The Physics of Rotary vs. Piston Engines

Created by Nick Perza, Gabe Dunlap, & Evan Reed
Contact: perza@email.unc.edu

This website was created as a project for the course Phys100 at UNC Chapel Hill for the following assignment. The goal of our website is to explain the physics concepts underlying rotary and piston internal combustion engines, as well as the advantages and disadvantages to both.

Both Rotary and Piston internal combustion engines have many physics principles in common:

How to Get the Engine Parts Moving

• Both engines get the power to propel their internal components from the the force applied by the combusted gas.
• This combusted gas does work on the engine, where work = force x distance or = pressure x change in volume.
• Air from the engine's intake is provided into the engine's combustion chamber where it is combined with chemical potential energy from gasoline that is also injected into this chamber via fuel injectors or a carburetor. Electrical potential energy from the car's battery is also used for many purposes. The most important for our concern is providing the spark plugs with the voltage necessary to emit a spark, often via a distributor to control the timing of the sparks. Together the air/fuel mixture ignites in the combustion chamber due to the spark resulting in the combustive gas and thermal energy that propels the pistons/rotors in the engine providing them with kinetic energy resulting in the torque that the engine produces.
• This combustion reaction follows the chemical equation 2 C8H18 (gas) + 25 O2 = 16 CO2 + 18 H2O which represents the ideal stoichiometric air/fuel ratio of 14.7:1. Running lower than this value is considered running rich (more fuel) and increases the performance of the engine providing better acceleration. Running above this value is known as running lean (less fuel) and can increase the gas mileage of the engine.

Work and Efficiency

• Thus, an internal combustion engine acts as a heat engine, a device that converts thermal energy into ordered energy as the heat flows from a hot object to a cold object. The thermal energy is converted into work (decreasing entropy) as heat flows from the hot engine to the cold atmosphere (increasing entropy in the atmosphere) via the exhaust to obey the 2nd law of thermodynamics. Energy is also conserved in this process.
• The work provided by an internal combustion heat engine can ideally be written as:
• work provided = heat removed from object x (temp. hot - temp. cold)/temp. hot.
• Thus, the greater the temperature difference between the hot and cold, the larger the fraction of heat you can transform into work.
• The efficiency of the heat engine can be calculated via carnot efficiency. The same idea applies to this as it did for the work provided by the engine. The engine needs to be as hot as possible and the cold side (outside) needs to be as cold as possible. Real engines never reach ideal efficiency and are normally around 30 percent. The carnot efficiency can be calculated via:
• Carnot heat engine efficiency = (Temp. Hot- Temp. Cold)/ Temp. Hot (Calculated in Kelvin)
• This efficiency can be maximized by increasing the compression of the engine, as increasing the pressure also increases the temperature. Compression ratios often range from around 8:1 to 12:1, but can reach as high as 15:1 in race engines. This compression is limited though as increasing the pressure and temperature too much will result in knocking. Knocking is when the fuel preignites spontaneously before the fuel reaches the combustion chamber and before the engine is ready to use it to extract work. This wastes energy and can possibly destroy the metal components inside the engine.

Transfering the Energy From the Engine to the Wheels and Measuring the Engine's "Power"

• Whether it is the pistons and connecting rods or the rotors, they apply their force to the crankshaft or eccentric shaft causing it to rotate, which also causes the flywheel to rotate. By providing a force to rotate the flywheel, the engine provides a torque that can be measured and also transferred to the transmission, driveshaft and differential (in RWD cars), axles, and finally to the wheels propelling the automobile.
• Car companies often advertise horespower and torque numbers for their engines to attract buyers. The torque number is simply the torque measured from the rotating flywheel. Horsepower is completely dependent on and calculated from this measured torque.
• Horsepower = (Torque x RPM)/5252, thus high horsepower is simply torque produced at high rpm's.
• Torque at low rpms provides good towing power such as in trucks, where as torque and "horsepower" at high rpm's provides good acceleration for high performance sports cars.
• Power output/torque is directly proportional to the displacement of the engine. Displacement is often referred to as the size of the engine measured in liters or cubic centimeters as it is defined as the total volume of air/fuel mixture that is displaced during one complete engine cycle (2 rotations of the crankshaft). This is simpler to measure in piston engines as it simply the volume of this mixture swept by all the pistons in the engine in a single movement from top dead center (TDC) to bottom dead center (BDC). The measurement of displacement is more controversial in rotary engines due to the 3 faces of the rotor and the difference in rotational rate of the rotors and eccentric shaft.
• Both types of engines often use forced induction applications such as turbochargers, supercharges, and nitrous oxide to compress and/or make the inducted air more dense to increase their efficiency and power output. Engines utilizing forced induction normally use lower compression ratios (~9:1 or lower) to prevent engine damage from increased internal pressure.

```Page 2: The Physics Behind Rotary Engines
Page 3: The Physics Behind Piston Engines