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By M Biesinger, R St C Smart

Diagnosis of the surface chemical factors playing a part in flotation separation of a value sulfide phase requires measurement of the hydrophobic and hydrophilic species that are statistically different between the concentrate and tail streams. Statistical methods, based on the monolayer-sensitive time of flight secondary ion mass spectrometry (ToF-SIMS) technique, have been developed towards this ultimate aim by measuring hydrophobic species (collector ions, dimers and metal complexes, polysulfides) as well as hydrophobic metal ions, precipitates and added depressant species. Reliable identification of specific mineral particles is central to this statistical analysis. A chalcopyrite/pyrite/ sphalerite mineral mixture conditioned at pH 9 for 20 minutes to study transfer of Cu from chalcopyrite via solution to the other two mineral surfaces, since this mechanism can be responsible for their inadvertent flotation in copper recovery, showed no statistical difference in the copper intensities on pyrite and sphalerite (selected from Fe and Zn images) after this conditioning. Principal component analysis (PCA) identifies combinations of factors strongly correlated (positively or negatively) in images or spectra from sets of data. In images, PCA selects these correlations from the mass spectra recorded at each of 256 ¦ 256 pixels in a selected area of particles. In the image mode, PCA has proved to be a much better method of selecting particles by mineral phase with clearer definition of particle boundaries due to multi-variable recognition. It has clearly separated a statistical difference in copper intensities between the sphalerite and pyrite phases. The PCA method has been applied to concentrate and tails samples collected from the Inco Matte Concentrator demonstrating extensive CuOH and NiOH transfer between the chalcocite (Cc) and heazlewoodite (Hz) minerals. Statistical differences illustrate the important discriminating depressant action of NiOH in flotation despite the activation of Hz by Cu transfer. The adsorption of the collector at specifically-identified Cu sites has been elucidated by the study. Importantly, the statistical analysis has been able to confirm some mechanisms and deny others proposed to control recovery and selectivity giving more focus on the control factors.

Jan 1, 2005

By L. Bloomquist, C. Arnoldi

"This paper describes how Automated Mining Systems (AMS) is evolving the state-of the- art in guidance systems for autonomous underground vehicles. The techniques, tradeoffs, and lessons learned from these systems are described, including the safety regime that has been implemented.First generation autonomous guidance systems for underground vehicles relied on infrastructure for the vehicle to follow. However, there are additional costs associated with that approach.The current generation uses a pair of laser range finders as its only guidance sensors. This system uses a minimum of infrastructure, in the form of a redundant system of location referencing. Advanced steering and drive control algorithms are incorporated into this generation of system.The next generation of infrastructureless guidance systems will be based on a 3D vision sensor, which was originally developed for autonomous Mars rovers and is being adapted for underground mining use. Results of early underground field trials are presented, along with a description of this emerging technology."

Jan 1, 2004

By Minghao Hu, Hongbo Zhao, Jun Wang, Wenqing Qin, Rui Liao, Central South University

"In the present work, X-ray diffraction (XRD) analysis, X-ray photoelectron spectroscopy (XPS) analysis and electrochemical analysis were carried out to investigate the intermediate species and electrochemical dissolution process of chalcopyrite in the presence of sulfur and iron oxidizing microorganisms. For bioleaching of chalcopyrite by the sulfur oxidizing microorganism Acidithiobacillus caldus, the redox potential was always lower than the appropriate value and chalcopyrite was mainly directly oxidized to polysulfide (Sn 2-), thus resulting in low copper extraction. As for bioleaching of chalcopyrite by the iron oxidizing microorganism Leptospirillum ferriphilum, chalcopyrite was mainly directly oxidized to polysulfide at the initial stage where redox potential was lower than the appropriate value and resulted in low dissolution rate. At the middle stage where redox potential was appropriate (about 350–480 mV vs. Ag/AgCl), chalcopyrite was mainly transformed to intermediate species of Cu2S rather than polysulfide, thus resulting in high dissolution rate. At the later stage where redox potential was higher than the appropriate value, chalcopyrite was mainly directly oxidized to polysulfide which caused the later passivation of chalcopyrite. Finally, a model of electrochemical dissolution process of chalcopyrite in the presence of sulfur and iron oxidizing microorganisms was provided.INTRODUCTIONBiohydrometallurgy is considered as one promising mineral processing technique in processing low grade ores due to the advantages of simplicity, low cost and eco-friendly. Chalcopyrite (CuFeS2) is the most abundant copper-bearing resource, accounting for appropriately 70% of the known reserves in the world, while is recalcitrant to bio-hydrometallurgy mainly due to the coated passivation layer (Klauber, 2008; Li, Kawashima, Li, Chandra, & Gerson, 2013). However, the detailed dissolution and passivation mechanisms of chalcopyrite bioleaching are still uncertain. The microorganisms assisting chalcopyrite dissolution can be mainly classified into three types, including mesophilic microorganisms (e.g., Acidithiobacillus ferrooxidans, Acidithiobacillus thiooxidans and Leptospirillum ferrooxidans), moderately thermophilic microorganisms (e.g., Acidithiobacillus caldus, Sulfobacillus thermosulfidooxidans and Leptospirillum ferriphilum), and extremely thermophilic microorganisms (e.g., Metallosphaera sedula, Sulfolobus sp., Acidianus sp., and Sulfurcoccus mirabilis). Moderately thermophilic microorganisms have a better prospect in the future industrial application of chalcopyrite bio-hydrometallurgy (Olson, Brierley, & Brierley, 2003; Rohwerder, Gehrke, Kinzler, & Sand, 2003). Hence, investigating the detailed dissolution and passivation mechanisms of chalcopyrite bioleaching by moderately thermophilic microorganisms is of important significance, which will provide essential information for promoting chalcopyrite bioleaching by moderately thermophilic microorganisms in laboratory or industrial plant."

