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By P. Bolsaitis, L. Skolnick

A model of metallic solutions is postulated which explains the energy of formation of alloys on the basis of changes in electron density around solute and solvent atoms and changes in pairwise interactions between atoms. The model is based on the Wigner-Seitz cell model of metals, with the electronegativities of the metals as the parameter for the electron-attracting power of the constituent atoms. In contrast to models based on the description of cohesive energy in terms of pairwise interactions only, which require an empirical, adjustable correction parameter to the Berthe-lot relations in order to predict negative energies of formation, the electron cell model accounts for both negative and positive energies on the basis of parameters of the pure components. Calculated heats of mixing based on published parameters of the pure metals are found to compare favorably to experimental values, despite the absence of any adjustable parameters in the model. THE formulation of an "exact" quantum mechanical model for the energy of cohesion of metals reduces ultimately to the many-body problem and for a complete solution would require the knowledge of wave functions and energy levels of all the particles in the system. The case of alloys is further complicated by the fact that the potential fields around the constituent atoms are different and the matching of boundary conditions in terms of the resulting wave functions is still an unresolved mathematical problem. It appears that in spite of the numerous investigations that have led to an elucidation of many properties of the metallic state, the formulation of the Hume-Rothery rules in 1931 marks the lone accomplishment toward simple, qualitative prediction of the energy of formation of alloys. More recently Friedel'' and Arafa have utilized the modern concepts of the electronic structure in metals in combination with the Hume-Rothery rules to arrive at quantitative estimates of the energy of formation of alloys with low solute contents. The relative success of the Hume-Rothery rules and Friedel's and Arafa's studies encouraged broaching the subject of formulation of a model based on realistic physical parameters and of conceptual and mathematical simplicity that could be applied to alloys regardless of concentration. On the basis of the free-electron theory, the cohesive energy of pure metals can be expressed as a function of "valence" (number of free electrons per atom), lattice parameter (or density), and the ioniza-tion energy. In addition to the electronic contributions to cohesion, one has to consider the pairwise exchange interaction energy between neighboring ion cores and the contribution from van der Waals forces. The energy changes upon alloying are viewed as resulting primarily from a redistribution of electron densities around the ions (a simplification of the more basic concept of a change of the wave functions of the electrons in the presence of a perturbing potential field). In addition there is a change in the pairwise interactions between neighboring ions which is usually the only factor taken into account in commonly used adaptations of the quasichemical theory. The electronegativities of the metals forming the alloy are used as the measure of the electron-attracting power of the ions in the alloy and the difference in electronegativities as the driving force for changes in electron energy on alloying. The interplay of pairwise interactions and electronic forces results in positive or negative energies of formation of alloys. Results obtained for systems to which the free electron model is best applicable are in good agreement with experimental values. 1) COHESIVE ENERGY OF METALS IN TERMS OF THE ELECTRON CELL MODEL The simplest physical model of a metal is that of a lattice of positive charges immersed in a sea of uniform, negative charge distribution represented by the

Jan 1, 1969

By Max Mason

In 1923 a Western mining company was experimenting with the device of an inventor designed to locate buried ores by radio. Because the progress was slow and the results were confusing, the company began to doubt the usefulness of the method and invited me to review the whole question of the application of physics to ore detection. I was fortunate in securing the cooperation of several physicists who had worked with me during the war on the problem of submarine detection. This group has been increased and has been studying the problem of physical exploration for ores since that time. It was evident that the problem is a big one, with many angles of approach. Its general features may be set down, in rough outline, as follows: The soils, rocks and ores hidden beneath the surface differ one from another in many respects. These differences may be made to furnish a clew for the physicists working from the surface. To bring these differences into action the physicist creates some kind of an effect which penetrates into the ground and is distorted and reflected when it meets boundaries between different sorts of underground structure. In other words, he sends a message down, and the rocks and ore send back signals in reply. In picturing this process, we should not regard the ground as dense and impenetrable. The kind of messages used pass through the earth about as readily as a sound wave travels the air. If, then, the fundamental procedure is to shout down questions in the hope that an orebody will hear and answer back to us, it is clear that a large part of the expert's study must relate to the kind of questions best suited to the temperament and intelligence of orebodies. It will be easier for the ore to reply to some of our questions than to others, and it is for us to find the right questions. In certain cases, we are spared the necessity of using a messenger, because nature has already provided one. For example, we already have a terrestrial magnetic field which automatically and continually conveys messages from underneath. We also have available the earth's gravitational field which furnishes us

Jan 1, 1929

By R. M. Bricka, T. J. Olin

Heavy metals contamination is an environmental problem at Army installations engaged in firearms training and munitions production. At these facilities, weathering and corrosion of expended munitions and leaching from wastewater lagoons, landfills and burn pits have resulted in heavy metals contamination of the soil. The principal metals encountered in firing-range soils are lead, copper and zinc. Cadmium and other metals, such as antimony, that are often incorporated in the munitions are sometimes seen in lesser concentrations. Mercury is associated with various propellants and, while present in much smaller concentrations, is of concern because of its acute toxicity. Chromium is primarily associated with plating operations. The transport of metals into groundwater has been confirmed at some locations, which has required treatment of the soil and groundwater at these sites. Certain treatment processes for contaminated soil produce metals-laden extracts, which also require treatment before reuse or disposal. Ion exchange is generally quite effective for removing metals from aqueous streams. However, resins are expensive and must be regenerated, and activated carbon is generally less effective for most metals and also requires regeneration. Therefore, alternative effective and economic sorbents are needed. Twelve sorbents were screened in initial batch testing. These included activated carbon, bark, chitosan, crown ether, corn cob, xanthate, clay (kaolinite and montmorillonite), peat moss, seaweed and reagent-grade zeolite (aluminosilicate, Sigma Product No. Z3125). Of these, zeolite demonstrated the highest capacity for Pb, Cr and Cd. For this reason, zeolite was selected for further testing in batch, kinetic and column studies. Materials and methods Zeolite. The zeolite used in the second-phase batch and column studies was obtained from a natural deposit of clinoptilolite-rich rock located in South Dakota (Rocky Ford SDH) (Desborough, 1996). Large blocks of the material were crushed and sieved into the following three particle size ranges: 0.5 to 1.0, 1.0 to 4.0 and 2.0 to 4.7 mm. This material demonstrates high structural stability in acidic solutions (pH 2.5) (Desborough 1996) and has a measured surface area of 30 m2/g. The measured total cation-exchange capacity (TCEC) was approximately 10 meq/100 g. This is well below what has been indicated for commercially available zeolite, which has been reported to be about 180 to 220 meq/ 100 g. The TCEC test was repeated (Method 9081, SW 846) using sodium acetate. The test resulted in a TCEC of 54.5 meq/100 g. The difference between values obtained for this material and published values for zeolites may be attributable to the greater heterogeneity in the material used in this study, compared to commercially available materials, or to the effect of the relatively large particle sizes utilized. Batch studies. Seven batch studies were conducted using synthetic metal solutions and soil extracts (Table 1). Extract composition: The P-extract was prepared by sequential surfactant extraction of organics from a burnpit soil followed by acid extraction of metals. The pH of this solution is approximately 1.1. A number of metals and organic compounds were present in the soil. Analysis of the extract was restricted to Pb, Zn and Cu concentrations for this study. The FBH extract was produced from a firing-range soil that was oxidized with a 0.01 M CaO solution and then extracted with 0.1 M acetic acid. This was filtered through 0.5-µm Whatman No. 5 filter paper and stored at room temperature. The pH of the FBH extract was approximately 4.5. pH Control: Calcium carbonate (CaCO3) may be present in the zeolite horizon or bed. Calcium ion (Ca") is released from the exchange sites when in contact with solutions containing ions for which it is more selective, such as lead. This results in a rise in solution pH over time. Acid washing removes most of the carbonates, eliminating the need for a buffer. Batch studies were conducted using both acid-washed zeolite (AW) and unwashed zeolite (UW) for performance comparison. The UW zeolite was rinsed with distilled deionized (DDI) water to remove fine soil particles. Both materials were dried at 105°C (220°F) overnight, so that the dry mass could be determined. Column studies. Ten column studies were conducted. Because it was expected to have the best hydraulic properties, the largest particle

