between the sails seems to have quite _{abig effect} _on, _the

efficiency of

the

sailS.

Undoubtedly, interaction between sails, _{particularly between main}

and foresail, is the most controversial subject _{among sailing theorists}

Broadly speaking, there are two schools of thought': _{those who maintain}

that the foresail accelerates the

air

_{past the leeward. tide lof the main=}

sail increasing the suction, and those who argue that the function of the foresail is as a sail in its own right, and a very efficient one at that.

The firstof:theory _{is sometimes called the nozzle}

or Venturi effect,

and owes a lot of its support. to the _{analogy with a, slotted aircraft wing.}

it One can often find in sailing, text books examples quoted by one or

other of these two schools of _{thought, giVing} _{correct' angles}

_of

trim for

the, foresail. _{FreqUently, however, these descriptions}

are quite contra,

dictory, the correct trim angle for _{the headsail has, on different}

occasions,

been recommended as anything, from

F to 0F= 20°,

Unquestionably a foresail _{can, by itself, be a very efficient sail,}

because

it has not the disturbing influence _{of the mast to upset the flow}

round the

sail and the pressure distribution _{on it,}

This appears to have been opn,,

firmed in the investigation done, by Warner' and Ober (Reference 1) _{on the}

_full

-

4 -=

(8)

scale yacht 'Papoose'. _{At the same time, the foresail} _{can also greatly} improve the flow of air over the leeward side of the mainsail, particularly if there is some overlap. (See Reference 2).

However, to obtain the maximum advantages from the foresail in both

these capacities simultaneously is _{difficult and for certain classes}

im-possible. _{'=ome class rules are so framed that the most}

efficient sails

configuration cannot be employed. _{Limitations in most class rules prohibit}

the use of outriggers to extend the _{sheeting of the foresail outboard of the}

gunwale, with the exception that in some cases the foresheet can be guided by a boom.

Somequantitctive information on how great is the influence _{of the}

foresail sheeting base on sail efficiency can be derived by analysis of the driving force curves in Figure 3.

As an example _{for a typical angle of heading} _(P

"A.) = 30°, the

driving force FR _{increases by about 20% if the sheeting angle}

6F is

1

increased from 7° to 15° _{At the same time, the corresponding}

increase

2

of heeling moment is about 3°5 only.

The significance of the sheeting base becomes more and more important

when bearing away off the wind. _{For the angles of heading}

_{(P - x)}

_{= 350}

and (P X) =-40° _{corresponding increments of driving force}

are 40% and

63% respectively, assuming that _{the sheeting angle} _6F _{can be increased}

1

from 7° to 20°. _{Figure 4 shows that there is a certain optimum in sheeting}

2

angle bF for a given heading (P X).

For a typical scope of heading to windward (P

- %) =

25° 35°, the

optimum sheeting angles 6F vary from 12° _{13° approximately.}

Figures 3 and 4 show that altering the trim angle of the foresail, with

the _{main held fixed, gives}

relatively larae chances in driv_ina force, _but

-

(9)

-5-very mall chanaes in heelina moment. _{On the other hand Figures 5 and 6}

show that changes in trim of the mainsail when the _{foresail is fixed}

affectr,..galthnotonlythdrivinforcl

moment.

For example, when heading ( X) = 300, the increase of the driving

force Fa _{due to closer sheeting of the main, is approximately 29%} _{but at}

the same time, the corresponding increase in _{heeling moment is about 42%.}

It is worthy of notice in Figure 5 that the vertical position of the

true C.E. is very near to the geometrical C.E. _{For the angles of heading}

1

(P -

x) = 17-f _{42f changes of vertical, true C.E. position} _{were + 4%}

only.

For the region of typical angles of heading to windward ( X) = 25°-35°,

the vertical position of the true C.E. is about 4% _{above geometrical C.E.}

Differences in the aerodynamic characteristics of _{the sail due to}

various wind speeds V = 30, 20 and 171 ft/sec0 _{are of a rather big}

order. From Figure 9 it can be seen that in the _region

( - %) below

25°, the attainable driving force coefficients

CR have a tendency to

drop when the wind speed increases. _{Some possible reasons for this}

are-Twist of the sails which increases _{following increase of}

the wind speed.

Deformation of the sail shape (camber) due to stretch of the sailcloth.

Increasing (with wind speed) sag of the forestay which affects

the camber of the foresail and also the _{floy between the two}

sails.

