Search Documents

There are presently no suitable underground mine production scheduling optimisation models available for application to sublevel stope mining. Scheduling underground production for maximum return is therefore still a manual process, which generally involves scheduling production from the next available highest cash flow stope within the operational constraints of the project. In most mining operations, the scheduling problem is too large and complex to guarantee truly optimal results through manual scheduling. This paper reviews some general optimisation studies that have been proposed for underground hard rock mining. Furthermore, an example of a mixed integer programming model is presented for a small conceptual sublevel stoping operation. Comparative results of a schedule generated by a mixed integer programming (MIP) production scheduling model and a manually generated model on a nine stope example is presented. Results indicate that the potential benefits of the MIP production scheduling model for the purpose of maximising NPV are significant. Finally, a new constraint was formulated to limit multiple exposures of fill masses for use in an existing MIP production scheduling model. Testing of the formulation took place on the central stope of the nine stope example, which showed that the formulation performed its task without breaking other operational constraints.

Jan 1, 2007

By D. P. Power

The development of an accounting code for the metallurgical industry has been debated for many years. Following the series of tumultuous economic events in the nineties and earlier this century that have affected business, there was much need for legislation to be passed to minimize potential risk. One of the consequences to affect the mining industry was the enhancement of existing geological codes for reporting. In parallel the sponsors of AMIRA have taken the brave step to develop a generic code for metal accounting that embraces the full gamut of industry. In this paper the code will be reviewed in the context of metallurgical accounting as it applies to coal preparation. This paper provides the background for this development and an insight into the mechanism for the debate for the generation of this code. The key elements of the code as it applies to the coal industry are explained but most importantly the key opportunities are highlighted.

Jan 1, 2010

The second annual student prize giving function of the South African Institute of Mining and Metallurgy was held in the Van der Byl Hall, University of Pretoria, on Thursday, 10th March, 1978. The main address (see opposite page) was given by Dr T. F. Muller, Chairman of Iscor.

Jan 1, 1978

By A. A. Hazell

Mine management by objectives by A. A. Hazel The procedure of setting production targets is illustrated in Appendix I of the paper. This procedure is intended only as a guide although the standards on which it is based were established by work studies and found subsequently to be well within the limits of a trained crew.

By J. P. Kirsch

This paper sets out to clearly identify all elements that make up an effective furnace feed system. These are outlined and the more common types of technology are listed. These technologies all play an important role in the final delivery of all feed materials to the furnace.

Jan 1, 2008

By F. J. J. Blaauw

This paper discusses a bold venture into the use of interactive computer graphics technology as the foundation of an overall integrated mining managerial system. The wide range of applications that can be addressed through the use of this technology is highlighted, and some discussion of the major facts of this project, which is still in its early stages, is provided.

Jan 1, 1987

By F. E. Steffens

The application of kriging in assessing the area rainfall in a weather modification experiment is complicated by the presence of many zero rainfall recordings on a given day, and the fact that the variograms seem to be quite different for the rainfall on different days. Indicator variograms are shown to be directly related to two sets of conditional probabilities. Probability kriging is used in estimating the probability of rainfall amounts above any cutoff at any point

Jan 1, 1987

This paper illustrates the application of numerical modeling methods, in conjunction with limit-equilibrium techniques, to the location of critical slip surfaces in slope-stability problems. Initially, the Spencer slice-based method of analysis is introduced, together with a dynamic-programming algorithm for slip-surface location. This limit-equilibrium method is assessed critically through the use of an illustrative problem. The technique is then extended to locate the critical slip surface for a similar slope, but with more complex constitutive and yield relationships for the material comprising the slope. To this end, the use of the stress field generated from a finite-difference program, together with a dynamic-programming search routine, is presented as an advanced technique of slope-stability analysis for engineers.

Jan 1, 1993

By D. J. Hallbom

A new graphical method termed the ?Design Curve Diagram? (DCD) has been developed to analyse non-Newtonian pipe flow data by relating the plastic Karman number to the plastic Reynolds number. Since the plastic Karman number is directly proportional to the pressure loss gradient and the plastic Reynolds number is directly proportional to the velocity, the DCD is essentially a non-dimensional pipe flow curve. This makes the DCD conceptually easier than the commonly used Hedström-Moody diagram. While, the DCD was developed for the analysis of yield plastic fluids (e.g., Bingham plastics), it is equally applicable to Newtonian fluids.