Jan 1, 1999

By L. R. Duncan, O. M. Wicken

Magnesium, the eighth most abundant element in the earth's crust, is found widely distributed in a variety of minerals. Among the more commercially important ones are magnesite (MgCO3), brucite (Mg[OH]2), dolomite (CaMg[C03]2), and the salts magnesium sulfate and chloride often found in natural brines. Among other commercially important magnesium-containing minerals are olivine ([MgFe]2Si04), talc (H2Mg3[Si03]4), and serpentine (H4Mg3Si2O9). These are valuable because of desirable characteristics given them by the magnesium content and its placement in the particular crystal structure. These minerals are the raw materials for a host of products including magnesium metal and several grades of magnesia or magnesia-containing materials for refractories, fluxes, fillers, insulation, cements, decolorants, fertilizers, and chemicals. Considering only those minerals valued for their magnesia or magnesium content, over 85% of the material tonnages are processed to be used as refractories. Dolomite, which is used in enormous tonnages for its physical properties in construction, has an important use as a refractory raw material in its own right and, after calcination, as a precipitant for magnesium hydroxide, which is an intermediate for the production of magnesia or magnesium metal. Magnesia from the reaction of calcined dolomite (or limestone) with seawater or magnesium-containing brines has supplanted much of the production of magnesia from mined magnesite, particularly in the United States. The best known of the minerals directly and widely exploited for magnesia content is magnesite, one of the calcite group of rhombohedral carbonates which includes calcite (CaC03), siderite (FeCO3), and rhodochrosite (MnCO3) among others. The members of this group enter into a wide range of substitutional solid solutions when the positive ions have similar radii. The radii of magnesium and iron ions are within 6% of each other; hence, magnesite and siderite form a complete series of which breunnerite (ferroan magnesite) is a well-known end member. However, the radius of calcium ion is 36% larger than that of magnesium ion, and only limited substitution exists at each end of the MgCO3-CaCO3 series. Dolomite is not a member of the calcite group, but results when calcium and magnesium ions alternate in equal number in an ordered structure among carbonate ions. The result of these relationships is that calcite and dolomite, often found intermixed with magnesite, occur commonly as identifiable crystal entities which can often be separated to a varying degree from the magnesite by various beneficiation techniques. Magnesite, when pure, contains 47.8% MgO and 52.2% CO.. The pure mineral is sometimes, but rarely, found as transparent crystals resembling calcite, but, preponderantly, magnesite contains variable amounts of the carbonates, oxides, and silicates of iron, calcium, manganese, and aluminum. Magnesite may be either crystalline or amorphous (cryptocrystalline). The crystalline form has a hardness of 3.5 to 4.0. The color may range from white to black with shades of yellow, blue, red, or gray. The color is not a fundamentally significant indicator of purity, but in a given deposit, an experienced person can often roughly grade magnesite by assessing color and crystallinity. The crystalline form of magnesite occurs in

Jan 1, 1983

By Carl Henrich

Aspen, the flourishing mountain- and mining-town of Pitkin county, Colorado, is located in the valley of the Roaring Fork, 11 miles above Glenwood springs, where that stream empties its waters into Grand river, a tributary of the Colorado. The Roaring Fork heads on the western slope of the Sawatch range near Grizzly peak, and runs in a general northwesterly direction to its junction with the Grand river. Of its numerous tributaries, Castle creek joins it just below the town of Aspen, the town being built on an extensive flat hounded on the northeast by the Roaring Fork and on the west by Castle creek. The latter heads at the junction of the Sawatch and the Elk mountains and flows northward between the two chains, until it empties into Roaring Fork. Opposite the town of Aspen, Hunter creek, coming westward from the western slope of Mount Massive, joins the Roaring Fork. About a mile north of Aspen, the bed of Hunter creek is at least 300 feet higher than that of the Roaring Fork at Aspen. Hunter creek forms thus, at its mouth, one of the best water-powers in Colorado. A portion of it is now utilized for electric lighting in Aspen, while in the near future, the whole of this magnificent natural power will be applied, through electric transmission, for hoisting, pumping and ventilating at different mines of the district. The mountain opposite the town of Aspen, on the east side of Hunter creek (which near its mouth flows southerly), is called Smuggler mountain, from the famous mine at the foot of it. On the other, or western, side of Hunter's creek (see map, Fig. I), a higher mountain rises, on the slope of which the regular dip of the Triassie or Upper Carboniferous red sandstone strata, alternating with white layers of the same rock, can be clearly seen from town. This mountain is called Red mountain, from the prevailing color of its rocky