As a result of these changes in working _{conditions affecting both}

sails, the drop in the driving force _{coefficient when}

(i3 X) = 30° and

wind speed V = 30 ft/sec (18 knot) is about 16% _{compared with that at}

wind speed V = 1701 ft/sec. (10 knots).

(10)

6-The vertical C,E0 position also varies with wind speed. From;

-Figure 9 it can be seen that the true C.E. goes down even below the

geometrical, C.E. a5 the wind speed increases. _{This is caused by the}

twisting of the sail. _{At greater wind speed the upper parts of the}

mainsail flutter, contributing less to the generation of the aerodynamic force than lower parts of the sail.

Bearing away, When fluttering of the sail becomes less and less, the

true vertical C.E. position approaches the geometrical C.E. It is

worth-while noting also that following changes in C.E. position, the values of

the heeling moment coefficient vary in a similar manner, Figures 10 and

11 show the difference between sails in the upright position and for 20° of

heel. _{Comparing driving force curves in Figure 11 it} _{can be seen that}

for the whole region of X), the attainable driving force when the

sails are heeled is smaller than when upright. _{For example, when} _(P _X) _30°

the losses in driving force due to heel are approximately 15%. The

changes in the heeling moment are similar to those of the driving force.

Some of the differenb-e between the two driving forcr.1 curves arises because

when sails are heeled the effective angle of incidence of the _{sail to the}

wind becomes less, both for gemetrical reasons and because of the greater influence of the sea on the sail,

The effect of this can sometimes be seen when a yacht is heeled to a

verylarge angle usually on the verge of capsizing, when the _{sail may get}

the wind on the leeside.

(11)

5. _Conclusions

In racing circles it is well recognised _{how vitally important the}

trim angle of the foresail is when _{close hauled.} _{Nothing can reduce}

speed like sheeting the foresail too hard. _{Freeing the foresail sheet by}

only two inches, or a-small outboard _{shift of its fairlead may make a}

radical improvement in the performance of a yacht. _{This is proved by the}

results shown in Figures 3 and 4.

The most important condition _{for effective interaction between the}

two sails is that the foresail _{should be trimmed in such}

a way that a

sub-stantial increase in air velocity _{occurs in the slot without the mainsail}

being backwinded. _{In other words it is necessary that the general direction}

of air flow on the leeward _{side of the main in the}

overlapping region be

tangential to the surface of the _mainsail.

If the camber of the foresail

is too large or if the sail is sheeted

to hard, excessive _{convergence of the slat produces}

a velocity component

perpendicular to the surface of _{the mainsail.}

The harmful effect of this

perpendicular component, which _{reduces the suction on the mainsail, will}

be most prominent _{immediately abaft the mast.}

From a study of pressure

distribition (Warner and Ober, _{F:ee Ref. 1) it is already known}

that the

suction just behind the mast is not very great. _{It is a particularly}

sensitive place on the mainsail

and gives the helmsman the first warning

that he is 'pinching' _{the sail.}

When the suction at this point is re-duced to such an extent that the pressure

difference between the windward

and leeward sides is _{nearly zero, the sail will}

flutter.

Oncethe sail starts to _{flutter near the luff,}

its smooth contour is

destroyed and with it the streamlifted flow over the rest of _{the sail.}

(12)

-8--It can be suggested that to minimise backwdnding, we

should-Use a flat foresail in combination with a mainsail fairly well

cambered in the overlal7ing region rather than vice versa.

Position the sails so that they are substantially parallel.

These two rules imply that not only is the _{converoence of the slot}

dmoortant but also its shape.

Probably the supporters of the Venturi theory will not wholly

agree with this, as with them, the more convergence the better.

How-ever, one should remember that an effect of acceleration of the flow

between sails is conferred by a change in speed, or direction of the

flow. _{The gap can, and should be nearly parallel in the}

over-lapping region, yet the foresail will still exert a powerful influence on the mainsail, by virtue of it turning the air flow to the advantage of the latter.

Comparing curves in Figure 3 with those in Figures 5 and 6, a very

important conclusion can be reached as to the respective roles played

by the foresail and mainsail, Figure 3 shows that altering the

sheeting angle of the foresail with the main being fixed, gives

large changes in c37iving force, up to 63% in the case of heading

N.) = 40, but relatively small changes in heeling moment. On the

.other hand, Figures 5 and 6 show that chal,ges in trim of the mainsail affect heeling moment considerably.

When tuning the sails the above remarks must be borne in mind.

The dual role of the foresail, as a sail itself and _{one which has a}

profound effect on the mainsail, makes it particularly important.

