I understand (from preliminary research) that when engine gets bigger, with a higher displacement that it is practically not possible to have a two stroke engine.
What are the implications in building a higher cc two stroke engines?
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Lubrication and cooling of two-stroke engines have always been the limiting factors. The bigger the engine, the bigger the problems. A big two-stroke will have a very short service life, even with constant maintenance.
Two-stroke engines burn oil in their fuel and burning oil causes pollution.
The charging of the cylinders by its port arrangements mean they are not fuel efficient. Burning more fuel inefficiently again gives more pollution.
The Communist East German Trabant was the last vehicle made with a two-stroke engine, you dont have to say anything else really.
The two-stroke today is used for machines such as lawn mowers and water pumps where its simple design with small size and minimal maintenance make it endurinly 'useful'.
I am not sure where you get the idea they haven't built larger displacement two stroke engines. Detroit Diesel built the 71 series which was very large displacement two stroke engines. From Wikipedia:
The Detroit Diesel Series 71 is a two-stroke diesel engine series, available in both inline and V configurations, with the inline models including one, two, three, four and six cylinders, and the V-types including six, eight, 12, 16 and 24 cylinders. The two largest V units used multiple cylinder heads per bank to keep the head size and weight to manageable proportions, the V-16 using four heads from the four-cylinder inline model and the V-24 using four heads from the inline six-cylinder model. This feature also assisted in keeping down the overall cost of these large engines by maintaining parts commonality with the smaller models.
These motors required a supercharger (roots type blower) in order to function, as a normally aspirated engine could not intake enough air to function properly. Due to this, the entire crankcase was under pressure. Some of the larger engines had both a supercharger and a turbo-charger placed inline to produce the amount of air flow needed to feed the monster. They also used exhaust valves (either two or four) to vent the exhaust. Since these engines are diesel fed, and diesel is in and of itself an oil, there was adequate amount of lubrication for these. The engine lifespan was good and viable. They quit building it in 1995 in favor of a four stroke design. I believe this was due to the 4-stroke design being more efficient.
To give you an idea how big the engine was, each cylinder displaced 71 cubic inches (hence the series name). The 24-cylinder engine displaced 1704ci (27.9l) and produced 1800 horse power. I don't have the torque number, but assume it was HUGE.
I believe what Allan has said about gasoline (petrol) 2-stroke engines is very true, but understand larger engines of the 2-stroke variety have been produced and were commercially viable.
I know this thread is a bit old, but Detroit Diesel and GM EMD (Electro-Motive Division) have many 2 stroke Diesels. The crankcases! Well they aren't pressurized. How it works is different to a smaller 2 stroke engine. Instead of the underside of the piston 'pushing' an air fuel charge up a transfer port, these engines have an air gallery around the cylinder liners. The cylinder block is machined to accept the cylinder sleeves. Immediately below the block deck is water and below that is an air gallery. The cylinders have the conventional ring of ports and the piston acts as the intake valve in the conventional sense. Pressurized air is supplied, usually but not always, by a Roots blower. Exhausting is effected by 2 or 4 valves in the cylinder head which are cam operated. The fuel delivery is by unit injector (one injector per cylinder pressurized at the cylinder and not by a remote injector pump). The injector is pressurized by a rocker arm and cam driven by the exhaust camshaft.
Detroit Diesel sizes are per cylinder i.e. 8V92 means V8 and 92 cu in per cylinder. 6-71 means inline 6, 71 cu in per cylinder. The EMDs are similar 16V645 means V16 and 645 cu in per cylinder. The EMDs are very common the world over particularly for electricity generation. They are used in tug boats and Diesel electric locomotives also.
Interestingly some EMDs have a hybrid turbocharger. A large (about 6' high) centrifugal blower is powered by the crankshaft for starting and idling and then exhaust takes over. An overrun clutch allows free spooling of the compressor.
The problem with all supercharged engines, as with normally aspirated engines, is power output is affected by altitude. The higher you go the less power you make. Turbocharged engines address this, so the rated power is maintained at all altitudes wheeled vehicles are likely to see. I mention this because the blower on 2 stoke Diesels DOES NOT ACT AS A SUPERCHARGER. It is a positive displacement air pump. Detroit Diesel categorize all their unturbocharged 2 stroke Diesels as N. N means natural. For example 8V92n as opposed to 8V92t. The Ns loose power with temperature and altitude increase, whereas the Ts maintain rated power because they have a turbo as well as the blower. Turbo Detroit Diesel 2 strokes have both the blower and the turbo. Similar to the the EMD hybrid turbo principal, the Roots blower is required for starting and idling then the turbo takes over. Unfortunately the blower parasitic pumping loss (paid for in fuel and power loss) is still applied as there is no means of disconnecting the blower. They do have a bypass flap and this saves 30% of the blower load by bypassing air when the turbo is pumping, but the blower rotors are still turning. The Hybrid design was proposed for Detroit Diesel Silver Series but were dropped because of cost in favor of the bypass flap but as mentioned the rotors in the blower are still always turning.
Perhaps you were thinking of 2-stroke gasoline engines when asking the question.
Evinrude built a 3.6 liter gasoline 2-stroke for outboard boat motors.
Interestingly the exhausts are in the V in this design, which is necessary as the carburetors need to inlet into the crankcase.
2-stroke supercharged diesels are really a completely different type of engine with different methods of lubrication and scavenging.
Just to ram the point home that 2-stroke diesels can really be very large, try over 1000 liters displacement: https://en.wikipedia.org/wiki/W%C3%A4rtsil%C3%A4-Sulzer_RTA96-C
Suzuki built two stroke gasoline motorcycle engines in the 1960's, 1970's which were every bit as durable as the four stroke motorcycle engines of similar displacement being offered at the time. Suzuki built a water cooler 3 cylinder 750cc two stroke motorcycle which a service life of over 100,000 miles without rebuild was not unheard of. I have one of these in my collection. This machine is now over 40 years old with over 40,000 miles on and it still runs fine. The motor has never been opened. I crossed the continent 3 times on a Suzuki 500cc two stroke two cylinder motorcycle. I sold this same motorcycle with around 50,000 miles on it, with no internal engine work ever having been done. I sold it to a fellow who took it across the continent for a 4th time. He called me when he had finished his tour of the country on that Suzuki. His only failure being a broken speedometer cable. That's where I lost track of the machine. These machines were built using the tech of the 1950's and 1960's, The last of which was offered for sale here in the States in 1977. There really is no telling where this tech could have gone. The EPA basically having regulated it into being economically unfeasible to pursue. With today's lubricants, metals and hybrid materials, there is really no telling where two stroke gasoline engines would be today.