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By Herbert Hoover

IT is always a pleasure for me to join in the Ameri-can Mining Congress, for not only has my own professional life been closely linked with the industry, but the Secretary of Commerce is specifically enjoined in the organic act creating the office to promote and foster the interests of the mining industry. And it is a vital part of our national life. It is one of those indus-tries without which. the nation could not go on for a week. It ranks second only to the agricultural industry in its contribution to our raw materials. Its production amounts to nearly 6 ½ billions annually, providing direct support to probably ten millions of our people through employment to about two million workers. But the in-dustry has a greater importance than even these figures indicate, for with agriculture, forestry, and water power it furnishes the raw materials upon which the whole work of our civilization rests. When the raw ma-terials of our mines emerge. from manufacture with the added expenditure of labor and capital upon them, they have a wholesale value of over fifteen billions of dollars. And in this, the second stage of their application, they give employment to another two million workers and support to about ten million more of our people. A large portion of these manufactured commodities must filter through the retail trade; their total value when delivered to the consumer exceeds twenty billions of dollars. And from this distribution arises the support of many more millions of our people. It is estimated that the products of agriculture when they reach . the consumer, with transportation, manu-facturing, and distribution costs added, have about the same value as the mineral industries-each of them thus contributing about one-quarter of our total na-tional income. No other continent has demonstrated its possession of such a magnitude of minerals as has ours, and such a bountiful distribution over our whole land. But our mineral resources differ in one essential from our other natural resources-they are not renewable. Agricul-ture, forests, and water power replenish their supplies from season to season. Some people conclude from the non-renewable character of the mineral supply that they must shortly be exhausted. The practical question is ,one of time, and time in these matters needs to be measured in generations, and apprehension of exhaus-tion needs to be tempered with many probabilities in-cluding the advance in technical methods of extraction. In some of our minerals, such as coal, iron, and building materials we can, through a knowledge of their geologi-cal structure and occurrence, make fairly good estimates of our reserves. We. know that they will outlast many generations of Americans. In non-ferrous metals and oil, geology affords us no great basis for an estimate of future supply. We only know of the occurrence of minerals of this type by actual exposure of them, and we can thus make no estimates except upon reserves which have been proved by actual development by the process of mining. To develop them ahead merely for national satisfaction of assured future supply would imply an unbearable waste of capital. The consequence is that in these groups there is never a demonstrable assurance of more than a few years' supply ahead of us. Yet we have never failed from year to year to find new deposits and extension of old deposits.

Jan 1, 1928

By Albert F. Hill

The manufacture of structural shapes in steel of uniform quality, which shall command the full confidence of the engineer, is a problem in practical metallurgy which is beginning to attract much attention in this country. The progress of the past fern years in the improvement of plant and processes has placed it within the power of the steel-maker to supply a material of such chemical composition as will meet the requirements; but this solves only in part the difficulties of the constractor. It is well understood that the influence of shop manipulations is a most decisive one upon the mechanical properties of the finished product; in many cases so great, in fact, as to cause an entire transformation in the character of the material, and to render it unfit for the service for which it was intended. On the other hand, mechanical treatment is frequently resorted to as an efficient corrective of certain undesirable properties, which may be due either to chemical composition or previous manipulation. This understood and accepted, it is evident that careful investigation of the effects of mechanical treatment is fully as necessary to the successful use of steel in engineering structures, as the investigation of the influence exerted by its chemical composition. All structural material has to undergo more or less mechanical treatment, such as shearing, punching, upsetting, etc. Each of these operations produces effects which are far more marked and decisive in steel than they are in iron, and means must therefore be adopted to counteract, or at least to modify, these effects before the material is permitted to enter the structure. The fact that both shearing and punching affect the tenacity and elasticity of steel has long been recognized; bat, through more recent investigations, it has been established that these effects are purely local, and are therefore susceptible of correction by other and simpler means than annealing. The importance of this discovery to the use of steel in structures is very great. The impracticability of