One should therefore give it priority when tuning the sails, and

if any compromise is required, this should be made on the mainsail rather than the foresail.

9

(13)

-The following conclusion _{can be derived as a guiding factor when} selecting the mainsail trim angle.

In light winds, when the main objective _{is to attain the maximum}

driving force FR, trimming the boom well amidship when _{close hauled,}

can be advantageous. _{At the first sign of the heeling}

moment becoming

too large, with increasing wind _{strength, the sheet should be eased.}

This

will bring the working condition of the _{sails closer to the strong weather}

FR

criterion _{max because we can reasonably assume that the}

sails are mom

required to develop a large driving force FR _{with a low heeling moment}

(Mom) _{and heeling force} _FH.

Under these conditions it is better to

ease the mainsheet for the gusts, and maintain _{the trim of the foresail}

constant.

As a rule the foresail is _{a splendid driving sail, with its C.E.}

relatively low. _{Easing the mainsheet will}

cause backwinding which can be controlled from a slight shaking

of the luff to the whole sail flogging.

This,. in turn, will reduce the driving force but to a greater _{extent will}

cause a large diminution of heeling moment.

Ihen discussing the vertical true C.E. position, experiments _carried

out on the X-ONE DESIGN CLASS _{rather confirm the designer's assumption}

about the geometrical C.E _{being reasonable.}

However, this does not mean

that longitudinal true C.E. _{position is also fixed relatively} _{near to}

geo-metrical C.E.

Interpreting Figures 8 and 9 it _{can be said that the cut of the sail}

and properties of the sailcloth, _{which predetermine the resulting}

camber,

are very important factors.

The deformation of the camber _{of the sail due to stretch of the}

sail-cloth or sag in the forestay (which _{depends on the wind strength)}

can

(14)

-greatly change the efficiency of a given rig.

Visual observations of the behaviour of differently cut foresails

during tests on the XONE DESIGN CLASS and DRAGON _{CLASS could suggest}

certain conclusions concerning the cut of the foresail in order to

reduce the harmful effect of backwinding.

It was already argued that the ideal closehauled working condition for an overlapping headsail and mainsail is for the two sails to be

essentially parallel in the overlapping region and that the foresail should

be relatively flat. As an illustration we can consider the case of a

typical foresail, as shown in Figure 12. _{If initially cut with a straight}

luff (most frequently recommended in text books on the subject) the sag aft

of the forestay when sailing to windward _{will produce camber in the sail,}

even supposing the foot and leech remain straight. _{From the sketch it is}

clear that the camber at the various sections

S1, S2 S3 will be different

depending on the relative proportion of the material which _{works aft.} _The

biggest camber will be produced somewhere close to section 537 where the

proportion of sag to the chord is the greatest. _{Thus the camber of the}

sail cut in this fashion will generally increase _{towards the head, which is}

an undesirable, but frequently encountered, trait in headsails.

Nhen cutting the foresail this factor must be borne in mind. The

sag of the forestay is of particular importance when dealing with _{a sail}

of high aspect ratio and the mean chord of the _{sail is relatively small.}

It is worthwhile noticing that the _{sag in the stay equal to 4% of the}

chord will produce a camber 1/77 assuming _{that when there is no} _{sag the}

sail is flat.

A camber of 1/7 is of a rather big order and can produce backwinding

(15)

even if there is no overlapping. _{Attempts to counteract the effect of}

forestay sag frequently follow the old salt's advice of "keep _{the jib stay}

bar taut". _{Although, like many others, there is} _{some sense in this saying,}

it should not be applied equally in all _{cases, as particularly in small}

craft, excessive tension may only bend the hull and _{mast and not reduce the}

forestay sag. _{Even in very strong, large keel yachts where this} _dictum

can be applied (to a certain limit), it will be found impossible _{to eliminate}

the sag completely.

It is necessary therefore to introduce corrections _{when cutting the}

curved luff, having excess material _{near the foot, but a deficit in the}

upper parts as shown in F igure 12.

In effect one is subtracting the _{sag of the forestay from the basic}

surplus allowance of cloth, in a similar, though reverse way, to that

which is used to compensate for mast bending _{on the mainsail.}

The best procedure to adopt is to _{guess at the sag and so make an}

approximate allowance but defer cutting thc sail _{finely until it has been}

tried in actual windward sailing. _{The basic aim when making such}

adjust-ment as may be necessary is to produce _{a relatively flat sail causing the}

minimum of backwinding.

In this report it Was not intended to deal exhaustively with the subject but only to indicate one of many aspects o2 sail cutting and its possible influence on sail efficiency.

