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By W. R. Bull

This paper examines water-only cyclone performance for the cleaning of fine coal, and the effects of changes in feed flow rate, feed pulp density, and vortex finder diameter. A model is presented for performance simulation which can be used to predict products obtained based on feed washability data.

Jan 1, 1987

Controlled blasting experiments in small development drifts were conducted at CANMET's Experimental Mine, from August 1992 to November 1993. The objective of these experiments was to develop suitable controlled blasting techniques for small development headings drilled by jackleg with 32 mm diameter holes. The experimentation also aimed to provide insight into blast damage mechanisms. Particular attention was given to the physical-mechanical properties of the rock and the rockmass structural data in order to make the results applicable to other geological environments. The drift faces were approximately 2.4 m by 2.4 m with 36 to 43 holes drilled to a depth of 2.4 m. Cartridged water gels, emulsions and semigelatin dynamite were used in the cuts and as primers, ANFO as the main explosive and decoupled 19 mm diameter semigelatin dynamite charges were used in the perimeter holes. Smooth blasting techniques and pre-splitting were tested in the underground mine. All the blasts were monitored with a multi-channel blast vibration monitor to which was attached sets of high frequency geophones and accelerometers. This first set of experiments has illustrated the efficiency of con-trolled blasting techniques to reduce blast damage and demonstrated the need for further research to improve the safe and efficient use of explosives.

Jan 1, 1995

By J. H. Daniel

The reduction of accidents will play an ever increasing role in the mining of coal and hardrock ores as mining operations become more mechanized, the equipment becomes more costly and sophisticated, and as mineral production exploits deeper and more marginal coal and ore deposits. The most effective means to reduce accidents is through the design of mining systems and equipment. Results of safety research by the U.S. Department of the Interior, Bureau of Mines, to design safer coal extraction and haulage systems and to reduce electrical accidents are presented.

Jan 1, 1991

By Jackson M. Langton

INTRODUCTION The Morenci-Metcalf district is located on the southern slope of the white Mountains in Greenlee County, Arizona. Both porphyry copper deposits are four to six miles northwest of Clifton, the county seat, and the new Metcalf mine is situated approximately one mile northeast of the Morenci open pit (Figure 1). Chase Creek, a south-flowing tributary of the San Francisco River, dissects the district and separates the two ore bodies. More than 1,200 exploration and development drill holes have been completed in the district and the Morenci-Metcalf ore bodies have been delineated on a 400-foot grid. Recently initiated drilling programs have revealed new data about deeper protore and associated hypogene alteration. This information, correlated with surface mapping and petrographic studies, was utilized to propose a plausible geochronologic sequence for this region. The reasoning behind this study has been helpful in locating new ore beneath leached capping indicative of only protore mineralization. The scope of this paper is to establish a practical solution to a highly theoretical problem of ore genesis and to familiarize the reader with stratigraphic, structural, and mineralogic events responsible for localizing ore in this district. Continued research will possibly alter the proposed time span and relative displacements, but it is doubtful that the order of events will vary significantly. Geochronologic conclusions are therefore presented as general hypotheses and additional geologic mapping,

Jan 1, 1972

By M. E. Rossi, J. A. Bassan, J. B. Novillo

Sampling and geological models are the basis of recoverable resources models. They are pillars of mineral resources and reserves estimation, and what geostatistical methods for grade estimation should rely upon. The resource model is best estimated if geostatistical methods make good use of sound geologic models. Data collection from the original drill holes, including field procedures and the quality assurance and quality control (QA/QC) of those samples are pillar one of a resource model. The second pillar of the model is the good use of the logged geological information, resulting robust geological interpretations, and the corresponding three-dimensional models of those interpretations. These models are partly subjective and mostly conditioned by the quality of logging and the geologist’s experience. They are also conditioned by the quality of the three-dimensional models built, regardless of the modeling method employed, traditional or implicit. Grade estimation is more commonly done by applying some geostatistical method and using the two basic sources of information, data and geologic model. Multiple stages are involved in this process, and in all of them there are uncertainties and risks that have to be dealt with. Knowledge, understanding, interpretation, and management of the model’s fundamentals are critical, given that they directly affect its accuracy and predictive quality. The mitigation of related risks allows for the creation of opportunities, generating value and reducing the project’s uncertainty. This paper discusses some of the key variables, uncertainties, and risks involved in the resource modeling process, illustrating with specific examples; discusses possible risk mitigation alternatives, and proposes best practices to avoid or mitigate those uncertainties. Emphasis is placed on taking advantage of technological advances without ignoring fundamentals. INTRODUCTION In the area of mineral resource estimation, one alarming trend that these authors have observed in the past 20 years or so is that the care and diligence in checking the work as it progresses has generally diminished. This is, perhaps, an unintended consequence of the availability of new technologies and tools that attempt simplify and speed up the work involved. This has led to a more casual attitude towards checks and balances that have to be in place at any given stage of the process before proceeding to subsequent stages, as best practices dictate. To some extent, some of these aspects are covered in international standards for resource estimates reporting (JORC, 2012; CIM, 2010). But these are broad, and do not specifically recommend best practices to a level of detail that would have an impact on certain aspects of the process. There are numerous references in the geology and mining journals and conferences that discuss the consequences of poor recoverable resource models (Baker and Giacomo, 1998; Vaughan, 1997).

