In In-depth Analysis of the Rotary Engine

    The invention of the combustion engine has made a significant impact on the world in the twentieth century. The creation of engine allowed for huge advances in many industries including the automotive industry and the aviation industry. Without the combustion engine, transportation as we know it would not exist.

    Since the combustion engine is used in so many different applications, many adaptations have been created to meet the needs of the industry. Once such adaptation of the combustion engine is the rotary combustion engine. German engineer Felix Wankel developed the rotary engine, as it is known today. Ramelli proposed the first designs for rotary engines as early as 1588. It was not until the automobile was invented in 1896 for more advanced plans for an efficient rotary combustion engine. In the 1900’s, Dr. Felix Wankel began to catalog possible configurations for a rotary engine. Wankel tested 862 configuration pairs of rotors and housings, of which 278 were impractical. In the end, Wankel thoroughly tested 149 pairs before creating the four-phase rotary piston engine in 1938.

    In order to understand the importance of the rotary engine, it is necessary to explain the design compared to a standard gasoline piston engine. In a conventional reciprocating engine, the pistons move linearly in the cylinders. This linear motion of the pistons must be transformed into a circular motion through a crankshaft. Although the design of reciprocating engines can vary considerably, the essential principal of linear motion is the same. The conversion of linear motion to rotary motion in a reciprocating engine is not necessary in a rotary engine, because the piston is designed to rotate. "In a piston engine, the same volume of space (the cylinder) alternately does four different jobs – intake, compression, combustion and exhaust. A rotary engine does these same four jobs, but each one happens in its own part of the housing. It’s kind of like having a dedicated cylinder for each of the four jobs, with the piston moving continually from on to the next." (Nice) The major parts of a rotary engine are the housing and the rotor. The housing is an epitrochoid in shape. (In depth analysis of epitrochoid will follow in the text.) An epitrochoid is generated by rolling a circle around another circle. The housing uses this shape to create three equal chambers. Each part of the housing is for one specific part of the process including intake, compression, combustion, and exhaust.

    In the center of a rotary engine is the rotor. The rotor has three convex faces and each face acts as a piston. The faces also have pockets to increase displacement because the greater the displacement, the more air/fuel mixture can be burned. At each of the apexes of the faces there are metal blades to create the seals between the chambers. The path of the rotor always allows it to maintain contact with the housing. This uniquely shaped rotor creates the area where the air and fuel mixture is contained for combustion. These chambers replace the cylinders of a conventional engine.

    The first phase in the four-phase rotary engine is the intake. When the apex of the rotor passes the intake port in the housing, the intake phase begins. At that moment, the volume of that chamber is at a minimum. As the rotor continues to moves the chamber expands, drawing the air/fuel mixture into the chamber. Therefore in a rotary engine there is no need for intake valves controlling the flow of the ports.

    The next phase is the compression phase. As the rotor continues to spin, the volume of the chamber begins to decrease. The fuel mixture is compressed and when the mixture reaches the spark plug it is at full compression.

    Then begins the combustion phase. At this point, the shape of the chamber is long and narrow. A rotary engine requires two spark plugs because it would take too long for the flame to spread with one spark plug. The two spark plugs ignite the mixture, creating pressure. This pressure builds and forces the rotor to continue the rotation.

    The last phase in the process is the exhaust. The rotor rotates past the exhaust port in the housing and the high-pressure gases flow out the exhaust. This completes the four-phase process and it starts again. As the rotor is spinning, each of the three faces is working on their part of the cycle. Therefore in one complete revolution of the rotor, there are three combustion strokes, not one.

