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By Harry H. Nowlan

A heavy development campaign progressed during the year 1936 in South Texas1, following up important discoveries made in 1935. Oil and gas wells completed during the year were 1473 against 704 in 1935. The drilling program reached its peak of operations in June in consequence of offset requirements made necessary principally in Duval County in the Seven Sisters, Loma Novio, Lopez and Cole fields. There were six new fields discovered during 1936 as follows: Rhode in McMullen County; Peters, El Mesquite and North Kohler in Duval County; Wood in Starr County and Colorado in Jim Hogg County. No discovery of unusual consequence was made during the year. The pools mentioned above are simply in the primary stages of development. The most intensive exploratory work during the year was in Duval, Webb and Zapata Counties. Considerable activity also prevailed in Starr and Brooks Counties. Much significance is attached to the California Company's discovery in the Alta Mesa field in Brooks County, which is considered to be a deep-seated salt dome. The Comitas field, in Zapata County, developed some surprisingly good production in a shallow sand at 900 ft. and is being followed by a heavy wildcat campaign throughout that area in search of like production. In Starr County an active wildcat campaign is in progress in a continued effort to find new fields northwest of the Sam Fordyce field, in Hidalgo County. This play continues in a northerly direction through Starr and Jim Hogg Counties. New Fields Rhode.—The Rhode field, in southeastern McMullen County, was opened in May by the Magnolia Petroleum Co. with a gas well in the Whitsett (Upper Jackson) sand at a depth of 1810 to 1822 ft., this test is located in the southeast corner of sec. 86 on the Rhode ranch. Four gas wells have been completed, proving up a gas area of 1000 acres, more or less. Development will be slow because of lack of market for the gas.

Jan 1, 1937

By J. F. Wilkinson

A high degree of accuracy is often required in mine-surveying, in order that expensive mining work may not be misdirected. The making of underground connections by drifts or shafts located as the result of surveys presents a crucial test of correctness not usually involved in any other class of surveying. In view of these considerations, the present notes and description of a survey made in June, 1890, for the San Francisco shaft of the New Almaden quicksilver-mines, may be of interest to members of the Institute who are surveyors. The purpose of this survey was to locate on the surface a vertical 2-compartment shaft (3.5 by 7 ft.), to connect with another vertical shaft, of practically the same size, which had been sunk a number of years before from an adit-level about 240 ft. vertically below the surface, to a deeper, so-called 600-ft. level. It will be seen, of course, that the most important matter was to secure an exact coincidence in vertical line, so that the resulting continuous vertical shaft from the surface should have no offset or irregularity at the point of junction between its two parts. The levels were of less importance; but, as the hoisting-works were to be placed in position and the new shaft permanently timbered from the start, its correct alignment was an essential requirement. The important features of the work, therefore, were the methods used in determining with certainty : 1. That the shaft was located in the right place in a general way; 2. That the ordinary inaccuracies of linear and angular measurements were so reduced as to insure correctness of location within certain defined and allowable limits. Instruments.—Thc instruments used were: a Buff and Berger transit-theodolite, with a 6-in. horizontal plate, reading to 10 seconds; a Heller and Brightly Y-level; a Chestermán steel tape, graduated in tenths and hundredths of a foot; and New York leveling-rods, graduated to thousandths of a foot.

