AN OTTO ENGINE DYNAMIC MODEL

Otto engine dynamics are similar in almost all common internal combustion engines. We can speak so about dynamics of engines: Lenoir, Otto, and Diesel. The dynamic presented model is simple and original. The first thing necessary in the calculation of Otto engine dynamics, is to determine the inertial mass reduced at the piston. One uses then the Lagrange equation. Kinetic energy conservation shows angular speed variation (from the shaft) with inertial masses. One uses and elastic constant of the crank shaft, k. Calculations should be made for an engine with a single cylinder. Finally it makes a dynamic analysis of the mechanism with discussion and conclusions. The ratio between the crank length r and the length of the connecting-rod l is noted with landa. When landa increases the mechanism dynamics is deteriorating. For a proper operation is necessary the reduction of the ratio landa, especially if we want to increase the engine speed. We can reduce the acceleration values by reducing the dimensions r and l.

Almost a quarter of the planet's population works directly or indirectly for the construction of machines.Most specialists are involved in the development and production of road vehicles.
If Otto engine production would stop right now, they will still working until at least about 40-50 years to complete replacement of the existing fleet today.
Old gasoline engines carry us every day for nearly 150 years."Old Otto engine" (and his brother, Diesel) is today: younger, more robust, more dynamic, more powerful, more economical, more independent, more reliable, quieter, cleaner, more compact, more sophisticated, more stylish, more secure, and more especially necessary and wanted.At the global level we can manage to remove annually about 60,000 cars.But annually appear other million cars (see the table 1).DOI: 10.14807/ijmp.v7i1.381In full energy crisis since 1970 until today, production and sale of cars equipped with internal combustion heat engines has skyrocketed, from some millions yearly to over sixty millions yearly now, and the world fleet started from tens of millions reached today the billion.As long as we produce electricity and heat by burning fossil fuels is pointless to try to replace all thermal engines with electric motors, as loss of energy and pollution will be even larger.However, it is well to continuously improve the thermal engines, to reduce thus fuel consumption.Planet supports now about one billion motor vehicles in circulation.
Otto and diesel engines are today the best solution for the transport of our day-to-day work, together and with electric motors.
Even in these conditions internal combustion engines will be maintained in land vehicles (at least), for power, reliability and especially their dynamics.

DETERMINING THE FIRST EQUATIONS
The first thing necessary in the calculation of Otto engine dynamics, is to determine the inertial mass reduced at the piston (1).
Then it derives the reduced mass to the crank position angle (2).
Lagrange equation is written in the form (3).

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Were used for piston the next kinematics parameters (4).

DYNAMIC EQUATIONS
The dynamic equation of motion of the piston, obtained by integrating the Lagrange equation ( 3), takes the form 5.
Dynamic reduced velocity (6) and dynamic reduced acceleration (7) are obtained by derivation:

NOTATIONS AND FIGURES
In the Figure 1 For the masses one uses the notations (18); see the Figure 2.
  the ratio between lengths of crank and rod;  The parameters c1-c4 take the forms (19):
The crank length, r, and the length of the connecting-rod, l, can be seen in the kinematics schema of an Otto mechanism (Figure 2).For a proper operation is necessary reduction of the ratio  , especially if we want to increase the engine speed (see the next diagrams).

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it presents the crank shaft.The relation (17) determines the elastic constant of the crank shaft, k.