Jan 1, 2007

By R. K. Brummer

A simplified two-dimensional plane strain numerical technique for the non- linear modelling of a tabular mining excavation in brittle host rock under high stress conditions is described. The model has been developed using relatively straightforward assumptions based on extensive underground investigation of the fracturing and deformation of rock at the stope face in deep gold mines on the Witwatersrand, together with observed rock behaviour under laboratory conditions. The reef rock is modelled as a linear string of yielding elements which interact horizontally, while the elastic rockmass remote from the reef is modelled using boundary element techniques. This elementary technique is shown to produce results which agree closely with the observed behaviour of the fractured rock during the mining of a remnant pillar

Jan 1, 1987

By K. Shin

Determining the anisotropy of rocks has in the past been difficult and rarely attempted in engineering practice. Here we have developed a new practical methodology for measuring orthotropic anisotropy that requires only one hollow cylinder specimen to determine the anisotropy of a set, even when the directions of the anisotropic axes are unknown. Autrefois, la détermination de l’anisotropie des roches était difficile et elle a été rarement essayée dans la pratique de l’ingénierie. Voilà c’est nous qui avons mis au point une nouvelle méthodologie pratique pour mesurer le coefficient de conductibilité thermique de l’anisotropie qui exige un seul spécimen du cylindre creux afin de déterminer l’anisotropie d’une série, même si les directions des axes anisotropiques sont inconnues. Früher war die Bestimmung der Anisotropie von Gesteinen ein schwieriges Verfahren, das in der technologischen Praxis nur selten in Angriff genommen wurde. Wir haben hier eine neue praktische Methodik zur Messung der orthotropen Anisotropie entwickelt, bei der nur ein Hohlzylinder an Gesteinsproben benötigt wird, um die Anisotropie einer Reihe von Steinen zu bestimmen, selbst wenn die Richtungen der Anisotropieachsen unbekannt sind.

Jan 1, 2003

By E. Hakami

The objective of the study was to estimate the largest shear displacement that could be expected on a pre-existing fracture located in the repository area, due to the heat release from deposited waste. Two-dimensional numerical analyses using UDEC have been performed. The maximum shear displacement, at the fracture centre, amounts to 0.2 – 13.8 cm depending on fracture parameters. The fracture extension, friction angle and shear stiffness are found to be the most important. Le but de cette étude est de déterminer le déplacement maximal en cisaillement qui puisse se développer le long d'une fracture préexistante en réaction à la chaleur dégagée par les déchets radioactifs enfouis dans la roche. Les analyses numériques ont été réalisées à l'aide du code 2D UDEC. Le déplacement maximal en cisaillement enregistré au centre de la fracture varie entre 0.2 et 13.8 cm en fonction des propriétés de la fracture. L'ouverture, l'angle de friction et la rigidité au cisaillement semblent avoir une influence dominante sur les résultats. Zielsetzung der Studie war die Abschätzung der maximalen Scherverschiebung, die auf einer innerhalb des Endlagergebietes existierenden Rissfläche infolge der Wärmeabstrahlung des eingelagerten Materials zu erwarten war. Es wurden zwei-dimensionale numerische Berechnungen mit UDEC durchgeführt. Die maximale Scherverschiebung im Zentrum der Rissfläche beträgt 0.2-13.8 cm, abhängig von den Risseigenschaften. Dabei hat sich herausgestellt, dass Rissgrösse,Reibungswinkel und Schersteifigkeit den grössten Einfluss haben.

Jan 1, 2003

Book news 1. Book reviews ? Prospecting in areas of desert terrain. London, The Institution of Mining and Metallurgy, 1985. 283 pp. £28 (members £25,20). Reviewer: J.S. Mostert This publication records the proceedings of a con¬ference convened to deal exclusively with prospecting in areas of desert terrain. The meeting, organized jointly by The Institution of Mining and Metallurgy (London) and the Ministry of Energy and Mines, Morocco, was held in Rabat from 14th to 17th April, 1985, and generated considerable international interest. Exploration cam¬paigns and case studies of successful discoveries in the desert areas of more than 14 lands are described. Since large areas of South Africa, Botswana, and Namibia are characterized by and and semi-arid terrains, this publication should be of considerable interest to explorationists and mining engineers engaged in the search for and development of mineral deposits in southern Africa. The fact that the desert terrains of southern Africa are host to a number of important base-metal (Aggeneys, Gamsberg, Prieska, and O'Okiep) and diamond deposits (Orapa, Jwaneng) has ensured continued interest in these areas from the viewpoints of exploration and mining.

