Title:
High speed displacement type hull
United States Patent 2185431


Abstract:
This invention relates to improvements in hull forms and more particularly to those forms of hulls which are adapted for high speed operation. Former high speed hulls have usually been of the planing type and while such hulls were capable of attaining desired high speeds, such former hulls...



Inventors:
Starling, Burgess William
Application Number:
US18843538A
Publication Date:
01/02/1940
Filing Date:
02/03/1938
Assignee:
ALUMINUM CO OF AMERICA
Primary Class:
International Classes:
B63B1/04
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Description:

This invention relates to improvements in hull forms and more particularly to those forms of hulls which are adapted for high speed operation.

Former high speed hulls have usually been of the planing type and while such hulls were capable of attaining desired high speeds, such former hulls were relatively unseaworthy and lacked lateral and longitudinal stability characteristics.

Their maneuverability characteristics were relatively poor and such hulls tended to pound exextensively in a seaway. All of these characteristics have hampered the use of such hulls for certain purposes, such as war vessels, passenger vessels and yachts where seaworthiness and stability characteristics were not only desirable, but in some cases absolutely necessary. Such latter types of vessels accordingly have usually been of the pure displacement type and even with such types of hulls expedients such as bilge keels were utilized to dampen the rolling period, that is, increase its time and decrease its amplitude. Displacement hulls also required the use of considerable power to attain speed, in fact more power was required with displacement hulls than for planing type hulls of comparable size.

In view of the foregoing, the hull form delineated in my copending application, Serial No. 93,358, filed July 30, 1936, was devised in order to provide a hull form which retained the efficiency at speed characteristics of planing hulls and which also provided the stability and seaworthy characteristics of displacement type hulls. These characteristics were obtained in my former hull by providing a novel form of hull bottom which provided desired lifting characteristics of the hull at speed with attendant decrease of wetted surface area, good maneuverability characteristics, good seaworthy characteristics, desirable stability characteristics and minimization of bow and stern wave.

All of the foregoing features were obtained with maintained displacement characteristics at all speeds which was provided for by the configuration of the bottom. This bottom was concave throughout the afterbody and in portions of the forebody in contact with the water at speed. The bottom was also provided with relatively increased angles of deadrise at the various stations and particularly in the stations of the afterbody.

Hulls of the form shown in my copending application, while affording the characteristics desired did, however, lack efficiency characteristics when operated at relatively slow speeds such as cruising speeds.

The present invention generally has for its object the provision of a hull form which will have not only the efficiency at speed characteristics of my former hull, but which also have even more efficient characteristics for the hull when driven at speed, for example, maximum speed. A further object of the present invention resides in the provision of a hull form which will have the efficiency at speed characteristics of my former hull or even better resistance characteristics as well as improved efficiency over my former hull when driven at relatively lower speeds, for example, cruising speeds.

It is a further object of the present invention to attain the foregoing objects while retaining all of the improved seaworthy characteristics, lateral stability characteristics, good maneuverability characteristics of my former hull. In fact, it is an object of the present invention to improve my former hull in these latter characteristics and to provide for improved operation such as further minimizing pounding in a seaway, improved maneuverability characteristics whereby turns may be effected with a relatively shorter radius than heretofore, less bow and stern wave and in general to provide improved operating and efficiency characteristics for the hull over former hulls, including the hull form of my prior application.

It is a further object of the present invention to provide a hull form and particularly a form of bottom which will provide desirable efficiency of operation characteristics, desired stability characteristics, desired seaworthy characteristics, desired low resistance characteristics, desired minimizing of bow wave and stern wave characteristics, desired free and unhindered flow of water along and under the hull in a hull in which certain of the design characteristics are modified with respect to the design characteristics of the hull of my former application. Such design characteristics are speed-length ratio, length-beam ratio, displacement-length ratio.

It is accordingly a further object of the present invention to provide a hull form and bottom which will have improved performance and operating characteristics as set forth above and wherein the hull is of a type having design characteristics of speed-length ratio, approximately between 2 and 4.5, length-beam ratio approximately between 8 and 10.5, displacement-length ratio approximately between 35 and 55. It is a further object of the present invention to provide a hull form with a new and novel bottom' configuration which is adapted for enhanced performance characteristics in hulls wherein the design characteristics are such that the speedlength ratio is approximately 3.1. The lengthbeam ratio is approximately 9 and the displacement-length ratio is approximately 40 at trial and approximately 50 at full load condition. It is a further object of the present invention to provide a novel form of hull bottom adapted for an enhanced efficiency of operation in hulls having design characteristics other than those disclosed in my former application and which modified design characteristics will be hereinafter set forth in further detail.

