US3517399A - Mooring apparatus having a free floating buoyant element - Google Patents

Description

June 30, 1970 W ET AL 3,517,399

MOORING APPARATUS HAVING A FREE FLOATING BUOYANT ELEMENT Filed March 4, 1966 INVENTORS. MAURICE HOROWITZ AND CLINTON S. MYERS United States Patent 0 3,517,399 MOORING APPARATUS HAVING A FREE FLOATING BUOYANT ELEMENT Maurice Horowitz and Clinton S. Myers, Fort Wayne, Ind., assignors to The Magnavox Company, Fort Wayne,

Ind.

Filed Mar. 4, 1966, Ser. No. 531,960 Int. Cl. B63b 21/52 U.S. Cl. 9--8 1 Claim ABSTRACT OF THE DISCLOSURE Mooring apparatus is provided with a buoy having optimum submergence and lift, and with a cable having optimum strength and length. When anchored in water, the buoy remains above the water and near the anchor for an optimum length of time under various conditions of the surrounding water and atmosphere.

This invention relates to an improved mooring apparatus having a buoyant element which is free floating within limits defined by a cable or other tethering means which is anchored at its base or bottom end.

More particularly, the present invention relates to a process for establishing various structural criteria for producing an optimum combination of float element and a tethering means for such float element and permitting the float element to move within circumscribed bounds.

For various reasons the art has long attempted to produce a flotation system which can be readily packaged and transported to a point of use and then fixed at a certain location within an ocean, lake or sea site for the purpose of accomplishing, among other things, certain monitoring functions. Flotation systems in general have been unsatisfactory and particularly deep anchored flotation systems for use in deep water in conjunction with oceanographic, communication, military, naval, fishery and transportation uses have been entirely unreliable because of the lack of processing information tying together cable size, length, or float size, etc. For one thing, such systems have uniformly lacked reliability because as the sea state conditions change, the float element would frequently break away from its mooring, thus destroying the system. In order to prevent such breakaway the flexible mooring element in the form of a cable, or the like, was made larger but this, in turn, necessitated a larger float, thus increasing the effects of drag and inertia for supporting the mooring cable and as a consequence, the flotation systems reached large proportions, making them ditficult to transport while still lacking any satisfactory degree of reliability. The problem was further complicated by the lack of establishing proper limitations on the cable or other mooring element length. For example, if the cable length equaled or substantially equaled the depth of the water body in which the flotation member was anchored then the strains developed on the anchoring means by the drag forces on the float became inordinately high and necessitated too great a size of the anchoring element to withstand such forces. On the other hand, if the mooring element was made longer the surface area over which the flotation element could migrate became so considerable that the information provided by the system was rendered indefinite by failing to pinpoint the location of information provided by the system. The severity of these problems increases as the desired mooring depth increases.

What is needed, therefore, is a reliably anchored flotation system adapted for use with scanning sonars, moored beacons, moored telemeters and other such applications.

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The present invention allows optimization of all parameters of the moored system thereby providing not only a high degree of reliability and long life but also allows the realization of a deep moored minimum weight system which is capable of being easily transported and launched even by airborne methods which heretofore has been highly impracticable.

It is one of the important features of the present invention to provide apparatus whereby moored systems can be readily established providing optimum system results wherein float size is related to a satisfactory cable or other tethering means and in which there is readily established a diameter, weight, and length of mooring cable enabling the system to withstand high currents and inertia forces. In providing a system of this type, a cable or other tethering element can be so designed that, in relation to a given size and configuration of float, there is produced a system which is reliably retained in place under sea state conditions ranging from tranquil to very heavy and which will maintain its assigned monitoring area regardless of the sea state condition or change of sea state condition.

It is a still further object of the present invention to provide apparatus having a combination float and anchoring system which are so related together that the combination can be of whatever size and weight desired, within ranges, of course, so that the system is readily transportable yet possesses the necessary structural strength for resisting breaking.

It is an important feature of the present invention that the float portion of the system has a surface buoyancy such that a portion thereof remains unsubmerged throughout sea state conditions ranging from tranquil to very heavy so that monitoring can occur and be transmitted substantially constantly regardless of the sea state condition.

