Is Flywheel Powered Car Feasible?


Donald E. Pauly

1 June 1974


(version 0.0)

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At first thought, the title of this article may appear ridiculous, but advances in technology have made it necessary to reconsider the subject. If a spinning flywheel were used to power a vehicle, two approaches might be used. One would be to operate a gear train to convert the necessarily high speed-low torque of the flywheel to the lower speed higher torque required for the wheels. The other approach would be to drive a generator with the flywheel, and use electric motors on each wheel.

If flywheels could be built to store sufficient energy to provide a useful range and speed, both methods would have the advantage of being able to recover the energy dissipated during braking and going down hill by spinning back up the flywheel during such operations. On the order of 25% of the total energy expended by a conventional car is used during descent of grades and braking. Thus, a corresponding savings in energy use could be realized.

The use of a gear train to reduce flywheel speed to wheel speed is hampered by the high reduction ratio necessary and also by the need for either a clutch and gear train or a rather inefficient fluidic torque converter. In either the all mechanical scheme or the electric one, a source of energy is necessary to spin up the flywheel when it runs down. The best source of this energy is the electrical outlet. Therefore, an electric motor would be needed to spin up the flywheel in the all mechanical car or the generator in the electric version could be made to function as an electric motor to spin up its flywheel.

Mr Richard F. Post has discussed the possibilities of an electric vehicle in the December, 1973 issue of Scientific American. He advocates the electric route. Since an electric motor is required in both the mechanical and electric designs, the mechanical version would have a weight penalty as a result of having to carry around a motor used only during spin up. In addition, the problems of clutch jerk or automatic transmission slip on the mechanical version make the all electric approach clearly superior.

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In order to determine how much energy must be stored in the flywheel, we will base our calculations on a 3,000 pound automobile having a range of 240 miles at 60 mph., or an endurance of 4 hours. We shall first determine the energy requirements of a conventional automobile of that weight.

A 3,000 lb. sedan was driven up to 65 mph., put in neutral, and allowed to coast until it slowed down to 55 mph. The average time needed to decelerate from 65 to 55 was about 10 seconds. This corresponds to about .045 g deceleration or in this case about 137 lb. of drag. Since the vehicle was traveling an average of 88 feet per second, and the energy used in foot pounds per second is the product of the drag and speed, we get about 12,025 foot pounds per second. There are 550 ft. lbs. per second per horsepower which is about 22 horsepower or 16 kilowatts. (1hp=.746 kw) To cruise at this speed for 4 hours would require 64 kilowatt hours. This test was done with nylon tires so the necessary energy would be less if radial tires, which have less rolling fiction, were used.

The maximum acceleration or deceleration possible with a car driven by friction of its wheels on the road is about one g. On wet roads, ice, or gravel it is much less. The wheels on a 3,000 lb. car will spin or skid if they attempt to exert more than about 3,000 lbs. of friction on the road during a rapid speedup or braking. At 60 mph (88 fps.) this gives 264,000 ft. lbs. per second or 358 kw. If the maximum power available from the flywheel is 358 kw., acceleration and braking above 60 mph would be reduced. This is probably desirable since a skid is very dangerous above 60 and extremely rapid acceleration is most important while passing or starting from a dead stop. Even with reduced acceleration above 60 mph., such a car would far outperform a conventional vehicle in that speed range. Conventional brakes would still be used as a backup in the event of an electrical failure.

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It is now necessary to determine how big the flywheel must be and how much it must weigh in order to store the required energy. To simplify the mathematics, let us assume that the flywheel is built in the shape of a wagon wheel with essentially weightless spokes. In that case virtually all of the mass is concentrated in the rim and all parts of the rim are moving at virtually the same speed. Therefore, the energy stored is E=mv2/2, where E is the energy stored in Joules or Watt seconds, and m is the mass of the flywheel in kilograms, and v is the velocity of the rim in meters per second.

