A project of Volunteers in Asia . E Des for &xter Kks.l.8 by: William G. Ovens Published by: Volunteers in Technical Assistance 1815 North Lynn St. Suite 200 P.C. Box 12438 Ariington, VA 22209 USA Paper copies are $ 4.95. Available froi?: Volunteers in Technical Assistance 1815 North Lynn St. Suite 200 P-0. Box 12438 Arlington, VA 22209 USA Reproduced by permission of Volunteers in Technical Assistance. Reproduction of this microfiche document in any form is subject to the same restrictions as those of the original document. . A DESIGN MANUL FOR WATER WHEELS PP with details for applications to pumping dater for village use and driving small machinery William G. Ovens c c\ VITA, Inc. 1975 LIST OF TABLES LIST OF FIGURES PART ONE: THE WATER WREEL TABLE OF CONTENTS I Introduction 1 II Formulation of the Problem 2 III Design Limitations - Advantages and Disadvantages 6 TV Theoretical Considerations for Design 7 A. Stall Torque 7 B. Power Output vs. Speed; Required Flow Rates 10 C. Bucket Design 21 D. Bearing Design 24 E. Shafts 28 F. Minor Considerations 31 V Practical Considerations for Design 32 A. Materials 32 8. Construction Techniques 33 C. Maintenance 35 PART Two: APPLICATIONS I Water Pumping 36 A. Pump Selection Criteria 36 8. Attachment to Wheel 46 c. Piping 55 II Other Applications 57 Sample Calculation An Easily Constructed Piston Pump: by Richard Burton ii iii 1 36 60 65 69 LIST OF TABLES Table I Stall Torque per Foot of Width Table II Horsepower Output for a Constant Torque Wheel per RPM per Foot of Width 12 14 Table III Water Power Input to Wheel per RPM per 15 Fact af Width to Maintain Constant Torque (hp.) Table IV Flow Rate in Imperial Gallons per RPM per Foot of Width of Wheel Required to Maintain Constant Torque 16 Table V 19 Estimated Maximum Output Horsepower for Constant Input Water Flow Rate Condition Table VI Upper Limits on Useable Flow Rates for Various Size Wheels 20 Table VII Table VIII Approximate Weight Carted by Each Bearing 27 28 Maximum Bearing Diameter Required for Various Loadings Table I? Standard Pipe Sizes for Use as Axles with Bearing at 12 inches from Wheel Edge 31 Table X Table XI Estimated Friction Factors 39 40 Peak Pump Piston Velocities for Pump Rod Attached Directly to a Crank on the Wheel Table XII Peak Force on the Pump Rod of a Piston Pump for Various Bores and Heads 41 Table XIII Volume of3Water in Various Sized Delivery Pipes (ft ) 42 Table XIV Inertial Force per Inch of Stroke for Various Volumes of Water at Various Pump Cycle Speeds 43 Table XV Horsepower Required for Water Pumping at Various Flow Rates and Heads 45 47 Table XVI Quantities of Water Pumped per Stroke for Various Bore and Stroke Sizes LIST OF FIGURES Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Schematic View of a Scotch Yoke Mechanism Figure 6 Sc).ematic Views of a Suitable Cam-activated Pump Rod Schematic Side View of Bucket Shape 9 Schematic View of Water Distribution on Wheel 11 Schematic View of a Slider-Crank Mechanism 48 Schematic View of a Trunnion-mounted Pump and Crank 51 52 54 - iii - PART ONE: THE WATER WHEEL I. INTRODUCTION Supplying power to many remote locations in the world from central generators using customary distribution methods is either economically unfeasible or will be many years in coming. Power, where desirable, will therefore need to be generated locally. Various commercial machinery is marketed, but the required capital expenditure or maintenance/running cost is beyond the capability of many potential users. Some effort has been expended at the Papua New Guinea University of Technology to devise low cost means of generating modest amounts of power in remote locations. This paper reports on one such project involving the development of low cost machinery to provide mechanical power. Regardless of the final use to which the power is put the natural sources of energy which can be utilized are fairly readily categorized. Among them: 1. Falling water 2. Animals 3. Sun 4. Wind 5. Fossil fuels 6. Nuclear fuels 7. Organic waste Sun, wind and water are free and renewable in the sense that by using them we do not alter their future usefulness. From continually operating cost considerations, a choice from among these is attractive. From -l- capital cost consideration hydro-power may be very unattractive. Sun and wind have obvious natural limitations based upon local weather conditions. Furthermore, for technological and economic reasons, solar power use is presently limited to applications utilizing the energy directly as part of a heat cycle. Animals require specialized care and continuous food sources. Conversion of organic waste to useable energy is being experimented with, with varying success, in several parts of the world. Whatever the form of the naturally occurring energy, it may be trans- formed, if necessary, into useable power in a wide variety of ways. The choice of method depends upon a complex interaction of too many con- siderations to enumerate fully here, but among them are: 1. the use to which the power will be put; 2. the form in which it will be utilized. This generally, but not exclusively, falls into the broad categories of mechanical and electrical; 3. the economic and natural resources available; 