Jan 1, 1985

By J. O. Roux

The Impala Platinum Limited Base Metals Refinery in Springs, South Africa, refines convertor matte containing base metals and PGM?s (platinum group metals) using a hydrometallurgical process. In addition to a PGM-rich concentrate that is further refined, the Base Metals Refinery produces nickel (in powder or briquette form), copper cathodes and cobalt powder. Five leaching stages are utilized to remove the base metals and impurities from the PGM concentrate. The project described in this paper involves a radical redesign of the second stage leach autoclave with the aim of reducing maintenance costs and downtime, increasing throughput and ensuring a safer working environment. The second stage leach process at the Base Metals Refinery, produces a PGM-rich residue through the extraction of copper and any remaining base metals from the first stage leach solid residue material. Leaching is performed in an autoclave operating at a pressure of 600 kPaG and a temperature of 140°C to 150°C. Concentrated H2SO4 is added to the feed to produce a solution with a free acid content between 10 and 30 g/L and a pH of less than 2. Oxygen is passed into the 1st and 2nd compartments of the autoclave. As a result of the aggressive, highly oxidizing conditions within the autoclave, the original design utilized a heavy wall carbon steel shell with lead lining and two layers of acid bricks. The bricks acted as a wear resistant material and ensured a low surface temperature at the skin of the lead lining, whereas the lead lining acted as a corrosion barrier to protect the steel shell. These brick lined autoclaves were heavy, maintenance intensive and prone to catastrophic failure. A radical autoclave redesign was needed to reduce the high costs of manufacturing, installation and operation. Finite element modelling was used to optimize the design and various high alloy materials were investigated for the application. Based on extensive test work, the carbon steel shell was replaced with duplex SAF 2205 stainless steel in the new design. The use of this highly corrosion resistant material, eliminates the need for the lead and brick linings and reduces the wall thickness requirements substantially, resulting in an increase in the available volume for the same external shell dimensions. The vessel is welded in circular sections to form an elongated, impermeable, cylindrical body, with several agitator nozzles and compartments. The first new duplex stainless steel unit has been in continuous operation for more than 24 months and its performance has exceeded the highest expectations. The design was so successful that a patent has been registered. The major benefits of the new stainless steel design include increased throughput, improved performance, less downtime and a safer working environment. Lead has been eliminated and replaced with a more environmentally safe material, and the total lifespan of the vessel has been extended. In addition, the autoclave project has made significant developments in advancing the field of welding and optimizing the integrity of welding quality standards in South Africa.