Jan 1, 2019

By Rodger C. Smith

The topic chat has been assigned to me ?Economic and Political Climate of the Potash Industry? is a function of two basic facts: 1. Potassium is absolutely essential to plant and animal growth. Along with nitrogen and phosphorus it is one of three major plant nutrients, the three nutrients required in largest quantities for plant growth. 2. United States is unequivocally an "have not" nation with regard to potassium. Quantity of potassium ores is limited and, more disturbing, the cost of production at all U.S. potash mines is marginal in comparison with the major producing countries, i.e. Canada and U.S.S.R.

Jan 1, 1983

By W. A. Mathews

We report on the progress of an automated mineralogical deportment of fluorine (F) in two portions of the Grasberg District for the development of metallurgical amelioration protocols for Cu sulfide concentrates. Fluorine detection limits in automated SEM technologies range from 1% (TIMA) to about 9% (QEMSCAN), however substitution in hydrophobic minerals or those reporting to concentrate is typically much lower (

Mar 2, 2022

By J. J. Zimmerman

Over-exposure to noise remains a widespread, serious health hazard in the U.S. mining industries. Most other categories of illnesses and injuries associated with mining have improved, with the exception of hearing loss. Mine Safety and Health Administration (MSHA) coal noise data from 2000-2004 show that the continuous mining machine is first among all equipment with 35% of the noise overexposures. Joy Mining Machinery, in collaboration with the National Institute for Occupational Safety and Health (NIOSH), is conducting research to reduce noise generated by continuous mining machines. This paper describes a ?JOY Designed for Noise Reduction? (JOY-DNR; Patent Pending) tail section as a noise control for reducing the noise overexposures of continuous mining machine operators. Underground results show a 45% and 65% noise exposure reduction for the operator when compared to a standard machine. Utilizing this newly developed noise control, along with previously proven controls, will provide continuous mining machine operators an opportunity to be within the MSHA-Permissible Exposure Limit (MSHA-PEL).

Jan 1, 2010

By H. Cetin

The availability of coal resources of selected 7.5-minute quadrangles of southwest Indiana was examined in this study. Resources were defined as original coal in place, remaining after mining, and currently available considering land-use and technological restrictions. The amount of coal mined from each study area varies depending on the mining practices of the companies operating within the area. Of the three quadrangle investigations, the available resources range from 50 percent to 79 percent of the original resources. Most of the coal resources under deep-minable category were not available because of technologic restrictions, such as insufficient coal thickness.

Jan 1, 1996

By P. W. Erickson

Development of the Twin Buttes mine entailed the largest known preproduction stripping job in the history of mining. It linked earthmovers and conveyor belts in a new approach to development of a pit that may reach, or even exceed, dimensions of 1 x 1-1/2 miles at the surface and go as deep as 1800 feet. The orebody to be stripped was covered by an average of 460 feet of alluvial gravels, which presented an initial stripping job of great magnitude. The initial pit layout and the original time schedule established early in 1965 called for the excavation and disposal of about 250,000,000 tons of alluvial overburden before the end of 1969. Allowing about a year for equipment delivery, this schedule left four years to do the job averaging about 62-1/2 million tons per year. In 1964 when The Anaconda Company undertook the development of Twin Buttes, it was recognized that special planning was necessary for the disposal of waste material and tailings. Environ- mental control was a prime consideration and is particularly sensitive in the Twin Buttes area due to the proximity to residential developments. Disposal of the 250,000,000 tons of alluvium, as well as future rock and tailing waste material, presented a problem which Anaconda engineers resolved by designing a plan to spread out much of the alluvium over an extended area, including a massive 11- 1/2 mile dike system which will impound mill tailing in three basins. The tailing will be impounded behind these-dikes to avoid wind exposure and blowing. The dikes also serve as a

