High stability low drag boat hull keel having inverted foil configuration

Abstract

A modified V-hull boat has a keel having a horizontal cross-sectional profile of an inverted foil. The leading edge of the keel is a sharp point and the front region of the keel tapers outward along the length of the keel until it reaches its widest point. The widest point is aligned with the center of gravity of the hull. The trailing edge is a rounded blunt edge. The aft region of the keel is substantially shorter in length than the front region of the keel.

Claims

1. A keel on a V-hull boat comprising: a keel having a horizontal cross-sectional profile of an inverted foil, wherein the keel comprises a leading edge, a trailing edge, a widest point that is aligned with the center of gravity of a V-hull boat, a forward region defined by the leading edge and the widest point, the forward region having a concave horizontal cross-sectional profile and a convex transverse cross-sectional profile; and, an aft region defined by the widest point and the trailing edge, the aft region having a concave horizontal cross-sectional profile and a convex side profile.

2. A keel on a V-hull boat comprising: a keel having a horizontal cross-sectional profile of an inverted foil, wherein the keel comprises a leading edge, a trailing edge, a widest point that is aligned with the center of gravity of a V-hull boat, a forward region defined by the leading edge and the widest point, the forward region being having a horizontal cross-sectional profile wherein two opposing leading edges are substantially straight proximal to the leading edge and concave proximal to the widest point, and a convex transverse cross-sectional profile; and, an aft region defined by the widest point and the trailing edge, the aft region having a concave horizontal cross-sectional profile and a convex side profile.

3. The keel of claim 1 further comprising a keel pad positioned aft of the keel and extending to a stern of a V-hull boat.

4. The keel of claim 3 wherein the trailing edge is blunt and ends at a front of the keel pad.

5. The keel of claim 1 wherein the leading edge is a point.

6. The keel of claim 1 wherein the leading edge of the keel begins at a point on a V-hull boat about 22% down the length of the hull, and the widest point is positioned about 70% down the length of the hull and the keel ends about 75% down the length of the hull.

7. The keel of claim 1 wherein the keel further comprises a tip having a side profile that is concave proximal to the leading edge of the keel straight proximal to the widest point.

8. The keel of claim 7 wherein the straight region of the tip has a slight downward sloping angle relative to the hull.

9. The keel of claim 1 wherein the widest point is located in the aft of the keel.

10. The keel of claim 9 wherein the forward region has a length five times a length of the aft region.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) A more complete understanding of the present invention, and the attendant advantages and features thereof, will be more readily understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein:

(2) FIG. 1 is a forward perspective view of a boat hull in accordance with the principles of the invention;

(3) FIG. 2 is a bottom perspective view of a boat hull in accordance with the principles of the invention;

(4) FIG. 3 is a side perspective view of a boat hull in accordance with the principles of the invention;

(5) FIG. 4 is another perspective view of a boat hull in accordance with the principles of the invention;

(6) FIG. 5 is another bottom perspective view of a boat hull in accordance with the principles of the invention;

(7) FIG. 6 is bottom plan view of a boat hull in accordance with the principles of the invention;

(8) FIG. 7 is a diagram of a chine of a boat hull having a bulge in accordance with the principles of the invention;

(9) FIG. 8 is a cross-section of a lifting strake or spoiler of a boat hull in accordance with the principles of the invention;

(10) FIG. 9 is a side view showing sections of a boat hull in accordance with the principles of the invention;

(11) FIG. 10 is a cross-sectional view of a boat hull in accordance with the principles of the invention;

(12) FIG. 11 is a cross-sectional view of a boat hull in accordance with the principles of the invention;

(13) FIG. 12 is a cross-sectional view of a boat hull in accordance with the principles of the invention;

(14) FIG. 13 is a cross-sectional view of a boat hull in accordance with the principles of the invention;

(15) FIG. 14 is a cross-sectional view of a boat hull in accordance with the principles of the invention;

(16) FIG. 15 is a cross-sectional view of a boat hull in accordance with the principles of the invention;

(17) FIG. 16 is a cross-sectional view of a boat hull in accordance with the principles of the invention;

(18) FIG. 17 is a cross-sectional view of a boat hull in accordance with the principles of the invention;