The tip speed of a flywheel is limited to a velocity that is below the point of disintegration. If the flywheel is in the form of a hoop, the stress is primarily one of tension in the hoop. The stress which occurs at a given speed is Sh=v2d/g, where Sh is the hoop stress in kilograms per square meter, v is the velocity in meters per second, and d is the density of the material in kilograms per cubic meter, an g is the acceleration of gravity in meters per second per second. It is necessary to determine the amount of energy that can be stored with a given material in order to select the best one.

Solving for v2 in the stress equation and substituting it in the energy equation we get E=(Shg/d)m/2. It is seen that the factor Sh/d is merely the strength to weight ratio. Therefore, for a given amount of mass, the best material for a flywheel is one having the highest strength. This may seem strange, but it is easily seen that if two flywheels of equal weight but different strength are spun up, the weaker one will fail at a lower speed that the stronger. As a result, aerospace materials having good strength to weight ratios are far better candidates that steel or other metals.

Although many materials including E glass (used to make fiber glass) are available, a new material, named Kevlar, appears to the best present candidate for flywheel use. Fused silica is better in performance, but is presently too expensive.

Woven Kevlar

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Kevlar has a breaking strength of about 500,000 psi. It is only operated at 300,000 psi, it has an expected life of 10 years with only a 1% probability of failure. Calculations here will be based on the latter figure. The 64 kilowatt hours of stored energy previously determined to be needed is equivalent to 236 million joules. Redesigning the body and the absence of a radiator will make possible a considerable reduction in aerodynamic drag. In addition, the lack of a differential would reduce friction as well as a reduction due to the use of radial tires. On this basis, 200 megajoules will be used for the necessary storage figure.

If a flywheel in the shape of a cylinder were made from Kevlar, the energy stored in it would be one half of that stored if it were in the shape of a wagon wheel. This is because the inner portions are moving slower than the tip. The wagon wheel shape cannot be used because of the excessive diameter needed and the difficulty in joining the spokes to the hub. The energy stored in a cylindrical flywheel is E=Shmg/4. Using 300,000 psi for Sh, 86.4 lbs. per cubic foot for d, 32.2 ft. per sec. per sec. for g, 200 megajoules for E, converting into metric units, and solving for m we get 1176 pounds.

If we hollow out a hole in the center of 1/3 of its diameter for the generator, we find the weight of the Kevlar required is *****math error 90% of the above weight or 1060 lbs.[12-(1/3)2=9/10] This may seem to be very heavy, but when it is seen that it replaces about the same combined weight of engine, transmission, differential, and gasoline, it becomes competitive. The resultant tip speed is about 4,000 per second or 2,700 mph. This high speed necessitates that the flywheel be operated in a high vacuum to prevent huge losses from air friction. It would be necessary to enclose the flywheel in a spherical shell to provide a vacuum chamber. Wires from the generator would be brought out thru seals in the wall of the sphere.

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A flywheel made from fibers such as Kevlar would be easiest to make by winding up the fibers to form a cylinder. Epoxy could be used to help hold it together. It can be shown from the calculus, that if a cylinder is to fit inside a given size sphere and have maximum volume, the diameter of the cylinder and its height must be in the ratio of square root of 2 or 1.414. If we choose a 3 foot diameter cylinder, its height must be 2.12 ft. and the sphere containing it will have a diameter of 3.67 ft. This height give the smallest possible spherical container for a given weight flywheel. The cylinder's volume excluding the hole in the center reserved for the generator would be 13.3 cubic ft. Since Kevlar weighs about 86.4 lbs. per cu. ft., the sphere will have the capacity for 1150 lbs of Kevlar fiber. This is sufficient to achieve the energy storage objective of 200 megajoules. A 3.67 foot sphere could be fitted inside a conventional automobile body with some redesign of the body.

Any high energy flywheel exhibits substantial gyroscopic effects. These effects give rise to large torques that tend to prevent any reorientation of the axis of the gyro. If a flywheel car was at the equator and its flywheel was mounted vertically, it would tend to resist the earth turning under it due to gyroscopic effects. It must precess to stay vertical as the earth turns under it but can do so only if a continual torque is applied to its shaft to force it to follow the earth's rotation.

