IN THE 19TH CENTURY the British physicist James Prescott Joule observed that if stretched rubber is warmed, it tends to contract. Having described the effect, Joule turned to other matters. About five years ago the phenomenon attracted the interest of Paul B. Archibald, who is associated with the Lawrence Radiation Laboratory of the University of California. He decided to put the effect to work in the form of a heat engine. His project illustrates the essential difference between scientific and engineering experimentation. The scientist experiments to discover and confirm the facts of nature's behavior; the engineer seeks to put those facts to use as economically as possible. Archibald describes his apparatus and experiments as follows:

"My first Joule-effect engine consists essentially of rubber bands stretched between the rims of a pair of disks [see Figure 1]. The assembly resembles a squirrel cage, except that the disks are canted with respect to each other at .53 an angle of about eight degrees. Each r: disk turns on its own shaft, but the facing ends of the shafts are joined by a flexible coupling that constrains the disks, causing them to rotate synchronously.

"The rubber bands alternately stretch and relax as the assembly rotates. Strands at maximum elongation, on the diverging side of the squirrel cage, dip into a tank of warm water at the bottom of the machine. The resulting increase in tension drives the engine.

"Water was selected for the heat transfer medium primarily because it has much greater thermal conductivity than air. The rubber bands could be warmed by radiant heat. On the other hand, rubber could be damaged by excessive heat if an overload caused the machine to slow down or stall.

"The water medium served still another purpose. I supposed that natural rubber would deteriorate rapidly. Synthetics worked, but in elongation and strength they did not compare favorably with natural rubber. For a time I assumed that the improvement of the engine depended on the development of a high-performance synthetic rubber that would be resistant to oxidation. Subsequent investigations disclosed that this was a misconception. Oxidation of natural rubber is not a problem if the rubber is kept wet by running the engine continuously. It is ozone rather than oxygen that degrades the material. Ozone is converted into oxygen in the presence of water.

"When I learned this, I ran the engine continuously. Gum-rubber tubing lasted for three months, whereas black vulcanized rubber tubing of the kind used in laboratories performed well for eight months. During this period the speed of the engine gradually decreased. I made no adjustments. None of the rubber strands broke, but gum rubber became: quite sticky and failed by depolymerization. The black vulcanized material crept slowly and lost its tension but did not appear to deteriorate in other respects. I could have reinstalled it at increased tension and thus extended its working life.

"The engine operated when the heat differential was negative, that is, when the temperature of the water was three degrees Celsius below the air temperature. The temperature differential is created by the evaporation of water from the rubber strands in the cooling cycle. A mechanical engineer who observed the operation of the engine on the negative heat differential said: 'Don't quote me, but if I didn't know better, I would say it is a perpetual motion machine.'

"A principal limitation of this design was that its enlargement would be difficult and costly. Some of the components were nonstandard. Moreover, the design imposed a flexural load on the two wheels. These problems were not insurmountable, but the game is lost if the engineering becomes complex and the final design is massive.

"At the time the engine was designed I was unaware of a similar engine that had been built about 50 years earlier This first Joule-effect engine was the result of a hunch on the part of William B. Wiegand, a pioneer in rubber chemistry whose subsequent work contributed largely to the fact that automobile tires now last five times longer than they did then. Wiegand's inspiration to construct a rubber engine came one afternoon in 1920 as he was lecturing to a group of students at McGill University. He later gave the following account: 'To demonstrate the Joule effect, I strung a bundle of rubber bands from the high ceiling of the lecture room and by a weight stretched them to 400 per cent elongation. When a battery of Bunsen burners was placed beneath the stretched rubber, the weight leaped upwards; when the burners were removed, the weight sagged. The students seemed impressed by seeing heat induce contraction. I shared their interest, but in addition I also saw Carnot's cycle: the reversible cycle in which heat is absorbed at high temperature and discharged at a lower temperature. Here, I thought, is a potential heat engine. Subsequently I shared my hunch with a collaborator, H. F. Schippel, who was endowed with mechanical genius. As a result we constructed two heat engines, one reciprocating (in the form of a pendulum) and the other rotating–a rubber motor.'