(19) FIG. 18 is a cross-sectional view of a boat hull in accordance with the principles of the invention;

(20) FIG. 19 is a diagram of a typical keel of the prior art;

(21) FIG. 20 is a cross-sectional view of five typical keel profiles of the prior art;

(22) FIG. 21 is another perspective bottom view of a boat hull in accordance with principles of the invention;

(23) FIG. 22 is a bottom perspective view of a keel of a boat hull in accordance with the principles of the invention;

(24) FIG. 23 is a side elevation will view of a keel of a boat hull in accordance with the principles of the invention;

(25) FIG. 24 is a bottom plan view of a keel of a boat hull in accordance with the principles of the invention;

(26) FIG. 25 is a cross-sectional view of a keel of a boat hull in accordance with principles of the invention.

DETAILED DESCRIPTION

(27) Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction and to the arrangements of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced and carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting.

(28) Disclosed is a hull design that improves the stability of a boat at low speed and efficiency at high speed. The forward region of the hull may have a bulbous, i.e. ellipsiodal, area that may be centered around the chine within the impact zone of the boat. The impact zone is the area or region of the hull impacted by water projecting upward due to the hull moving through water and is generally in a region extending from about 15% to about 35% down the length of the bottom of the hull. Modified chines and strakes may by combined to reduce drag at lower speeds typical of a flatbottom boat while also having the stability of a deep hull boat at higher speeds. Lifting strakes, or spoilers, may also contribute to reduce drag. An aft centerline pad may also be incorporated into the hull design.

(29) The hull may also have a mid and aft ellipsoidal fullness aft of the forefoot and forward ellipsiodal fullness. The ellipsoidal fullness may continue to a lesser extent all the way to the transom. Without being bound by theory, the inventor believes that the mid and aft ellipsiodal fullness may work synergistically with the forefoot and forward ellipsiodal fullness to allow for a more natural water flow and makes for a smoother ride in large chop conditions.

(30) The chine near the bow may be of a conventional design, but may include a bulge or fullness in the impact zone. Aft of the bow, in the area at the aft end of the forefoot and forward ellipsiodal fullness, the chine flat may become wider and may sweep around the mid and aft ellipsoidal fullness. The deadrise angle of the hull in this area may gradually flatten until it becomes a continuation of the chine flat as one wide surface on each side of the hull. This wide chine flat may continue aft with a slight negative deadrise angle. The wide chine flat may vary in deadrise and width, and may be stepped. The hull and chine flat in accordance with the invention may create extremely high levels of stability both at speed and when stationary in wave and cross wave conditions.

(31) A keel may begin at a point aligned with the impact zone and extend aft along the centerline to a point near the hull's center of gravity. The keel may be shallow keel and extend aft widening along a convex path and having concave sides. The keel may blend into the hull with a large radius. The keel may have a tear drop shape similar to an airfoil, but in a direction opposite to a NACA keel, i.e., the opposite of a typical foil keel design. The aft end of the keel may taper to a fine section to promote clean water flow. The keel may promote natural water flow, and may enhance slow speed and at rest stability especially in cross waves, and works together with the forward ellipsiodal fullness and the mid and aft ellipsoidal fullness to create a smoother ride in large chop conditions. A flat centerline pad may provide lift at speed and is also used to control planing attitude in extreme conditions.

(32) On each side of the hull there may be one or more lifting strakes also to be known as spoilers. The outboard edges of the spoilers may be lower than the inboard edges (negative deadrise) and the inboard and outboard edges may be blended into the hull with a radius on each edge. Without being bound by theory, the spoilers may create lift and may simultaneously interact synergistically with the keel and with the wide aft chine flat to create a smoother, more stable ride in large chop conditions and in slow speed or when stationary in cross wave conditions.

(33) FIGS. 1-6 show one exemplary embodiment a boat hull 100 in accordance with the principles of the present invention. The boat hull 100 may be generally described as having a modified V-hull. The hull 100 includes a keel 120, a spoiler 170 and a lifting strake 140. The lifting strake 140 runs parallel to and equidistant from both the keel 120 and the spoiler 170. The hull 100 has a V-shaped forward region, and the hull bottom twists down the length of the hull and the lateral region 184 flattens out as it travels down the length of the hull 100 so that it becomes a chine flat 180 which extends to the stern.