Jan 1, 2016

The paper describes the reasons for the development and for the selection of systems which were finally adopted; further estima- tion and design engineering problems, as well as experience with large screens in operation. Advantages, disadvantages and the final li- mits of screen dimensions are indicated.

Jan 1, 1984

By R. V. Ramani, George W. Luxbacher

Computer simulation of mine ventilation systems, after a slow start in the early sixties, is gaining increasing acceptance for planning, design, and evaluation purposes. Numerous programs are readily available from government, university, consulting, and industry sources. The computer adage "garbage in, garbage out" is as applicable in ventilation engineering as in any other application of computers, and has been responsible for the questionable results obtained in some instances. The source of input data for a ventilation simulation is most often a pressure-quantity survey of the mine, or, in the case of a new mine, information derived from a survey of an existing mine which has conditions similar to those expected in the new mine. The crucial step is to generate simulation input data from the ventilation survey. Problems such as quantities that do not balance, pressure gradients opposite to measured air flow, differences in the pressure datum in a multi-shaft mine, modeling of leakage, and deviations in flow from the square law (H=RQ2) are frequently encountered and must be resolved. The purpose of this paper is to discuss these aspects and to propose procedures which can lead to input data for valid simulations of mine ventilation systems.

Jan 1, 1982

By Tim Neil, O&apos

Copper price rebounds A worldwide scramble for diminishing supplies of copper has pushed the red metal's price to more than $2.20/kg ($1 per lb), the highest level since 1980. The first nine months of 1987, world copper production was down 1% from a year ago, while consumption rose 7%. Demand has been fueled by economic strength in several countries, particularly Japan, South Korea, and Taiwan. The price has also been helped by interest rate declines that have prompted manufacturers to build up inventories. In addition, China is expected to be a major buyer in 1988 as it stocks up for its five-year industrialization plan. There appears to be no sign of any significant increase in copper supplies until later 1988 or early 1989. This means supplies probably will remain tight for some time even if world economic activity slows. Strikes and other production problems slowed world output of copper in 1987. As a result, copper supplies are the lowest they have been in 14 years. World inventories currently total 625 kt (690,000 st). That is not much above the 585 kt (645,000 st) level reached in 1974 when the price of copper rose to a record $3.84/kg ($1.74 per lb). This makes all the more interesting what Chile, the world's largest copper producer, has been doing lately. Chile has been the world's largest copper producer since 1982, when it overtook the United States. Table 1 shows Chile's copper grades, reserves, and production at its mines. Chile contains roughly one-fifth of the world's copper reserves. At present production rates, these reserves would last for more than 100 years. In 1986, Chile produced 1.4 Mt (1.5 million st) of fine copper, up 3%. Chile accounted for 17% of the world's copper output.