Jan 1, 2009

By R. R. M. Cousens, W. S. Garrett

Discussion: L. T. Campbell Pitt: When Mr Garrett and I discussed the design and construction of plugs and bulk head doors to resist great water pressures in mines about ten years ago, we visualized an emeregeny when there would be no time for site preparation. We could not however, anticipate a problem of such magnitude and urgency as the one described in the paper under discussion. The paper very clearly describes the flooding and the measures taken to save the mine. The complete flooding would have been a national disaster. The account of the combat between man and water reads like the account of a military operation. It was an endeavour which achieved success because there was a master plan, tenacity and, in fact, heroism. The paper is of necessity a long one. In my contribution I will mention some historical facts and factors that I believe have relevance to the flooding and the saving of the mine. It is of great satisfaction to me to have been one of the two initiators of a new approach to underground plug design and construction. The investigation was taken over by a Chamber of Mines Committee which combined our early work with further research and the resulting data had a significant bearing on the West Drie emergency plug designs. The final plug length was correctly based on the requirements to obviate leakage. A plug to have structural strength only would have been very much shorter but so ineffective as to have become a waste of labour, material, and in consequence, wasted the limited time available to prevent flooding of the whole mine. The figure of 75 lb per sq in. sheer stress provided a very ample margin, in my opinion, but under the very difficult site conditions and the limitations of plug material suitable for the very unusual construction, justified such a figure. There must have been considerable temptation to reduce the safety margin due to the urgency to complete and commission the plugs, but it is much to the credit of the directors of this operation that nothing less than a safe design was permitted. In about 1945 Blyvooruitzicht Gold Mining Company, which was then mining in to the West Driefontein area to assist in early development, decided to protect themselves from a possible inrush of water from the latter mine. A bulk head door was accordingly designed and installed on 2 level between 1945 and 1948 at 4,218 ft below surface. Since West Driefontein paid for it, Gold Fields consulting mechanical engineers collaborated with their colleagues of Rand Mines who completed their design after a few modifications were agreed. This door was never used to prevent an inrush into Blyvooruitzicht but the exercise was very useful to Gold Fields when the high pressure doors initially installed on 10 and 12 levels between Nos. 2 and 3 shafts to enable isolation of one section of the mine from another were designed. At that time the capacity of West Driefontein to cope with an inrush of water was comparatively small because the storage in stoped areas and the installed pump capacity were much less than in later years. These doors together with others of the same design were later moved to the lower levels served by sub vertical shafts. In addition, doors to prevent flood water entering the pump chambers on 18 level were installed at each end of that level, and designed for a head of 360 feet so that water would have to reach 16 level before the pumps were flooded. All these doors were called upon to hold water and it is reported that only a small plug in one of the doors and a 4 in. dia flanged pipe joint failed. The lesson is that in these cases the smallest details warrant as much attention as the major ones. That these were the only equipment failures when so much depended on equipment, is very much to the credit of design engineers, both of the Gold Fields head office and companies who supplied both mechanical and electrical equipment. Until I had read the paper I wondered why the policy of isolation by bulk head doors was not continued as the development moved eastward towards the Bank Compartment and particularly when it pierced the Bank dyke. The reasons have been given in the paper. It was unreasonable to expect provisions to be made to counter the remote contingency that the large installed pumping capacity and mine capacity to store water would be exceeded during a peak inrush. When pumps were being considered for West Driefontein, it was decided that the Gold Fields standard underground main pumps at that time of 1 million gallons per 24 hours would be too small. Three alternatives were considered. 1. Very large units that would require underground sub assembly and dismantling of both pump and motor. 2. The largest pump and motor that could be conveyed as a complete pump or motor from surface to the pump chamber. 3. Pumps of higher speed to reduce dimensions and weight. It was decided to adopt alternate 2 because of avoidance of transporting pumps in parts and assembling underground. Alternative 3 was not favoured because high speeds would have introduced problems of more exact rotor balancing. I believe the decision was correct and in the crisis enabled comparative easy transport of pumps and motors to surface for overhaul and, if required, transfer to other pump stations. The standard pump thus became a 10 stage 1,500 rpm pump with a capacity of approximately 2 million gallons per 24 hours against a static head that varied

Jan 3, 1969

By T. K. Roy

INFACON XI has no doubt earned the distinction as the first such Congress in India. This prestigious occasion could become a reality of a long cherished dream of the Indian Ferroalloy Producers, consumers and ex-porters. The International Committee of Ferro Alloys (ICFA), South Africa, the august body for organising INFACON, every three years, could be convinced by the Indian Ferro Alloy Producers? Association (IFAPA) to award INFACON (XI) to India. This Congresss, organized by IFAPA, has opened a window for the Ferroalloy Community of India, the up-coming Asian Tiger, to register their strength and weakness to the world forum with the principal objectives of evolving long and short-term optimum road-maps for development. It is to be reckoned that India is poised to be a steel giant by 2020 when it is envisaged that the steel production may reach a level of 120 million tons of which significant proportion has to be in the categories of alloy and special steels, requiring standard and high grade ferroalloys. Keeping the above objective in view, the theme of this Congress has been rightfully designed as ?Innovations in Ferro Alloy Industry.? This Congress has also earned a distinction of more than eighty papers, finally selected for inclusion in the Proceedings. More than 100 internationally and nationally reputed experts in the field of ferroalloys (technology and manufacturing practices as well as world scenario) have been approached for critical review of abstracts and selection for the proceedings. It needs to be mentioned without the cooperation received from ICFA the high standard of INFACON could not have been assured. The papers are suitably grouped under seventeen heads, starting from world situation to production and operation followed by present and future technologies and finally to modelling and simulation. It is a Herculean task to the Technical Committee to fit these papers in proper sequence. The Commit-tee members kept no stone unturned to ensure the cogency with the subject matters and at the same timekeeping the flexibility of interests of the participant, especially in the context of three parallel sessions. The Proceedings containing only refereed papers of high quality, will serve the entire gamut of ferroalloy industry and will also highlight the present status of concerned countries. The areas of attention to make the industries globally competitive and at the same time laying emphasis on the prevailing practices, will help the industry leaders to formulate an appropriate global approach. Following the break-through step, instilled by INFACON XI, the Proceedings will be available both in bound and in searchable electronic CD-ROM format. I, as the Chairman of the Technical Committee would like to express thanks and high appreciation to all the Committee members for their whole hearted efforts in all respects without which it would not have been possible to complete these proceedings in the scheduled time. Technical Committee desires to place on record their gratitude to Organising Committee for their synergic cooperation all through in successfully executing multifarious tasks, associated with such a grand international technical Congress.