Jan 1, 1883

By S. Inaba, K. Taguchi, T. Uenaka, I. Mizuguchi, K. Umeji, H. Isako

At Kobe Steel Ltd., various improvements in pellet quality have been carried out since beginning lime-fluxed pellet production. Especially, dolomite-fluxed pellets, developed in 1975, have superior high temperature properties. With this improvement, successful BF performance has been achieved. But, in order to achieve more successful BF performance, improvements of physical properties such as the shape factor, reposed angle, and the bulk density are desired. Now, crushed pellets have been developed for the improvement of those characters. The test operation with these new pellets in Kakogawa No. 2 BF was carried out with successful results. This report describes the development of crushed pellets and their use in BF.

Jan 1, 1986

By M. Duclos, A. Sawatzky

A simple model has been developed which describes the steady-state solute distribution in Ti-H type systems above the eutectoid temperature in the presence of a temperature gradient. The solute distribution is dependent on the shape of the phase boundaries. An interesting result, and one that is not observed at steady state in thermal diffusion below the eutectoid temperature, is the existence of a two-phase region. The heat of transport for hydrogen in a titanium, Q*a, over the temperature range 275" to 650.C is determined to be 4500 * 230 cal per mole. The heat of transport for hydrogen in B titanium, QB* over the temperature range 320" to 590.C is found to be 630 ± 200 cal per mole. It is also shown that thermal diffusion provides a method by which phase bounduries above the eutectoid may be determined in Ti-H type systems. IN modern technology materials are being used at constantly increasing temperatures under greater temperature gradients. Thus atomic migration in metal alloys due to a temperature gradient (thermal diffusion) may in some cases occur to an observable extent. The thermal diffusion of hydrogen in zirconium has in recent years received considerable attention1-' because of the use of zirconium alloys in nuclear power reactors. The thermal diffusion kinetics below the eutectoid (547°C) are fairly well understood. At steady state the solid solution, a, and hydride, 6, phases are completely separated with the hydride precipitating at the lower temperatures. No experimental work has been carried out in the a + B region although Droege4 suggested that a complete separation of the two phases, as observed at temperatures below the eutectoid, might not always occur. In the present investigation a simple model has been used to determine the steady-state solute distribution under a temperature gradient in Zr-H type systems heated above the eutectoid temperature. The solute distribution is shown to be dependent on the shape of the phase boundaries in the constitutional diagrams and several typical cases are discussed. The model has been applied to Ti-H. This system was chosen in preference to Zr-H because of its much lower eutectoid temperature (-300°C as compared with 547.C), thereby reducing experimental errors due to oxidation and hydriding. The heats of transport for hydrogen in the a and B phases of titanium also have been determined since they were required to compare the proposed thermal diffusion model with experiment. THEORY In the presence of a temperature gradient the atomic flux in a single-phase region of a two-com-ponent system of which the atoms of only one component are diffusing is given by:' J = - U\dx + RT3 dx) which can be written as: j-D(dn/dt +Q*n/RT2)dt/dx [11 J - -D\dT + RT2)dx [1] where D = diffusion coefficient, n = solute concentration, T = absolute temperature, R = gas constant, dT/dx = temperature gradient, and Q* = heat of transport. At steady state (J = 0) Eq. [I] leads to the solute distribution: n = noexp Q*/RT where no = a constant depending on total solute content. The heat of transport Q* can be experimentally determined from the steady-state distribution. In the present paper we shall determine the solute distribution in systems having the constitutional diagram exemplified by Ti-H shown in Fig. l.' As shown, N,(T) and NB(T) are the equilibrium solute concentrations in the a and 0 phases at temperature T. Lines AA' and CC' define the region of interest to us. The following assumptions are made: 1) Steady-state conditions prevail. 2) In a single-phase region all points on an isotherm have the same thermodynamic potential so that the composition over an isotherm is uniform. If a two-phase region exists, thermodynamic equilibrium is found only at phase interfaces. However, we assume the component of the concentration gradient along an isotherm to be small so that the composition in each phase is approximately the same as at the interface and is given by the constitutional diagram, Fig. 1. 3) There is appreciable diffusion of only one component. 4) We shall consider only the case where Qa*, QB*, and Qg*, the heats of transport for solute diffusion in the a, B, and 6 phases, respectively, are positive. This has been observed for the thermal diffusion of hydrogen in zirconium3 and titanium.10 We will show that the steady-state solute distribution above the eutectoid is primarily determined by the heats of transport and the temperature dependence of Na(T) and Np(T). It may be quite different from the steady-state distribution below the eutectoid. For example, we will see that, under certain conditions,