4. availability of suitable maintenance facilities; 5. whether the machinery must be portable or not. II. FORMULATION OF THE PROBLEM In the absence of a specific request from government or any outside body, the decision was taken based primarily on the obvious abundance of available water power to investigate broadly the design possibilities for low cost machinery to produce small amounts of mechanical power. One immediately obvious potential application is the generation of electric power, but for reasons mentioned under "Other Applications" in Part Two -2- this has not been pursued. However, in many places, villages are located at some distance from the traditional source of drinking water. The principal intended use for the power generated by the machine dis- cussed in this manual has been the pumping of potable water for dis- tribution to a village. The project, thus, has included construction of a simple pump attachment also. Several other potential uses are discussed later. Limits on the scope of the project were decided based upon numerous considerations: 1. Minimum of capital expenditure indicated a device which could be constructed locally of inexpensive materials with no specialized, expensive components or machinery required. 2. 3. 4. 5. Local construction suggested the desirability of design details requiring only simple construction techniques. Since the installation was likely to be remote (indi- cating a probable shortage of local skilled tradesmen) maintenance, if any, would have to be minimal and simple. The device should be such that repair, if any, could be carried out on-site with parts and necessary tools light enough to be carried easily to the site. The usual considerations of safety mcst apply with the knowledge that the village children could not/would not be kept away from the device. -3- I decided to conecratrare on investigating the feasibility of using the water ubeel, it being the device which seemed most likely to optimize the criteria set out above. There are other types of machines suitable for creating mechanical power from hydro sources, but none, known to me, can be constructed with such simple techniques requiring so low a level of trade skills as the wooden water wheel. Water wheels are in use in various parts of the world now. Many have been constructed on an ad hoc basis and vary in complexity, efficiency -- and ingenuity of design and construction. The basic device is so simple that a vorkablo wheel can be constructed by almost anyone who has the desire to tr 4. Wwever, the subtleties of design which separate adequate from inadecltire models may escape those without sufficient technical training. The number of projects abandoned after a relatively short life attests to the fact that designers/builders often have more pluck than skill. It seems desirable to attack the problem in a systematic fashion with an objective of establishing a design manual for the selection of proper sizes required to meet a specific need and to set out design features based on sound engineering principles. I offer the following as an attempt to et that objective. The wheel consists of buckets-to hold the water-fixed in a frame and arranged SP that buckets and frame tagether rotate about a centre axis which is oriented perpendicular to the inlet water flow. Traditional designs employ the undershot, overshot or breast configurations. In the undershot wheel, the inlet water flows tangent to the bottom edge of the wheel. In the overshot wheel, the water is brought in tangent to the top edge of the wheel, partially or fully filling the bucket. It is carried in the buckets until dumped out somewhat before reaching the lowest point -4- on the wheel. The breast wheel has water entering the wheel more or less radially, filling the buckets and then again being dumped near the bottom of the wheel. Typical efficiency values vary from a6 low as 15% for the undershot to wei1 over 50% for the overshot with the breast wheel in-between. We shall concentrate on the overshot wheel a6 being the most likely choice to give Blax power output per dollar cost, or per pound of machine, or per manhour of construction time based upon expected efficiences. Miti- gating against this choice is the need for a more complex earthworks and race vay with the overshot wheel where the water must be guided in at a level at least as far above the outlet as the diameter of the wheel. The undershot wheel, of course, may be merely set down on top of the stream vith virtually no preparation of raceway necessary. But in many streams the rise and fall with heavy local rainfall is spectacular, so flood protection would be a major consideration for any type of device. The simplest flood protection is a channel leading from the river to the installation, vith inlet to the channel controlled to keep flood water in the main stream. Since a diversion channel would probably be required -Fay, the odds are very good that a suitable location to employ an overshot &eel can be found for most installations. In the event that the overshot installation is impossible, the undershot wheel straddling the diversion channel is simple to use. Another consi eration which makes the overshot wheel attractive