The torque that will cause a given precession of a flywheel is given by t=2Efp/frg, where E is the energy stored, fp and fr are the frequencies in revolutions per minute of precession and rotation, and g is the acceleration of gravity in meters per sec. per sec.. Using 200 megajoules for E, 9.81 meters/sec2 for g, .00069 rpm. for fp (one revolution per day), and 25,500 rpm. for fr (4,000 ft. per sec. tip speed and a 9.42 ft. circumference gives 425 revolutions per sec.) gives 1.1 meter kilograms of torque or 8 foot lbs. If the upper and lower bearings are 3 ft. apart, they would be subjected to about 2.7 lbs. of side load in opposite directions.

If the precession speed of the flywheel were 1 per second, the side load on each bearing would be about 640 lbs. This is not unreasonable for bearings that must support normally about 600 lbs. each. With 600 lbs. side load on the bearings a 30 realignment of the flywheel could be accomplished in 30 seconds in the event the vehicle were parked on the side of a hill with a 30 slope.

Unfortunately, solid cylinder flywheels have a hidden stress problem, as Mr. Post has pointed out. If thin rings are used, the only stress is tangential. However, as the thickness of the rings is made greater, a radial stress appears and grows as the thickness does. It increases the closer we get to the inside edge of the thick ring or cylinder. **Omit** In addition, the tangential force increases as we move inward from the outer edge of the flywheel. It reaches a maximum at a distance from the center that is equal to the geometrical mean of the inner and outer diameters. ***Incorrect The radial stress buildup is more important of the two since it is much larger than the tangential stress.

Kevlar in epoxy has only about 2% of its normal tensile strength when stressed in a direction perpendicular to its fibers. Its strength lies almost exclusively in its ability to withstand the stretching of the fibers along their length. Due to its small tensile strength perpendicular to the fibers, it is unsuitable for use in thick walled cylinders. Mr Post has proposed that a thick walled cylinder should be built up from thin walled cylinders of progressively smaller diameter with the smaller ones fitting inside the larger. Rubber or other resilient spacers would separate each ring. This would prevent the stretching of each ring from being able to expand the one inside it. As a result, radial tensile forces would be eliminated.

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In a metal flywheel, failure sends deadly shrapnel thru anything near it except thick concrete or steel barriers. However, fibers fail by shredding rather than by cracking. As a result, they do not produce shrapnel and can be contained in a vacuum by a relatively thin aluminum sphere. If a Kevlar flywheel should fail, the main effect would be considerable heating of the fiber and shell. Kevlar has a specific heat of about 0.5. If the entire energy of 200 megajoules were transformed into heat the 1100 lbs. of Kevlar would rise in temperature by about 360 F. This would not melt the material or give rise to explosive gas pressures.

Since rapid changes in the slope of the surface on which an automobile travels occur, a means must be provided to gimbal the flywheel so that it does not have to follow these pitch and roll changes immediately. Any attempt to effect a pitch or roll change of more than a few degrees per second would probably force the flywheel off its bearings and cause total destruction.

The sphere enclosing the flywheel could be mounted inside a cubical cage made of rods with roller bearings in the center of each rod. A system of springs attached to the sphere could provide a restoring force when the flywheel is turned from its normal position. A pulley arrangement could change the point of application of spring pressure by 90 in order to precess the sphere back to its proper place. In the event that the car was driven onto a slope greater than a predetermined limit, perhaps 45, or was turned over, and automatic release of the restraining springs could be initiated. The flywheel could then rotate freely inside the cubical cage without damaging itself.

A set of springs would be necessary to keep the sphere from spinning during braking or acceleration. This torque is not as great as that necessary to precess the sphere back to the vertical axis of the vehicle. It would be on the order of 100 ft. lbs. at maximum flywheel rpm. or 300 ft. lbs. at minimum rpm. These figures are for maximum acceleration or braking efforts. Ordinary operation would require much less torque.