Jan 1, 1901

By Fred H. Lippold, Wm. H. Wolf

Methods of fair payment for excavating, supporting, and concrete lining tunnels have been sought by various owners for years. Tunneling techniques have changed with the development of equipment-from the hand-mucking operation to the machine mucker and, most recently, to machine-boring; from tunnel supports using timber sets to steel sets to rock bolts and, most recently, to shotcrete support; and from hand-placing the concrete lining using wooden forms to pumping or pneumatic placing using steel forms. As tunnel construction techniques advanced, so did methods for payment for the work performed. The recent development of tunnel-boring machines, or "moles," is precipitating another change. These changes have led to some difficulty in providing proper payment for the various items of work for different types of tunnels. As a major construction agency engaged in water-resources development in the western states, the U.S. Bureau of Reclamation has long been aware of the need for clarification of payment provisions in tunnel construction. The Bureau has some 150 miles of tunnels completed on its projects and about 50 miles of tunnels under construction. In this construction, the Bureau has benefited by the advance made by contractors in improving the techniques of tunnel excavation. To assure that the Bureau has an up-to-date approach to payment provisions, the Chief Engineer recently established a "standard" method of payment for all types of tunnels. It is believed that this new method of payment will be equitable for all contractors bidding on various types of tunnels using the diversity of methods of excavation now available to them. These payment provisions provide for different quantities for excavated tunnels using the blasting technique or using machine-boring techniques. In this way, the contractors have a choice in excavation methods and an equal opportunity to be low in their bids. We believe this will be an incentive to all contractors to be as progressive as the development of new equipment economically allows.

Jan 1, 1970

By E. Ryba, D. J. Michel

SAMPLES of REZn2 (RE = rare earth) intermetallic compounds prepared by a variety of techniques have been shown to exhibit an extensively twinned micro-structure.1-4 We have recently conducted compression tests at room temperature on specimens of HoZn2 prepared by a powder metallurgy technique.' The microstructures of specimens before and after testing are shown in Fig. 1. The "before" specimen, Fig. l(a), shows the basic twin structure of this material. Fig. l(b) shows the microstructure of the "after" specimen just below the fracture surface and reveals considerable cross-twinning as well as additional

Jan 1, 1970

By Victor Phillips, J. P. Blair

Jan 1, 1952

By A. C. Rand

The invention to be described in this paper is the work of Frederic A. Halsey, Engineer for the Rand Drill Company, of New York, and its use mill abridge the notable wastefulness of power of the striking rock-drill, and, at the same time, increase its capacity for work. That the older type of rock-drill is wasteful in power, is generally admitted; the cause being the use of steam* without expansion, arid the "cushion" of the blow, by the incoming steam upon the lower † end of the piston before the cutting tool strikes the rock.

Jan 1, 1885

By R. S. Lewis

IN a recent study1 of the evolution of engineering education 1870 was taken as the initial point, as it is said to mark the transition from the poineer era in American engineering education to an era of rapid growth and consistent development. Prior to the founding of Rensselaer Polytechnic Institute in 1824, West Point Military Academy was the principal source of formal engineering training. In 1849 Rensselaer revised its program on the model of the leading French technical schools. Lawrence Scientific School was estab-lished at Harvard and Sheffield Scientific School at Yale in 1847. The University of Michigan pioneered in en-gineering instruction in the West, offering its first course in 1853 and awarding its first degree in 1860. Other important steps in -the progress of engineering education were the founding of Columbia School of' Mines in 1864, the opening of Massachusetts Institute of Technology in 1865, and the founding of Cornell Uni-versity and the Thayer School of Civil Engineering at Dartmouth in 1867. From its organization in 1852 until 1871 the Ameri-can Society of Civil Engineers was virtually the only national society of engineers. In 1871 the American Institute of-Mining and Metallurgical Engineers was founded, to be followed later by the Mechanical En-gineers in 1880 and the Electrical Engineers in 1884. This expansion and diversification of the engineering profession was paralleled in the colleges, and by 1885 the plan of different curricula in the major branches of engineering was soundly established.

Jan 7, 1927

By A. Tobey Yu

The recent adverse economic climate has added further impetus to the demand for better-grade and lower-cost raw materials, for which increasingly larger quantities of muck are being moved and processed at higher unit labor costs. As a result, the cost impact of handling and shipping has never been as keenly felt by the mining industry as it is today. Thanks to joint innovative efforts by users and manufacturers, new and improved automated bulk-handling systems and devices are now blossoming everywhere to give the mining man the tools he needs to move ore, waste and concentrates more efficiently and economically.