(34) The boat hull 100 has a bow 112 and stem 114. Those skilled in the art will appreciate that the term stem is used to refer to the leading edge of a boat hull. The hull 100 has a total length defined by the bow 112 and the transom 116. The bottom 118 of the boat hull 100 is generally defined as the portion of the hull 100 below the chine 182. The length of the bottom 118 is generally defined as the distance between the transom and the point 115 where the stem 114 intersects the chine 182. Generally, when identifying a position on the hull 100 by the approximate percentage of the distance along the hull length, it is in reference to the length of the hull bottom 118 below the chine.

(35) The keel 120 is aligned with the centerline 122 of the hull 100. In this embodiment, the keel begins at a point on the hull bottom 118 about 20-25% aft of the bow and continues aft to a terminal end 124 to a point about 75-80% from the bow 110. Without being bound by theory, the inventor believes that the keel 120 provides both lift and lessens impact in rough water.

(36) The bottom 118 of the hull 100, for clarity in defining certain aspects of the invention, may be characterized as having regions. The regions of the bottom 118 between the keel 120 and the lifting strake 140 is referred to herein generally as the medial region 130. The region of the bottom 118 between the lifting strake 140 and the spoiler 170 is referred to herein as the intermediate region 160. The region of the bottom 118 between the spoiler 170 and the chine 182 is referred to herein as the lateral region 184. The lateral region 184 has almost the same dead rise angle and is almost parallel to the medial 130 in the intermediate 160 regions of the hull in the forward region 110 of the hull 100. As the lateral region 184 extends aft, it twists from the forward configuration into a substantially horizontal configuration, thereby forming the chine flat 180.

(37) Referring to FIGS. 3 and 4, the boat hull 100 has an impact zone 104 located within a region 15-35% down the length of the hull bottom 118. This is the region where water impacting the forward region 110 of the hull 100 is projected into the air by the force of the impact with the hull 100 as it travels through the water.

(38) Referring to FIGS. 5 and 6, the region 174 of the hull bottom 118 located aft of the spoilers 170 is radiused, i.e. is curved rather than having a pointed angle. This facilitates the movement of water and a more natural manner. The spoilers 170 typically have a terminating end 178 located at substantially the same point along the length of the hull 100 as the widest point 126 of the keel 120. For clarity, the lifting strakes 140 are not shown in FIGS. 7-13. However, in the other figures it may be seen that the lifting strakes 140 has terminating ends 148 closer to the bow than the terminating ends 178 of the spoilers 170. FIG. 6 also shows a pad 217 extending from a step 215. In some embodiments, the pad 217 may be referred to as a trimtab. Generally, the step 215 is relatively small, only an inch or two. This additional step 215 and pad 217 improve maneuverability of the vessel.

(39) The region 186 of the chine 182, in accordance with the principles of the invention, has a slight bulge 185 as shown in FIG. 7. V-hull boat designs typically include components that are substantially parallel to one another. It is common for the chine, strakes and other components to follow the lines of the hull itself and run parallel. A hull 100 of the present invention, however, includes a region 186 within the impact zone 104 more or less centered around the chine 182 having a bulge 185 that is not parallel with the other components of the hull 100 and extends outward from line 187 which illustrates a normal curve of a chine parallel to the hull bottom 118. Without being bound by theory, the inventor believes that the bulge 185 engages water projected upward in the impact zone and uses the force of the water to stabilize the hull 100 to provide a smoother ride and/or facilitate planing of the hull and/or improve maneuverability of the boat.

(40) Both the lifting strake 140 and the spoiler 170 may have a substantially triangular cross-section similar to common strakes. Optionally, the lifting strake 40 and the spoiler 170 may have a modified design with a convex lateral side 142 and a concave medial side 144 as shown in FIG. 8. Without being bound by theory, the inventor believes that the medial curvature along the strakes and spoilers facilitates a natural water flow, thereby improving efficiency of the design and providing a smoother ride of the boat itself.

(41) FIGS. 9-18 show section profiles A-Iof the hull 100 along the lateral, or transverse, planes identified in FIG. 9. Section A is 15% down the length of the hull bottom 118. Section B is 21% down the length. Section C is 26% down the length. Section D is 35% down the length. Section E is 44% down the length. Section F is 59% down the length. Section G is 71% down the length. Section 8 is 77% down the length. Section I is 97% down the length.