Jan 1, 1988

By R. M. Hudson

Equilibrium constants have been determined for the jeaction C (in steel) + H2O = CO + H2 as a function of carbon content (0.013 to 0.74 ujt pct) and temperature (1200° to 1800°F) by using a flow system in which the water-vapor content of various gas mixtures containing hydrogen, carbon monoxide, and nitrogen was systematically controlled. The equilibrium partial-pressure ratio K1 = PcoPH2/PH2O was obtained for two low-carbon steels and four Fe-C binaries from a series of runs made at each temperature. By comparison of Ki with the analogous ratio for the reaction C (graphite) + H2O = CO + H2, the activity of carbon in steel (ac) was comDuted for each temperature and carbon content studied. From these data values of the equilibrium constants for two other carburization-decarburiza-tion reactions of importance were estimated. The chemical compositions of the two steels and four Fe-C binaries used are given in Table I. Specimens of Steel E were cut from a 0.035-in.-thick commercially box-annealed and temper-rolled lot of a low-carbon low-metalloid steel. Steel F was a commercially hot-rolled rimmed steel that was cold-reduced at the Laboratory to a 0.059-in. thickness. Fe-C binaries A, B, C, and D were vacuum-melted and poured, hot-rolled, pickled, and cold-reduced at the Laboratory to furnish specimens 0.035 in. thick. Sheet specimens were cut from all lots to approximately 3/4 by 3 in. by gage and were vapor-degreased with trichlo-roethylene and weighed before heat treatment. Heat treatments were carried out in a hinged-top Hevi-Duty electric furnace with a Vycor-glass tube. When the furnace was at the desired

Jan 1, 1965

By Missy Isaman

"Mixed ground tunnels come in all kinds. In rock tunnels with possible faults and high pressure water, the challenges are many. With the advent of Crossover TBMs, contractors can minimize machine wear in such conditions while maximizing efficiency. The newest generation of Crossover is exemplified by two projects in Albania and Turkey. A 5.56 m Crossover TBM destined for Turkey’s Gerede Water Transmission will be assembled using Onsite First Time Assembly (OFTA) from within an existing tunnel. The unique machine will bore through 30 fault zones requiring the TBM to be sealable to up to 20 bar so pre-consolidation grouting can be done. If boring under pressure is required, the TBM will bore sequentially using the screw conveyor fore and aft gates. Skewing further towards hard rock, a unique 6.2 m diameter Double Shield TBM with Crossover features was designed for Albania’s Moglicë Headrace Tunnel. The machine features closure doors and a sealing system to contain inrushes of water until they can be grouted off. This paper will discuss the unique aspects of the Crossover designs, including their inception as based on past projects in difficult ground, and their utilization at the two current projects. INTRODUCTION Specialized tunnel boring machines have been made for years to tackle specific types of ground conditions. Traditional types of TBMs bore within a specific set of ground conditions. If a project is located in a competent granite face, then a Main Beam machine is a good solution. In soft ground, Earth Pressure Balance (EPB) machines are the method of choice. Years of experience and engineering advancements have made both types of machines fast and economical solutions for tunneling. Unfortunately not all ground conditions are a perfect swath of one material, and the need for a more diverse machine is apparent."

Jan 1, 2016

By R. W. Guard

ALTHOUGH etching techniques have been developed for revealing dislocation sites in several metals and ionic crystals,h t is valuable to extend the technique to new metals. An etch pit method for nickel has been developed on the basis some suggestions of Dr. John R. Cuthill of the National Bureau of Standards who had observed etch pits in creep specimens of nickel. The etchant used was proposed first by wensch2 for revealing grain size in nickel. The present paper describes the evidence that the technique can be used to reveal dislocations and gives the conditions under which etching can be carried out. The specimens examined were vacuum melted high-purity Ni (99.985 pct Ni) and commercial "A" nickel (99.8 pct Ni). Both materials contained greater than 0.008 pet C and had been annealed in nitrogen or dry hydrogen at 1100o to 1200°C. This gave a grain size of 1.5 mm in the high-purity nickel and 0.050 mm in "A" nickel. Tensile specimens (0.254 in. diam) were deformed from 0.25 to 10 pct at room temperature and then heated for 1/2 hr at different temperatures from 400" to 900°C. The specimens were sectioned longitudinally then polished electrolytically in 60 pct H2SO4 and etched in 35 pct H3PO4 solution at 0.2 to 0.4 v for 30 sec to 3 min. The best method for setting the proper voltage for etching is to increase the voltage until gas bubbles are evolved vigorously from the specimen and then cut it back by 10 pct. It is necessary to heat the specimen above 500°C after deformation in order that etch pits will be formed. This "decoration" treatment permits carbon to segregate to the dislocation rendering them sensitive to etching. It was demonstrated that carbon was the decorating impurity by decarburizing some specimens in wet H2 at 1200°C. The susceptibility to etch pitting was lost following this treatment but could be restored by carburizing in contact with graphite. Some rearrangement of the dislocations in the as-deformed structure occurs on heating at 500oC and above so that the technique can not be used to study the nature of dislocation patterns in deformed specimens. Extended etching does not change the number of pits although the background becomes rough and the pits quite large. The polycrystalline specimens with various strains were examined after annealing at different temperatures. Typical patterns are shown in Figs. 1 and 2. In the unstrained specimen, Fig. 1, the density of pits is 2.5 X 10' per sq cm. All grains show pits regardless of their orientation although there is a