The results shown in Figure 4 encourage one to take the liberty of

emphasising the fact that sail design is at least _{as significant as hull}

design on the performance of a yacht.

A current question of great interest _{to English yacht designers is the}

rather shattering success in off-shore _{races of beamy shallow draft}

(16)

-12-American centreboarders built under the C.C.A. rules. Both on rating and handicaps these have virtually eliminated the competition of the

narrow, deep keeled yachts. This rather unexpected result, from the

point of view of hull designers, is being attributed to the differences between the hull types, particularly to the supposed high efficiency of fins

having a large centreboard. Even the recently introduced changes in C.C.A.

formula support this view by taxing more heavily than before, broad beam, shallow draft centreboarders.

Without decrying the advantages to be gained from these hull

conceptions, it would be worthwhile considering also their effects on the

sails. For off-shore racing and cruising where close-hauled performance is

not usually of predominant importance, sail rig on a wide sheeting base is considerably superior to the usual rig found on the traditional narrow hulled English yacht.

(17)

,",archaj, Chapleo, A.Q. 3. Marchaj, C.A. Chapleo, A,Q.

REFERENCES

Author _Title

1. E. ':arner, _{'The Aerodynamics of Yacht Sail'}

S. Ober

'Visual Observation of the Flow Round the Sail of a Model Yacht'.

A.C.Y.R. Paper No, 33.

'Preliminary Note on Results of Rigid. Sail Tests in the Unheeled Position'. A.C.Y.R, Paper No. 37.

- 14.-C.A.

(18)

UNIVERSITY OF SOUTHAMPTON Department of

Aeronautics & Astronautics

ADVISORY COMMITTEE FOR YACHT RESEARCH

WIND TUNNEL TESTS OF A 1/3rd SCALE MODEL OF AN

XONE DESIGN YACHT'S SAILS

by

CA Marchaj

(19)

ot. el it re -5 51.1_- ift J ----"- To. .1 ' c

t

, .. r 3 51

,

.'1. k ' e at

y

A-One D.2:.sign Class Sails in Heeled Position (Heel 200)

9

1,

-" - o ece

(20)

FIGURE I.

X ONE - DESIGN CLASS.

Scale

1:3, Mainsail Luff. 6

Fool'

3' 8"

Area

14.5 sq. ft.

No. I. Staysail

Area

_{6 sg. ft.}

Total area

.

20.5 sg.ft.

2

AR (Main).:Vf

4.4. AR (Jib

:-.

3.9. Turntable

7i

4 --

-2' 6

3

8

_Turntable.

Axis

_{of rotarion.}

3 0 Vertical

position

of

geom. C.E.

Axis of rotation.

86

Mast 5 -Boom.

(21)

-J

Lip

I 5

I0

5 15 50

_20°

5

250

30 30°

35 Heading, (0-

N.)

350

40 40°

( D )

FIGURE

2. qconstanl)

0F 20

F = 15( A F lOc

x

F = 71.

4

3 '2

20°

(22)

_o Lu (-9

200

Heal:fin N

25°

30°

350

_

40 °

F = 20

F

I 5

F = ° F= Heeling moment.

Driving force

FR. v)4'-LS m

5°(constont)

40 5 20

(23)

0

App. wind. FIGURE

4.

Driving

force

FR

(43, _?\), 350

°

(is

-X=32 '2

(f3-0

X): 30

- N)= 25

0

.5

10

15

₂₀

F Sheeting angle in degrees

71/2 1216

102.

4 _-

_{A)7 27}

22

(24)

3 FIGURE 5.

30

35

40 _{p - X) in ,degree.}

eF

7 lit 7 r c cop

0--4 0

_-

in degrees.

30

35 '5

*20

2 5, 15

20

25

Geomer C.E.

(25)

5 0

4 0

3 0

0

FIGURE 6.

Mom. , (g

-,I5

,10

(g- X) in

degrees. 0

2 0

cy,

10

20

25

30

35

15

.05

(26)

IJ '17 5

0

FIGURE 7

50

IF

20 2 0

Con stall/.

20

-Drag coe ff. - CD.

" foe

_ v

=30 ft/sec.

(-18 knots.)

20 bo."" (-12

0v

171 10 )

4Istc

1-5 -J 0

10

2 15

30

35

40

1.0 L C D

(27)

-FIGURE 8.

115 15

20

7

4

25

30

35

40

___ AT/

300 fti sec. (.18

n)

171

10 kn) ±_- 20.0 kn) MA 11 11 .in degrees.