The present invention is not limited to an environment of sea water; the apparatus is usable for any moored or float system comprised of a liquid surmounted by a gas. The apparatus may also be equipped, if desired, with sub-surface floats and canisters but it is essential to the present invention that the required cable tethering length will exceed the total depth so that the float will not impose excessive strain on the cable as it is tended to move by surface current forces. At the same time the cable must not be so excessively long so that the float extends over an excessive area and provides excessive forces tending to submerge the float because of the period of the waves being less than the response time supplied by the float buoyancy. It is, of course, necessary that the cable float have suflicient slack so that it can maneuver in the waves without becoming submerged and without imposing excessive forces upon a taut or short cable (or other tethering means) during such maneuvering.

It is, therefore, one of the important accomplishments of the present invention to establish a moored system which will satisfy the system requirements of: (1) nonsubmergence of the surface float; (2) nonbreaking of the cable or other tethering means; (3) minimum length and cross-sectional area of the cable or other tethering means; (4) minimum horizontal displacement of the float from the anchor; and (5) survival in specified currents and winds.

Other objects and features of the present invention will become apparent from a consideration of the following description which proceeds with reference to the accompanying drawings, wherein:

FIG. 1 is a schematic view showing a float, a tethering means and anchor and illustrating the various forces and directions of forces which act upon the float;

FIG. 2 illustrates the position of the float in different sea conditions.

Referring now to the drawings, a flotation member designated generally by reference numeral 10 which floats at the surface 12 of a body of water and has a submerged portion and an unsubmerged portion which remains unsubmerged in sea conditions ranging from tranquil to high sea conditions except those which are extremely turbulent, and then only temporarily.

Below the surface of the float is an attachment point 14 for a cable or other flexible member 16 which is secured to point 14 at one end and is attached at the opposite end 18 to an anchor 20 which is fixed at the bottom 22 of the body of water. The buoy or float is subjected to a substantial number of external forces; these forces influence the movement and flotation of the buoy and such forces must be taken into account in determining whether the float can remain afloat with at least a portion of it unsubmerged in the various sea rate conditions and also whether the float can respond rapidly enough to the sea state conditions so that its inertia will enable it to respond quickly enough to ride on top of the Waves. Also, such external forces determine whether or not a given float is adequately tethered, that is, whether it is held Within the strength limitations of the mooring system.

In an analysis of the problem, it is necessary to relate the float size and float requirements to the capability of the mooring system to hold the float within bounds and prevent its breaking away regardless of the sea state conditions.

In order to accomplish these ends, the optimum values of the various float parameters are set forth by simultaneously equating the relationship of the submergence, Y of the float, which is the distance from the water level to the lowermost point of the float, the tension T, which is the tension of the cable at its point of attachment with the float, and the angle, which is the cable angle at the point of attachment, all to the drag and lift factors operating on the float, including those parameters affecting the drag due to the water surrents, D as well as those due to air currents, D

The above parameters together with the drag, D per unit length of the cable are further differentially related, in order to establishthe cable dimensions such as the length, L, mass, M, volume, V, and displacement, X, of the float from the anchor for assumed values of the cable tension. The dimensions which result from assuming a given tension are used to balance the tethering system or anchoring system against the float system and allows the determination of whether the cable is either too large and hence too cumbersome, expensive and nontransportable or, conversely, if the cable is too small, in which case the cable will be excessively long or too weak.

It is found that in the system of the present invention for a float of given configuration immersed at the surface by a fixed amount, specifying the cable tension at the surface uniquely determines the cable angle and the physical dimension of the float. This discovery enables all portions of the system to be analyzed, varying only one parameter, namely, that of the cable tension at the surface. The system once properly configured can then be disposed within a given area and function as a moored scanning sonar, moored beacon, moored telemeter or the like. The system of the present invention enables the design and computational proceeding using the laws of hydrodynamics and opens up a systematic procedure for establishing the cable diameter, weight, and length and the float size, for a system adapted to withstand high currents of both sea and air, and waves.

Previous to the present invention it was virtually impossible to provide any deep anchored system for oceanographic communication, military, naval, fishery and transportation uses and have the system survive reliably over a period of time. The system further establishes the draft permitted for the float and the cable angle required for developing the necessary resistance under assumed current and wave conditions while withstanding breakage. The length of the cable is designed so that it is greater than the immersion depth and yet is not so long as to create an excessively large and hence indefinite monitoring area. In other words, what is rendered is a cable long enough to reduce tautness and allow the float to maneuver in the waves while at the same time producing a cable of optimum weight and low volume.