Further and other objects of the present invention will be hereinafter set forth in the accompanying specification and claims and shown in the drawings which show by way of illustration a preferred embodiment and the principle thereof and what I now consider to be the best mode in which I have contemplated of applying that principle. Other embodiments of the invention employing the same or equivalent principle may be used and structural changes made as desired by those skilled in the art without departing from the present invention and within the spirit of the appended claims.

In the drawings: Figures 1 and la, taken together, with Fig. la to the right of Fig. 1, show longitudinal elevational views of one embodiment of the improved vessel and hull. The afterbody is shown on Fig. 1 and the forebody on Fig. la.

Figs. 2 and 2a, taken together with Fig. 2a to the right of Fig. 2, are half plan views of the afterbody and forebody. The afterbody is shown on Fig. 2 and the forebody is shown on Fig. 2a. Fig. 3 is a view generally similar to Fig. 1, but taken on a scale in which the vertical scale is increased with respect to the fore and aft scale to permit a clearer showing of the configuration of the buttock lines.

Figs. 4 and 4a, with Fig. 4a taken to the right of Fig. 4, is a view similar to Fig. 2a in which the beam scale is increased with respect to the fore and aft scale to permit the showing of the various water lines and their configuration, which showing cannot be properly shown on the smaller scale view-Fig. 2a.

Fig. 5 is a view of the fore and aft body plan showing the cross-sections at various stations.

Fig. 6 is curve diagrams showing the angles of dead-rise at various stations, the progression of such angles and equations for the curves.

Fig. 7 is curve diagrams showing comparatively the total resistance factor of the instant hull as compared with another vessel.

Fig. 8 is displacement curve diagrams showing the comparable displacement of the instant hull at different stations with a comparison displacement curve for a high speed hull now in use.

Pig. 9 shows righting arm curves of the instant hull form at different displacements.

In the various drawings, similar reference characteristics are used on different views and conventional marine nomenclature is adopted.

Reference characters BLP-I, BLP-2, BLP-3 refer to buttock line planes. Reference letters B--, B-2, B-3, etc., refer to the buttock lines on corresponding numbered planes. The buttock lines of the bottom comprise the lines of intersection of the bottom surface with longitudinal vertical planes (such as BLP-I, BLP-2, etc.) parallel to the fore and aft vertical center line plane or the fore and aft plane of symmetry of the hull which is designated VCP. LWL refers to the load water line plane of the hull at trial displacement. Various water lines are designated WL- I, WL-2, WL-3, etc. The reference letter CL refers to the chine line. KL refers to the line of the keel knuckle and DL and DL' refer to the deck lines. The bottom is generally designated as BT and the two sections of the bottom one on each side of VCL are respectively designated BT' and BT". S designates the side portion and TS the top sides.

The bottor- portion BT of the hull may be generally stated to comprise two warped or twisted surface portions or sections which, as stated, are marked BT' and BT" on the drawings. Each bottom surface or section comprises a portion which in the afterbody is considerably concave in crosssection at all stations. From amidships forward the concavity of the bottom sections gradually diminishes, becoming flat at approximately station 8 and thereafter changes to and becomes progressively more convex at successive stations towards the stem. The buttock lines B-1, B-2, etc., are generally convex in the forebody, but the curvature of these buttock lines reverse in the afterbody, becoming concave. This configuration of the buttock lines in the afterbody is clearly shown on Fig. 3.