is the ease vit ich it can handle trash in the stream. First, the water shoots over the wbee1 and so trash tends to get flung off into the tail- race witbout catching in a bucket. Secondly, there are not usually the tight spaces between race and wheel in vhich trash can jam. Somewhat -5- closer fitttig arrangements are required with breast and undershot wheels to get good efficiency. III. LIMITATIONS - ADVANTAGES AND DISADVANTAGES The wheel is a slow 6peed device limited to service roughly between 5 and 30 rpm. Consequently this limits its usefulness as a power source for electricity generation or any other high speed operation because of the step up in speed required. Although not a great problem from an engineering viewpoint, adequate gearing or other speed multiplying devices involve increasing complexities in terms of money, potential bearing problems, and maintenance. The slow speed is advantageous when the wheel is utilized for driving certain types of machinery already in use and currently powered by hand. Coffee hullers and rice hullers are two which require only fractional horse-power, low speed input. Water pumping can be accomp- lished at virtually any speed. Slow speed output of a wheel cannot of course, directly power a centrifugal or axial pump. The positive dis- placement "bucket pump" or suction lift pump already in use in various villages normally operates at well under 100 cycles per minute and can be adapted for use in conjunction with a wheel at slow speed. This of course, has been done for hundreds - maybe thousands - of years else- where. Devices of this type have relatively low power output capability. The power output depends upon the dimensions of the wheel, the speed and the useable flow rate of water to the wheel. As an example, a recon- structed breast wheel installed in a museum in America of 16 ft. out- side diameter and with bucket depth of 12 in. operating at 7 rpm, with flow rate of 28 cubic feet of water per second had an estimated power -6- output of 18.5 hp (14 kv) (calculated at an efficiency of 100%). Actual output on that vheel has not been measured but would be less than 10 hp (7.5 kv). A 3 ft. OD, I l/2 ft. wide model constructed by the author is in the fractional horse-power range. Already mentioned once, it is worth emphasizing that a useable water wheel can be built almost anywhere that a stream will allow, with the crudest of tools and elementary carpentry skills. Iv. THEORETICAL CONSIDERATIONS A. Stall Torque The stall torque capacity of the machine, ignoring the velocity effect of the water impinging on the stalled buckets, is easily calculated by a simple summation of moments about the shaft due to the weight of water in each filled or partially filled bucket. Obviously this will depend in part on the amount of spillage from the bucket which in turn depends on bucket design. Bucket configurations used in the 18th and 19th century varied depending on the skill of the builder. They were empirically determined on the criterion of maximizing torque by maximizing water retention in the buckets while recognizing that optimum design on this criterion also required increased construction complexities. Buckets of shape shown schematically in a side view, Fig. 1, were used for overshot and breast configurations. The straight sided buckets are less efficient but simpler to construct. The width of the bottom of the bucket was typically l/4 of the width of the annulus where that configuration yeas chosen. Purely radial buckets were used in undershot wheels. -7- It is convenient to use three of the wheel's dimensions for . calculation of the torque capacity of the wheel: the outside radius, r; the wheel width, w, i.e., from side to side; and the annulus width, t, defined as t = (outside diameter - inside diameter)/2. See Fig. 1. The ratio of the annulus width, t, to the outside radius, r, is important to wheel design as there are practical limits to the useful values which may be employed. In this paper only ratios 0.05 <t/r < 0.25 are considered. For smaller ratios, the potential output per foot of diameter of the wheel is considered too low to be practical. For larger values, the buckets become so deep that l there is insufficient time to fill each one as it passes under the race exit. Also, since the torque and power depend upon having the weight of water at the greatest possible distance from the wheel axis, increasing annulus depths increases total wheel weight faster than it increases power output. The result is that if more power is needed it is better to increase the O.D. than to increase the annulus width to values exceeding t/r = 0.25. In this way the wheel weight and the structural components to support that weight remain economically most advantageous for a given power output. Historically, wheels have tended to have t/r values around 0.1 to 0.15. Upper limits on wheel width have tended toward approximately l/2 the O.D. because of structural problems with wider wheels. It can be estimated that the overshot wheels operate with the equivalent of approximately l/4 of the buckets full. That is, the -8- Figure 1. Schematic side view of bucket shape. Upper: Flat bottomed bucket. Lower: Straight sided bucket. -9-