20

25

30

35

40

(28)

'3 0 LJJ C) FIGURE 9. 5 ° F

.20°

1

constant.

FH

171 f

t/sI

c.

v = 20 0

-ft/s-ec.

300 ft sec.

CE.

20

25

30

35

40 3'

Vertical

position

of

geometr. C. E. if = = Geome tr. C.E. M

(29)

0

-FIGURE

10.

0 115

120

I L CD , 0 -74- 4 2 72

40

I -5

). 4 2

V;

25

30

35 I 0

x- Upright

0 - Hee 1

20

40 (f3

_ A )

DYaq coe ff - C D. CL (63 0 0

35

CD

(30)

c

40 3 0

20

0

10

8 6 .

4

0 2 >

0

FIGURE H. =

(0°

F 17 120 15 15

20

25

30 X Upr ght

0 Heel 20°

35

40(

_ N

Mom --0 (13

FR

(P_

N C7s

20

25

30

35

40 -

N)tn degrees

-p

(31)

FIGURE 12.

Sag in

forestay

s

Chord.

Curved line

of cut of the

A,

luff

in

order

to minimise back Winding.

(32)

F

7IP

Mom. FR

v = 20 ft/sec.

FH

Vert.

CE

pos.

CL CD CR CL/CD

Page 1.

15

4.50 .95

14.00.25

4.60

6.60

3.05

3.03

0.46

0.67 .097

.123

.085

.47

.68

4.73

5.47

171-

20

221

25

271-

30

321- 35 371.

40

6.55

8.20

0.80 _11.60

_13.10

_14.40

_15.40

_15.85

_15.95

15.85

1.20

1.40

1.55 2,05

2.65 3.5)

4.45 5.1-0

6.40

7.35

20.0

25.5

30.5

35.5

40.0

44.5

47.0

49.0

50.5

0.83

1.48

2.23

2.95

3.71

4.17

4.50 4.6Q

4.63

4.61

8.19

9.68 _11.38

12.85

14.22

15.36

16.07

16.40

16.87

3.12

3.15

3.12 _3.12

_3.13

_3.06

_3.05

_2.98

_2.99

0.84

1.01

1.19

1.34

1.48

1.58

1.63

1.64

1.63 .144

.169

.210

.272

359 .456

555 .656

.755

.152

.229

.302

.381

.428

.461

.480

.475

473 .84

.99

1.17

1.32

1.46

1.58

1.65

1.68

1.73

5.87

5.93

5.65

4.94

4.12

3.46

2.94

2.16

(33)

( F FH

Vert.

CE

pos.

CL CD CR CH CL/DC

Page 2

15

4.45

0.90

12.5

0.28

4.53

2.76

0.46 .092

.029

0.46

4.95 17-L-6.50

1.10

18.7

0.90

6.52

2.87

0.67 .113

.092

0.67

5.90

20

8.25

1.30

24.5

1.60

8.21

2.98

0.85 .133

.164

0.84

6.35 22i

10.05

1.55

29.5

2.38

9.89

2.98

1.03 .159

.244

1.01

6.50

25

11.75

1.95

35.5

3.20

11.47

3.10

1.20 .200

.328

1.10

6.02 271-13.45

2.45

40.0

4.05

13.08

3.06

1.38 .251

.415

1.34

5.49

30

14.75

3.40

44.0

4.70

1,;-.31

3,08

1.51 .318

.482

1.47

4.77

3 2 i -;

15.05

4.00

47.5

5.15

15.51

3.06

1.62 .410

.528

1.59

3.97

35

16.40

5.00

49.0

5.31

16.31

3.01

1.60 .513

.545

1.67

3.29 37h-16.50

6.05

49.5

5.25

16.78

2.95

1.69 .620

.538

1.72

2.73

40

16.50

7.10

50.0

5.16

17.20

2.91

1.69 .728

.530

1.76

2.33 42-i-16.25

8.05

51.0

5.04

17.41

2.93

1.66 .325

.517

1.79

2.02 D M = 5 °

v = 20 ft/sec.

10°

Mom.

(34)

M = 5°

= 12

v = 23ft/sec.

Pave 3.

Mom, FR FH

Vert,

CE

pos.