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Due to the vacuum present in the spherical chamber and the very high rotational speeds present, conventional bearings cannot be used. Mr. Post advocates that magnetic bearings be used. Strong permanent magnets of the same polarity would be mounted on both the flywheel and spindle. They would repel each other to hold up the flywheel, thereby providing a frictionless bearing. Other magnets would be mounted inside the hole in the flywheel to act as the field in a generator-motor. Windings for the generator-motor would be wound on the stationary spindle. Back up mechanical bearings, that would not normally be in contact with the flywheel, could support it if a severe jolt were experienced and the bearing magnets were not strong enough to prevent frictional contact.

With permanent magnets for its field, an AC generator would have an output voltage proportional to rotation speed. If the flywheel speed was constrained to a 3 to 1 range, 8/9 of the total energy could be recovered. This is because the energy stored varies as the square of the speed, leaving 1/9 of the original energy remaining at 1/3 of the initial speed. Without compensation therefore, the output voltage of the alternator would drop to one-third of its initial voltage as the flywheel approaches rundown.

If a 3 phase system is used, switching from delta to wye configuration would yield an increase in voltage by the square root of 3 or 1723. If this switch were automatically accomplished at a rotation speed of 57% of maximum, the voltage variation would be a maximum of 32% high and 24% low. These changes would be within limits that would lend themselves readily to electronic control.

The frequency of the alternator output would depend on the state of charge of the flywheel but would be in the range of 140 to 400 cycles per second. The frequencies involved are low enough to be controlled by readily available triacs and rectifiers. A dc voltage bus could interconnect the wheel motors and the flywheel alternator. During normal running of the vehicle,

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energy from the alternator would be rectified by turning on a sequence of triacs. This dc would be fed to the wheel motor armatures to provide them with power. Wheel torque would be controlled by changing the field current in the wheel motors. Speed control would be achieved by controlling the torque. Reversal of direction can be achieved by reversing the field current. When starting from a dead stop, the voltage on the armatures would be electronically reduced to prevent useless high starting currents.

The voltage to be used on the distribution bus depends on several factors. It should be low enough so as not to constitute an undue shock hazard to humans coming in contact with it. In addition, lower voltages can be handled by less expensive semiconductors. If higher voltages are used, the current required will be less, which would greatly reduce the size of the wiring required. Higher voltage motors and generators are substantially lighter that their lower voltage counterparts. It is desirable to be able to run standard 120 vac motors from the vehicle's electrical system with minimum conversion. AC motors would be need for such purposes as air conditioning, heater fans, and miscellaneous other accessories.

A distribution system having a positive 120 volt line and a negative 120 volt line appears to be a good compromise between the requirements. By merely switching back and forth between the two polarities at 60 cycles per second, standard ac motors could be operated and accessory power could be made available at remote locations such as camping or construction sites. Lights and cooking power would make camping much more enjoyable. The ability to run a welder for several hours would make a flywheel powered vehicle invaluable for remote construction work. If 2 kilowatts were used for air conditioning in summer or for electric heating in the winter, only 8 kw. hours would be used during a 4 hour drive. This would only reduce the range of the car by about 15%. In the even that the flywheel on a vehicle ran down away from a source of power, another similar vehicle could quickly give it a partial charge sufficient to reach a source of power by means of jumper cables.

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A considerable amount of electronics will be needed to control wheel speed, reverse direction, provide no skid braking, and give the desired acceleration. This would be done by varying the direction and amount of field current in the wheel motors. To brake, field current in the motors would be increased which would increase armature voltage. This higher voltage would reverse the current in the alternator and raise the speed of the flywheel, thus returning energy to it. To accelerate, the field current would be reduced, lowering armature voltage in the wheel motors which would draw current from the alternator, slowing down the flywheel and speeding up the car.

Normally, (except during cross country driving) a flywheel would be charged overnight when it approached rundown. In local driving this would occur less often that a conventional vehicle needs to be refueled. The lack of idling losses in the flywheel car and its ability to recover energy during braking would save much energy in urban driving, thereby considerable extending its intervals between charges. The 55 kw. hours in the flywheel could be obtained from standard household 220 volt lines. A power level of 6 kw. would fully spin up the flywheel in 8 hours. This power is comparable to that drawn by an electric range with its oven and a few burners on, for cross country driving, charging stations would have to be built that would be able to spin up the flywheel in about 10 minutes. Water cooling of the alternator windings might be necessary during high rate charging.