In the various views, the various stations will be numbered with numerals and for convenience, stations from 0 to 20 have been delineated. Station 0 is adjacent the bow and station 20 adjacent the stern. Deadrise angles are referred to and such angles comprise the angles between the horizontal and the chord lines of the bottom which extend from the keel knuckle to the chine line. Hereinafter the terms "length-beam ratio", "speed-length ratio", and "displacement-length ratio" will be referred to. "Length-beam ratio" is'the length in feet divided by the beam in feet and is expressed "Speed-length ratio" is the speed in knots per hour divided by the square root of the length in feet and is expressed In certain cases this refers to the maximum attainable speed. "Displacement-length ratio" is 50 the displacement in long tons divided by the cube of another ratio, such ratio comprising the length in feet divided by 100. "Displacement-length ratio" is expressed thus D 55 \100/ Hulls of the typical form herein shown and described are particularly adaptable for vessels having a length-beam ratio approximately be- 60 tween 8 and 10.5, a speed-length ratio approximately between 2 and 4.5 and a displacementlength ratio approximately between 35 to 55. A particularly efficient hull is one having the following design characteristics. Length-beam 65 ratio 9, speed-length ratio 3.1, displacementlength ratio 40 at trial and 50 fully loaded.

Afterbody The present hull in the afterbody section is 70 provided with a bottom BT form of two.sections or portions BT' and BT" each of which is disposed at each side of the vertical center line or plane of symmetry. Each section is generally concave and in the afterbody there is a substan- y7 tial degree of deadrise all along the afterbody.

The progression of the angles of deadrise at the different stations is shown in Fig. 6. The buttock lines are generally convex in the forebody and reverse and become concave in the afterbody towards the stern.

Forebody From amidships forward the deadrise angles 10 progressively increase to greater and greater extents at successive stations towards the stem.

The progression of deadrise angles is delineated in Fig. 6. In the forebody the bottom surface is slightly less concave at station 9 (just forward of amidships). From this point forward the concavity gradually diminishes, becoming substantially flat at station 8 and thereafter gradually progressively becoming convex to a greater and greater degree as the stem is approached. In the forebody section there is a pronounced chine line CL, beginning at about station 2 and extending aft. Forward of station 2, the chine line gradually disappears and the side portion S comprises a surface which is smooth and continuous with the bottom portion.

In the forebody the buttock lines B--, B-2, etc., are generally convex as delineated in Fig. la.

Sides and top sides 80 The sides and top sides may have any desired shape or configuration.

Deadrise angles Fig. 6 shows the angles of deadrise at the vari3ous stations. The solid curve shows the actual angles of deadrise as derived from the body plan at the various stations, and the dot and dash curves show the general trend of the progression of deadrise angles. As delineated, it will be noted that there is a tendency for the value alpha, the angle of deadrise, to oscillate about a general smooth curve. Mathematically the general smooth curve may be represented quite closely by the equation 45 Alpha=10.2+68e-.15on In the above equation, alpha is the deadrise angle in degrees and n is the station number. n may be any selected station number from 0 to 20. e is the Naperian base, i. e., 2.7183--etc. The oscillatory part of the curve may be represented quite closely by the term 2.5 cos ((n-61)) The expression 55 ir(n-1) 6 is a number expressing angle in radians.

Accordingly, the solid or actual deadrise angle 60 curve may be represented very closely by the general equation Alpha=10.2+68(e-.'150)+2.5 cos (1 ( ) The foregoing two equations are adaptable for approximately specifying the angle of deadrise at any selected station, either for the mean curve or the actual curve shown in solid lines. By the use of such equation the angle of deadrise at a particular station may be computed with fair accuracy. To illustrate, assume station n to be 10.

-.150X n=-.150X10 or -1.5 The value of e -1.5 can be found to be .223. MulIg tiplying 68X.223 gives 15.16. Adding this to 10.2 gives 25.36 which is an angle quite close to the actual deadrise angle at station 10. At station 10 the second portion of the equation drops out as will now be shown.

/ir(n(10)-1)\ - 3.1416X9 2.5 cos 6 2.5 cos 4.712 radians 1 radian= 57.30 4.712X57.3=2700 Cos of 2700=0 10 Therefore, 2.5x0=0 and such portion of the equation is of no consequence at this station 10.

Solving the large equation for another station, sfa.v 13. gives the following: -.150X13=-1.95 6 -- 2X3.1416 radians=6.2832 e-l.5=.1423 20 68X.1423=9.68 57.3X6.2832=3600 10.2+9.68=19.88 cos 360°=1 and is+2.5X1=2.5 19.88+2.5=22.4 which is quite close to the angle of deadrise at station 13.

It has been demonstrated by towing tank tests that performance characteristics of a desired hull 25 and particularly desired reduction of resistance involve a coordination of design characteristics such as speed-length ratio, length-beam radio, displacement-length ratio, with the shape and configuration of the bottom. The hull herein 30 shown and described discloses such required coordination of features in the best manner now known to me and affords a hull form which has been found on tests to be exceedingly efficient.