Jan 1, 2007

By C. L. E. Swartz, I. J. Barker, J. H. Schubert

A dynamic simulator of the leaching and adsorption cascades of a gold plant was developed and used to compare the effect of various disturbances on the overall efficiency of the plant. These comparisons show which disturbances most critically need to be controlled to optimize plant performance. The simulator was based on an existing gold plant. Dynamic and steady-state data were collected on the plant and were used in the modeling of the process. Simple dual-rate models are used to describe the leaching and adsorption processes. Mole-balances of various species take into account the changes of concentrations in the leach, and also the movement of pulp and carbon up and down the adsorption cascade. Fluctuations in the flow rate, density, and cyanide concentration of the feed to the leach have a negative effect on the efficiency of the leach, while carbon attrition was found to be an important factor in decreasing the efficiency of the carbon-in-pulp (GIP) section. Badly regulated transfers contribute towards the decreased efficiency of the GIP section, but overflows and carbon leakage have only a limited long-term effect. Various carbon profiles and transfer schemes were studied, and the results indicated that a slightly heavier loading at the bottom of the cascade is beneficial, while the type of transfer is relatively unimportant.

Jan 1, 1993

By D. Duncanson, R. J. Davidson, C. G. S. Schmidt, G. A. Brown, J. D. Taylor, N. W. Hanf

The development of a cyanidation route for the treatment of gold-plant gravity concentrates is described. This work was carried out as a natural consequence of earlier improvements to the recovery of gold in the gravity sections of existing gold plants. Concern about the environmental aspects of the conventional amalgamation process was further motivation in the development of an alternative procedure. It was found that the partial pressure of oxygen in solution was the most critical reactionrate determining factor. The rate of gold dissolution was shown to be controlled by the reaction rate below approximately 25°C and by diffusion above that temperature. Thus, the efficiency of pulp agitation and oxygen partial pressure permitted a high degree of control over the rate of gold dissolution. The use of oxygen rather than air significantly increased the dissolution rate of both gold and silver. The solubilities of sodium, calcium, and potassium aurocyanide complexes under simulated reaction conditions were studied, and it was established that the values for the sodium and calcium complexes were limited, requiring the use of lower pulp densities and higher reaction temperatures for the treatment of very high-grade concentrates. The presence of excessive amounts of tramp iron in such concentrates of up to 25 per cent by mass was found to result in poor gold dissolution owing to the cementation of gold under certain reaction conditions. The maintenance of high oxygen partial pressures, together with high cyanide concentrations, high pH levels, and the presence of calcium in the system, all aided in passivating the tramp iron. Copper, gold, and iron were shown to be the main cyanide-consuming elements. Optimum gold dissolution was obtained in a closed bench-scale reactor incorporating a flotation-machine type of agitator for effective pulp agitation and oxygenation, the oxygen being recirculated. The reactor was designed to operate under a very small positive pressure. After reaction times of 2 to 6 hours at temperatures in the region of 30°C, both the gold and the silver dissolution averaged 99,S per cent. In the case of very high-grade concentrates, it was shown that gold could be floated in the same reactor by drawing off the flotation concentrate through a port in the reactor. A flotation recovery of 87,4 per cent of the gold in 3,9 per cent by mass was obtained. The recovery of osmiridium from cyanide-leach residues and the electrowinning of gold from the pregnant liquors were also considered as processing aspects in the treatment of gold-plant belt concentrates. Final table tailings with a gold concentration of 10to 12 gft were obtained. The results of the investigation strongly suggested that an alternative cyanidation route for the treatment of gold-plant concentrates was technically feasible, provided the system included effective agitation and oxygenation. In the case of lower-grade concentrates, cyanidation followed by the electrowinning of gold appears to be the simplest route, while, for high-grade concentrates, flotation and smelting of the concentrate followed by cyanidation of the flotation tailings are suggested. The use of oxygen rather than air for sparging the pulp would depend largely on the grade of material to be treated. A preliminary comparison of the costs related to the amalgamation and cyanidation processes for the recovery of gold from such concentrates indicated very similar capital and operating costs. It was concluded that other considerations, e.g. toxicity, safety, and lower labour requirements, were more important than such small cost differences. Furthermore, the 'opening' of the gold-plant gravity circuit, which would be made possible by a cyanidation route, would further reduce the operating costs because of the subsequent decrease in the tonnage to be treated.