Jan 1, 1974

By F. S. Knoll

Magnetic separation employing superconducting technology is now accepted within the Kaolin processing industry, proving the value of this technology and its ability to operate reliably even at the most remote site. Developments in superconducting magnet engineering, including cryogen free operation, combined with experience in mineral processing enables new forms of Wet and Dry superconducting magnetic separation to be developed. Applying the high magnetic force advantages at 5 T else available from such magnets to other materials is now a reality. High magnetic force mineral separating system developments are reviewed allowing the mineral processor to take advantage of a technology that is no longer confined to the laboratory.

Jan 1, 1997

By M. Polat

Variations in flotation rate by particle size and specific gravity have been investigated for three different bituminous coals. The flotation rates for various components were determined by separating the products of bulk flotation into size-specific gravity fractions. The effects of feed size and reagent addition on the flotation response of individual size-specific gravity fractions were evaluated.

Jan 1, 1994

By K. T. Brashear, N. Ripepi

"Over recent years, specifically following the MINER Act of 2006, an increasing number of manufacturers of underground mine seals in the United States have begun using a form of pumpable cement or shotcrete to create barriers separating the working and abandoned sections of underground coal mines. This seal material, while generally considered to be homogenous and solid, contains a network of microcracks, voids, and delaminations. Generally, it has been assumed that methane (CF4) leakage around these seals is a result of movement around the boundary interface between the seal and surrounding strata. Using a perfluorinated tracer compound, perfluoromethyl-cyclohexane (PMCH), the movement of gases can be monitored through seal material to observe how gases move though the material, both intact and with faulting in the material. This paper documents two large experiments where the movement of PMCH was monitored in the field, along with modeling confirmation using 3D visualization software. INTRODUCTION According to a report in 2007, there were over 14,000 active mine seals in underground U.S. coal mines alone (Zipf, Sapko, & Brune, 2007). These seals are used for both ventilation and safety purposes, to direct the flow of air away from the abandoned area of the mine and to help eliminate the propagation of explosions that can occur on the outby side of the mine seal. The atmosphere on the outby side of these seals typical consists of low levels of methane that have the potential of producing leakage along the face of the seal on the inby side. Methane leakage around mine seals has historically been attributed to the permeability between the seal and mine interface (McPherson, 1993). According to the United States Bureau of Labor Statistics (BLS) between 2003 and 2012 an average of 17 deaths occurred annually in underground bituminous coals mines. The only time during the ten-year period where the fatalities were higher than the average was in 2006 and 2010, years which had three major explosions occurring in underground coal mines in West Virginia and Kentucky. Two of the explosions were propagated through the mine by seal failure or methane leakage around newly poured seals (Light, et al., 2007) (Gates, et al., 2006). These recent events, and new regulations regarding seal strength (MINER Act), have created a need to monitor the condition of underground mine seals. BACKGROUND Measuring the permeability of solid materials, such as concrete or seal materials, can be a valuable tool in the field of non-destructible testing (NDT). By using an inert gas, such as nitrogen, injecting the gas into a solid structure, and measuring the resultant flow rate and pressure differential, this can provide valuable information about the structure. Studies have shown permeability can be affected by the stresses applied to the structure, as well as temperature and moisture (Choinska, Khelidj, Chatzigeorgious, & Pijaudier-Cabot, 2007) (Abbas, Carcasses, & Olliver, 1999)."