Jan 1, 1970

By G. F. Moulton

Extraction of minerals from Searles Lake brines has taken place since 1873. Early operations for borax and raw trona found on the surface were expanded after 1914 to include potash, salt cake, and soda ash. A new soda ash plant now in operation will double area production. The evaporite beds were formed by desiccation of eastern Sierra runoff. The resulting series of brine-bearing salt beds supply the fluids necessary to feed the area chemical plants. Production methods include evaporation and crystallization for potash, borax, and salt cake; carbonation of brine to recover soda ash; and organic extraction of borax.

Jan 1, 1982

By R. L. Tobie

The degree of automation that has evolved in the dumping and hoisting of ore at the 3A and 3B hoisting shafts of the San Manuel mine is discussed. Motormen underground now dump their own trains at shaft pockets with rotary car dumps which operate semiautomatically. The ore is then drawn out of the 1200-ton shaft pockets into measuring baskets in skip loading stations, loaded into bottom-dump skips, hoisted, and dumped into coarse ore bins on the surface, in a fully automated operation. In an underground control room on the 2075 level midway between 3A and 3B shafts, car dumping, skip loading, and hoisting systems are monitored on lighted control panels which mimic each step in the operation. Here skip loading and dumping are viewed on closed-circuit television.

Jan 1, 1972

By AIME AIME

ALBERT PORTEVIN, distinguished French physical metallurgist .and savant, has been added to the Institute's list of Honorary Members. Professor Portevin's work in collaboration .with A. M. Garvin represents one of the greatest steps ever made in understanding the heat-treatment of steel and the function of steel-alloying elements. In addition, he has published the results of important work, on the castability of ternary alloys, on the determination of oxygen and-oxides in steel, and on high-temperature oxidationn and scaling of steel. Notable also are his studies on methods of testing metals, on the constitu¬tion and structure of alloys, on founding and welding, and on alloys of aluminum, magnesium, and copper. Professor Portevin was horn in Paris in 1880, entering

Jan 1, 1938

Copper ores from small mines in the area south of Tucson, where the Twin Buttes mine is located, were first operated in the 1880's. Today this area is one of the great copper mining centers of the world. In 1963, Anaconda Company acquired the property from Banner Mining Company and in recent years joined with AMAX in a 50/50 partnership to work the Twin Buttes property. From the beginning, Anaconda had relied on conveyors to remove overburden, oxide material for eventual leaching, and ore from the open pit. In the large st preproduction stripping program in mining history, Anaconda in a four-year period (1965 to 1969) removed 266 million tons of overburden of an average depth of 500 ft (152 m) lying over the ore body. The alluvium overburden was stripped by scrapers carrying 70 to 80 tons and push-loaded by two D9 tractors operating in tandem. The scrapers delivered their loads to bins which fed a 60 in. (1.52 m) conveyor having a capacity of 8500 tph. The 25% slope belt conveyor, which was 2100 ft (640 m) long, transported the material to the brow of the pit, where it was transferred to an 8300 ft (2530 m) surface belt to a 1000 ton loadout bin. At this point, the overburden was trucked to the sites of the tailings ponds, where it was used for dam construction. During 1976, the one billionth ton of overburden was removed from the Twin Buttes mine. The Twin Buttes quartz monzonite porphyry contains only scattered mineralization of which chalcopyrite is the most abundant mineral, associated with chalcocite, covellite, minor bornite, and several oxide minerals. Oxidation has progressed to variable depths of up to several hundred feet below the base of the alluvium. Because of the depth of the sulfide and oxide ores and hard rock waste, two in-pit crushers and conveyor systems were also installed for their transport out of the pit; and in 1976 a third crusher and conveyor system was installed lower in the pit for waste rock only. The two initial crushing and conveying systems were designed to handle any of three functions: crushing waste to be disposed of by a rail-mounted stacker -conveyor, crushing oxide ore for conveyor and then truck transport to stockpiles for future leaching, and primary crushing of sulfide ore for conveyor transport to the two 30 in. by 70 in. (0.76 by 1.78 m) secondary crushers and the two 7 ft (2. 13 m) standards and four 7 ft shortheads in the third and fourth stage crushing plant. A third standard crusher has been in- stalled recently. Mining is done by 15 yd (11.5 cum) shovels which load 100- and 150-ton