Jan 1, 1961

By A. Pytlik, W. Masny

"Underground mining is subject to various natural hazards such as seismic events, rockbursts, fire, and gas (methane). In general, an increase in the extraction depth causes an increase in the likelihood of these hazards, especially seismic activity and rockbursts. Dynamic phenomena such as rockbursts and tremors have been recorded on six continents: Europe (Poland, Russia, Czech Republic, Germany, and Slovenia), Asia (India, and China), North and South America (USA, Canada, and Chile), Africa (South Africa), and Australia. To select appropriate mine working supports for such dynamic phenomena, the performance characteristics of such support types must be determined under both static and dynamic load conditions.This article presents information regarding the application of rockbolts in Polish underground hard-coal mines. Dynamic phenomena occurring in the mines from 2004–2013 are also characterized. A methodology developed at the Central Mining Institute (GIG) for the laboratory testing of rockbolts is presented. In this methodology, the bolts are loaded by the direct impact of a free-moving mass (up to 20 000 kg) at speeds of up to 1.2 m/s. The facilities at GIG used to test the support under static and dynamic load conditions are characterized, and the results of laboratory tests on yielding bolts with a nominal capacity of 420 kN are presented. These types of bolts are commonly used for reinforcing steel arches and the surrounding rock mass in Polish coal mines. The results of the laboratory testing of yielding bolts are discussed.IntroductionSeismic events such as rock bumps and tremors occur with great frequency during underground mining. These phenomena have been reported in such countries as Poland, Czech Republic, Germany, France, Slovenia, Russia, India, China, the USA, Canada, Chile, South Africa, and Australia (Brauner, 1991; Potvin, Hudyma, and Jewell, 2000; Kidybin??ski, 2003; Driad-Lebeau et al., 2005; Li, Cai, and Cai, 2007; Whyatt and Loken, 2009; Durrheim and Riemer, 2012; Holub, Rušajova, and Holec?ko, 2011). Descriptions of the dynamic events and their effects in the form of damage to or destruction of supports have been presented in many publications, both for hardrock mines as well as for coal mines (Brauner, 1991; Dubin??ski and Konopko, 2000; Heal, 2010; Heal and Potvin, 2007; Simser, Joughin, and Ortlepp, 2002; Kaiser and Cai, 2012; Cai 2013; Nierobisz, 2013; Mark, 2014; Masny and Prusek, 2015). One of the main goals of the research has been to develop methods, criteria, and guidelines for the selection of an optimal and safe support for mine workings located in areas of rock bumps or tremors. Example of such studies include the Canadian Rockburst Support Handbook (Kaiser, McCreath, and Tannant, 1996), or the principles presented in the literature (Li, 2010; Cai, 2013)."

Jan 1, 2016

By K. B. Nowels

Data pertaining to pipe line flow for both oil and gas in horizontal or nearly horizontal pipe lines are both extensive and accurate. However, the pipe formulas used to determine pressure drop for flowing fluids (liquids and gases) under conditions of horizontal flow are not generally applicable to flowing oil and/or gas wells. Except for some data developed in small laboratory set-ups, little or no information was available concerning flow of oil and gas mixtures in vertical pipes, when, in 1928, the writer began the development of a method for computing pressure drops in the pipes of flowing oil wells, as outlined in this paper. In 1929, Urenl presented some findings based on laboratory experiments in which vertical flow of an extremely heavy crude oil was induced by means of air through a 2-in. pipe, 41 ft. long. The friction factors derived from the experiment, as well as values for pressure drop per 100 ft., are not believed satisfactory in their application to flow problems in the field. Versluys,2 also in 1929, presented a mathematical development of the theory of flowing oil wells, and in 1930, gave a companion paper3 setting forth some principles governing the choice of length and diameter of tubing in oil wells. Since the termination of the study presented in this paper, another valuable contribution pertaining to the problem of vertical flow was made by Moore and Wilde.4 Although there were writings dealing with the principles of the gas-lift, a search of the available literature indicated that specific information on vertical flow was lacking with the exception of the writings of Uren, Versluys, and Moore and Wilde, to which reference has been made.

