From your first Post: -
[[i]i]"a)The process of the combustion of the mixture begins before the piston arrives at the “top dead point” and it means that the movement of the piston to the ”top dead point” is counteracted by the total pressure: the sum of the degree of the compression, and the increasing pressure of the inflamed mixture, and that results in loss of the power."
It is true that combustion starts just before TDC, this is deliberately done for two reasons,
1) There is an ignition delay after fuel is injected before combustion starts, and combustion itself is a "Chain reaction", it starts slowly and grows exponentially, therefore to achieve maximum pressure just after TDC injection has to start well before TDC and combustion will start a little later but still before TDC in order to achieve optimum efficiency. Modern Electronically controlled common Rail fuel injection systems achieve this very well, under all running conditions, while simple mechanical injection systems could only be optimised for one type of fuel, at one speed and load.
2) As the piston is being pushed upwards by the connecting rod on the compression stroke the bearing surfaces of the bottom end and Big end are all under load, at TDC the crank changes direction and if there was not enough pressure on the piston, both the connecting rod and piston would continue upwards under the influence of inertia, until all the clearance in the bearings had been taken up and the BE bearing hammered on the Crankshaft journal and the Top End bearing hammered on the Gudgeon Pin. When the engine fired, and the pressure started to force the piston down to transmit force to the crank, the bearings would be hammered again. This would obviously be very damaging to the engine, and has to be avoided by keeping the load on the bearings in the same direction throughout the cycle rather than having it alternating.
.b) The change of a coefficient of the tangential force to the force working on the piston from the value of 0 up to the value of 1. 2.The engine of the internal combustion uses in the best case scenario only 75 % of the fuel and 25 % goes in the exhaust pipe and the muffler. Namely, this part of the fuel is burning in the catalyst. But catalyst is the very expensive device and it requires the substantial part of the powerful of the engine for pumping the fuel through a dense net of the surfaces of the catalyst. There are several reasons for this phenomenon and one of them is the very short time of the process of the burning. The average time of the burning of the fuel in the cylinder is 0.001sec. In other words the effectivity of the engine depends on the length of the motion of the piston. But the length of the motion of the piston is directly related with the size of the crankshaft and this relationship limits the length of the motion of the piston.
I have never heard of any engine that is 75% efficient. When I started as an Engineer we used to say that, for a large marine engine 1/3 of the Chemical Energy in the fuel is converted into useful Mechanical Power, 1/3 into waste heat in the exhaust gas and 1/3 into waste heat in the cooling water. At that time typical car engines were about 15% efficient, less efficient that a coal fired Scotch Boiler powering a triple expansion steam engine.That is why using this waste heat is so important to Plant Efficiency as opposed to engine efficiency. The improvements over the last 45 years have increased Engine efficiency to about 40%.
If the engine is being operated correctly no fuel should be burnt in the catalyst, and it should not require a great deal of power for the exhaust gas to flow through the catalyst. Obviously the catalyst causes a slight pressure drop in the gas flow and hence a slight increase in the back pressure at the engine, reducing its efficiency slightly and raising the exhaust temperatures slightly. If there is a significant pressure drop the catalyst is dirty and requires cleaning.
As I have said before, the tangential force does not cause a significant loss of power/ energy, because there is no movement in the direction of that force. The friction between the cylinder and piston may be slightly increased by this transverse force, but not sufficiently to reduce the efficiency of the engine.
The catalysts are fitted in the exhaust Gas system, not the fuel system so I am not sure why you are talking about pumping fuel through the catalyst?
The duration of combustion does not greatly effect efficiency, we are not using the force of the explosion to drive the piston, we are releasing energy (through the combustion process) to heat the working fluid (the excess air over the stoichiometric ratio) as the air is heated it tries to expand, generating the pressure that drives the piston. Also, as has been pointed out, modern engines using Electronically controlled Common Rail Fuel Injection, can inject fuel as many times as desired throughout the power stroke, so combustion duration can be maintained over longer periods by making multiple sequential injections of small quantities of fuel, starting before TDC and continuing throughout the power stroke.
I agree that the longer the length of the stroke, the more the Gas is expanded and the less energy is passed into the exhaust pipe, that is why some large 2 stroke engines for big Tankers have a 2 metres long stroke, and they use a conventional crankshaft without any problem, but usually they run at about 60 RPM flat out to optimise the propeller efficiency. However, with a shorter stroke engine that energy can be recovered in an exhaust gas boiler or an exhaust gas power turbine. However, if the expansion stroke were too long there would be insufficient energy in the Gas for it to exhaust properly, there is a limit to how far you can increase efficiency by lengthening the stroke, there comes a point where the pressure is so low that it does not overcome friction in the engine!
"3. The significant influence on the fuel efficiency makes also a short time for the exhaustion of the burned mixture. It means that the new portion of the fresh air-gas mixture is mixed with remains of the burned mixture. These phenomenon decreases the powerful of the engine."
The short time for the exhaust gas to leave the cylinder is common to all 2 stroke engines and one reason why 4 stroke engines tend to be more more efficient, although they tend to have a lower power to weight ratio.
Opposed piston engines have Uniflow scavenging as do the large poppet valve engines like the Sulzer RTA and later engines. Until the demise of Doxford, Sulzer always claimed that there "loop scavenging" design gave superior scavenging to Uniflow, however, it is evident that Uniflow scavenging avoids the problem of the New charge of air mixing with the previous air/ fuel charge.
"4. When the piston is at the “top dead point”, the compressed mixture is ignited. It is known that for the full and complete combustion of the fuel vapor desirable the high temperature and the high pressure. But immediately, when the piston passed the “top dead point”, it starts to move down with the significant increasing of the space above the piston. With the spread of the flame front of the mixture in the combustion chamber the first portions of the mixture will burnt at the high temperature and the high pressure. But the latest portion of the hot mixture burns under the condition of the sharply declining of the pressure and the falling of the temperature. For this reason, the part of the mixture does not have the time to burn or not burn fully."
This is simply not true!! I have never heard of modern engines pumping excess fuel into the exhaust pipes, until the fuel system is set up incorrectly, even high speed engines have plenty of time to burn all the fuel.
I have spent a considerable amount of time searching for a way to make you understand that the angle of the crankshaft does not effect the efficiency of the engine.
The best analogy I have come up with is Electrical. In A.C. circuits driving Electric Induction motors the current flows out of phase with the voltage by an angle known as the phase angle. The product of multiplying the Voltage with current that is in phase with it (Cos. Fi of the total current) is the true power, in kW. The Re active power, the Volts multiplied by the vector of current acting at Right Angles to the Voltage, is known as Wattless power, because it does not have any power, because no Voltage is acting in phase with it.
It is similar with the resolution of forces on the connecting rod, you resolve them into a force acting in line with the movement of the piston, which produces true power, and a force acting against the side of the cylinder, which does not produce any power and could also be described as Wattless".
It is always better to ask a stupid question than to do a stupid thing.