Jan 1, 1970

Abbey, Robert Graham, District Mgr.. The W. W. Sly Mfg. Co., 50 Church St.. New York, N. Y. '21 Abbott, A. N., Mines Supt., Mazapil Copper Co., Ltd Concepcion del Oro, Zac., Mexico. '28 Abbott, Argyle Campbell, Dev. Dept., E. I. du Pont de Nemours & Co., Wilmington, Del. '29 Abbott, Clarence E., V.P., Charge of Raw Materials, Tenn. Coal, Iron & R. R. Co., 1242 Brown-Marx Bldg.. Birmingham, Ala. '04 Abbott, Louis Benjamin, Chief Engr., Elkhorn Div., Consolidation Coal Co., Jenkins, Ky. '16 Abeel, George H., Jr., Cons. Min. Engr Box 427, Santa Monica, Cal. '18 Abel, Albert E., Asst. to Pres., Valley Mould & Iron Corp Hubbard, Ohio. '19 Abel, Raymond L., Asst. Prof., Dept. of Pet. Refin., Univ. of Pittsburgh Pittsburgh. Pa. '28 Abeel, Leo M., Research Engr., Sullivan Concentrator Chapman Camp, B. C., Canada. '31

Jan 1, 1932

In 1970, the federal Clean Air Act was passed, promulgating limits on the emissions of sulfur dioxide (SO2) from large stationary sources that would affect local air quality. The brunt of this regulation was felt by the electric utility industry, especially those units generating electricity with coal-fired boilers. The law hastened development of a new industry, flue gas desulfurization (FGD), which is composed of three major segments: the electric utility, the FGD equipment suppliers (the scrubbing modules), and the scrubbing chemical suppliers. Dravo's experience suggested the equipment end of the business, but market analysis recommended investigating the chemical processes involved in the removal of the SO2 gas. This resulted in the formation of Dravo Lime Co. to manufacture and market reagents to the FGD industry. This paper will briefly describe the Thiosorbic lime scrubbing process and review Dravo's innovative mine and calcining facility.

Jan 1, 1982

"The zinc concentrator of the Butte & Superior Copper company, shown on the opposite page, represents an industry which is coming into importance in Butte. The existence of large bodies of zinc ore in some of the silver veins of Butte has been realized for years, but it is only recently that some of them have proved amenable to successful concentration. Most of the zinc ores thus far found in the camp are mixed with considerable pyrite, but those found in the Black Rock and Elm Orlu mines contain very little pyrite, so that a concentrate low in iron is possible.The Butte & Superior mill is rated at 1,200 tons daily capacity. The ore is sphalerite, most of which is finely disseminated through a hard quartz gangue, with small quantities of galena, pyrite, chalcopyrite, rhodocrosite and rhodonite. In mining, the included granite and the low grade vein matter are sorted out and used for waste filling so that the ore as it goes to the concentrator will carry about 20 per cent of zinc, 1 per cent lead, .25 per cent copper, 8 to 10 ozs. silver and a little gold. The ore bodies ranging from 5 to 103 feet in width, are mined by the square set method and filling of stopes with waste rock.The ore is hard and tough requiring extensive crushing and grinding equipment, consisting of Blake and gyratory crushers, 54-inch and 42-inch high speed rolls, Chili mills, Tube, and Conical mills. All of the lead con¬centrate and part of the zinc concentrate are recovered in the upper part of the mill by jigs and tables. The classifier overflow and the re-ground jig and table tailings go to settling tanks and from there to the Hyde Flotation process, where the balance of the zinc concentrate is recovered, and the tailing go to waste."