Jan 1, 1932

By James D. Noll, Eileen Birch

In a previous study, the e?cacy of commercial and prototype impactors for sampling diesel particulate matter (DPM) in coal mines was investigated. Laboratory and ?eld samples were collected on quartz-?ber ?lters and analyzed for organic and elemental carbon. Coal dust contributed a minimal amount of elemental carbon when commercial cascade impactors and prototype impactors, designed by the University of Minnesota (UMN) and the US Bureau of Mines (BOM), were used to collect submicrometer dust fractions. Other impactors were not as e?ective at excluding coal dust. The impactors evaluated in that study were either not commercially available or were multi-stage, expensive, and di?cult to use for personal measurements. A commercial version of the BOM impactor, called the DPM Cassette, was recently introduced by SKCs. Tests were conducted to evaluate the performance of the DPM Cassette for measuring diesel-source elemental carbon in the presence of coal dust. Bituminous coals from three mines in two di?erent coal provinces were examined. The dust particle diameters were small and the coal dust contained a high percentage of carbon, there by giving a worst-case condition for non-anthracite coal mines. Results for the DPM Cassette were essentially identical to those obtained by the BOM impactors in a previous study. At a respirable coal dust concentration of 5.46mg m3, which is 3.8 times the regulatory limit, the DPM Cassette collected only 34µg m3 of coal-source elemental carbon.

By Nancy Estrada, Jane Nowell, Cathy Jennings, Debra Yniguez, Carol Lavery, Kristin Harrer

Pilots of the MH-60S helicopter are exposed to continuous whole body vibration (WBV). Pilot fatigue is a growing operational concern due to the increased frequency of extended durations of missions (6-8+hours) in support of Operations Iraqi Freedom and Enduring Freedom. Endurance aspects of the currently used rotary wing seating systems were not optimized for the longer missions and wide range of pilot anthropometric measurements, which is now typical of naval aviation. The current seating systems were designed primarily to meet crashworthiness requirements, not for the wide range of pilot anthropometry or to mitigate WBV. Albeit, an issue, pilot fatigue and reduced mission effectiveness are also critical concerns. Current Hazard Reports indicated that pain in pilots’ legs and backs begin two to four hours into the flight and increase with time. Mission readiness also decreases with an increase in flight duration due to the constant distraction of pilots shifting in their seats while trying to get comfortable. Froom, et al [2] reported a dose-response relationship between the length of military helicopter flights and back discomfort. He also concluded that this pain is typically dull, over the lower back, and its prevalence and intensity are dependent on the total flight hours of exposure. Methods This study evaluated WBV produced in the pilot seating systems onboard the MH-60S. The purpose of the study was to test and compare the effectiveness of two different seat cushions, the current seat cushion versus an anti-vibration seat cushion. Both seat cushions were measured for acceleration levels averaged over five-minute intervals using a triaxial seat pad accelerometer. The recordings were completed for a 3-hour straight and level flight. A frequency analysis from 0-80 hertz (Hz) was conducted on all acceleration measurements to determine the dominant axis and frequency of the pilots’ vibration exposure. The results were then compared to the applicable Threshold Limit Values (TLVs) established by the American Conference of Governmental Industrial Hygienists (ACGIH) [1] and the International Organization for Standardization (ISO) 2631.1 [3] to determine the MH-60S pilots’ permissible exposure time for both seat cushions. Results The results of the study showed that for both seat cushions the vibration levels of the z-axis at 16 Hz had the shortest allowable exposure duration, according to the ACGIH TLVs. In the z-axis at 16 Hz, the MH-60S’s current seat cushion’s acceleration levels indicated an exposure time limit of approximately 6 hours, while the anti-vibration seat cushion’s acceleration levels pierced the 8-hour exposure time limit curve. This is shown in the graph below.