In such hull there is a novel progression of angles 35 of deadrise at the various stations from stern to stem. As shown in Fig. 6 such angles of deadrise commencing at the ster at successive stations toward the bow first diminish somewhat in degree thereafter they progressively increase 40 again at successive stations in a somewhat greater degree or in somewhat greater increments. As amidships are approached while the deadrise angles increase from station to station the increment of angles from station to station is 45 again somewhat less than at the stations relatively nearer the stern. From amidships forward in the forebody the rate of increase or increment of increase in angles of deadrise at successive stations becomes greater and greater from 50 station to station towards the stem. The progression and change in the angles of deadrise at the different stations and the angles of deadrise themselves at the various stations are coordinated with the cross-sectional configuration at 55 the bottom at related stations, i. e., with the concave configuration which is generally concave in the afterbody which diminishes in concavity forward of amidships, becomes flat and thereafter convex and progressively more and more convex 60 towards the bow.

It is all of the foregoing factors and features taken together and coordinated with one another as well as coordinated with the design characteristics previously mentioned, such as 65 V L D TL d (L a \ which provide the improved characteristics of a 70 hull as a whole.

General characteristics The afterbody section generally follows the lines of my previous hull in that the deadrise 75 angles are so selected as to provide along the bottom of the afterbody a dihedral angle configuration which will displace a substantial volume of water and extend relatively deeper into the water at all points and sections of the afterbody.

Accordingly, the hull form will maintain substantial displacement characteristics both at rest and upon lifting of the same at high speeds. The dihedral angles along the afterbody sections of the hull also provide dynamic stability of the hull when listed and at speed.

Lifting of the hull at speed and decrease of wetted surface area is provided for by the configuration of the hull bottom particularly by the concave configuration in the afterbody. The reversal of the buttock lines aft assist in providing lift for the hull at speed. In practice at speed, the wetted surface area is decreased about 8% in a hull having a speed length ratio of 3.1. By providing the convex configuration in the forebody there is less change of longitudinal trim at high speed than with the hull form delineated in my copending application above referred to. The convex forebody configuration furthermore minimizes pounding in a seaway. The convex configuration of the forebody taken with the concave configuration of the afterbody affords a desired minimum of total resistance at low and cruising speeds. The convex configuration of the forebody taken with the concave configuration of the afterbody further cooperates to reduce total resistance of the hull when driven at higher or maximum speeds.

Maneuverability characteristics are also excellent. For example, a hull may turn with a turning radius of one-third the turning radius necessary with hulls of displacement type now in use.

Desired improved lateral stability and sea*orthy characteristics are secured and bilge keels and other rolling expedients can be dispensed with.

Tests have demonstrated that efficiency at cruising speeds may be somewhat enhanced by trimming the hull down slightly by the head. In practice, with a hull of a length of 300 ft. a change of total trim of two feet will enhance the efficiency of operation at cruising speeds by a material percentage, for example by about 10%.

Change of longitudinal trim to improve operating efficiency at cruising speed may be obtained in various ways, for example, liquid fuel can be shifted from tanks which are relatively aft to tanks which are relatively forward.

Tests have demonstrated that the present hull presents improved characteristics over previous hulls now in use and also over the hull form delineated and described in my copending application. The delineated angles of deadrise in the afterbody and forebody, the concave configuration of the afterbody section which extends throughout the afterbody and which concave configuration gradually diminishes in the forebody just forward of amidships, then becomes flat and thereafter becomes progressively more and more convex, all contribute to improved hull characteristics. Such improved characteristics include those previously mentioned, diminished total resistance at low and cruising speeds, diminished resistance at higher speeds, including maximum speeds, seaworthy characteristics, desired diminution of bow and stern waves, improved easy flow of water along and under the hull and improved lateral stability. The improved efficiency of the hull with respect to very t fast displacement type vessels is shown by the curves on Fig. 7. These curves indicate the percentage of resistance of the present hull form compared with high speed vessels of comparable size of the best known modern practice.