Jan 1, 2015

By J. A. Cremeens, D. D. Overton, J. C. Varnier

"Slope failures that occurred in 2008 and 2009 at the Pikeview Quarry in El Paso County, Colorado, USA were investigated using three-dimensional discrete element modeling methods. Large scale block sliding failures occurred along weak bedding planes that dip steeply into an excavation located at the toe of the slope. Several mining sequences at the toe of the slope were simulated to evaluate the effects of various degrees of extraction and backfill on slope stability. Slope stability back analysis was conducted using pre-failure and post-failure conditions to determine the joint shear strength properties. Laboratory testing was also conducted to determine intact rock properties. Three-dimensional discrete element analysis was uniquely applicable to this evaluation because it allowed representation of shear stress of the basal sliding surface and it afforded evaluation of several scenarios of extraction and backfill at the toe of the slope. INTRODUCTION The Pikeview Quarry is an aggregate quarry located approximately five miles northwest of Colorado Springs in El Paso County, Colorado, USA. The quarry has been operated by several owners since the early 1900s. The Pikeview Quarry has been a major source of construction aggregate for the Colorado Springs area for many years (MSHA 1986). In the 1950s, the site was mined by Peter Kiewit and Sons to provide limestone for the construction of the nearby Air Force Academy. A large scale slope failure occurred on December 2, 2008, which stopped mining activity at the Pikeview Quarry. A second, related slope failure occurred on September 13, 2009. The second slope failure was located immediately adjacent to the initial December 2008 failure. The objective of this publication is to discuss the three-dimensional slope stability evaluation. The causal relationships of slope instability are not within the scope of this publication. However, omitting the precursors to slope failure would limit understanding of the nature of the slope stability evaluation. The regional and local geology and the history of slope instability at the Pikeview Quarry aid in understanding these precursors. Two main failure mechanisms were hypothesized during the failure investigation to explain the triggering of the 2008 and 2009 large slope failures at the Pikeview Quarry. Both mechanisms are given equal credence in this publication. Quarry excavation was a key factor in the slope instability for both failure mechanisms. The objective of the three-dimensional model was to evaluate the effects of extraction and backfill at the toe of the slope with respect to slope stability. GEOLOGY Regional and local geology are both important factors in slope instability at the Pikeview Quarry. Geologic structure at the quarry is related to regional mountain building and basin development associated with the Laramide Orogeny and the Rocky Mountains. Lithologies at the Pikeview Quarry are also related to regional trends. Localized geologic features, primarily related to weathering and erosion, have also been major contributing factors to slope instability at the Pikeview Quarry."

Jan 1, 2017

By David Beck, Eko Wibowo, Hendri Silaen, Andres Sugiyanto, Karl Llewelyn

PT Freeport Indonesia’s Deep Mill Level Zone mine is one of the deepest block cave mines in the world and is in mountainous terrain in West Papua, Indonesia. The mineralization is hosted in a skarn deposit in a structural setting that is complex at the footprint, mine and regional scale. Large seismic events and significant episodes of rapid rock mass deformation are potentially critical geotechnical risks during this ramp-up stage of mining. Understanding the interaction between stress, strain, rock mass strength and geological structures is essential to minimize the hazard and engineer control measures to help ensure the safety of the employees while achieving production targets. This paper discusses how the seismicity and excavation damage have been shaped by the interactions between the mine and geological features, and how this affects strategic mining decisions. Additionally, the paper presents a summary of the mitigation measures used for mining the DMLZ in the safest and most productive way. These include improvements to geotechnical characterization of rock mass and structure, dynamic ground support designs, production scheduling for desirable cave propagation and a seismic monitoring system with re-entry protocols.

Apr 26, 2022

By Craig M. Sams

Matching mill? drives to mill power draws is a relatively new practice with the introduction of variable speed drive arrangements. Semi-autogenous grinding (SAG) mills are the focus of this paper as ball and rod mill characteristics are easily charted as charge loading and speed change. In addition, a look at types of drives available in the market and mechanical ratings is outlined to match the specifics of each drive.

Jan 1, 1991

By JIAQI JIN, Joe Milbourne, Maoming Fan

Gold is very important to support the financial system, and to be used in industries of the jewelry, high-tech fields such as electronics and aerospace, etc. Gold is mainly extracted from three types of ores: primary ore (vein gold), placer (alluvial gold) and associated ore. Cyanide was widely used in gold ore flotation to depress gangue minerals and leaching/cyanidation. The process of extracting gold from gold ore, its separation and flotation concentrate, specifically through a technique called cyanidation or cyanide leaching. This method, which has been dominant since the 1970s, utilizes a dilute solution of cyanide to dissolve gold from the ore. While effective, the use of cyanide raises environmental and safety concerns due to its high toxicity. Cyanide spills can have severe environmental consequences. This has led to the exploration of alternative, environmentally friendly reagents. This paper discusses processing results using the alternative flotation depressants such as sodium sulfite (Na2SO3), etc. to produce a goldrich flotation concentrate for sale to a smelter or as feed to an alternative leaching agent. and methods to extract gold from ore without relying on cyanide.