"Wiegand and Schippel developed reciprocating motion by constructing a compound pendulum, which is a rod that carries bobs at both ends. The pendulum swung on a knife-edge bearing supported by anvils fastened to an apparatus stand. Power was obtained from a strip of rubber stretched between a lug on the upright support just below the knife-edge and a second lug on the pendulum rod close to the lower bob. The upright support also carried a piece of sheet metal in a vertical plane parallel to the plane in which the pendulum swung. The metal served as a screen that shielded the rubber from a source of radiant heat when the pendulum vibrated at low amplitude.

"Heat was radiated horizontally from a source behind the apparatus. At higher amplitudes of vibration the pendulum carried the rubber beyond the shadow cast by the metal. At these large excursions the rubber absorbed heat from the radiant source. The resulting contraction of the rubber pulled the pendulum back into the shadow, where the rubber cooled in preparation for the next cycle Of heating. Wiegand and Schippel made the period of the pendulum relatively long, about 15 seconds, so that the rubber could cool adequately between heating intervals.

"Wiegand's rubber motor resembled a bicycle wheel with rubber spokes [see Figure 3]. The rim of the bicycle wheel was supported in the horizontal plane by a vertical rectangular frame. Both the wheel and the frame rotated on a fixed vertical shaft with a crank at its center. The hub of the wheel turned on the crankpin.

"Heat was provided by a hot plate fixed to the vertical shaft. A candle generated the heat. As the wheel turned, the eccentric position of the hub caused the rubber to stretch more on one side of the wheel than on the other. The hot plate, located at the point of maximum elongation, warmed the rubber and induced rotation.

"In a description of the rotary engine published in 1925 Wiegand wrote: 'Space does not permit a closer examination of the Joule effect. Perhaps enough has been said to justify the opinion that we may get further if for a time we think less about the hypothetical mechanism of the Joule effect and get right down to a quantitative engineering study of its thermodynamic realities. I hope someday to build a five-horsepower rubber motor. It will be a fascinating job to determine the proper bore and stroke for maximum efficiency. The bore will be the tension on the thermal members; the stroke is represented by the cyclic range of elongation employed. Speed will be governed by advancing or retarding the heating element exactly as in the small motor just described. There is even the vision of huge rubber motors in Malaya and Ceylon converting the sun's energy into useful work, or into electrical or chemical energy!'

"Although Wiegand's vision has not been fulfilled, rubber engines are still of interest, apart from the fact that they make fascinating toys. They are relatively inefficient compared with steam engines or internal-combustion engines. They cannot compete for the same costly fuel. There is, however, an unoccupied niche in the realm of power generation that may someday be filled by rubber engines or an equivalent mechanism. We have no engine at present for the conversion of heat into mechanical work at low temperature. The French have made heroic efforts to extract energy from thermal gradients in the ocean. Many others have constructed workable solar engines. Wiegand's engine might contend with conventional sources of power in regions where the cost of fuel is zero. The prospects of the rubber engine in such regions may well turn on the economics of its construction and the collection of heat

"An elegantly simple version of the engine has been designed by Roger Hayward, who illustrates "The Amateur Scientist" [see "The Amateur Scientist"; SCIENTIFIC AMERICAN, May, 1956]. In Hayward's version, as in Wiegand's, stretched rubber bands replace the spokes of a wheel. The rim of the wheel is a cardboard ring. A sewing needle serves as an axle on which the wheel turns in the vertical plane. Heat from a lamp causes the rubber strands to contract on one side, thus shifting the center of gravity and generating rotation. This design is simpler than the Wiegand engine but is limited by the force of gravity. Accordingly its further development is of little interest.