Jan 1, 1889

By Arthur B. Cummins

Diatomite is a siliceous rock of sedimentary origin, which may vary in degree of consolidation, but which consists mainly of the fossilized remains of diatoms. These are microscopic algae of the order Bacillaria. Diatomite is a unique form of silica, there being nothing else found in nature or produced by the manufacturing arts, that has its characteristic physical structure. There are numerous sediments which contain some diatom residues, admixed with a substantial amount of other materials-clay, carbonates or silica. While these are classified as diatomaceous silts, shales, or mudstones, they are not properly diatomite, a designation which is restricted to material of such qualities that it is suitable for commercial uses. The terms diatomaceous earth and kieselgur are synonymous with diatomite. The expressions infusorial earth and tripolite are obsolete. Diatomaceous silica is a definition best used to distinguish the basic component of diatomite, that is, the substance of the silica shell itself and is the major constituent of beneficiated diatomite or processed diatomaceous products. Some highly indurated materials, such as cherty shale, porcelanite, and opaline cherts which have resulted from diagenetic changes cannot be considered as diatomite although they may have been derived therefrom. On the other hand, diatomaceous oozes or loose sediments consisting mainly of diatom residues with or without much organic matter are source materials in process of becoming diatomite. Composition and Properties Pure diatomite is composed of opaline or hydrous silica, with small amounts of associated inorganic components-alumina, iron, alkaline earths, alkali metals, and minor constituents, all of which may occur in solid solution or as an essential part of the opal complex. Crude diatomite on the other hand may contain variable amounts of organic matter and soluble salts, and the usual contaminants of sedimentary formations-particles of rockforming minerals, sand, clay, or carbonates. As occurring in nature, diatomite contains an unusual amount of free water, which may vary from 10 to 60 pct or more. Diatomite, in the dry deposits which are characteristic of most of the important world deposits, occurs as a lightweight, comparatively light colored, "chalklike" material. The apparent density (dry basis) in situ varies from 20 to 40 lb per cu ft. The structure may be either massive or finely stratified. The earth is highly porous, usually soft and easily friable. It is nonreactive with acids and may be tentatively identified by the above characterizations. Confirmation is by microscopic examination which readily reveals the nature of the material. In deposits which contain organic matter the appearance of the material is totally different. The color may vary from light tan or gray to brown, greenish or nearly black. There is frequently difficulty in distinguishing it in the field from peatlike materials, but the difference is readily apparent after calcination. Powdered diatomite or diatomite products have an apparent density (loose weight) of 5 to 16 lb per cu ft, wet densities of 10 to 30 lb per cu ft, specific gravities 1.9 to 2.35, index of refraction 1.42 to 1.48. Diatomite is essentially micro-amorphous, but does show some tendency toward orientation in structure after a cristobalite pattern. Amorphous silica has been considered as a random association of cristobalite crystallites, the size of which are only slightly larger than a unit cell.20 The prop-

Jan 1, 1960

By P. K. Hopke, A. Hubbard, K. H. Leong, J. J. Stukel, K. Nourmohammadi

INTRODUCTION In order to understand the transport and deposition of radon daughters in mine atmospheres, it is necessary to know the variation in the attachment of the daughter atoms to particles as a function of particle size, composition, number density, relative humidity, temperature, and radon concentration, the free gaseous diffusion coefficients of the daughters, and the variation in the mass transfer of the activity, both free and attached to particles, to mine surfaces as a function of particle size distribution, surface roughness of the mine walls, and the flow conditions. If all of these parameters are known in a model system, it should be possible to understand the transport and fate of the airborne radioactivity in real mines under certain well-defined flow conditions. There have been a number of recent investigations of the attachment of radon decay products to particles 1-4, but there are still a number of unanswered questions regarding the process. However, it is clear that for most real mine atmospheres, the vast majority of the activity is attached to particles. The size distributions for the activity-bearing airborne particles have been studied 5,6, and it has been found that most of the activity resides on particles with diameters in the range of 0.05 µm to 0.3 µm with an average mass median diameter between 0.1 and 0.2 µm. The behavior of the unattached radon daughter species has also been recently studied[ 7], and many of the previous problems regarding the value of the diffusion coefficient for Po-218 have been resolved. A major problem in the understanding of the airborne transport of radioactivity in mines is the lack of detailed knowledge of mass tranfer to and fluid flow over rough walls under fully developed turbulent flow conditions. This paper will report the progress on a project that is designed to obtained that information. MATHEMATICAL MODEL DEVELOPMENT Deposition of particles on smooth surfaces in turbulent flow has been extensively studied. A comprehensive review of these results has been prepared by Sehmel 8. There has not been such a comprehensive study of particle deposition on rough walls under such flow conditions. In recent years, only a single model has been proposed to explain such deposition 9,10 and in both of these papers the flow structure in the rough walled pipe was not taken fully into account. As part of the work being conducted on this project, a more complete model was outlined in a previous report [11]. The basic theory will be reviewed to provide a context for the flow measurements to be reported. The flux of particle deposited on the walls of a pipe in a turbulent flow is derived from the one dimensional form of Fick's law as given by [N = Dpdpp/dr (1) where N is the flux of particles deposited per unit area per unit time, D is the total eddy diffusivity of the particles, p is the airborne concentration of particles, and pr is the distance measured from the center of the pipe. The rate of deposition is best expressed by a deposition velocity Vp = NIP pb (2) where P b is the mean particle concentration in the sulk flow. The shear radius, V/ut and the shear velocity, u , are used to calculate a nondimensional distance, and velocity, respectively, where v is the kinematic viscosity of the fluid. The nondimensional form of equation 1 is given by Vd = DP dpp(3) V dr+ where Pp = Pp/ Ppb(4) By integrating equation 3 from the rough wall stopping distance, S , to the center of the pipe, the deposition velocity can be obtained. In order to make this calculation, it is necessary to have accurate descriptions for the particle eddy diffusivity, stopping distance, and shear velocity in order to insure that the influence of the flow structure has been properly accounted for. The shear velocity can be determined experimentally from the shear stress evaluated at the wall, Tw, and the fluid density, ut =VT w/p = ub V f/2 (5) where ub is the mean bulk axial velocity. The wall shear stress for a given pressure drop, dP/dL, and hydraulic diameter, Dh, is]