    There are many advantages of the rotary engine compared to the piston engine. A rotary engine is lightweight and compact. Therefore the engines can fit in very small cars and increase fuel economy to due the reduction in weight. The engine’s action is smoother because of a lack of a reciprocating action. Everything in a rotary engine spins continuously in one direction. Where as a piston engine has parts moving in completely different directions and have to make sudden changes in direction. The rotor in a rotary engine is also internally balanced with counterweights to eliminate any vibrations. It also has much fewer moving parts because of the ingenious design. It does not have valves, connecting rods, cams, or timing chains. The lack of moving parts, creates to a more reliable engine. The engine also produces a constant torque curve because of the lack of valves. Where as a piston engine has peak torque only when the engine is working at a certain revolutions per minute. The engine also remains cooler during combustion, therefore lessening engine fatigue for longer life. Lastly, a rotary engine has lower nitrogen oxide emissions than a piston engine.

    There are a few disadvantages of the rotary engine compared to the piston engine. The rotary engine’s high surface to volume ratio is more inefficient. The engine is less thermodynamically efficient than a piston engine. Another disadvantage were the original design flaws. In early rotary engines, the seals between the rotor and the housing were not perfected therefore not burning all of the fuel and having high fuel consumption.

    The mathematics behind the rotary engine is very advanced. The housing shape is the most important mathematical aspect of the rotary engine. An epitrochoid is the curve produced by a point on one circle as it rolls around another circle. The equations for epitrochoids depend on the two radii of the circles and the distance of a point from the center of the circle.

The equations for an epitrochoid are:

Let R = Radius 1

Let r = Radius 2

Let P = Point on the circle

Let h = Distance of Point P from center of the circle

X = (R +r)cos(t) – hcos(((r +R)/(r))(t))

Y = (R +r)sin(t) – hsin(((r +R)/(r))(t))

    Another area of mathematics in the rotary engine is the compression ratio. The compression ratio is the ratio of the volume of air when it is first introduced in the intake chamber and the volume of air just prior to be ignited. The different compression ratios will affect the amount of pressure release because a higher compression ratio means more oxygen can be ignited. If the compression ratio is too high, the compressed air with ignite itself like a diesel engine, which would be very detrimental to a rotary engine. Therefore calculating the compression ratio is key to engineering a reliable rotary engine.

Compression Ratio = (A_max / R²) / (A_min / R²)

    There is more advanced math involved with the design of the rotary engine that involves the use of integrals and the thermodynamics of the engine. These areas of mathematics would be too involved and complicated to outline in a paper of this nature. Highly trained engineers to this day are working with the mathematics of this engine to perfect its performance and efficiency.

    Through continued engineering and development research on the rotary engine many improvements have been made on the seals, fuel injection, integral electronic control, intake design, weight reduction, and turbocharging. The Mazda RX-7 improved its fuel consumption by 9.4 percent and it’s power output by 8 percent in three years. When sales stopped of the RX-7 in 1995, no rotary engines remained on the automotive market. Although a new and improved RX-8 with a rotary engine is supposed to debut in 2003.

    I chose to analyze the rotary engine because I have always been fascinated with engines. I was familiar with the basic design of the piston engine and I wanted to learn more about the rotary engine. I had first heard of the rotary engine in the Mazda RX-7 and wanted to investigate the advantages and disadvantages of the design compared to a piston engine. The questions I am asking are interesting because not many people are familiar with the rotary engine although it is such a magnificent design. To full understand the mathematics involved in rotary engines, one must understand geometry, algebra, integrals, parameters, and trigonometry.

    Looking back on the project, I found finding sources the most difficult task. The rotary engine is not the most popular topic, therefore finding the mathematics involved in the design was somewhat challenging. I don’t think I would have done anything differently if I was to complete this project again. If I were to continue explorations in this topic, I would like to test different shapes for the housing to try to find other possibly efficient designs.

    In conclusion, the rotary engine is a unique approach to the common internal combustion engine. Not only does it solve many of the problems associated with reciprocating engines, but also produces more power with better efficiency in a smaller more compact design. The rotary engine is able to accomplish this feat because of advanced mathematics

Evarts, Eric. "The Rotary Engine." Christian Science Monitor Feb. 2000: p23.

Marr, Allan. "Advantages and Disadvantages of Rotary Combustion Engines." Internet. 5 May 2002. <http://www.monito.com/wankel/advantages.html>.