The curve of Fig, 7 shows the ratio of resistance of the hull form of the instant application to that of a comparable high speed vessel now in use with both at equal displacements of about one thousand tons. The total resistance of the comparable vessel at any speed length ratio is taken as 100%. This is shown by the straight horizontal line at the 100% ordinate. The curved line shows the percentage of resistance of the instant form as compared to the other vessel at various speed-length ratios from 1 to 3.2. At a speed-length ratio of 1.33 the percentage of resistance of both vessels is the same. From this point on up to higher speeds, the hull of the instant form decreases in percentage of resistance by the amount shown between the straight line and the curve. In practice the comparable vessel attains a maximum speed at a speed-length ratio of 2.25 as indicated by the X mark at such point. This represents the highest speed possible under present engineering practice.

It will be noted from the curve that the resistance of the present hull is decreased by about 29% at maximum speed and such decrease is attained wholly by virtue of the hull form.

Accordingly, the instant hull may be driven at higher speeds than the former hull, the power required at any given speed being in direct ratio to resistance. While at extremely low speeds, the present hull form is not as efficient as the comparable vessel, the present hull is more efficient at such speeds than my former hull. The data from which the curve of Fig. 7 was plotted was obtained from towing tank tests and from calculations based thereon.

Fig. 8 shows comparable displacement curves of the present hull and a comparable vessel of the prior art at their design trial trim and with equal displacements. The solid line represents the displacement curve for the present hull form and the dot and dash line represents the displacement curve of a comparable vessel. The abscissas represent the various stations. The ordinates show the cross-sectional area of the hulls below the water line at the various stations.

It will be noted that the dot and dash displacement curve shows much less area over the greater portion of the forebody and that its maximum ordinate is greater than that shown by the solid line curve. The maximum ordinate on the dotted line curve is well abaft of amidships instead of being close to amidships as shown with the solid line curve. In the afterbody the curve of areas is much fuller for the full line curve than the dotted line curve. The prismatic coefficient is about 5% greater in the present form over the old form. The prismatic coefficient is equal to the area under the curve divided by the area of the rectangle including the curve.

The solid line displacement curve of Fig. 8 may be represented quite closely and approximately by the following equation: Y=0.60 sin n-0.06 sin --+0.48n-0.0014n2 20 20 where Y is the decimal equivalent of the crosssectional area at any station n from 0 to 20, con- 70 sidering the cross-sectional area at station 10 as unity. On the displacement curve, the numbers ;o the right of each ordinate show the decimal equivalent or coefficient. The numbers to the left )f each ordinate show the actual area in square feet of a 270 foot vessel of about 750 tons displacement. The area designated is the area at trial or designed load water line. As shown on Fig. 8, the station to station distance for the pres6 ent hull form is 13.50 feet.

As previously stated the actual displacement characteristics of the instant hull at various stations along the hull is shown by the solid line displacement curve of Fig. 8. While a particular relation of decimal coefficient is referred to in the specification and in certain claims, my invention is not limited to the exact coefficient disclosed, but to reasonable variants thereof which are not of such degree as to substantially detract from the general efficiency and advantageous features of the hull herein delineated and described. It may be mentioned, however, that a substantial departure from the displacement curve characteristics here delineated will detract from the operating efficiency and performance characteristics of the hull in one way or another. The displacement curve equation, while following quite accurately the actual displacement curve, does at certain points somewhat depart from it, the maximum discrepancy being about 7%. Such variation is not, however, considered excessive, but within the scope of the present invention.

The curve shown in Fig. 9 shows the value of the righting arm in feet plotted against the angle of heel and degrees for a typical vessel embodying the improved hull form of the present application. The upper curve shows the righting arm for a typical vessel having a length of 285 feet and a displacement of 940 tons plus 10% or 1034 tons, whereas the lower curve shows the righting arm for the same vessel with a 20% increase of displacement or 1128 tons. With both of the curves it will be noted that there is an upward inflection of the curves and corresponding increase of the righting arm beginning at about 45 degrees for increased angles of heel greater than 45 degrees. As shown the maximum ordinate on both curves is about 90 degrees.

With comparable vessels of the prior art the Srighting arm curve levels off or even decreases for increased angles of heel over 45 degrees. Accordingly, the present hull form affords greater stability at sea. The curves of Fig. 9 have been plotted from data derived from physical tank tests of models.