At 5 cents per kilowatt hour, a full charge would cost $2.50. Compare this with a tank of gasoline costing $8.00. Due to the vastly reduced number of moving parts, lubrication and maintenance expense would be virtually eliminated. Extensive use of aluminum to prevent rust would make possible a car that should last well in excess of 10 years. The total cost of a flywheel car should be in the range of $7,000, but its increased performance and durability should more than make up for the price.

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Since a flywheel powered vehicle requires no combustion, its performance on cold winter mornings and mountaintops would be phenomenal compared to the internal combustion vehicle. There would be no danger of carbon monoxide poisoning when sitting in an electric vehicle to keep warm. Without the constant explosions of a gasoline engine, driving would be quiet and vibration free. Incredible acceleration and the ability to climb steep grades would make the flywheel car a delight for mountain driving. With its superior aerodynamic design and horsepower capability it should be an excellent racing car.

The no load running losses of the alternator should be on the order of 15 watts. The flywheel would therefore lose only about half its energy if the vehicle were not used for 3 months. In a conventional vehicle the carburetor would most likely be clogged by sediment and the gasoline would have deteriorated by that time, not to mention a discharged battery.

In the typical conventional vehicle discussed earlier, we might expect to get about 18 miles per gallon at 60 miles per hour. Gasoline delivers about 136 megajoules per gallon when it is burned completely. On this basis the efficiency is seen to be about 13%, if 22 horsepower is delivered to the wheels. On aircraft power plants, efficiencies on the order of 25% are typical, but this is because they are running at 75% of maximum power and do not have to change speed during cruise. Turbine engines are lighter and require less maintenance for the same horsepower but they are more costly and have about the same fuel consumption.

The efficiency of refineries is on the order of 85%. This is due to the heat necessary to refine gasoline. Since fuel is used to pump pipelines or run tankers, the transportation efficiency for gasoline is only about 90%. Due to evaporation losses the efficiency of gasoline storage is about 98%. Multiplying these three factors by the internal combustion engine efficiency of 13% gives and appallingly low fossil fuel efficiency of 9.7%.

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The efficiency of modern fossil fuel power plants is on the order of 40% for electricity delivered at its destination. The efficiency for cruise of a flywheel car is the product of the efficiency of its conversion of commercial ac power, flywheel motor efficiency, flywheel generator efficiency, power control efficiency, and wheel motor efficiency. Using 90% for wheel motor efficiency and 99% for the others gives a figure of 86%. Multiplying this by the efficiency of the power plant gives a total fossil fuel efficiency of 34%.

It is seen that a gallon of oil burned in a power plant and used to power a flywheel car will go 3.5 times as far as the same gallon used to power a conventional car. About half of all the oil used in the U.S. is for transportation. One third of the total oil used is presently being imported. If the half that is used for transportation were reduced by 3 to 1 by mass adoption of flywheel vehicles, the U.S. would not have to import any oil. This would provide immense worldwide bargaining power if we were self sufficient in energy.

The eventual use of nuclear or solar power to produce electricity on a large scale would allow vehicles to be totally independent of fossil fuels. With the advent of silica fibers or even stronger ones, flywheel powered aircraft would become feasible. Large flywheels could be built to provide emergency backup power or act as peaking units for commercial power generation.

With no engine to produce carbon monoxide and nitrogen oxides, a society converted to flywheel cars would find that the air in its city streets was breathable again. Since the power plants producing electricity would be burning 3.5 times less fuel that the I.C.E. vehicles burned before, the overall pollution would have to be a least 3.5 times less. Actually, since power plants have good control over their combustion and have the ability to install precipitators, the net reduction in air pollution would be well in excess of 3.5 to 1. Power plants are ordinarily in sparsely populated areas which further reduce urban pollution by dispersal.


Donald E. Pauly

The author is an electronic engineer with two patents
a commercial pilot with Airplane and Helicopter ratings.