Jan 1, 1913

By José Aloisio Paione, Eudes Prado Lopes

The geophysical exploration carried out by the Brazilian government through the Mineral Resources Development Co. (CPRM) to discover and develop Brazil's mineral resources is discussed. Particular mention is made of procedures specially adapted for contracting companies specialized in geophysics, CPRM's activities, statistical data from study programs, as well as the financial investments committed. More than 500 000 km of aerogeophysical surveys have been carried out by CPRM in the last four years, and it is expected that more than 600 000 km will be flown in 1974 and 1975, at an investment of approximately $30 million.

Jan 1, 1977

By R. E. Shinkosk

This paper outlines the development of a program for increasing the life of woolen bags used for filtering Dwight-Lloyd gases by treating the bags and gases with hydrated lime. Methods and apparatus are described for determining alkalinity of dusts, acidity and breaking strength of bag cloth. Procedure and results, based on several years of operation, are presented. DURING 1939, additional facilities were constructed in the Dwight-Lloyd Blast Furnace and Baghouse departments at the Selby, California, Plant of the American Smelting and Refining Co. In order to handle adequately the increased volume of gases from the resultant increase in production, it was necessary to increase gradually the amount of water used for cooling gases ahead of the sinter machine baghouse. As a result of this increased water cooling, the average bag life dropped from 27 months in 1939 to 14 months in 1941. (Table I). This drop in life meant an increased. bag cost, as well as lower recovery of dust and some curtailment of operation. During 1941, it was found new bags showed as high as 0.3 pct acidity* after two weeks of opera- tion and as much as 2.0 pct acidity after some months of operation. This high acidity was present in spite of the fact that free oxide or relative alkalinity of the unburned dust ran from 5 to 6 pct. In view of these circumstances, a twofold program was started in Nov. 1941.t Part one of this program consisted of vigorously dipping all new bags in a weak lime solution, containing 50 lb of hydrated lime per 50 gal of water. Part two consisted of feeding fine, dry, hydrated lime into the gas stream intake of the sinter baghouse fan. Apparatus for feeding this lime is shown in fig. 1. All baghouse chambers are shaken in rotation about once each hour. On alternate hours, the baghouse operator places 50 lb of hydrated lime (one sack) into the lime feeder, starts feeder and immediately starts the bag shaking machinery. The rate at which lime is fed is set to coincide with the approximate time necessary to shake all sinter bag-house chambers, or about 15 min. It is felt this method of lime addition is most effective for getting lime into the woolen bag fabric. The amount of lime so fed averages about 600 lb per day. The amount of lime fed per day is varied to keep a minimum relative alkalinity of 9 pct in the unburned sinter dust. A daily dust sample is taken for alkalinity by allowing dust to accumulate in a sample pipe over a 24-hr period. This sample pipe, placed in any chamber cellar, is 2 in. in diam, 4 ft long, is sealed on the inner end, and capped on the outer end. It has a 1/2 in. slot cut for 18 in. along the tip end. This slot faces upward and allows the pipe to fill gradually with dust as bags are shaken. Breaking strength of bags has, in most cases, been the deciding factor in bag replacement. Bags that normally test 100 psi breaking strength when new are replaced when they test under 35 lb. The method for determining breaking strength is shown in the description accompanying fig. 2. Since the start of the liming program in 1941, bag life has increased from 14 months to an average of over 23 months, with a consequent material decrease in bag cost per year. Acidity, as per cent sulphuric acid, may be determined by means of a Beckman pH meter as follows: From a piece of bag cloth. which has been thoroughly cleaned of dust, a 5 g sample is weighed on a balance. Cut the sample into fine pieces and place in a 400 cc beaker. Add 100 cc (measured) of distilled water and stir vigorously. Filter on suction funnel, holding cloth pulp in beaker with a stirring rod. Wash cloth sample and filter wash water four additional times, each time with 20 cc distilled water, the last time squeezing cloth pulp over funnel. Discard pulp and rinse funnel and filter paper. Pour wash solution jnto measuring graduate and make up to exactly 300 cc with distilled water. Place into clean 600 cc beaker and measure the pH on meter. The per cent acid in bag cloth is read from the following table:—