While the present invention is not limited to the exact angles of deadrise herein referred to and not limited to the extent of concavity or convexity at the various stations as shown, it may be mentioned that departure from the design delineated in substantial degree will seriously affect operating efficiency of the hull and particularly affect the resistance characteristics of the hull and my invention embraces such relation of deadrise angles and concavity and convexity of the bottom as will provide enhanced operating efficiency in a material degree, over vessels in common use and more particularly provide improved efficiency substantially approaching or equalling the showing of Fig. 7. While a particular relation and degree and progression of angles of deadrise are referred to in the specification and in certain claims, my invention is not limited to the specific or exact degrees referred to, but to reasonable variants thereof which are not of such degree as to substantially detract from the efficiency here delineated and described.

The material used in the hull plating, decks and frames is preferably one of the lighter ma76 terials such as aluminum or alloys thereof. Such materials are particularly adaptable for the present hull form inasmuch as displacement may be reduced with attendant advantages. Utilizing such materials, the speed may be increased A of one percent for each one percent reduction in displacement. A particularly efficient hull form employing such materials for its plates and frames is one having a speed-length ratio of 3.1, a length-beam ratio of 9, a displacement-length ratio of 40 to 50 and a displacement of about 1,000 long tons. Such a hull with the bottom configuration here delineated and described is capable of being driven at a maximum speed exceeding the hull shown in my former application and at a speed which exceeds the speeds of comparable displacement type hulls now in use. The attainable speed for such latter vessels being increased by about 25% for the same power. A hull of the characteristics of the form here described and with the plates and frames of such lightweight materials is capable of being driven at higher speed ranges with a substantial power saving.

At lower speeds there is also considerable saving in power due to decreased lower resistance. Attainable speeds of. over fifty knots may be secured with the instant hull form with the design characteristics mentioned.

The present hull shows at maximum speed, a change of longitudinal trim about 30% less than that of a comparable vessel of the prior art. What I claim is: 1. A displacement type hull adapted for high speed operation with reduction of wetted surface area at speed, said hull comprising a bottom portion intermediate the keel knuckle and chine line, said bottom portion including an afterbody and forebody with a pair of bottom defining sections, one on each side of the vertical center line plane of symmetry, each section defining and affording a warped water contacting surface which at all stations throughout the afterbody is concave in cross-section from the keel knuckle to chine line and which section in cross-section in the forebody gradually diminishes in degree of concavity, then becomes flat and which section at stations in the forebody forward of the flat section and approaching the stem becomes progressively more and more convex in cross-section at successive stations for the purpose described.

2. A hull according to claim 1, wherein the o0 angles of deadrise of the section of the bottom portion adjacent the stern and at stations forward thereof to amidships are of such degree to afford substantial displacement characteristics to the afterbody with the hull at rest, which characteristics are maintained with the hull lifted at speed, said angles of deadrise in the forebody progressively increasing in degree from station to station from amidships toward the stem and being coordinated to each other and to the angles of deadrise in the afterbody to afford improved diminished resistance characteristics at various speeds, including cruising speeds, intermediate speeds and maximum speed.

3. A displacement type hull adapted for high speed operation with reduction of wetted surface area at speed, said hull comprising a bottom intermediate the keel knuckle and chine lines of the hull, said bottom including an afterbody and a forebody with a pair of bottom defining portions one on each side of the vertical center line plane of symmetry, each portion defining and affording a warped water contacting surface which at all stations throughout the afterbody (i. e., from 10 to 28) is concave in cross-section from keel knuckle to chine line, and each portion in cross-section at the various stations of the forebody from 10 to 0 first gradually diminishes in concavity, then becomes flat and which at stations in the forebody forward of the flat section and approaching the stem becomes progressively more and more convex in cross-section at successive stations, said bottom portions being each provided with deadrise angles alpha at various stations n approximately according to the following equation: Alpha= 10.2+68(e-.1n)+2.5 cos ( (n7 1) 15 to provide in cooperation with the concave and convex configuration of the bottom, a hull form having improved characteristics substantially as described.