Feb 22, 2026

By W. M. Ma, Daniel W. H. Su, K. Centofanti, Yi Luo, W. L. Zhong, Syd S. Peng

2.1 INTRODUCTION When total extraction of an opening of sufficient size is reached in a horizontal coal seam, the roof strata in the overburden deform continuously to reach a new equilibrium condition. The severity of deformation decreases upward toward the surface. As the downward saggings of the strata propagate and reach the surface, there will be a depression zone on the surface directly above, but extending beyond the edges of the underground opening. This is the surface subsidence basin or surface subsidence trough. The surface subsidence basin is circular in plan view, if the coal seam is horizontal and the mined-out opening is square in shape. But it is rectangular with rounded corners or elliptical if the coal seam is horizontal and the mined-out opening is a long- and thin rectangle or a short-rectangular, respectively (Fig. 2.1). Most underground openings (e.g., longwall panel) assume rectangular shape when total extraction has been completed. Theoretically the edges of the subsidence basin are the points of zero subsidence. But it is difficult to exactly locate the points of zero subsidence. Therefore in practice the points with vertical subsidence of 0.4 in. (10 mm) are used. The final subsidence basin is that which exists long after the mining has been completed, because its magnitude and shape are quite different from the dynamic subsidence basin formed while the face is moving. 2.2 CHARACTERISTICS AND TYPES OF DEFORMATION IN THE FINAL SUBSIDENCE BASIN For a horizontal coal seam, every point in the subsidence basin moves toward the center of the basin. Subsidence is maximum at the center of the basin. Any cross-section that passes through the point of maximum subsidence and either parallel to AB or CD line (Fig. 2.1) is a major cross-section along which principal directions of surface movements occur. However among those infinite numbers of major cross-sections, two specific ones are of special significance, not only because the magnitudes of surface movements are the largest, but also because they are the most easily identifiable directions, i.e., one that is parallel to the faceline at the center of the basin (CD in Fig. 2.1) and' the other is that perpendicular to the faceline but parallel to the diction of face advance (AB in Fig. 2.1). Nearly all the subsidence data obtained in the US have been derived from these two cross-sections, although some cross- sections parallel to CD but near the edges of the panel have also been included. In addition to moving horizontally toward the center of the basin, every point in the basin also subsides vertically. The magnitude of subsidence increases toward the center of the basin. Therefore surface subsidence is a three-dimensional problem and should be treated so in all cases. On all the major cross-sections, only principal subsidence and principal displacement occur. Since subsidence and displacement vary continuously in every major cross-section, three additional deformation components are de- rived, i.e., slope, curvature, and strain. On all other non-major cross-sections on the other hand the five components are accompanied by two additional components, i.e., twisting and shear strain. The seven components of the surface movement are defined as follows (Fig. 2.2): 1. Subsidence, S. On any cross-section, the vertical component of the surface movement vector is called surface subsidence. It generally points downward. But sometimes it points upward in areas ahead of the faceline or beyond the edges of the opening. In such cases it is a surface heave which is usually less than 6 in. 2. Displacement, U. On any cross-section, the horizontal component of the surface movement vector is called surface horizontal displacement. It generally points toward the center of the subsidence basin. But in steep terrain, it moves along the downdip direction 3. Slope, i. On any cross-section, the difference in surface subsidence between the two end points of a line section divided by the horizontal distance between the two points is called the surface slope of the section. 4. Curvature, K. On any cross-section, the difference in surface slope between two adjacent line sections divided by the average length of the two line sections is called the surface curvature of those two line sections. There are two types of curvature: con- vex or positive curvature and concave or negative curvature. 5. Horizontal strain, e. On any cross-section, the difference in horizontal displacement between any two points divided by the distance between the two points is called horizontal strain. If the distance between the two points is lengthening, it is tensile strain with positive sign. Conversely, if it is shortening, it is compressive strain with negative sign 6. Twisting, T. On the surface of the subsidence basin, the difference in slope between two parallel line sections divided by the distance between the two line sections is called twisting. 7. Shear strain, y. Shear strain is the changes in internal angles of a square on the surface of the subsidence basin or on any major cross-section. It is the summation of the differences in incremental (or decremental) lengths between the two opposite sides divided by the original distance between the two opposite sides. More precisely, the surface deformation indices (i.e., slope, strain, curvature, twisting and shear) are defined by derivatives of surface movement components. For simplicity, the x- and y-axes of the cartesian coordinate system are set to be parallel and perpendicular to the cross-section of interest, respectively. In such a coordinate system, slope and curvature along x direction are the first and the second derivatives of the vertical components (S) of surface movement with respect to x, respectively, or i, = ds/dx and kx = d2s/dx2. Horizontal strain along x direction is the first derivative of the component along x direction of the horizontal displacement,