Jan 1, 1978

By James K. Stanley

PREFERRED orientation, particularly in irons and low-carbon steel, is a phenomenon that is both of considerable importance and theoretical interest. At times it is a liability and at other times an asset. In deep-drawing operations, preferred orientation is extremely undesirable because it necessitates trimming operations and increases scrap loss. Furthermore, oriented metals are likely to crack more easily than randomly oriented material because the forming of symmetrical and unsymmetrical shapes out of preferentially oriented metals and alloys increases the probability of rupture in regions of high stress, owing to differential ductility.1 In the electrical industry, on the other hand, preferentially oriented silicon irons are in demand for transformer application because of the improved magnetic permeabilities in the rolling direction.2 This phenomenon of preferred orientation in soft magnetic materials has been responsible for the tremendous improvement in transformer design and construction in recent years. Directional properties in metals have received a great deal of attention in the metallurgical literature,3-9 in which much of the information reported about orientation has been obtained by conventional methods, mechanical properties and X-rays. A wealth of data has been obtained and often at a great expenditure of time. The recent introduction of the magnetic torque measurements on ferromagnetic materials provides a very simple and rapid method of evaluating orientation. The judicious use of the method can supply important in- formation, but it should be borne in mind that such studies must be supplemented by X-rays, optical methods,10 and etch and pressure figures" to get a rational under- standing of the orientation phenomena. No claims are made that the magnetic torque of evaluating orientation will reveal the behavior of the metal in deep drawing. For this purpose the accepted tests for deep-drawing quality must be used. For a good drawing 'stock, which must have low impurities, desirable grain size, ductility, strength, hardness, good surface, random orientation, and good recrystallization behavior, it cannot be expected that any simple test will be satisfactory for appraising all the factors. The only factor on which the magnetic method can be used is orientation, which is, of course, of considerable importance. When directionality can cause a 10 to 15 per cent change in tensile strength and a IOO to 300 per cent change in tear length,12 it goes without saying that a reliable as well as rapid method for detecting these changes would be desirable. There are certain inherent advantages in testing orientation by the torque method: The method is rapid with the proper type of equipment; no elaborate preparation of specimens is required-it is only necessary punch or machine a disk of the sheet material and insert it into the testing device.

Jan 1, 1943

By G. H. Alani, H. T. Kennedy

One of the major difficulties in predicting the performance of oil reservoirs from their early pressure history lies in the uncertainty of estimating the volume of the liquid hydrocarbons contained in them. As a first step in filling this need, an equation was developed to determine the Inolal liquid volume of pure hydrocarbons over a wide range of temperature and pressure. The second step consisted of adapting the equation to apply to mixtures, with the heary hydrocarbons expressed as c The equatious are similar in form to van der Waals equation. hut the constants a and b tire considered as furnctions of temperature. In addition to the gas constant R, there are four constants characteristic of each hydro- When comptired with experimental values jound in the literal the. the average absolute deviation in the calculated molal volumes is found to be a Maximum of 0.33 per -cem for any of the pure liquid hydrocarbons studied. This maximum deviation was that found when comparing the calculated and observed values over a temperature range of 86° to 482°F and a pressure range from the bubbl-point ro 10,000 psis. The equations expressing the correlation for. mixrurrc were developed from 647 experimental measure-rilents of volume on 47 bouom-hole samples covering ; temperature range of 72" to 250°F and a pressure znge from bubble-point ro 5,000 psig. The average absotute deviation was found to he 1.6 per cent with the maximum for any measurement of 4.9 per cent. INTRODUCTION Accuratc information of the pressure-volume-temper-iiture behavior of hydrocarbon liquids is of considerable importance in the field of both applied and theoretical science and, especially, in the solution of petroleum reservoir engineering problems. These PVT relationships can be expressed graphically, in tabular form or as equations of state. Equations of state for gases have been developed based on the ratio of pressure, temperature and volume to the pressure, temperature and volume at the critical points of the hydrocarbons. These equations have been successful in yielding values fairly accurate for reservoir engineering purposes. For liquids, however, relations of this type are more complex and have not yielded useful results. The composition of reservoir liquids is normally expressed in terms of the moles of hydrocarbons C,? C,. C,. elc, per mole of mixture. The composition must include the fraction of a mixture such as C,,, which cannot be separated with reasonable time and effort into specific hydrocarbons. Although there are several equations of state having variable degrees of accuracy applicable to pure liquid hydrocarbons, none includes a means for estimating the volume of mixtures as a function of temperature. pressure and composition expressed in this manner.