4. A displacement type hull adapted for high 20 speed operation with reduction of wetted surface area at speed, said hull comprising a bottom intermediate the keel knuckle and chine lines of the hull, said bottom including an afterbody and a forebody with a pair of bottom defining portions, one on each side of the vertical center line plane of symmetry, each portion defining and affording a warped water contacting surface which at all stations throughout the afterbody (i. e., from 10 to 20) is concave in cross-section from keel knuckle to chine line, and each portion in cross-section at the various stations of the forebody from 10 to 0 first gradually diminishes in concavity, then becomes flat, and at stations in the forebody forward of the flat section and approaching the stem becomes progressively more and more convex in cross-section at successive stations, said bottom portions being each provided with deadrise angles alpha at various stations n approximately according to the following equation: Alpha=10.2+68(e-.150)+2.5 cos ((n-1) said bottom portions being also shaped and proportioned to provide a displacement curve where45 in the decimal coefficient Y of cross-sectional area at any station n from 0 to 20 is represented approximately by the following equation: Y rn 3srn 0 Y=0.60 sin -0.06 sin ---0+0.048n-0.00140n2 said deadrise angles and displacement curve relation of the hull providing in cooperation with the concave and convex configuration of the bottom a hull form having improved characteristics substantially as described.

5. A displacement type hull adapted for high speed operation with reduction of wetted surface area at speed, said hull comprising an afterbody and a forebody with a bottom therefor between the keel knuckle and chine lines of the hull formed with a pair of bottom defining sections of warped contour for contact with the water, said sections being disposed one on each side of the vertical center line plane of symmetry, each of said sections at all stations from 10 to 20 in the afterbody being concave in cross-section from keel knuckle to chine line, each of said sections in the forebody at station 10 to 0 first gradually diminishing in concavity, then becoming flat and thereafter at successive stations towards the stem successively and progressively becoming more and more convex in cross-section, said hull also having speed-length ratio characteristics substantially intermediate 2 and 4.5, length-beam ratio characteristics substantially intermediate 8 and 10.5, displacementlength ratio characteristics substantially intermediate 35 and 55.

6. The hull according to claim 5 wherein the deadrise angles alpha of the bottom sections at the various stations n are approximately as represented by the following equation: Alpha= 10.2+68(e-.-o5)+2.5 cos ( )(n-1) L. ine nun according to claim 5 wherein the hull is proportioned to provide a displacement curve wherein the decimal coefficient Y of crosssectional area at any station n from 0 to 20 is! represented approximately by the following 15 equation: Y=0.60 sin --0.06 sin --+0.048n-0.00140n2 20 20 8. The hull according to claim 5 wherein the 20 hull is proportioned and the bottom sections thereof shaped to provide a displacement curve wherein the decimal coefficient Y of cross-sectional area at any station n from 0 to 20 is represented approximately by the following equation: 25 Y=0.60 sin n-0.06 sin -2+0.048n-0.00140n2 20 and wherein the deadrise angles alpha of the bottom sections n from 0 to 20 are approximately as represented by the following equation: 30 Alpha=10.2+68(e-.'l"7)+2.5 cos (R-1) 9. A displacement type hull adapted for high speed operation with reduction of wetted sur- 35 face area at speed, said hull comprising an afterbody and a forebody with a bottom therefor between the keel knuckle and chine lines of the hull formed with a pair of bottom defining sections of warped contour for contact with the 40 water, said sections being disposed one on each side of the vertical center line plane of symmetry, said bottom being also shaped to afford buttock lines which are generally convex in the forebody and which reverse and change in curvature be- 45 coming concave in the afterbody, each bottom defining section having angles of deadrise of substantial degree not less than a minimum of substantially 12* at any station in the afterbody to provide substantial displacement characteristics 50 to the hull which characteristics are substantially maintained at speed whereby lateral stability is improved, each of said sections at all stations from 10 to 20 in the afterbody being concave in cross-section from keel knuckle to 55 chine line, each of said sections in the forebody at station 10 to 0 first gradually diminishing in concavity, then becoming flat and thereafter at successive stations towards the stem successively and progressively becoming more and more con- 60 vex in cross-section, said convex configuration of the forebody bottom and concave configuration of the afterbody bottom cooperating with the angles of deadrise at the respective stations to provide a hull having low resistance at cruising speeds and low resistance at higher and maximum speeds substantially as described.