Jan 1, 1951

E. O?C. Acker Truman H. Aldrich Walter H. Aldridge Anson W. Allen John H. Allen W. Lawrence Austin W. S. Ayres David Baker John Henry Banks Alonzo F. Bardwell Robert Bentley Andrew A Blair Walter M. Brodie Fredrick Burbidge H.H. Burden Charles Butters

Jan 1, 1939

By Cyril Stanley Smith

Jan 1, 1949

University of Michigan Press, Ann Arbor, Mich. The publications of the various divisions of the University are issued by the Press A large number of scientific treatises and books are listed in the catalogue of the Press but only a few of them are of a nature to be given here. In the Scientific Series, vol 3 should be cited, The geology of the Netherland East Indies, by H A Brouwer; price, $3 plus 15 cents postage. Some of the volumes of the Michigan Academy of Science, Arts and Letters, also issued by the Press, contain papers on geology. Specifically:

Jan 1, 1933

A special committee on the Classification of Surface Mining Methods was appointed by the A.I.M.E. Board of Directors on Nov. 17, 1939. The committee was headed by Gerald Sherman, and the members were Chester A. Fulton, C. F. Jackson, Earl E. Hunner and Arthur Notman. The following form of classification was reported to the Board by the Committee on May 16, 1940, as its unanimous recommendation. SURFACE MINING Dry Mining Bottom Benching Bank Mining < Top Benching Dry Mining Dry Mining Bottom Benching Hydraulic Mining Pit Mining Dredging Dry Mining Top Benching Wet Mining Top Benching River Bed Dredging Subaqueous Mining Lake Bed or Dredging Ocean Bed (Hand Mining Ground Sluicing Hydraulicking Dredging In most cases the terms used in the accompanying outline define themselves. Bank Mining is distinguished from Pit Mining by its situation. In Pit Mining the ore is taken from an operation below the level of the surrounding surface. In the secondary classification, Bottom Benching is an operation in which a bench is attacked from below, but the material mined might be hauled up out of the pit or moved out horizontally or downward.

Jan 1, 1940

By Fred Wise

THE Getchell mine, a comparatively recent gold discovery, is in the old Potosi mining district, Humboldt County, Nevada. All ore is mined from open pits using Diesel shovels and gasoline trucks. Two types of ore are mined, oxide and sulphide. Oxide ores are siliceous or shaly; sulphide ores either gougy, siliceous or shaly. In mining, the sulphide ore is segregated into hard and gougy ore, because the gouge must be dried before it can be crushed, The oxide ore is not segregated. GENERAL METALLURGY The oxide ore is the leached outcrop that overlies the sulphide ore body. All of the iron and arsenic sulphides found in the sulphide ores have been thoroughly oxi-dized, The sulphur and arsenic have been leached out while the iron is present as hematite and limonite. The oxide ore is amenable to direct cyanidation, and although no visible free gold is present it is released at a comparatively coarse grind. The sulphide ore is more refractory, since the gold is all of micron size and some of it is locked in fine sulphides. It has been established microscopically that the free gold is coated with an impervious shell, which is probably some form of iron compound. The sulphide ores contain from 1.5 to 2 per cent of arsenic, which is present as orpiment and realgar with minor amounts of arsenopyrite. The orpiment and realgar are of a later mineralization than the gold and are barren. Roasting and washing of the sulphide ore prior to cyanidation is necessary to eliminate the arsenic, to alter the gold coating from an insoluble form to a soluble form, and to release the gold associated with the fine sulphides. Washing the ground calcine in weak sulphuric acid, trona, or hot water are beneficial in the order named, but to date the water is the best from an economic standpoint. Metallurgical tests as well as plant practice indicate that a certain amount of gold cannot be recovered even by going beyond economic practices, On this basis metallurgical results are viewed in the light of an optimum tailing rather than a per-centage of extraction.