By C. W. Haworth, M. G. Hall

THE diffusion of copper in silver has been studied by Sawatzky and Jaumot1 and Cahoon and Youdelis.2 Sawatzky and Jaumot measured tracer diffusion in single crystal specimens but the 12.9 h half-life of CU64 limited the time of the diffusion anneal to about 50 hr, and in consequence the minimum temperature of the investigation was 716°C. Cahoon and Youdelis employed polycrystalline diffusion couples, and measured the interdiffusion coefficient over the range 0 to 2 at. pct Cu. These experiments were performed at temperatures down to 630°C and a discontinuity in the Arrhenius plot was observed at -700°C. The high D-values at lower temperatures were attributed to the effect of grain boundary diffusion. The present experiments were undertaken to investigate this anomaly and study the low temperature region of the diffusion of copper in silver. The method employed single crystal samples and a plated source of copper. Silver single crystals 2½ by 4 in. sq were grown from zone-refined silver bar (>99.99 pct Ag) by the Bridgeman technique, and $ in. thick slices were cut by spark machining. The specimens were electro-polished, and a 2 µm layer of copper was electroplated on to the planar surface at one end of each specimen using a potentiostatic voltage source. The following solution was used for plating: CuSO4 . 5H2O 125 gm H2SO4 (S.G. 1.8) 53 ml H2O 1000 ml The diffusion couples were sealed in capsules, in an argon atmosphere, and were annealed at either 701, 597, or 498°C. The temperature measurements were made to an accuracy of *l°C After the anneal, the penetration of copper into the silver was determined using an electron probe micro-analyzer. 100 sec scaler measurements of the intensity of Cu Ka! X-radiation were performed at 2 to 5 µm intervals along a line normal to the source, with a beam potential of 25 kv. Allowances were made for the background radiation, and the dead-time of the counting system in the normal way, and the intensity ratios were corrected to weight concentration by the method of Duncumb & de-Casa.3 For the analysis of the diffusion profiles, it was first observed that the copper layer did not completely dissolve in the host crystal for the specimens annealed at 498 and 591 whereas for the specimen annealed at 701°C, a single phase solid solution was formed. For the 498" and 597°C specimens, the concentration of copper in the silver at the interface was therefore constant throughout the anneal and the analysis for a

Jan 1, 1970

By James K. Stanley

Preferred orientation, particularly in irons and low-carbon steel, is a phenomenon that is both of considerable importance and theoretical interest. At times it is a liability and at other times an asset. In deep-drawing operations, preferred orientation is extremely undesirable because it necessitates trimming operations and increases scrap loss. Furthermore, oriented metals are likely to crack more easily than randomly oriented material because the forming of symmetrical and unsymmetrical shapes out of preferentially oriented metals and alloys increases the probability of rupture in regions of high stress, owing to differential ductility.' In the electrical industry, on the other hand, preferentially oriented silicon irons are in demand for transformer application because of the improved magnetic permeabilities in the rolling direction.2 This phenomenon of preferred orientation in soft magnetic materials has been responsible for the tremendous improvement in transformer design and construction in recent years. Directional properties in metals have received a great deal of attention in the metallurnical -literature,3-9 in which much of the information reported about orientation has been obtained by conventional methods, mechanicai properties and X-rays. A wealth of data has been obtained and often at a great expenditure of time. The recent introduction of the magnetic torque measurements on ferromagnetic materials provides a very simple and rapid method of evaluating orientation. The judicious use of the method can supply important information, but it should be borne in mind that such studies must be supplemented by X-rays, optical methods,10 and etch and pressure figures" to get a rational understanding of the orientation phenomena. No claims are made that the magnetic torque of evaluating orientation will reveal the behavior of the metal in deep drawing. For this purpose the accepted tests for deep-drawing quality must be used. For a good drawing stock, which must have low impurities, desirable grain size, ductility, strength, hardness, good surface, random orientation, and good recrystallization behavior, it cannot be expected that any simple test will be satisfactory for appraising all the factors. The only factor on which the magnetic method can be used is orientation, which is, of course, of considerable importance. When directionality can cause a 10 to 15 per cent change in tensile strength and a IOO to 300 per cent change in tear length,12 it goes without saying that a reliable as well as rapid method for detecting these changes would be desirable. There are certain inherent advantages in testing orientation by the torque method: The method is rapid with the proper type of equipment; no elaborate preparation of specimens is required—it is only necessary to punch or machine a I-in. disk of the sheet material and insert it into the testing device.