(42) FIG. 10 shows section A which is located near the forward edge of the impact zone 114, and shows the bulge 185. The dead rise of the hull bottom 118 is greatest here. The lateral region 184 has a slightly smaller dead rise angle, due in part to the bulge 185. FIG. 11 shows section B which is located just aft of the bulge 185. Here, the lateral region 184 still has a dead rise angle slightly less than the dead rise angle of the medial and intermediate regions 130 and 160, respectively. FIGS. 12 and 13, showing lateral sections C and D, respectively, also show the lateral region 184 having a dead rise angle almost equal to the dead rise angle of the other regions of the bottom 118. This is due more to the flattening and decreasing dead rise angle of the medial and intermediate regions 130 and 160 as they move down the length of the hull bottom 118 than it is to a change in the dead rise angle of the lateral region 184. The bulge 185 in this embodiment is positioned in the forward region of the impact zone. The bulge may optionally be located at a different place within the impact zone or throughout the entire impact zone 114. Those skilled in the art will appreciate that the bulge 185 does not greatly diverge from a line 187 parallel to the other regions of the hull 100. The bulge 185 may optionally be larger or more pronounced. However, this is not necessary in order to obtain the beneficial results provided by the present invention.

(43) The spoiler 170 can be seen in sections A-G as positioned within the crux formed at the medial end of the lateral region 184. The keel 120 begins near section C shown in FIG. 12 and is first noticeable in section D shown in FIG. 13. The keel 120 reaches its highest and widest point near section G shown in FIG. 16. Section H, shown in FIG. 17 is aft of the keel. FIGS. 17 and 18 show sections H and I, respectively, where the keel pad 150 can be seen. Sections F-I show the lateral region 184 where it has become a chine flat 180 having a dead rise angle of about zero. The dead rise angle of the chine flat may preferably be between 5 and 5. Referring to FIGS. 17 and 18, it may be seen that the aft region of the hull bottom 118 includes three flat regions, the two chine flats 184 and the pad 150. In addition, the medial region 130 and intermediate region 160, while not flat, have a relatively small dead rise angle.

(44) Inverted Foil Design of Keel

(45) The art of keel design is almost as old as the art of boatbuilding itself. FIG. 19 shows a typical keel 200 and some basic components. Inclusion of this Figure is intended to introduce some basic terms so that the design of the present invention may be better understood. Keel 200 is attached to the bottom 202 of a boat 204. The length of the keel 200 where it meets the boat bottom 204 is generally referred to as the root chord 206. The length of the keel 200 along its lower edge is generally referred to as the tip chord 208. The distance from the root chord 206 to the tip chord 208 is referred to as the span 210. The length of the keel 200 halfway along the span may be referred to as the mean chord 212. The sweep back angle 214 is the angle between a vertical line and the leading edge 216. The aspect ratio of the keel 200 is given by dividing the span 210 by the mean chord 212.

(46) FIG. 20 is also provided primarily for reference and shows the four most common NACA foil designs typically considered the standards for keel design in the boating industry. NACA refers to the National Advisory Committee for Aeronautics, and those skilled in the art of boat and keel design are familiar with the NACA foil designs shown in FIG. 20. These designs all include a blunt leading edges 220 and a trailing edges tapering gradually to points 222. These profiles are shown as horizontal cross-sections of the keels. This cross-section may be seen when viewing the keel from directly below it, which may be referred to as a bottom plan view. Optionally, this may also be referred to simply as the horizontal cross-section of the keel.

(47) FIGS. 21-25 show the keel 120 and aspects of its design in more detail. Keel 120 has an inverted foil design in accordance with the principles of the invention, has a configuration similar to an airfoil, such as those promoted by NACA and considered fairly standard in hull design, but is inverted in accordance with the principles of the present invention. The keel 120 is shallower than most keels with a very low aspect ratio. The keel 120 is narrow at its front 124 and widens as it moves aft. The keel's widest point 126 is proximal to the center of gravity of the hull 100. Aft of point 126, the keel 120 tapers downward along a curved aft region 127 and intersects the bottom 118 of the hull 100 at the forward end of the keel pad 150. Without being bound by theory, the inventor believes that the shape of the aft region 127 of the keel 120 directs or allows the water to flow naturally back together over the flat keel pad 150 and feeds/directs it to the propeller or propellers.