Jan 1, 1981

By J. C. Holm

ALTHOUGH the main constituents of Portland cement are the oxides of calcium, silicon, aluminum, and iron, characteristics of the cement are seriously affected by such contaminants in the raw materials as magnesium, phosphorus, sodium, potassium, sulfur, and others of lesser importance. Sources of cement raw materials comprise a long list of minerals occurring in nature in various degrees of purity. The calcareous raw materials are generally limestone of purity varying from calcite to cement rock (a low-grade limestone of natural, almost correct chemical composition), chalk, marl, seashells, coral, and coral sand. The argillaceous raw materials supplying silicon, aluminum, and iron are mainly various forms of clay and shale, to which may be added silicious sand, iron ore, bauxite, or kaolin for minor adjustment of the chemical composition. The quality of Portland cement in this country, as in most parts of the world, is controlled by rigid specifications limiting both its chemical and physical characteristics, and cement manufacturers must comply with these specifications to market their products. Brandon Raw Materials: An unusual deposit of marl, limestone, and clay occurs 12 miles east of Jackson, Miss., near the village of Brandon. The deposit is of sedimentary origin and of relatively young geological age. Layers of marl vary from putty-like consistency to such hardness that it can be cut with a knife. Interspersed between the layers of marl are bands of limestone varying from very soft to hard. the compressive strength of the hardest layers exceeding 15,000 lb per sq in. The layers of marl range in thickness from a few inches to about 25 ft. The limestone bands seldom exceed 2 to 3 ft but often occur in thinner veins in the quarry face. Above the top layer of the deposit, which may be marl or limestone, a layer of clay ranges in thickness from a few inches to more than 20 ft. Part of this clay is harvested with the raw material to supply part of the argillaceous components, but most of it is stripped as overburden and wasted. A highly silicious clay of extreme fineness, harvested from the bottom of the quarry below the marl and limestone bands, is to correct the silica content. Fig. 1 shows typical examples of the interrelation of the various materials, based on drill logs obtained during exploration of the deposit. The marls vary in moisture content in the bank from 15 to 30 pct and contain up to 70 pct -200 mesh particles and up to 40 pct —10 p particles. A large percentage of the fine fraction is within the colloidal range, making the marl extremely sticky. The limestone beds range in hardness from that of the hardest marl to a medium hard limestone and in moisture content from 2 pct to approximately 14 pct. The line of demarcation is often difficult to draw and the moisture content is possibly the best means of classification. The ratio of soft to hard material is not constant throughout the deposit, but the average is approximately 70 pct soft to 30 pct hard material. Through the years this deposit had been repeatedly explored by cement companies and rejected as unsuitable for cement manufacture, mainly because of physical characteristics. In 1950, after careful exploration of the deposit and comprehensive laboratory and pilot plant tests of the raw materials, officials of Marquette Cement Mfg. Co. of Chicago were convinced that a practical and economical method of processing the raw materials had been devised and authorized construction of a new plant that began production in December 1951. Marl and limestone, common raw materials for Portland cement, usually occur in such a manner that they can be worked separately. Their harvesting and processing normally have presented no difficult problems, as standard equipment and methods are available for handling either sticky or hard materials. No other cement plant utilizes a deposit of the nature of that at Brandon, however, and for this reason no prior art was available for design. When properly blended, the raw materials produced an excellent cement without additives. Basic problems to be solved in designing the cement plant were:

Jan 1, 1957

By Arthur Green

A GROUP of 13 cities situated in Los Angeles and Orange counties in Southern California is engaged in constructing an aqueduct to carry water from the Colorado River at a point near Parker, Arizona, to a distribution point sear Riverside, California. The aqueduct will have a total length of approximately 241 miles, and is designed to deliver 1605 cu. ft. of water per second, or a little more than one billion gallons per day. The aqueduct crosses a barren, desert waste and the project includes approximately 91 miles of 16-ft. tunnel. The large amount of tunnel driving that has been done in this country in the past few years has resulted in some remarkable developments in equipment and methods. The building of the Colorado River Aqueduct, with its 91 miles of tunnels, has called on the best engineering knowledge in the country. New and better equipment has been designed for all phases of the work, and this equipment has been coordinated and adapted to the various conditions with a high degree of efficiency. The result has been that records for tunnel driving have been set under adverse natural conditions that exceed the estimates for progress under good conditions. All of the tunnels in the main aqueduct, except the Valverde and Bernasconi at the western end, have a finished diameter, inside the concrete lining, of 16 ft. Fig. 4 shows a section of the tunnel with the concrete lining in place. Fig. 5 illustrates the finished tunnel in three typical sections. The standard tunnel grade is 3.432 ft. per mile in the 16-ft. tunnels, but the Valverde and Bernasconi tunnels have a steeper grade and a finished diameter of 15 ft. 3 in. The rough bore of the large main aqueduct tunnels averages 12.95 solid cubic yards of material per foot of advance in timbered sections and 10.76 solid cubic yards per foot in unsupported sections.

Jan 1, 1936

By Frederick C. Tompkins

A complete service system was established for the monitoring of personnel exposure to N02 based upon the use of passive dosimetry. This system is structured such that minimum effort is required of the user: manufacturing, analysis, reporting, and record keeping functions are provided by the service organization. A field evaluation program was carried out in a dieselized mine to assess the performance of two passive dosimeters, the Walden GASBADGE TM dosimeter, and a tubular dosimeter developed at New York University. Side-by-side comparisons were carried out to evaluate dosimeter suitability for monitoring in the field, and to assess relative accuracy characteristics.

Jan 1, 1976

By Donald L. Johnson

REVIEWS on the applications of optical ellipsometry to the study of polycrystalline metal surfaces and oxidation-corrosion processes have been presented by Kruger and Hayfield, and white.' In view of the ability of this method to measure differences in film thicknesses to below 10A, ellipsometry was used to study nitrogen chromium surface reactions during the early stages of growth. Chromium specimens in the form of a vapor-deposited film on glass substrate were exposed to purified nitrogen for selected time increments at 700°F. This temperature was selected because it gave the best combination of exposure time and thickness change. Ellipsometer readings were taken immediately after exposure to determine polarizer and analyzer angles using monochromatic light at 5000A.2 After each set of readings was obtained, the specimens were exposed for an additional increment of time in nitrogen and a new set of readings taken. Film thickness was computed from LUCy's3 equation for nonabsorbing thin films. In Lucy's derivation, two equations for computing thickness were obtained. Peterson and Bashara4 have discussed the validity for using one of these equations when an independent value of the refractive index is used. The film was assumed to be Cr2N (Ref. 5) and was determined to be optically isotropic. Optical isotropy was determined by rotating the films about the surface normal and noting that the azimuth and phase difference did not change. Since Cr2N is reported to be hexagonal, it is assumed that optical isotropy results from randomly oriented grains of very small size. The thickness was computed using refractive indexes varying from 1.6 to 2.0. The maximum variation in computed thickness over this range for a given exposure was 20 pct. The data reported are based on a refractive index of 1.8. Reference readings on the metal surface were taken just prior to nitrogen exposure. No attempt was made to deoxidize or denitride the metal surface after vapor deposition, although specimens were observed to gain approximately 2A per day in air at room temperature. Twelve experimental exposures were made on a single sample over a total accumulative time of 132 min. Additional experiments over longer time intervals were made to determine the effect of heat up and cool down during and after exposure. As a result of these experiments, the thickness computed for each exposure was increased by 4A. Time profiles based on the linear law are similar to the oxidation profiles for many metals.' The rate of accumulation of the nitride film is rapid at first and slows down as the film thickness increases. The parabolic law x2 =k1t +k2 [11 gives a straight line in Fig. 1; therefore, it is concluded that the kinetic behavior is parabolic. Sey-bolt and Haman5 reported similar results for CrlN on chromium at 1000°C although the order of the thickness was much greater (10-3 cm). Analysis of thickness data based on other values of refractive index shows that the curves are shifted vertically but retain the same shape. According to Mott,7 it is expected that for thin films k2 is zero in Eq. [I]. Since the plot in Fig. 1 is linear through the origin, k2 is zero and the parabolic nature of the film growth is further indicated. The parabolic rate constant, calculated from the slope in Fig. 1, is 4.4 x 10-16 sq cm per sec. The corresponding work (+) required to bring an electron from the metal into the oxide is estimated to be 1.5 ev.7 The author thanks professor N. M. Bashara and D. W. Peterson, Electrical Materials Laboratory, University of Nebraska, for making the ellipsometer available and providing technical assistance. The Electrical Materials Laboratory is supported by the office of Naval Research, NONR 3718 (01). This work was partially supported by the Engineering Experiment Station and the Mechanical Engineering Department, University of Nebraska.