Jan 1, 1944

By James K. Stanley

Preferred orientation, particularly in irons and low-carbon steel, is a phenomenon that is both of considerable importance and theoretical interest. At times it is a liability and at other times an asset. In deep-drawing operations, preferred orientation is extremely undesirable because it necessitates trimming operations and increases scrap loss. Furthermore, oriented metals are likely to crack more easily than randomly oriented material because the forming of symmetrical and unsymmetrical shapes out of preferentially oriented metals and alloys increases the probability of rupture in regions of high stress, owing to differential ductility.' In the electrical industry, on the other hand, preferentially oriented silicon irons are in demand for transformer application because of the improved magnetic permeabilities in the rolling direction.2 This phenomenon of preferred orientation in soft magnetic materials has been responsible for the tremendous improvement in transformer design and construction in recent years. Directional properties in metals have received a great deal of attention in the metallurnical -literature,3-9 in which much of the information reported about orientation has been obtained by conventional methods, mechanicai properties and X-rays. A wealth of data has been obtained and often at a great expenditure of time. The recent introduction of the magnetic torque measurements on ferromagnetic materials provides a very simple and rapid method of evaluating orientation. The judicious use of the method can supply important information, but it should be borne in mind that such studies must be supplemented by X-rays, optical methods,10 and etch and pressure figures" to get a rational understanding of the orientation phenomena. No claims are made that the magnetic torque of evaluating orientation will reveal the behavior of the metal in deep drawing. For this purpose the accepted tests for deep-drawing quality must be used. For a good drawing stock, which must have low impurities, desirable grain size, ductility, strength, hardness, good surface, random orientation, and good recrystallization behavior, it cannot be expected that any simple test will be satisfactory for appraising all the factors. The only factor on which the magnetic method can be used is orientation, which is, of course, of considerable importance. When directionality can cause a 10 to 15 per cent change in tensile strength and a IOO to 300 per cent change in tear length,12 it goes without saying that a reliable as well as rapid method for detecting these changes would be desirable. There are certain inherent advantages in testing orientation by the torque method: The method is rapid with the proper type of equipment; no elaborate preparation of specimens is required—it is only necessary to punch or machine a I-in. disk of the sheet material and insert it into the testing device.