(48) The spoilers 170 have terminal ends 178 approximately aligned with the end of the keel 120. The terminal ends 148 do not extend as far aft as the spoiler terminal ends 178 or the keel 120. Without being bound by theory, the inventor believes that by having the spoilers 170 and the keel 120 longer than the lifting strakes 140, water flowing over the hull 100 flows more naturally, creating less friction and more stability at both low and moderate speeds.

(49) The front of the keel 124 has a relatively sharp leading edge 224. Leading sides 129 of the keel 120 provide a very gradual increase in width of the keel 120 along its length 118. The bottom plan profile of the keel 120, i.e., the shape of the keel 120 when viewed from directly below, shows how the leading edges 129 of this embodiment are substantially straight along the first third of the length of the keel 124 and curve gradually as they approach the widest point 126 of the keel 120. The leading sides 129 however have a slightly concave transverse profile 121 as shown in FIG. 25.

(50) The keel 120 widens as it travels down the hull until it reaches its widest point 126. The keel 120 is located along the centerline of the keel and its leading edge 224 is located in the same region as the impact zone of the hull. That is, the keel 120 typically begins between 15% and 30% down the length of the hull bottom 118. The widest point 126 is aligned with or very close to the center of gravity of the vessel. The aft region 127 of the keel 120 extends from the widest point 126 to the trailing edge 131. The trailing sides 133 are substantially straight close to the widest point 126 and become convex as they approach the trailing edge 131. Thus, the bottom plan profile of the keel 120 when viewed from below has a profile similar to a NACA foil, but inverted. Or, as explained above, the keel 120 has a horizontal cross-sectional profile of an inverted NACA foil.

(51) As shown in FIG. 23, the aft region 127 has a convex side profile, with the leading edge 152 curving into the keel pad 150. It may also be seen in FIG. 23 that the tip 125 of the keel 120 is concave in the front region 124 of the keel 120 and substantially straight at a point about 25% down the length of the keel all the way to the widest point 126. The straight region of the tip 125 has a slight downward sloping angle relative to the bottom 118 of the hull 100. Thus, the keel increases in cross-sectional area along of the length of the keel until it reaches its largest point, the widest point 126.

(52) The aft region 127 curves down in a concave manner along trailing edge 152 and joins the hull bottom 118 at or near the forward end of the centerline pad 150. In this embodiment, the keel 120 begins at about 22% down the length of the hull bottom 118, has a widest point at about 70% down the length of the bottom 118 and ends at about 75% of the length of the bottom. The forward region of the keel 124, measured from the front edge 224 to the widest point 126, is therefore about 5 times the length of the aft region 127 of the keel, measured from the widest point 126 to the end 131 where it meets the forward end of the centerline keel pad 150. In this embodiment, the widest point is located in the aft of the keel, and may preferably be about aft of the total length of the keel.

(53) The flat centerline pad, or keel pad, 150 is positioned aft of the keel 120 and extends to stern of the hull bottom 118. The function of the keel pad 150 is to keep the aft end on centerline from digging in at low speeds and in turns, which allows the boat to pivot within its own length on a point at the end of the keel at any speed. It also assists in bringing an early onset to planing during acceleration. Without being bound by theory, the inventor believes that the flat keel pad 150 serves two purposes. First, it is a dedicated support for the vessel's riding or planning angle. Second, it acts as a step and allows the vessel to pivot at high speed and at all speeds giving the vessel greater maneuverability.

(54) The medial region 130 of the hull bottom 118, defined as the area of the hull bottom on both the port and starboard sides of the keel 120 between the lifting strakes 140. The medial region 130 extends from the bow all the way aft to the transom 116. In this embodiment, it has a deadrise angle of about 40-45 degrees at the bow 112, which twists and flattens, to about 17-20 degrees at the transom 116 This medial region 130 is bounded by the keel 120 inboard and the lifting strake 140 outboard. The medial region 130 is believed to function to dynamically lift the boat at speed and to provide the primary buoyancy area of the hull when planing.