Jan 1, 1967

By R. A. Flinn, R. D. Pehlke, D. R. Glass, P. O. Hays

Knowledge of the depth of penetralion of an oxygen jet into the bath of the oxygen converter and of the correlation of penetration with driuing pressuve, lance heighl, and nozzle throat area is vital to the understanding of converter operation. If the penetration is too shallow, then severe and hazardous slopping takes place. On the other hand, if the jel penetrates entirely Lhvough lhe bath for an apprcciublc period of time, bottom damage occurs. In addilion to measurement of the penetralion of the jel, knou~ledge of the circulatory movement in the bath is also of interest in order to evaluale various theories oj-concerter operating behavior which have been published. In this investigation, experimental converters were buill of IOU- , 300-, and 4000-lb capacity. Four independent methods were used to determine penelralion: the onset of bottom marking, a nitrogen bubbler probe, observation througlt an optical syslew built into the oxygen lance, and direcl viewing of the jet issuing from the bottom of the vessel. Good correlation zuas obtained, and empirical relalions for pvedicling perletration were found. These relations were conjzrmed by bottom marking tests in 55- and 110-ton vessels. Within the operaling conditions employed in these tests, the depth to which a single oxygen jet penetrated zuas found lo vary according to the relatiorl ThE technical literature is replete with data concerning the successful use of the basic oxygen furnace or converter in steelmaking. Experimental data are lacking, however, on the vital factors of the depth of penetration of the jet into the bath and the induced circulation. Commercial operating conditions usually have been the result of cut and try experiments in lance manipulation until satisfactory results were obtained. There have been, however, two hotly argued opposing theories concerning desirable depth of penetration and these are exemplified by the Schwarz and Miles patents1,2 on one hand and the Suess patent3 on the other. The Schwarz patent teaches that the jet, issuing from the nozzle at supersonic speed, penetrates deeply "so that the reactions between the iron and the oxygen and between the oxygen and the rest of the smelting components take place in the center of the bath". Specific operating suggestions are given by Miles.2 By contrast, the Suess patent calls for surface Circulalion was investigated by lour methods: by direct observation in 200-lb open baths, by the use of graphite rudders in the 300- and 4000-lb converlers, by direct observalion through an oplical system in the lance, and by various models al room temperature. All were in excellent agreement and indicated that the motion of the bath ulas up at the center, radially outluavd at the surface, and down at the sides. Experi-ments in small and in commercial vessels indicate that it is essential to operate with a jet penetration of approximately 50 pct of the bath depth. Surface blowing results in low oxygen eficienty and in hazardous conditions which may render the process inopeuable. RejYactory dartzage al the bottom of the vessel is only encountered when the jet penetrates to the bottom, and this can be avoided by properly applying the penetration formula. The application of this en/pirical formula in commercial peraations is best when limited to combinations of lance size, pressure, and height which are typically encounteved in the use of a single-hole lance. blowing so that "...the oxygen jet does not penetrate deeply into the molten metal bath and is confined to an impingement area at the central portion of the bath surface". These references are given merely to illustrate the basic differences between the two schools of thought and to point out the need for measurement of penetration for the sake of the operator. For example, it is shown later that inefficient and even dangerous conditions can arise if improper blowing conditions are used. Differences are also evident between the two schools of thought as to the mixing, circulation, and agitation which is to be accomplished by the jet. The Schwarz patent states that "surface contact is not sufficient in most cases to bring about quick reaction, the same as the blowing of the gas over the bath surface or the mere blowing of the gas onto the bath surface". The patent goes on to call for active mixing. In contrast the claims of the Suess patent call for "discharging a stream of oxygen ... to an extent to avoid material agitation of the bath by the oxygen stream". In this patent the circulation is said to be downward in the center and up at the sides of the vessel. A number of investigators4-12 have explored penetration and circulation in transparent models. In general, it is agreed in these tests that the circulation is upward at the center (along the sides of the jet cavity),

Jan 1, 1968

T.B.King (Depaytment of Metallurgy, Massachusetts Institute of Technology)— A valuable contribution of the authors is in the factual information which they have been able to gather; this type of information is quite difficult to obtain. In many respects, however, it would have been better if they had not subsequently embarked on a discussion of the chemistry of the converter process. It seems inconceivable that the authors do not refer to the papers of Schuhmann and his associates14 which have set the thermodynamic foundation for the whole copper smelting operation. In addition, a very useful review on the physical chemistry of copper smelting by Ruddle 5 appeared as long ago as 1953. An examination of this literature would have convinced the authors that there is no cause to be surprised at a correlation between the magnetic content and the silica content of converter slags, though they rightly point out that one should distinguish between the total magnetite content of the slag and the amount of magnetite which may be considered to be in solution. It is not true that the lowest melting converter slag is that corresponding to the eutectic between ferrous oxide and silica. The simplest slag system which can be considered is a three-component system, since both ferric and ferrous iron are present. As Schuhmann, Powell, and Michal have shown, there are lower melting compositions than this eutectic in the ternary system. The most unfortunate impression given by this paper is that the driving force for chemical reaction is determined by the heat of reaction: of course the entropy change must be taken into account. It would have been more correct to list, in Table VI, values for free energies of formation. Nor can it be said that the data in Table VI represent the "best available data." They do not corregtond with any of the recent, acknowledged sources. F. E. Lathe and L. Hodnett(author's reply)— We are pleased that Dr. King finds the factual information in our uawer of some interest. Dr. King suggests that it would have been better if our analysis and discussion of the data had been omitted, largely because our list of references is so. incomplete. If he will carefully read our introduction, he will see that the questionnaire was sent out in the hope of obtaining data which would throw light on certain questions relating to the use of converter refractories. We did not attempt (nor would the AIME have published!) a complete review of the literature on copper converting, as Dr. King has apparently assumed, nor indeed a complete analysis of the data submitted, but tried only to find a sound basis for the choice of refractories, taking into consideration common variations in converter practice. We hope our paper indicates that, by raising the silica content of the converter slag and operating at a higher temperature, the normal circulating load of magnetite can be greatly reduced, and the whole reverberatory-converter operation improved to a major degree, with resultant important savings. Under such operating conditions, chrome-magnesite brick may be expected to stand up better than those of straight magnesite. Regardless of the choice as between these brick types, however, we find the cost of converter refractories to be so low in comparison with other converter costs as to justify operation under the more severe conditions suggested. Valuable as are the papers by Schuhmann and associates and the book by Ruddle, we make no apology for omitting reference to them, nor for using heats of reaction without mention of entropy changes or free energies of formation. Our primary object was to interest the practicing copper metallurgist, with whose language we may claim to be fairly familiar; we think it would have been unwise to include the highly theoretical phases of the subject which Dr. King suggests. The interest shown in our preliminary paper presented at the New York meeting in 1956, and the trends in practice whtat we have observed since that time, suggest that we did not wholly miss the target. In conclusion, we sincerely hope that Professors King and Schuhmann will independently review the data obtained in our questionnaire and submit a paper giving their own recommendations as to the choice of refractories and the particular converter operating conditions which will result in the lowest overall cost of copper smelting and converting.