Jan 6, 2006

By L. B. Rothfeld, R. L. Dolzani

This paper presents preliminary results of a US Bureau of Mines (USBM) study of potential costs of compliance with possible federal regulations for copper heap and dump leaching. The regulations could arise under amendments to the Resource Conservation and Recovery Act (RCRA) and/or the General Mining Law. Estimates are given for the cost of compliance with possible technology standards that would require the use of liners and closure caps regardless of terrain and underlying geology and hydrology. This cost is compared to the cost of compliance with 1992 state requirements for terrains typical of those found at existing copper leach sites in the southwestern United States. Incremental compliance costs are found to widely exceed screening criteria used by the US Environmental Protection Agency (EPA) to denote significant economic impact.

Jan 1, 1995

By Charles George, Ronald Faul

The cementing process has been used in approximately 2.5 million oil and gas wells to seal, protect and isolate various downhole formations against communication. It has been adapted to other more specialized situations such as solution mining and sealing salt storage reservoirs. The technical literature contains very few papers specifically dealing with the cementing process for these applications, yet there have been many special projects in various parts of the world that are novel. These will be highlighted in this review. This paper also presents a comprehensive review of the various techniques used in cementing wells drilled for the recovery of soluble salts and brines. It also covers the application of cementing techniques to a large number of wells drilled for the storage of hydrocarbons in South Louisiana.

Jan 1, 1985

By Robert M. Lewis

Silica sand deposits are usually contaminated with various heavy minerals which must be removed to make the silica useful for flat-glass production. Research was undertaken to develop a better procedure for producing flat-glass-grade silica. Batch tests revealed that anionic detergent-type reagents had considerable promise. Pilot plant tests were run to compare the effectiveness of anionic detergent-type reagents with petroleum sulfonate in the removal of heavy minerals from a potential glass sand. Another slightly modified commercial procedure also was evaluated for comparison. In the pilot plant trials, utilization of the anionic detergent potation reagents did not produce quite as good results as petroleum sulfonate. It is likely that flat glass-grade sand could be produced with the anionic detergent reagents if more extensive pilot plant tests were conducted.

Jan 1, 1977

By Bruno Kneipel Neto, Mylena Inaiê Correia, Fabricio Cerqueira, José Francisco da Silva Filho

The automotive industry, when aiming to increase the resistance to corrosion, uses in the Body in White (BIW) concept the galvanized steels. The hot-dip galvanized steels that stand out most are known as GI steels. They are formed by the zinc element and by phases of intermetallic intermediate iron-aluminum-zinc compounds. The characteristic properties of the GI coating are directly related to the formation of the intermetallic layer, which is responsible for providing the connection between the metal substrate and the coating layer. In this context, two different types of steel (SAE1005 and TRIP780 steel) were used for laboratory characterization of their intermetallic layers through metallographic techniques. The results of the tests showed that the inclined section metallographic inlay technique allows obtaining a larger region of analysis of the intermetallic layer. For the surface analysis, it was observed that the chemical solution used in the preparation of the samples was effective, making possible an analysis more specific about the intermetallic layer formation, distribution and morphology.

Oct 12, 2019

PURPOSE: Evaluate practical technological advances in hearing protective devices for use in different mining environments. RESEARCH SUMMARY: Previous NIOSH research shows that miners develop hearing loss much more quickly than nonoccupationally noise-exposed individuals. Also, miners experience a greater severity of hearing loss than would be expected for nonoccupational noise-exposed persons of the same age and sex. As described in the National Occupational Research Agenda, problems created by occupational hearing loss include (1) the reduced quality of life due to social isolation and unrelenting tinnitus, (2) impaired communication with family members, the public, and coworkers,(3) a diminished ability to monitor the work environment (e.g., warning signals, equipment sounds, etc.), (4) lost productivity and increased accidents resulting from impaired communication and isolation, and (5) expenses for workers? compensation and hearing aids.

Jan 1, 2000

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By Jean-Michel Rendu

In most circumstances, the traditional methods of. ore reserve estimation for large undulating sedimentary deposits, such as coal and iron formations, do not allow the accurate prediction of grade for mining blocks. The problem is Particularly accute when the mining blocks are small with respect to the thickness of the geological zones in the deposit, and when there are significant grade changes between the foot-wall and hanging-wall of these zones. A simple geostatistical model has been developed, which takes into account the grade changes not only in the direction of the geological strata, but also in the direction normal to these strata. The genesis of sedimentary deposits and the resulting geological properties of these deposits were considered in the development of the model. The model has been successfully applied to the evaluation of a large coal deposit. Eventhough some practical difficulties have been encountered, for example when part of a geological zone was missing or had not been sampled, these difficulties have been .resolved. Both the theory and its practical application are presented in this paper.

Jan 1, 1979