10. A displacement type hull with an afterbody and forebody having bottom surface portions on each side of the vertical center line of symmetry which are each concave in cross-section in the afterbody which gradually diminish in degree of concavity and thereafter become convex in the forebody, said hull having the angles of deadrisealpha of the said bottom surface portions at various stations n from 0 to 20 approximately as represented by the following equation: Alpha= 10.2 + 68(e-*150)+ 2.5 cos ((n -1) said hull having displacement characteristics at various stations n from 0 to 20 substantially according to a displacement curve represented by the following equation: 15. A hull according to claim 1 wherein the hull comprises stations 0 to 20; stations 0 to 10 being in the forebody and stations 10 to 20 being in the afterbody, and wherein the bottom portions of the hull are also shaped and proportioned to provide a displacement characteristic at various stations n from 0 to 20 substantially according to a displacement curve represented by the following equation: where Y equals the decimal coefficient of crosssectional area at any station n from 0 to 20 with such coefficient at station 10 unity.

15 11. A hull according to claim 10 wherein the hull has speed-length ratio characteristics substantially intermediate 2 and 4.5, length-beam ratio characteristics substantially intermediate 8 20 and 10.5 and displacement-length ratio characteristics substantially intermediate 35 and 55.

12. A hull according to claim 10 wherein the hull has a speed-length ratio of approximately 3.1, a length-beam ratio of approximately 9 25 and a displacement-length ratio of approximately between 40 to 50.

13. A hull according to claim 1 wherein each bottom defining section has angles of deadrise of substantial degree at any station in the after0body to provide substantial displacement characteristics to the afterbody with the hull at rest, which characteristics are maintained with the hull lifted at speed and for also providing improved lateral stability, said sections in the fore85 body having angles of deadrise progressively increasing in degree from station to station from amidships towards the stem and being coordinated to each other and to the angles of deadrise in the afterbody to afford diminished resistance 40 characteristics at various speeds including cruising speeds, intermediate speeds, and maximum speed, said angles of deadrise of the afterbody bottom sections and of the forebody bottom sections also affording progressive increase of the righting arm for increased angles of heel greater than 45 degrees whereby improved stability at sea is obtained.

14. A hull according to claim 1 wherein the angles of deadrise in the afterbody bottom sections are at a minimum at a station slightly forSward of and adjacent the stern and wherein the angles of deadrise of the bottom sections at the stern are increased with respect to said minimum, and wherein angles of deadrise in the afterbody bottom sections progressively increase in degree from station to station from the station having the minimum angle of deadrise to amidships, and wherein the angles of deadrise in the forebody bottom sections also progressively increase in degree from station to statior 4 towards the stem for the purpose described.

where Y equals the decimal coefficient of crosssectional area at any station n from 0 to 20 with 15 such coefficient at station 10 unity.

16. A hull according to claim 1 wherein the bottom portions of the hull at stations in the afterbody, i. e. from 20 to 10, are also shaped and proportioned to provide a decimal coeffi- 20 cient at stations 20, 19, 18, IT, 16, 15 and 14, substantially approximating 0.4290, 0.4623, 0.5197, 0.5971, 0.6905, 0.7852 and 0.8739 respectively, taking the cross-sectional area at station 10 as unity whereby an increased prismatic coefficient. 25 is afforded in the afterbody for the purpose described.

17. A displacement type hull adapted for high speed operation with reduction of wetted surface area at speed, said hull comprsing an after- 80 body and a forebody with a bottom therefor between the keel knuckle and chine lines of the hull formed with a pair of bottom defining sections of warped contour for contact with the water, said sections being disposed one on each 35 side of the vertical center line plane of symmetry, each of said sections at all stations from 10 to 20 in the afterbody being concave in crosssection from keel knuckle to chine line, each of said sections in the forebody at station 10 to 0 40 first gradually diminishing in concavity, then becoming flat and thereafter at successive stations towards the stem successively and progressively becoming more and more convex in crosssection, said hull having a speed-length ratio of approximately 3.1, a length-beam ratio of approximately 9 and a displacement-length ratio of approximately between 40 to 50.

18. A hull according to claim 9 wherein the hull has speed-length ratio characteristics substantially intermediate 2 and 4.5, length-beam ratio characteristics substantially intermediate 8 and 10.5 and displacement-length ratio characteristics substantially intermediate 35 and 55.

19. A hull according to claim 9 wherein the hull has a speed-length ratio of approximately 55 3.1, a length-beam ratio of approximately 9 and a displacement-length ratio of approximately between 40 to 50.

SWILL;AM STARIGNG BURGESS. 6