Jan 1, 1960

By Donald W. Gentry

Introduction The mining industry is perhaps best characterized by the numerous and abnormally high risks associated with the business of mining and by its most basic assets - ore deposits, people and technology. At the most fundamental level, it is the quality and effective utilization of these basic assets that determine a mining company's ability to compete efficiently in the international market place. The gold industry has received much attention in recent years and especially in recent months, for good reason. This commodity serves as an excellent platform for the subsequent discussion of these three basic assets and their role in mining's future. Facets of the gold industry The fate of this noble metal in recent times illustrates some of the various risks associated with the mining industry and the importance of high-quality assets, whether they be ore deposits, people or technologies. The following comments pertaining to the gold industry help place proper focus on subsequent discussions. All monetary amounts given are in US dollars. Throughout 1997, falling gold prices broke record after record: first hitting three-year lows, then a 12-year low in July and finally an 18-year low at year's end. From Jan. 1 through Dec. 31, 1997, the price of gold fell by more than $2.57/g ($80/oz), or some 22%. The decline in gold-mining profitability and stock prices was even more dramatic. At the beginning of 1997, the 20 largest gold producers in North America had a market capitalization of approximately $44.5 billion. At year's end, this market cap had fallen to $26.2 billion, a reduction of 41%. The total market cap of all the world's gold companies fell from $71 billion to $46 billion, a 35% drop (Serwer, 1998). Analyses suggest that, at a spot gold price of $9.65/g ($300/oz), only one, or possibly two, North American gold-producing companies can make money when break-even or "total costs of production" are considered. While strong hedge positions mitigate this situation in the short term, clearly, this is an industry in desperate straits. For example, write-downs for North American producers in 1997 were approximately $2.5 billion. Speculative short positions in 1997 were near historical record highs and generally exceeded long positions by factors of 9:1 or 10:1. Much of this is driven by some US commercial banks, hedge fund managers and commodity speculators who can significantly move gold prices sharply over short periods of time by selling gold they do not own in the expectation they can buy it back at a lower price before they have to deliver. These signifcant short positions are likely to continue as long as central banks are willing to sell or loan gold to financial institutions that in turn make the gold available to speculators who hope to capitalize on price fluctuations. The Far East accounts for approximately 26% of the annual demand for gold. Including India, the region accounts for 43% of total demand. More than 85% of the physical demand for gold is for investment jewelry in Asia and the Middle East. This demand is extraordinarily price sensitive. The fairly recent turmoil in Asian markets and economies, combined with currency devaluations throughout the region, have made gold more expensive (30% to 50% in local currencies) for those peoples most likely to treat gold as a safe investment haven. Higher interest rates also have reduced the amount of money they have to spend on consumer goods such as jewelry. All of these recent Asian events are deflationary in nature. Deflation, if coincident with rising unemployment, could result in significant dishoarding of gold. There is one key fact to remember when analyzing

Jan 1, 1999

By Erick F. Weiland, John W. Lindemann

Introduction Minerals exploration is one step in the mining industry's task of providing raw materials to basic industries. The industry's provision of raw materials involves identifying and evaluating resources, converting them to reserves, and intelligent, economic exploitation of these reserves. The mineral process focuses on identification and evaluation. Reserves are ore bodies and ore bodies are, by definition, wasting assets. Therefore, if an adequate provision of raw materials to basic industry is to continue, these wasting assets (ore bodies) must be replaced with new or different reserves as current reserves are depleted. Minerals exploration is a geologic problem and is fundamentally deductive, flowing from the general to the specific. Past exploration methods and philosophy have amply supplied the resources to meet the demands of an industrial society. During the past decade, however, the framework where mineral resources were identified, defined, and evaluated has changed. Mineral explorationists no longer can rely solely on the successful past methods to provide the necessary resources for our complex society. Productive explorationists must effectively and efficiently use tools and procedures that will maximize exploration efforts. Past tools need not be abandoned, but should be critically reviewed and revised in light of current scientific knowledge and technical advances. Future explorationists will view their craft not as a single discipline, but as a thoughtful integration of geophysics, geochemistry, and geostatistics for solving interrelated problems. This integration of the geosciences will lead to successful mineral exploration. Not only will the productive explorationist generate new information, he will master the use of existing data for identifying and evaluating a mineral resource. The mineral exploration process consists of incentives, ideas, finance, area, staff, time, and luck. The exploration process that stems from the interaction of these elements has three stages, each bound by a major decision point. They are selection, reconnaissance, and definition. Subsequent evaluation and exploitation phases are considered more the function of mining engineers than the exploration geologist. Mineral exploration endeavors that have been productive have three attributes fundamental to success: commitment, competence, and persistence. Commitment Commitment is believing that exploring for mineral resources is worth performing. While the mining industry is the focus of this commitment, government and society must also be committed to the concept of mineral reserve identification through exploration activity. Government demonstrates its commitment by providing access to land for exploration and, if it is successful, exploitation can take place. Realistic legislation relating to taxation, land use, reclamation, and environmental constraints is indicative of government commitment to intelligent resource use. The public must come to terms with mineral resource evaluation and extraction. Without some form of commitment from the public, availability of mineral resources vital to basic industry will be largely in the control of a foreign and potentially unstable mining industry. Commitment to a mineral resource identification-evaluation-extraction system must be shared equally by government, society, and the minerals industry. The scope and direction of this commitment varies, with the industry's commitment to explore for mineral resources being the most apparent. Industry commitment is the belief at all levels of exploration (from senior corporate executives to individual field and support staff) that exploration is worth performing, that exploration goals can be met, and that their particular organization is the best and the only group that can successfully accomplish the project. Commitment can be considered at three