"The Wiegand engine is not limited in this respect. The force that induces rotation depends not on the weight of the wheel but on the tension of the rubber. The performance of the Wiegand engine would seem to be limited by three factors, namely the strength of the metal frame, the heat conduction of the rubber strands and the distribution of the radiant energy.

"After learning of the Wiegand and Hayward engines I built another model that combines selected features of all three designs [see Figure 5]. The crankshaft of the Wiegand engine has been retained. The pipe frame has been replaced by a wheel that turns in the vertical plane, as in the Hayward engine, but the spokes are of metal. The rubber strands stretch between the rim of the wheel and a stationary crankshaft. The engine runs in warm water, as in my initial design.

"This is an amazingly simple engine to build. Using an empty 14-inch aluminum reel designed for 16-millimeter motion-picture film, a few pieces of Teflon for bearings and ordinary rubber bands, I made a model in two hours. The throw of the crankshaft is 5/8 inch. The engine runs at a speed of about 12 revolutions per minute in water at a temperature of 50 degrees C. when the relative humidity is 50 percent. It starts itself when the water is three degrees C. warmer than the surrounding air.

"The size of the engine can be increased easily, because all principal stresses are either in tension or in direct compression. The loading on the bearings is radial in all cases and is high in none. Most of the tension on the rubber is balanced by another strand of rubber on the opposite side of the hub. Output power can be increased not only by using a wheel of larger diameter but also by multiplying the number of rubber strands. Moreover, the shaft of the engine can support any reasonable number of wheels.

"The power output of rubber engines that use water as the medium for transferring heat is limited by the rate at which heat is removed from the strands by evaporation. To use the analogy of the steam engine, the problem of increasing power output lies in the condenser, not in the boiler. Results of experiments in which a thermocouple was slipped inside a stretched rubber band indicate that at a relative humidity of 50 percent the cooling interval is some 10 times longer than the heating interval. The cooling portion of the cycle can be decreased by increasing the flow of air across the rubber strands or by spraying the rubber with cold water.

"So far I have not attempted to measure either the amount of power that would be expended for cooling the strands or the amount that would be gained. If the mechanism were to be cooled by a fan, the power required by the fan should be obtained from the engine. The scheme is difficult to realize in a small model.

"It is not difficult to measure the starting torque with a spring balance or to count the number of revolutions per minute. Such measurements enable the experimenter to make a reasonable estimate of the output power of the model. Specialists who design steam engines assume on the basis of a time-honored rule of thumb that maximum output power is developed when an engine runs at half its maximum speed and that the torque at this speed is half the starting torque. Measurements made with a Prony brake usually confirm the rule. My first engine, which ran for eight months, developed about one watt of power with four ounces of rubber.

"The starting torque can be estimated from Joule's law. If a strand of rubber is stretched so that the retractive force is 10 pounds at 21 degrees C. (300 degrees Kelvin) and then heated to 65 degrees (338 degrees K.), the tension amounts to 10 x 338/300, or 11.27, pounds, a net gain of 1.27 pounds. The torque can then be calculated by taking into account the number of rubber strands and the mechanical advantage of the system, which includes the throw of the crankshaft and the angle at which the strands exert force with respect to the throw of the crankshaft. I measured the starting torque of the model experimentally and also computed what it should be. The results agreed.

"I found that it is much more difficult to estimate the speed, even though many of the influencing elements are apparent. My engines ran at about 10 to 12 revolutions per minute under no load. Speeds of up to 20 revolutions per minute were observed.

"A major influence is the amount by which the rubber is stretched when the strands are installed. The amount of tension that is developed by the Joule effect increases with the elongation of the stretched rubber. Moreover, the cross section of the rubber varies inversely with elongation, but the rate of heat transfer to and from the rubber increases with elongation. The mass of the rubber, for a given length of the strand, varies inversely with the elongation, as does the total flow of heat.