Jan 1, 1992

By R. J. Smith

Hornestake's Mclaughlin Mine is the first commercial application of pressure oxidation pretreatment of gold prior to cyanidation. Inherent to the autoclave process are several liquid/solid separations. Flocculant consumption represents a significant portion of the consumable reagent costs at McLaughlan. This paper focuses on the efforts of the Operating, Metallurgy and Engineering groups to improve thickener operation and minimize flocculant consumption. An operating philosophy incorporating feed solids control, increasing flocculant dilution water and minimizing flocculant solution shear has resulted in a reduction in 1986 flocculant costs of $0.054/t ($0.06 st) versus 1985 costs. Additional changes are projected to result in a further cost reduction of $0.20/t ($0.22/.st) in 1987.

Jan 1, 1988

By Dale R. Ralston, Roy E. Williams, Gerry V. Winter, George L. Bloomsburg

GENERAL STATEMENT Data frequently can be collected by several dif¬ferent methods. The method required for the nec¬essary precision for inflow prediction to mines should be selected and other methods avoided. Pre¬cision monitoring or measuring techniques fre¬quently require more time, expertise, and expense in their implementation that may not be justifiable. The temporal distribution of the data needs also may dictate the method used for data collection. Continuous recording devices may be required for time sensitive data whereas point measurements of other parameters may be adequate. Data needs will vary as the hydrologic investigation proceeds. In¬itial data needs may require only a qualitative col¬lection of data such as the areal distribution of precipitation. Subsequent data needs may require the measurement of ground water levels to the near¬est hundredth of a foot. Data requirements can be difficult to fulfill for ground water systems. This is particularly true for anisotropic, heterogeneous hydrostratigraphic units since the hydrogeologic parameters vary both ver¬tically and areally. Techniques exist for determining the storage characteristics of both unconfined and confined hydrostratigraphic units but these pro¬cedures require the installation of multiple wells in the same unit which may be impractical. Specific tests are discussed subsequently that permit the determination of vertical hydraulic conductivity. Data collected from field procedures or tests are generally preferred to laboratory derived data. This is especially true for hydrogeologic parameters such as hydraulic conductivity. SURFACE WATER SYSTEMS Precipitation Precipitation data can be collected from sources that maintain a historical record. The US Depart¬ment of Commerce, National Oceanic and Atmos¬pheric Administration (NOAA), maintains weather observation stations across the country. Such a sta¬tion frequently can be found near a proposed mine site but the type of weather data collected varies from station to station. Fortunately, precipitation data are collected ubiquitously. The data collected by NOAA can be purchased for the area of interest in the form of monthly and annual tabulations. Private weather stations constitute a second source of precipitation data. Existing data usually are analyzed by one of three methods. The station average method merely sums the depth of precipitation at each station and divides the sum by the number of stations as fol¬lows: [ ] where Pavg is the average precipitation (L), P, is the depth of precipitation at station i (L), and N is the total number of stations. This method is applicable where there are a relatively large number of stations uniformly distributed across the area (Hjelnfelt and Cassidy, 1975, pp. 71-72). The second method, called the Thiessen poly¬gon method, weights the precipitation at each sta¬tion in direct proportion to the area it represents without consideration of topography. The stations are plotted on a map and perpendicular bisectors are drawn on the lines connecting the stations. The polygons formed by these bisectors constitute the area that the precipitation for that station repre¬sents. The overall precipitation can be calculated with the following equation:

Jan 1, 1986