The effect of waves is to tend to submerge the float unless the response time supplied by the float buoyancy is sufliciently less than the period of the waves. The size of the float and the tethering cable must be in a balanced relationship under the various environmental conditions. Such balance must result in a float which will not submerge and yet which will not be too bulky; the cable must neither be too short and hence overly taut and large and cause the lack of float maneuverability or be too long so as to cause indefiniteness in monitoring. The specific problem then is to provide a system having a tethering cable and float which will neither break the cable nor submerge the float under strong currents and high surface waves. These requirements are to be combined Within a system embodying minimum Weight and volume of cable. This invention satisfies the requirements of the system as to:

(1) Nonsubmergence of the surface float.

(2) Integrity of the cable.

(3) Small volume to meet packaging requirements.

(4) Minimum horizontal displacement of the float from its anchor.

(5) Survival of the system in specified wind and water currents.

The system (containing floats, canisters, etc. of any size and shape and independently of the gas which is above any kind of fluid subject to the currents, wind and waves) can be provided as follows:

STEP 1 Establishment of the relationship for optimum submergence, Y of the floatz' The submergence, Y is the distance from the top of the liquid to the bottom of the float 10. The optimum submergence will fall between the two extremes of no submergence and total submergence. Analysis of these two extremes are as follows when a sea state condition of zero exists, ie a condition whereby there is current flow but no wave action.

If Y equals zero, i.e. float not initially submerged, the drag forces on the float are a result of, and equal to, only those wind forces above the surface of the liquid. With the float not submerged, the lift due to liquid displacement is negligible and the vertical downward force will result only from the payload or weight, P, of the float. Payload refers to the weight of the float including its contacts, but does not include the Weight of the cable. Under this condition, the float will assume something less than the initial no submergence position since it must sink at least sufliciently to support the payload or weight.

If Y equals 2R, the maximum vertical dimension of the float, then the drag forecs on the float will be equal to the liquid currents alone and the lift will be at a maximum because of total submergence. The ratio of the lift, L, to the drag D, will determine the cable angle, 15. The drag force from the current will generally be at a maximum when Y equals or is greater than 2R because the current can operate against the entire float when it is fully submerged.

It is desirable to obtain a maximum ratio of lift to drag so as to minimize the inclination of the cable from its vertical position, hence mooring the float with a minimum amount of cable.

The relationship for an optimum Y is as follows:

Y, is chosen so that:

Equation 1 and:

=Density of the liquid py=DIlSltY of the gas C Drag coefficient of the float in the liquid for horizontal motion C :Drag coefficient of the float in the gas for horizontal motion V =Current velocity in the liquid V =Wind velocity in the gas B (Y :Area of float projected on a vertical plane below gas in liquid 5 (Y :Area of float projected on a vertical plane above liquid in gas and:

M (Y )=Volume of float in liquid M (Y )=Volume of float in gas =Density of liquid Density of gas P=Payload or mass of float g=Gravity This relationship for Y is valid for any size and shape of float, for any type of liquid or gas and for any drag coefficients.

Establishment of the relationship for tension, T, and cable angle,

Having established the relationship of the float submergence, Y lift, L, and drag, D, of Step 1 we may proceed to establish the relationship for the cable tension, T, and cable angle, in terms of L and D.

Thus:

T =L +D Equation 2 and:

L J5 tan (180-1 Equatio 3 where T=Tension of the cable at point of attachment to float =Angle of the cable with the horizontal at point of attachment to the float L=Lift as defined under Step 1 D==Drag as defined under Step 1 STEP 3 Determination of T, L, D and for the flotation system:

The aforementioned parameters of T, L, D and as are now made to simultaneously satisfy Equations 1, 2 and 3 thus resulting in four unknowns for the three equations; however, since We may vary one of the unknowns, as for example T, we can then proceed to select and establish the remaining three unknowns, namely the lift, L, drag, D, and cable angle, 41. The optimum tension, T, is selected applying the specifications and requirements on system weight, non-submergence of the float, etc. as set forth previously.

Having now established the flotation system we combine this with establishment of a favorable mooring system which shall be determined in Step 4.