CD H CL/CD 15

4.40

0.95

12.00.22

4.50

2.67

0.45 .097

o23

0.46 4,63

171

6.45

1.10

18.00.89

6.48

2.78

0.66

.113 .091

0.67

5.85

23

8.10

1.25

23.01.60

8.04

2.86

0.83 .128

.14

0.83

6.1-7 221

9.85

1.55

28.5

2.31

9.69

2.94

1.01

.159

.937

0.99

6.35

25

11.70

1.90

34.03.22

11.49

2.96

1.20

.195 .330

1.18

6.17

271

13.30

2.40

38.5

4.02

12.91

2.98

1.36 .246

.412

1.32

5.53

33

14.00

2.95

42.5

4.84

14.28

2.98

1.52 .303

.496

1.46

5.02 32-16.15

3.70

46.0

5.55

1.60

2.95

1.66

.300 .570

1.60

4.37

35

16.80

4.75

48.5

5.76

16.47

2.94

1.72 .487

.591

1.69

3.53

371

17.00

5.75

49.0

5.79

16.98

2.89

1.74

.590

.594

1.74

2.95

40

16.95

6.70

49.0

5.77

17.29

2.84

1.74 .687

.592

1.77

2.53

421

16.80

7.80

49.0 5.60 17.64

2.78

1.72

.000

.575

1.81

2.15

CbM L

(35)

Page 4.

(,)34)

L D Mom. FR FH

Vert

CE

Pose

cL

CD CR CL/CD 15

3.95

0.95

11.7

0.10

4.06

2.89

0.41 .097

.012

0.42

4.16 17*

5.95

1.10

13.30.74

6.00

3.05

0.61 .113

.076

0.62

5.41

23

7.65

1.25

23.01.45

7.62

3.02

0.78 .128

.149

0.78

6.12 2*

9.45

1.50

28.5 2.')3

9.03

3.07

0.97 .154

229

0.95

6.30

25

11.45

1.65

33.5

3.18

11.15

3.01

1.17 .190

.328

1.14

6.19

13.25

2.30

39.04.08

12.82

3.04

1.36 .236

.419

1.32

5.77

30

14.85

2.8t0

43.0

5.01

14.25

3.02

1.52 .288

.514

1.46

5.30

32,17

16.20

3.40

46.5

5.64

15.48

3.00

1.66 .348

.598

1.59

4.77

35

17.10

4.25

49.5

6.33

16.44

3.01

1.75 .435

.649

1.69

4.03 37*

17.70

4.95 53,5

6.84

17.04

2.96

1.82 .508

.702

1.75

3.57

40

13.05

5.95

51.5

7.07

17.66

2.92

1.85 .610

.725

1.31

3.03 42*

18.10

7.40

53.0

6.78

18.34

2.89

1.86 .759

.695

1.88

2.45

CD

M = 5°

V = 20ft/sec.

F = 15°

H

(36)

v = 20ft/sec. Page 5. (

-/\)

L D Mom, F R FH Vert. CE pos. CL L C R C H CL/CD 15 3.45 1.00 10.5 0.08 3.60 2.92 0.35 .103 3.45 17i 5.90 1.10 17.7 0.73 5.96 2.97 0.61 .113 .075 0.61 5.36 23 7.55 1.30 22.5 1.36 7.55 2.98 0.78 .133 .139 0.77 5.81 22L-9.25 1.50

20.02.15

9.12 3.07 0.95 .154 .220 0.93 6.17 25 11.35 1.D0

34.03.18

11.06 3.08 1.16 .185 .326 1.13 6.31 27i 13.10 2.25 38.5 4.06 12.66 3.04 1.34 .231 .416 1.30 5.82 30 14.60 2.75 42.5 4.92 14.02 3.03 1.50 .282 .505 1.44 5.31 34-16.05 3.30 45.0 5.84 15.30 3.01 1.65 .338 .601 1.57 4.87 35 17.05 4.10 48.5 6.42 16.31 2.97 1.75 .421 .j5 1.67 4.16 37c 17.65 4.35 50.5 6.90 16.95 2.96 1.81 .498 .708 1.74 3.64 40 18.00 5.85 51.5 7.09 17.54 2.93 1.85 .600 .726 1.80 3.08 42i 18.20 7.15 52.0 7.03 18.25 2.85 1.87 .733 .721 1.87 2.55

(37)

Page 6.

Morn.

Vet.

CE

pos.

