First the electric drive has always been the most efficient from an energy to power point of view. The problem was and is storage of the electrical power till it was needed. In the old streetcar that problem was solved with the overhead wires, thus stayed competitive with buses till people thought in terms of the cost this year (In any five year period, buses are cheaper, but they wear out quicker then Streetcars, so if you look at 20 year periods, Streetcars win hands down).
Now, one way to get the use of electric power is vehicle without access to overhead wires is to use an engine to produce the electrical power. What are called "Diesel" railroad engines have always done this, the actual drive on a diesel is electricity, the diesel is just a generator.
Batteries are another way to store electrical power for later use, they are NOT as efficient as generators, but are getting close. The big drawback is batteries to weigh a good bit of mass (Through that is getting lower, but even Lithium batteries have some weight). Thus the ideal situation is just enough batteries to get the vehicle from point a to point b. The problem is present electrical storage is not that great, gasoline still has more power in it then any battery is expected to have for at least another 20 years (and that is assuming the present increase in battery storage capacity, which some people do not think will continue). Thus today, most cars are designed only to operate 15 to 30 minutes on battery power alone. That is good for a lot of people, but not most people.
To get around this problem, the hybrid was adopted. It is a variation of the Diesel Railroad engine concept, i.e. a generator that charges the batteries AND provide extra power when needed. The gasoline engine turns off when the batteries are full and the electricity from the generator is NOT needed to propel the car.
As I like to point out Diesel Locomotive and diesel-electric drive (the most common drive on not only sea going ships but barges on the rivers) have been used for decades. Now, these were designed never to be turned off for some power was always needed somewhere on ships (and to a lesser degree on Locomotives) but if you turned the engines off, some locomotives and ships would still have enough power to stop safely.
The biggest waste on a gasoline or diesel engine is running it when it is not needed. With a Hybrid system, the actual power to propel the vehicle is electrical power and batteries can do that in most situations. Occasionally you will need extra power and the gasoline engine will cut in to provide that power, and then cut out when it is not needed.
Gasoline and diesel engines are at these least efficient when they are idling. This just eats up fuel. With conventional gasoline or diesel engine, the engines has to idle when the extra power that the engine can provide is not needed. In a hybrid during those low power needed period the engine cuts off and the electrical batteries provide all of the needed power TILL it is time extra power is needed and the gasoline or diesel engine is kicked on till the extra power is NOT needed.
Thus a hybrid system permit the max efficiency of both the electrical drive and gasoline/Diesel engines, for where one is weak the other is strong. At idle or constant speed electrical power is all one needs, when rapid acceleration is needed the gasoline/Diesel engine is kicked in till the extra power is no longer needed then the gasoline/Diesel engine is cut out. This is why such systems get 40 to 60 miles per gallon. It is the result of taking two system and integrating them where one is weak and the other is strong and making an overall stronger system.
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