Jan 11, 1983

By Hjalmar W. Johnson

It has long been accepted that blastfurnace practice varies to some degree with the coke used. While the qualities desirablc in iron have been known for some time, the qualities in coke that produce such iron have not been established. There are no objective standards for blast-furnace coke, which is usually described in general terms, as good or bad. Many experienced operators believe that coke cannot be measured objectively except by using it in the furnace, noting the result, and labeling the coke according to furnace operations. This is admittedly unscientific, and besides is useless for the two main purposes for which a measure of coke quality is needed: (I) to produce the best possible coke from the coals and equipment on hand; (2) to test new coals and determine their value for blast-furnace coke. In seeking such an objective measure, much work has been done on tumbler tests, shatter tests, sizes of coke, porosity, specific gravity, reactivity or combustibility and other tests, but as yet very little has been published in which conclusive correlations have been established between such objective measures and furnace operation. In our study of the problem during the past 8 years we have developed no new measures of coke quality, but we have collected data that are presented here in the hope that they may assist in further work, so that at some future time there may be developed such positive measures. The purpose of this paper is to show that there are variations in coke and that such variations do influence the operation of blast furnaces. At the same time we must remember that there are variations in blastfurnace operation and it may be the blast furnace that is at fault. This correlation of coke properties with blast-furnace operation will be worked out in the following steps: . Discussion of a period when a change in the coke resulted in an increase in efficiency on one furnace and a decrease in efficiency on another. 2. Adaptation of the inefficient furnace to the available coke so that normal efficiency was restored. 3. The use of radial distribution: a discussion of the effect of size of ore layer in adapting blast-furnace operation to the coke. 4. An example of a change in size of coke and the detrimental influence on the pro duction of one furnace. 5. An example of a change in size of coke, together with manufacturing data, to show why it changed, the conclusion being that coke is a product with an optimum value. 6. Illustration of the fact that coke has different optimum values on two furnaces, with discussion on adaptation of operation so the optimum values will be the same. 7. Limitations of the use of screen tests as an objective measure of coke quality. 8. Importance of uniformity in coke. Functions of Coke and Qualities Required to Perform These Functions Coke has three important functions in a blast furnace: (I) to furnish most of the

Jan 1, 1942

By Hjalmar W. Johnson

It has long been accepted that blastfurnace practice varies to some degree with the coke used. While the qualities desirablc in iron have been known for some time, the qualities in coke that produce such iron have not been established. There are no objective standards for blast-furnace coke, which is usually described in general terms, as good or bad. Many experienced operators believe that coke cannot be measured objectively except by using it in the furnace, noting the result, and labeling the coke according to furnace operations. This is admittedly unscientific, and besides is useless for the two main purposes for which a measure of coke quality is needed: (I) to produce the best possible coke from the coals and equipment on hand; (2) to test new coals and determine their value for blast-furnace coke. In seeking such an objective measure, much work has been done on tumbler tests, shatter tests, sizes of coke, porosity, specific gravity, reactivity or combustibility and other tests, but as yet very little has been published in which conclusive correlations have been established between such objective measures and furnace operation. In our study of the problem during the past 8 years we have developed no new measures of coke quality, but we have collected data that are presented here in the hope that they may assist in further work, so that at some future time there may be developed such positive measures. The purpose of this paper is to show that there are variations in coke and that such variations do influence the operation of blast furnaces. At the same time we must remember that there are variations in blastfurnace operation and it may be the blast furnace that is at fault. This correlation of coke properties with blast-furnace operation will be worked out in the following steps: . Discussion of a period when a change in the coke resulted in an increase in efficiency on one furnace and a decrease in efficiency on another. 2. Adaptation of the inefficient furnace to the available coke so that normal efficiency was restored. 3. The use of radial distribution: a discussion of the effect of size of ore layer in adapting blast-furnace operation to the coke. 4. An example of a change in size of coke and the detrimental influence on the pro duction of one furnace. 5. An example of a change in size of coke, together with manufacturing data, to show why it changed, the conclusion being that coke is a product with an optimum value. 6. Illustration of the fact that coke has different optimum values on two furnaces, with discussion on adaptation of operation so the optimum values will be the same. 7. Limitations of the use of screen tests as an objective measure of coke quality. 8. Importance of uniformity in coke. Functions of Coke and Qualities Required to Perform These Functions Coke has three important functions in a blast furnace: (I) to furnish most of the

Jan 1, 1942

By J. W. Snavely

A practical mathematical treatment is presented for the determination and control of conveyor belt acceleration, particularly for conditions of starting where vertical curves are involved. A typical sample problem is analyzed, with required calculations, to clarify the procedure. THE part that acceleration plays in starting a belt conveyor and its effect on belt conveyor design are well understood in a general way. Its practical importance is easily overlooked, however, and under some conditions, it is absolutely necessary to give the problem of acceleration detailed study. Most handbooks on conveyor belting design adequately present basic data for the determination of acceleration values. This paper will only attempt to present practical thinking and a convenient method of treatment of acceleration in belt conveyor design. Mathematical Analysis In working out the various problems of conveyor belt acceleration, the starting point, as presented by the handbooks, is the familiar formula of "force of acceleration is equal to the mass times acceleration." By expressing these fundamental quantities in terms of belt conveyor design, it is possible to arrive at the unsuspected conclusion that the acceleration time for horizontal belt conveyors is independent of the load, and instead, dependent upon the belt speed, the type of drive arrangement and drive pulley, and the idler coefficient of friction. The mathematics leading to this conclusion are shown in Table I, which has been prepared to show this derivation. While at first the conclusion just given may not seem to be reasonable, further reflection indicates that obviously the type of drive pulley and the type of drive do affect materially the tension in the conveyor belt, and thus, as clearly shown, the time of acceleration is dependent upon the factors mentioned. Inasmuch as all of the factors except time are predetermined by the belt conveyor design, it becomes relatively easy to establish the accelerating time and to reduce further this time determination to a simple graph from which the time in seconds can be read directly. Such a graph is given in Fig. 1. The table appearing on Fig. 1 should be explained further. For a given belt speed, the time of acceleration can be expressed as a percentage of the belt speed. The time of acceleration is also dependent on the drive arrangement, and changes in the drive arrangement consequently change the time of acceleration. It further follows that for a given belt speed, the time expressed as a percentage of that belt speed also changes with the type of drive. Obviously then, it becomes possible to graph the percentage of speed for .each type of drive against the belt speed and accelerating time, after which, for a given belt speed and type of drive, the time can be read directly in seconds. Two constants were established for Fig. 1, the first one being the limiting of the maximum acceleration tension to 35 pct of the full load operating tension in the belt. The purpose of this is to limit the total tension imposed upon the belt during the acceleration period to 135 pct of the full load operating tension, 'which is the amount required to start or breakaway the fully loaded belt conveyor from rest. The other constant is the friction factor used for the idler equipment, which has been established as 0.022. For installations where it is necessary to establish the values of acceleration, invariably high grade idler equipment is used, and it has been established from field experience that 0.022 for the idler friction factor is amply conservative. The use of this friction factor for idlers must be tempered with judgment, of course, for occasions will arise where more power than indicated is required to start, even with the very best of equipment, such as low temperature operations that tend to congeal the grease in the bearings and thus produce additional friction drag. An inspection of the table in Fig. 1 affords a convenient rule of thumb method for determining the acceleration time, which conveniently can be 5 pct of the belt speed in seconds. The 5 pct of belt speed figure is close to the average for most types of drives. In using Fig. 1 it must be emphasized that it applies accurately to horizontal belt conveyors only.