CD CR CL/CD 15

3.05

1.05

10.5

0.22

3.21

0

0.31 .108

-2.9

17!IT

4,75

1.10

15.7 o.38

4.86

3.23

0.49 .113

.039

0.33 4,32

20

7.15

1.33

22.5

1.23

7.13

3.13

0.73 .133

.1Z)

0.74

5.50 92-9.00

1.50

27.6

2.05

8.38

3.11

0.92 .154

.210

0.91

6.00

25

10.95

1.80

33.03.01

10.69

3.09 1./2./85

.309

1.10

6.09 27,2i-12.05

2.30

38.8

3.99

12.62

3.07

1.34 .236

.409

1.29

5.68

30

14.60

2.75 /;3.0

4.92

14.03

3.06

1.50 .282

.505

1.44

5.31

.)n_'_

5-,

15.00

3.30

46.0

5.75

15.17

3.03

1.63 .333

.590

1.56 4,82

35

16.95

3.95

49.0

6.48

16.15

3.03

1.74 .405

.665

1.66

4.29

37-!

17.65

4.55

5110.5

7.13

16.77

3.01

1.31 .466

.731

1.72

3.88

40

18.20

5.40

51.5

7.57

17.43

2.96

1.87 .553

.776

1.79

3.35 42!.i-18.50

6.55

53.0

7.68

18.06

2.93

1.90 .672

788

1.85

2.85 Sm

= 5°

F = 20°

V

23 ft;

D

(38)

(

Page 7.

L

cor

Nom. FR FH

Vert.

CE

pos.

CL

CD CR 1-1 Mom. 15

0.75

0.90

3.0 -.68

0.95

3.16

0.07 .092

0,

17-3.40

0.85

10.0 1 .21

3.50

2.86

0.35

087 .022

0.359 y, 0

20

4.85

0.95

14.7

0.77

4.80

3.02

0.50 .097

.o79

0.502 .052

S, /6

2*

6.55

1.10

19.7

1.49

6.47

3.05

0.67 .113

.153

0.663 .076

25

8.40

1.35

25.5

2.34

8.17

3.12

0.86 .139

.240

0.839 .092

t,20

271-10.35

1.70

30.5

3.26

9.96

3.06

1.06 .175

.337

1.023 .107

o7

33

12.10

2.10

36.0 4,23

11.51

3.12

1.24 .216

.434

1.180 .118

3*

13.65

2.55

40.0

5.19

12.87

3.11

1.43 .262

.533

1.322 .130

.5:34

35

15.10

3.20

43.5

6.05

14.21

3.06

1.55 .328

.621

1.463 .139

4.71 37c

15.90

4.00

46.0

6.50

15.05

3.06

1.63 .410

.667

14545

.141

3

40

16.65

5.00

48.5

6.87

15.95

3.04

1.71 .513

.705

1.635 .142

3. 3 3

42:L-16.70

6.15

49.0

6.76

16.46

2.98

1.71 .632

.693

1.690 .138

2,70

CDM 100

= 17V (const.)

V

= 23 ft/sec.

F R/ CR M .

(39)

(

= 15°

F 171°

Vert.

CE Mom. FR FH

pos.

C C CH MoF cR/cM D R

Page 8.

°C) 1/ 3.79

3 oy

15

0.10

0.80

2.0 -.74

0.31

17.11.50

0.74

5.5 -.27

1.66

3.31

0.15 .077

20

2.75

0.75 10.3+.24

2.84

3.63

0.28 .077

.025

.292

.023 221

5.15

0.85

15.5

1.19

5.09

3.05

0.53

.087

.122

.522

.077

25

7.05

1.05

20.5

2.03

6.83

3.00

0.72 .108

.208

.702

.099 271

8.83

1.30

25.5

2.92

8.41

3.03

0.90

.133 .298

.863

.115 30 10.45

1.60

30.03.85

9.84

3.05

1.07

.164 .297 1.010 .128 321

11.95

2.00

34.04.73

11.12

3.04

1.23 .205

.485

1.142

.139 35

13.35

2.50

37.5

5.62

12.35

3.04

1.37

.256

.577

1.267

.150 371 14.50

3.20

40.0

6.29

13.45

2.97

1.49

.328

.645 1.360 .157 40

15.35

4.05

42.5

6.76

14.35

2.96

1.58

.416 .694

1.472

.159 421 15.80

5.20

43.5

6.85

15.15

2.87

1.62 .534

.703

1.554

.157

20ft/aec,

D

R/

(40)

=

5°

F

200 V =

30 ft/sec.

vert.

CE

_pos.