(55) The intermediate region 160 is the strip of bottom 118 outboard of the lifting strakes 140 and inboard of the spoiler 170. The intermediate region extends from the stem 114 all the way aft to the transom 116. It has a deadrise angle identical to the medial region 130. The inventor believes that the intermediate regions 160 function to provide dynamic lift at moderate speeds as the boat gets up on plane.

(56) The lateral region 184 is the strip of bottom 118 outboard of the spoiler 170 and inboard of the chine 182, which extends from the stem 114 to the transom 116. The portion of the intermediate region 160 located past the terminal end 178 of the spoiler 170 transitions into the lateral region 174 by a fillet, or radiused area, 174 running from the terminal end 178 of the spoiler 170 to the transom 116. The fillet 174 is believed to allow the water to flow smoothly without abrupt changes of direction from the deadrise below to the much flatter deadrise of the chine flat 180. The intermediate region 160 has a deadrise angle of about 50-52 degrees at the bow, which twists and flattens into the chine flat which has between a 5 and 5 degree deadrise. The function of Area 4 is to provide dynamic lift at sub-planing speeds in order to start the boat up on plane. Trim tab pockets are set in the aft end of Area 4 to mount adjustable trim tabs should they be needed.

(57) When in motion, the keel 120 and the lifting strakes 140 feed water flowing through the lifting strakes 140. The keel 120 is a vertical appendage to the hull on centerline, which adds longitudinal running stability to improve yaw control while planing. This structure tapers from thin at the bottom to thicker at the top, and has a small fillet at the transition to medial region 130. The purpose of this is to provide a gentle turning of the water flow from horizontal up and over onto the deadrise angle of region 130 without abrupt changes that cause hydrodynamic drag. The keel 120 may run aft from about 20-25% aft of the bow, to 75-80% of the length from the bow where it terminates with a radiused end to aid in developing a combination of flow separation and smooth rejoining of the water as it flows from the rear end.

(58) The lifting strakes 140 works with the keel to provides positive lift and continues to create the softness of the ride these areas provide. The lifting strakes 140 are shaped in a triangular manner pointing downward and has a radios inside of the lifting strake 140 helping to create the curl of the natural shape of waves both providing lift and softness of the ride in a choppy or rough sea. Outside the lifting stakes 160 continues the genital ellipsoidal shape of the hull 100 and feeds the water out and aft. The spoilers 170 also provide lift both forward in the lager V area and moving aft to the chine flats 180. The Lifting Strakes 140 run from the bow aft to approximately 75% of the length of the hull. These strakes run approximately parallel to the chine, instead of tracing a waterline or buttock. In the midsection the lifting strakes flatten to horizontal, which causes the boat to run at a low bow trim angle near 0 degrees. These strakes also separate water flow from the area 2 strip, reducing friction and thus provide dynamic lift when the boat is fully planing.

(59) The spoilers 170 also provide softer looser water or soiled water to the chine flats 180 aft relieving friction of wetted surface of the hull 100. The chine flats 180 are wider than most of any hull designs. The chine flats 180 provide stability at rest and on plane at high speed and in a side rougher sea. The chine flats 180 also provide a positive buoyancy giving and assisting the keel 120 and the lifting strakes 140 and the hull 100 a direct attitude from rest to a full plane without squatting, digging or typically raising the bow high out of the water which also allows the vessel to reach a plane and high speed in very shallow water. The chine flat 180 has a step 215 5 to 10% forward of the transom 116 relieving friction of the wetted surface of the hull 100. The chine flats 180 are assisted by the bracket or 210 which is also a step.

(60) Whereas, the present invention has been described in relation to the drawings attached hereto, it should be understood that other and further modifications, apart from those shown or suggested herein, may be made within the spirit and scope of this invention. Descriptions of the embodiments shown in the drawings should not be construed as limiting or defining the ordinary and plain meanings of the terms of the claims unless such is explicitly indicated.

(61) As such, those skilled in the art will appreciate that the conception, upon which this disclosure is based, may readily be utilized as a basis for the designing of other structures, methods and systems for carrying out the several purposes of the present invention. It is important, therefore, that the claims be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the present invention.