"I found it interesting to measure the Joule effect. It is relatively easy to set up the required apparatus. A metal tube of convenient length can be used as an oven. A rubber band is connected by an inside hook to a pipe cap at one end of the tube. A companion hook at the opposite end of the tube passes through a hole in the second pipe cap and is connected to a spring balance.

"Temperature inside the tube can be measured with a thermocouple. The oven can be heated electrically by a helix of Nichrome wire wound over a layer of asbestos paper wrapped around the tube. The amount by which the rubber is stretched can be controlled by varying the position of the movable hook inside the oven. The Joule effect can be investigated by plotting temperature against force at various percentages of elongation. The experiment generates a family of graphs.

"Although the power and efficiency of the engine increase with the elongation of the rubber, the useful life of the material decreases. Hence the designer confronts still another engineering compromise. According to published data, natural rubber can be elongated 600 percent: a rubber band two inches long can be stretched to about 14 inches before it breaks. At elongations approaching this limit, however, rubber is extremely prone to damage. My engines were operated at an elongation of 300 percent, which avoided the problem of breakage.

"The diameter of the rubber strands, whether in the form of tubing or of solid strips, is also of interest. Most of my initial experiments were made with tubing that had an outside diameter of 1/8 inch and a bore of 1/16 inch. Recently I have been using solid rubber bands. My second engine, made with bands 1/8 inch wide and 1/32 inch thick, ran at about six revolutions per minute at a water temperature of approximately 40 degrees C.

"The rubber was then replaced with bands that measured 1/16 by 1/16 inch. The speed doubled to 12 revolutions per minute at the same water temperature. Thus encouraged, I decided to try even smaller bands. I could not find thinner ones at local stationery stores.

"It occurred to me that thinner rubber can be found in the core of a golf ball. In the ball I opened the rubber measured .1 inch wide and .01 inch thick. It had been elongated 1,000 percent during the wrapping process. Attempts to install strands of this material in the engine were extremely frustrating, and I finally abandoned them.

"Although these particular experiments are not conclusive, there seemed to be no increase in the engine's speed as had been anticipated. Perhaps it would be useful to investigate rubber strands of very small cross section. The resistance to the motion of small strands in water would doubtless become increasingly important as the cross section diminishes and would finally determine the maximum speed of the engine. As Wiegand suggests, the determination of the optimum size and elongation of the rubber is a fascinating job.'

"An intriguing aspect of the final model that I built with the film reel is its simplicity. Material for constructing the model can be found, in large part, in odds and ends that accumulate in nearly every household. If natural rubber were still used for automobile inner tubes, even this part of the construction could be a salvage item.

"Sunlight provides a suitable source of energy for the engine, as Wiegand envisioned. Collecting solar heat is not difficult. I made a source that consisted of a shallow reservoir lined with black tar paper for absorbing sunlight. The assembly was insulated with straw, not because straw is a better insulator than rock wool but because it costs less.

"The reservoir was filled with water to a depth of about six inches. A layer of white mineral oil was poured over the surface to retard evaporation. The entire assembly constituted a fairly effective heat trap and reservoir. During the daytime the temperature of the water rose to a minimum of 65 degrees C. Even though the water temperature dropped at night and in cold weather, it always remained from five to 15 degrees C. above the temperature of the surrounding air–a temperature differential sufficient to keep the rubber engine running 24 hours a day."

Bibliography

TENDENCIES IN RUBBER COMPOUNDING. W. B. Wiegand in Transactions: Institution of the Rubber Industry, Vol. 1, No. 3, pages 141-170; October, 1925.

UNITED STATES PATENT No. 1,889,429. November 29, 1932.

THE RUBBER PENDULUM, THE JOULE EFFECT, AND THE DYNAMIC STRESS-STRAIN CURVE. W. B. Wiegand and J. W. Snyder in Transactions: Institution of the Rubber Industry, Vol. 10, No. 3, pages 234-262; October, 1934.

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