CL CD

2279

3,78

5,0/

5:07

1/, 6

4,gy

4 y

37

_{3, gy}

Page 9

15

4.2

2.20

9.0 - 1.03

4.63 -0.191

.100

.41

17L

7.4

2.65

20.5 -.30

7.86

2.60

0.337 .121

-.014

.358

.93

20

11.22.95

31.5 + 1.07

11.54

2.73

0.512 .135

.049

.526

1.43 .0343

22-15.7

3.40

43.5

2.87

15.80

2.77

0.715 .155

.131

.720

1.98 .0662

25

19.8

4.00

55.0

4.76

19.65

2.80

0.903 .182

.216

.895

2.50 .0864

27.33-23.8

4.70

66.5

6.83

23.27

2.86

1.085 .214

.321

1.06

3.02 .1063

30 2 8.1

5.65

78.5

9.16

27.13

2.89

1.280 .258

.418

1.24

3.57 .1170

34-32.5

6.70

90.0

11.70

31.00

2.90

1.480 .306

.533

1.41

4.10 .1300

35

35.8

7.70

97.5

14.25

33.72

2.99

1.630 .351

.650

1.54

4.15 .1460

3-4

38.7

8.80

104.0

16.57

36.06

2.89

1.764 .402

.756

1.64

4.74 .1595

40

40.7

9.95

111.0

18.58

37.56

2.96

1.857 .453

.847

1.71

5.06 .1675

42

41.2

11.40

114.0

19.68

33.05

3.00

1.880 .518

.897

1.73

5.20 .1725

L COT Mom. FR FH

(r.)\).

CR/Cm

(41)

Page 10

cb-A

L Dr

Mom. FR FH

vert.

CE

pos.

CL CD CR CH Cm CR/CM 15

2.30

0.75

9.00 -0.12

2.41

0.32

.105

-.017

0.337

1.26

17-L-- 4,20 0.'60 14.00 4-0.50

4.25

3.30

0.59

.112

.070

0.595

1.96

.0357 20

5.50

0.90

18.50

1.03

5.48

3.37

0.77

.126 .144

0.768

2.59

.0556

2* 6.85

1.10 22.01.60

6.75

3.26

0.96 .154

.224

0.945

3.08

.0728 25

8.35 1.35 26.02.31

8.13

3.20

1.17 .189

.323

1.137

3.64

.0887 27-- -- 9.65

1.70 30.02.95

9.34

3.21

1.35

.238

.413

1.310

4.20

.0985

30 10.75

2.05 33.03.61

10.33

3.19

1.51 .288 .506

1.446

4.62

.1095

32i11.70

2.55 35.03.12

11.23

3.11

1.64

.357 .578

1.573

4.90

.1180

35 12.30

3.10

36.5

4.52

11.85

3.08

1.72

.434 .632

1.660

5.11

.1240 37-L712.70

3.65

37.5

4.84

12.29

3.05

1.78

.511 .677

1.720

5.25

.1290

40 13.05

4.35

36.5

5.07

12.77

3.02

1.83 .610

.710

1.780

5.39

.1316

4* 13.15 5.30

39.04.98

13.26

2.94

1.84 .742

.679

1.855

5.46

.1276 M =

5°

\100 F = 200 V

= 17.1

ftXec.

e4/

3, c25-

4. 27

41/

4:2iy

s", zy

_45-,

_2,97

_{4 yg}

_{3, o}

0 4 rg

(42)

'(p-A

Hoel, re

20°

C M6.1 10°

\bF

=. 17*

vert.

Mom. -R "H , CE

_pos.

CL

20 ft/sec..

CD CH ivl

0 A SID

_4,47/

6-,78

0

'C) 4,,44

333 2,33

15 L0.0

.85

0,0

- 82'

,22

0.00 .087

17*

2.00 .80

6,5

,16

2.15

0.205 .082

20

4.00

..85

12.0 ± .57

4,Q5

0,41

.6087

.058

.416

.047

22*

5.50 .95

1.23

5.44

0.56 .097

,126

.558

.075

25 -7.10

1.10

22.0 2,01

6.90 0073

.113

,206

,2708

.091

8.75

1.35 26,5

2.84

8.38 0,90

.137

.292

.860

.107

30

10.20 170 30-5

3.63 9,68'

1.05 .175

.372

.993

.119

11.45 2.10 34.5

4.38

10.78

1.17 ,216

.450

1,107

.127

12.55

2.70

36.5

4.99

11.82 1,29

.277

.512

1.213 .137

37*

13.50

3.40 -39.5

5.53 12.77'

1.38

6349

.567

1.310 .140

40i

14.15

4.25

41.5

5.84

13.57

1.45 .436

0599

1.383 .141

42*-14.40'

5.10 4205

5.98

14.05 1048

.523

.614

1,442

.141

Page 11

'K. =