Jan 1, 1940

By C. S. Matthews, J. L. Mahaffey, W. M. Rutherford

This paper gives results of an experimental study of the sweep efficiency of a miscible displacement in a five-spot. The study was carried out in a parallel-plate glass model in which effects of diffusion were scaled at or near the molecular diffusion level. The experiments show that very early breakthrough (25 to 35 per cent of pore volume (PV) injected) may be expected in miscible floods because of the unfavorable viscosity ratio. However after 1 PV of displacing fluid is injected, the sweep rises to a reasonable value (50 to 60 per cent). Photographs show that small slugs of less than 10 per cent of PV tend to dissipate before breakthrough. A minimum slug size of 15 per cent of PV would appear to be necessary even in a relatively homogeneous formation. Presence of a slug whose viscosity is inter-mediate between that of oil and gas increases the sweep efficiency of the oil-gas system. In a typical system the sweep at breakthrough rose from 26 to 37 per cent of PV for a 25 per cent slug. The increase in sweep brought about by use of a large slug could well pay for the extra deferment cost of the additional slug material. INTRODUCTION Most miscible displacement processes involve the displacement of oil with fluids of much lower viscosity and density. The displacement process at these adverse viscosity and density ratios is dominated by instability phenomena, i.e., viscous fingers and gravity tongues. These phenomena have highly adverse effects on oil recovery. Although a number of laboratory studies have been made to determine the effect of adverse viscosity ratios on five-spot sweep patterns,l,2 the scaling of diffusion effects is uncertain. In the series of scaled model studies reported herein, an attempt was made to scale diffusion. Model studies of miscible displacements in which molecular diffusion predominates are per-mitted by controlling the parallel plate spacing which reduces convective mixing to arbitrarily small levels. To decide how this scaling relates to any particular Geld displacement necessitates an estimation of diffusion effects for the natural rock being considered and conditions under which displacement will be conducted. The approach normally taken is to extrapolate data obtained from stable miscible displacements performed in the laboratory, such as those presented by Brigham et al.3 The validity with which such an extrapolation can be applied to an unstable flow system has yet to be established. If this approach is accepted, a family of oil recovery curves can be generated for a single viscosity ratio based on Brigham&apos;s observation that the magnitude of the dispersion coefficient is dependent, among other things, upon specific rock properties. Objective of our test was to define the lower limit of this range by presenting the case where dispersion effects were reduced to the molecular diffusion level in both the transverse and longitudinal directions.

Jan 1, 1967

Jan 1, 1949

By Charles A. Lindberg

It will be generally agreed that the most important accessory to a rail haul operation is the railroad type locomotive crane. The oldest and still most common type is the steam crane, a self-contained steam power plant, coal fired, complete with boom and hoisting machinery and mechanical drive capable of propelling the unit on its own power at speeds up to 15 mph on the level, and hauling, if necessary, a car for transport of the objects being handled. Usually, for greater mobility and safety, this crane and flatcar are moved around the pit by a switcher locomotive. Crane capacities range from 25 to 40 tons, these loads being handled with the shortest radius of boom and with outrigger. Boom lengths are 55 to 60 ft long, usually with heavy lift main blocks at 40 ft boom lengths. Lifting capacities with booms at maximum radius are approximately 20 % of maximum rating. Free capacities, namely without outriggers, range from 65 (at minimum radius) to 55% (at maximum radius) of the above capacity values.