Jan 1, 1953

By J. W. Snavely

THE part that acceleration plays in starting a belt conveyor and its effect on belt conveyor design are well understood in a general way. Its practical importance is easily overlooked, however, and under some conditions, it is absolutely necessary to give the problem of acceleration detailed study. Most handbooks on conveyor belting design adequately present basic data for the determination of acceleration values. This paper will only attempt to present practical thinking and a convenient method of treatment of acceleration in belt conveyor design. Mathematical Analysis In working out the various problems of conveyor belt acceleration, the starting point, as presented by the handbooks, is the familiar formula of "force of acceleration is equal to the mass times acceleration." By expressing these fundamental quantities in terms of belt conveyor design, it is possible to arrive at the unsuspected conclusion that the acceleration time for horizontal belt conveyors is independent of the load, and instead, dependent upon the belt speed, the type of drive arrangement and drive pulley, and the idler coefficient of friction. The mathematics leading to this conclusion are shown in Table I, which has been prepared to show, this derivation. While at first the conclusion just given may not seem to be reasonable, further reflection indicates that obviously the type of drive pulley and the type of drive do affect materially the tension in the conveyor belt, and thus, as clearly shown, the time of acceleration is dependent upon the factors mentioned. Inasmuch as all of the factors except time are predetermined by the belt conveyor design, it becomes relatively easy to establish the accelerating time and to reduce further this time determination to a simple graph from which the time in seconds can be read directly. Such a graph is given in Fig. 1. The table appearing on Fig. 1 should be explained further. For a given belt speed, the time of acceleration can be expressed as a percentage of the belt speed. The time of acceleration is also dependent on the drive arrangement, and changes in the drive arrangement consequently change the time of acceleration. It further follows that for a given belt speed, the time expressed as a percentage of that belt speed also changes with the type of drive. Obviously then, it becomes possible to graph the percentage of speed for each type of drive against the belt speed and accelerating time, after which, for a given belt speed and type of drive, the time can be read directly in seconds. Two constants were established for Fig. 1, the first one being the limiting of the maximum acceleration tension to 35 pct of the full load operating tension in the belt. The purpose of this is to limit the total tension imposed upon the belt during the acceleration period to 135 pct of the full load operating tension, which is the amount required to start or breakaway the fully loaded belt conveyor from rest. The other constant is the friction factor used for the idler equipment, which has been established as 0.022. For installations where it is necessary to establish the values of acceleration, invariably high grade idler equipment is used, and it has been established from. field experience that 0.022 for the idler friction factor is amply conservative. The use of this friction factor for idlers must be tempered with judgment, of course, for occasions will arise where more power than indicated is required to start, even with the very best of equipment, such as low temperature operations that tend to congeal the grease in the bearings and thus produce additional friction drag. An inspection of the table in Fig. I affords a convenient rule of thumb method for determining the acceleration time, which conveniently can be 5 pct of the belt speed in seconds. The 5 pct of belt speed figure is close to the average for most types of drives. In using Fig. 1 it must be emphasized that it applies accurately to horizontal belt conveyors only.

Jan 1, 1952

By J. W. Snavely

A practical mathematical treatment is presented for the determination and control of conveyor belt acceleration, particularly for conditions of starting where vertical curves are involved. A typical sample problem is analyzed, with required calculations, to clarify the procedure. THE part that acceleration plays in starting a belt conveyor and its effect on belt conveyor design are well understood in a general way. Its practical importance is easily overlooked, however, and under some conditions, it is absolutely necessary to give the problem of acceleration detailed study. Most handbooks on conveyor belting design adequately present basic data for the determination of acceleration values. This paper will only attempt to present practical thinking and a convenient method of treatment of acceleration in belt conveyor design. Mathematical Analysis In working out the various problems of conveyor belt acceleration, the starting point, as presented by the handbooks, is the familiar formula of "force of acceleration is equal to the mass times acceleration." By expressing these fundamental quantities in terms of belt conveyor design, it is possible to arrive at the unsuspected conclusion that the acceleration time for horizontal belt conveyors is independent of the load, and instead, dependent upon the belt speed, the type of drive arrangement and drive pulley, and the idler coefficient of friction. The mathematics leading to this conclusion are shown in Table I, which has been prepared to show this derivation. While at first the conclusion just given may not seem to be reasonable, further reflection indicates that obviously the type of drive pulley and the type of drive do affect materially the tension in the conveyor belt, and thus, as clearly shown, the time of acceleration is dependent upon the factors mentioned. Inasmuch as all of the factors except time are predetermined by the belt conveyor design, it becomes relatively easy to establish the accelerating time and to reduce further this time determination to a simple graph from which the time in seconds can be read directly. Such a graph is given in Fig. 1. The table appearing on Fig. 1 should be explained further. For a given belt speed, the time of acceleration can be expressed as a percentage of the belt speed. The time of acceleration is also dependent on the drive arrangement, and changes in the drive arrangement consequently change the time of acceleration. It further follows that for a given belt speed, the time expressed as a percentage of that belt speed also changes with the type of drive. Obviously then, it becomes possible to graph the percentage of speed for .each type of drive against the belt speed and accelerating time, after which, for a given belt speed and type of drive, the time can be read directly in seconds. Two constants were established for Fig. 1, the first one being the limiting of the maximum acceleration tension to 35 pct of the full load operating tension in the belt. The purpose of this is to limit the total tension imposed upon the belt during the acceleration period to 135 pct of the full load operating tension, 'which is the amount required to start or breakaway the fully loaded belt conveyor from rest. The other constant is the friction factor used for the idler equipment, which has been established as 0.022. For installations where it is necessary to establish the values of acceleration, invariably high grade idler equipment is used, and it has been established from field experience that 0.022 for the idler friction factor is amply conservative. The use of this friction factor for idlers must be tempered with judgment, of course, for occasions will arise where more power than indicated is required to start, even with the very best of equipment, such as low temperature operations that tend to congeal the grease in the bearings and thus produce additional friction drag. An inspection of the table in Fig. 1 affords a convenient rule of thumb method for determining the acceleration time, which conveniently can be 5 pct of the belt speed in seconds. The 5 pct of belt speed figure is close to the average for most types of drives. In using Fig. 1 it must be emphasized that it applies accurately to horizontal belt conveyors only.

Jan 1, 1953