Jan 1, 1978

By E. Pothas, P. R. Jochens, L. B. McRae, D. D. Howat

SYNOPSIS The phase equilibria, viscosities and sulphur capacities of titaniferous slags were determined in the composition range of CaO = 30 to 0 per cent, MgO = 0 to 30 per cent, SiO2 = 19.69 per cent, AI.O. = 13.12 per cent and TiO2 = 37.19 per cent. The phase equilibria were determined by high temperature microscopy, the viscosities were measured using a rotating outer cylinder viscometer and the sulphur capacities were evaluated from the results obtained by equilibrating the slag in a gas stream of CO, CO2 and SO2. The behaviour of these titaniferous slags under reducing conditions was examined. Possible use of the slags for aggregate, or slag-cement, and the possibility of extracting the TiO2 are discussed. CONTENTS INTRODUCTION PHASE EQUILIBRIA VISCOSITIES DISCUSSION OF THE PHASE EQUILlBRIA AND THE VISCOSITY VALUES EFFECT OF REDUCING CONDITIONS SULPHUR CAPACITY DISCUSSION OF THE SULPHUR CAPACITY VALUES POSSIBLE USES CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES INTRODUCTION The latest phase in the exploitation of the mineral wealth of the Bushveld Igneous Complex is the erection of a plant by the Highveld Steel and Vanadium Corporation Limited near Witbank to produce steel and vanadium-rich slag from the titaniferous magnetites occurring in this rock formation. These titaniferous magnetites occur as segregations in the gabbro body and the TiO2 is mainly present within the structure of other constituent minerals but also occurs in smaller amounts as ilmenite and ulvospinel. The vanadium is thought to be present in the iron oxide phase due to isomorphous replacement of the iron. Until very recently, it was feared that the high titania content of these titaniferous magnetites would militate against their value as useful iron ores. However, the design of an integrated plant to produce both steel and vanadium-rich slag, and in which the iron-making process is conducted in submerged arc furnaces instead of in

By G. W. Holl, E. G. Fairon

A review of some aspects of shaft design by G. W. HOLL, Pr. Eng., Associate of the Mine Managers Association of South Africa (Fellow)- and E. G. FAIRON, Pr. Eng., F.S.A.I.E.E., M.I. Cert. M.E.E., M.I.Mech. E., (Visitor) The reasons for the choice of vertical shafts in preference to inclined shafts of comparable capacity are set out, and the conclusion that the former are superior in virtually all circumstances is substantiated. The shapes of vertical shafts sunk during the past sixty years are recorded, and the shapes of those sunk during the past decade are analysed. From this analysis it is clear that circular and elliptical (and quasi-elliptical) shafts are the shafts of the future and that the rectangular shape will conceivably become obsolete. The determination of the size of shaft is discussed and it is forecast that shafts of a diameter of 13 metres and over will probably be sunk without difficulty in the years to come. The depth of the shaft is determined intrinsically by the Mines and Works Regulations applicable to factors pf safety of winding ropes and the design of the winding system. The Blair winder is the most suitable winder for hoisting rock, men, and material from a depth of, say, 3000 metres on an economic basis. Tertiary shafts will, therefore, be unnecessary in future deep-level mining projects at the limit of depth now envisaged. A few other factors relating to shaft design are described.