Jan 3, 1950

By A. L. Mowry, John T. Norton

Isothermal sections of the pseudo-ternary carbide systems TiC-VC-ZrC, TaC-VC-ZrC, and NbC-VC-ZrC have been examined. The sections contain an inverted U shaped two-phase field whose maximum extent is 77 molecular pct for Tic, 64 pct for TaC, and 51 pct for NbC. lsoparametric lines were determined which show the curvature of the single-phase field and the direction of tie lines in the two-phase field. It was not possible to show any relationship between atom size and the extent of the two-phase field. REVIOUS work&apos; on the solubility relationship of several pairs of refractory cubic monocarbides from the group Tic, ZrC, VC, NbC, and TaC has shown that, with the exception of the system VC-ZrC, they all form continuous series of solid solutions. It was demonstrated that the limited solubility in the case of VC-ZrC system was primarily a question of the size factor, the size difference between vanadium and zirconium being greater than the limiting value of about 15 pet. It is interesting to consider the results of combining these isomorphous carbides in groups of three and to determine the isothermal section of the pseudo-ternary diagram at, for instance, 2000°C, a temperature that will assure an equilibrium structure in a reasonable length of time. In the ternary systems where the three pairs form complete solid solution series, it is probable that the isothermal ternary section would be a single- phase field, although this is not necessarily the case. However, if one pair of carbides has a very limited solubility, then there must be a two-phase field of some extent, and it is the purpose of the present work to examine the extension of this field and to determine if it can be related to the nature of the third carbide. This condition is fulfilled if the VC-ZrC pair, which has only limited solubility, is combined with Tic, TaC, or NbC. The relative sizes of the metal atoms undoubtedly play a role in the extent of the single-phase field, and the values obtained from the pure carbides, assuming close-packing between metal and carbon atoms and a carbon atom diameter of 1.54A, are

Jan 1, 1952

By Louis A. Panek

The purpose of this paper is to present a method of designing safe and economical arch structures that are to be constructed of concrete or directly of original earth materials. The experimental data used to illustrate the design method are taken from Bucky and Fen tress,1,2 and the application of the ideas presented by them is extended by obtaining an additional set of curves from which arch structures may be designed. This design method is based upon the following principles of similitude: A scalar model made of the same material as that of the full sized structure will behave similarly to its prototype if the density of the model is increased in the same proportion as its linear scale is decreased. Let R represent the scale or model ratio, namely, the ratio of a prototype linear dimension to the corresponding model linear dimension. The effect of increased density may be obtained by rotating the model in a centrifuge at a speed such that the centrifugal held exerts on the model an accelerative force R times the accelerative force of gravity. Under these conditions; (I) model unit stresses are equal to corresponding prototype unit stresses, (2) the ratio of the prototype deformation at a given point to the model deformation at a similar point is equal to the scale ratio, R, and (3) the model and the prototype will behave similarly within and beyond the elastic limits of strain. According to the above relations, such models can be used to solve the following problems: I. The dimensions of the most economical safe arch structure for a given load. 2. The miaximum safe roof span underground for given geologic conditions. The procedure is described briefly as follows. Tests are made by rotating in a centrifuge a number of models that repiesent a variety of prototype loads and dimensions. From the experimental data, curves are plotted to show the relations between these loads and dimensions. The curves are used to solve directly the problems stated above. Structural design is based upon the working (safe) stress of the material of construction, which is established by applying a factor of safety to the experimentally determined ultimate strength of the material. In conformity with this principle, each model is gradually loaded until failure occurs. A safety factor is then applied to the results. If a safety factor of 4 is used, a given model at failure represents a safe prototype, the linear dimensions of which are equal to one-fourth the model ratio at failure times the corresponding model dimensions. The safe model ratio is computed from the following formula: Safe R =(1/4)4p2n2r/g=p2n2r/g [I] in which: n = centrifuge revolutions per second at model failure; r = radius of rotation of the model in feet; g = 32.2 ft/sec2.

Jan 1, 1949