Jan 1, 1944

By P. Chiotti, G. R. Kilp

IN the study of zinc-zirconium1 and zinc-uranium2 systems, vapor-pressure measurements were made in order to establish the equilibrium phase diagrams for a pressure of 1 atm. In each of these systems, only zinc has an appreciable vapor pressure over the temperature range investigated. The zinc pressure was measured over a sufficiently wide temperature and composition range to permit calculation of the standard free energy, enthalpy, and entropy of formation for the compounds ZrZn, ZrZn2, ZrZn3, ZrZn6, ZrZn14 , and U2Zn17. In these calculations the compounds were treated as line compounds. Although the exact composition range was not determined, metallographic and thermal data indicate that the solubility range for these compounds is small. It is to be noted that the compound initially reported to correspond to the formula UZn9, 2 has been shown by the crystal structure work of Makarov and vinogradov3 to correspond to the formula U2Zn17,. The crystal structure is similar to that for the compounds Th2M17, investigated by Florio,4 et al; here M represents iron, cobalt, or nickel. Therefore, thermodynamic calculations are based on the formpla U2Zn17 EXPERIMENTAL The dew-point method employed to measure the vapor pressure of zinc over uranium-zinc alloys has been described previously.2 The same procedure and apparatus were used in measuring the zinc pressure over zinc-zirconium alloys. In the case of alloys in the two-phase region consisting of a zirconium and the compound ZrZn, the Knudsen effusion method was employed to obtain a few values in the temperature range 600" to 560°C. In most cases, tantalum crucibles were used to contain the zirconium alloys. THERMODYNAMIC PROPERTIES OFU2Zn17 A least-squares treatment of the vapor-pressure data obtained for 35 and 65 wt pct U alloys in the temperature range 650° to 940°C gave lOg10PAtm = 7,713/T + 6.33 Here, as in following equations, T represents degrees kelvin and P represents the zinc vapor pressure in atmospheres. The probable errors for the two constants were calculated to be 60.68 and 0.0563, respectively. This relation represents the equilibrium dissociation pressure for the reaction U2Zn17 (s) - 2U(s) + 17Zn(v) The solubility of zinc in solid uranium is negligible and the only additional information required to calculate the free energy of formation of U2Zn17 is the free energy of vaporization of pure zinc. K. K. Kelley5 gives the relations, AF°= 30,902 + 6.03Tlog T + 0.275 X 10-3T2 - 45.03T

Jan 1, 1961

By J. E. Chappelear

We are concerned with the problem of calculating the forces produced by passing waves on a submerged object (in particular a drilling barge) located on the ocean floor. We employ the linearized theory of waves (the Airy1 theory), since solutions are generally more easily obtained in such a theory. It will be indicated how an approximate solution to the problem can be obtained for waves of finite height by use of a linear combination of Airy waves. We shall assume the submerged object has an infinite length, thus neglecting diffraction and making the problem two-dimensional. We find that there is not a considerable difference between our solution and the usual engineering solution. The force, as a function of time, is plotted in Figs. 4 and 5, together with the usual solution for easy comparison. So far, no experiments have been found to compare with the results. As will be shown, the calculations can be extended to waves of finite height (Stokes2-Struik3 waves) in an approximate fashion. This can be done by calculating the force produced by each Fourier component of the wave, separately, and omitting the coupling between the various harmonics produced by Bernoulli's theorem. The problem and its boundary conditions will be briefly stated. We seek a function, +, the velocity potential, which is harmonic, ?2?=0...........(1) and which satisfies the boundary conditions ??/?n =0 .......(2) (the normal derivative of + is zero) on the ocean floor and the sides of the barge, and s??/?y = ?..........(3) on the ocean surface, where s = g/w2........(4) The physical reasons for these choices and an interpretation of ? are given by Lamb.' As previously stated, we assume also that the problem is two-dimensional. We set up our coordinates such that x = 0 is the center of the barge and y = 0 is the ocean floor. The coordinates are shown in Fig. 1, together with the location of the barge on the bottom. Our solution may be decomposed into a function which is symmetric about x = 0,?e, and one which is antisymmetric, +,, ? = ? + ?o...........(5) Thus directly above the barge we have as boundary conditions that for x = 0, ?o = 0, ...........(6) and ??e/?x = 0........(7) Now, far from the barge, we have that (for x positive and assuming the waves are incident from the left) ?e ? Ae cosh ky cos k (x + a) , . . . (8) and ?e ? Ao cosh ky cos k (x + ß) . . . . (9) where + means ". .. approaches ... for x large." Let us put Ae, Ao, and k equal to one, and remember that, in accordance with the derivation of Eq. 3, a sinusoidal time factor is to be supplied. Then we may rewrite Eq. 8 for ?e, and we find that

Jan 1, 1958