STEP 4 Determination of cable parameters:

Having established the previous relationships and parameters for the float, We may proceed to select a cable having a diameter, d, and a wet weight, W, per unit length. A set of currents, V(y), are chosen at each depth portion, y, and upon knowing the drag coefficient of the cable we may proceed to solve for the cable dimensions by utilizing the following differential equations, expressing the equilibrium of each differential length of cable.

and

COS 45 =0 Equation 5 where:

T:Cable tension W=Cable wet weight per unit length =Angle between cable and motion into current measured counterclockwise from motion to cable s=Cable length F=Tangential drag per unit length and where the function of D which is the drag per unit length of cable when cable is normal to the stream, is obtained from the following relationship:

D /2 C I d where:

C=Dimensionless drag coeflicient of cable in fluid stream =Mass density of fluid V =Velocity of fluid d=Diarneter of cable STEP 5 Simulated test and final design:

After having established a given float system and anchorage system, the system is then tested in a simulated sea, in sea state ranging from sea state 0, using size 2R, starting tension, T, starting angle, starting submergence, Y total length, L, cable diameter, D, cable wet weight, W (per unit length), having specified currents V and wind V The system is tested using simulated waves of x and y motions which involves solving the differential equations relating to the cable motion. The mathematics for the sea state condition is well established and reference may be made to sea state chart in book entitled Waves and Beaches, pages 48-49, Table II, by Willard Bascom, published by Anchor Books, Doubleday & Company, Inc., Garden City, New York, in 1964; also Hydrographic Oflice Publication No. 9, entitled American Practical Navigator by Bowditch, published in 1958, pertinent references being on page 1059, Appendix R entitled Beaufort Scale with Corresponding Sea State Codes. The system is tested to determine whether the float will submerge in sea state 5 or cause the cable to break in sea state 8. There is thus established a final design of the system which combines the necessary performance and compactness of size. The system has assurance of survival in a severe storm as well as maintaining the necessary float condition. The foregoing design parameters are applicable to moored systems containing subsurface floats and canisters and also applies where the cable varies along its length in physical properties desired. The design parameters are also applicable to a nonmoored system, especially one which utilizes a long cable suspended below the float such as commonly used in sonobuoy equipments, by considering such system as being anchored by a cable whose bottom portion has a Youngs modulus of zero.

In the design of a system in accordance with the invention, the flotation system and the mooring system are related so that optimum values can be obtained for the submergence, size, and shape of the float and for an optimum diameter, weight, density, and volume of the cable. These relations are all established with environmental conditions in mind, including the sea state, wind currents, water current, etc. so that the system will reliably function in retaining the float within a prescribed area and without breaking during various sea state conditions. The physical parameters of the cable and of the float combine optimum values including air transportability, appropriate size, flotation, strength and mass so that the system will have a degree of reliability in use not heretofore obtainable.

The arrived at system is tested in sea state conditions ranging from tranquil to violent and the system operates so that the float remains above water at sea state and will survive sea state 8. Such a system is optimum from the standpoint of performance and size and will survive reliably at its moored position.

Although the present invention has been illustrated and described in connection with a single example embodiment, it will be understood that this is illustrative of the invention and is by no means restrictive thereof. It is reasonably to be expected that those skilled in this art can make numerous revisions and adaptations of the invention, and it is intended that such revisions and adaptations will be included within the scope of the following claims as equivalents of the invention.

What is claimed is:

1. A mooring system adapted to be launched from an aircraft for deployment in a deep water environment, said mooring system comprising anchoring means Which is adapted to be fixed at the bottom of a body of water, flexible mooring means secured at one end to said anchoring means, a float operatively secured to the upper end of said flexible mooring means and adapted to be movable at the surface of the water within circumscribed bounds in accordance with a radius of movement from an anchored reference point provided by said anchoring means,

the distance of movement of said buoy being in accordance with a distance X determined for a given submergence distance Y and a tension T within the strength limitations of such cable, the relationship of the foregoing being in accordance with:

T =L +D and having a length s defined by the relations:

and

where W is the unit wet weight of said mooring means, is the angle between said flexible mooring means and the motion ofthe surrounding water, F is the drag of said flexible mooring means for the surrounding conditions of the water, and D is the drag per unit length of the flexible mooring means normal to the motion of the surrounding water.

References Cited UNITED STATES PATENTS 3,005,909 10/1961 Grandoff 244-136 X 412,341 10/1889 Languet 98 3,176,982 4/1965 ODaniell 98 X 612,109 10/1898 Hutchins 98 3,101,491 8/1963 Salo 98 3,295,489 1/1967 Bossa 98 X FERGUS S. MIDDLETON, Primary Examiner J. L. FORMAN, Assistant Examiner

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