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In many mechanical devices, friction is the cause for reduced performance and general wear down, and it must be minimized as much as possible (sometimes friction is openly welcomed, such as the connection between a tire and the ground). It prevents moving parts from reaching maximum potential. Parts rub against each other, thereby converting kintetic energy into heat energy.
In a modern internal combustion engine's cylinder, a piston is sent downwards by the fuel/O2/ignition burn, which forces the attached connecting rod below to turn the crankshaft. Since the crankshaft is directly below the piston, the ignition must occur right when the rod/crank point has just passed top dead-center on its way back down in order to keep the crankshaft moving. The only problem is that the position of the rod at this time is at an angle, and causes the piston to press against one side of the cylinder wall. This pressure slows down the piston's downward movement and power is lost, while unwanted excess heat is built.
The tangential engine addresses this natural flaw by having the crankshaft offset to the side, instead of directly under the cylinders. This way when ignition occurs, the position of the rod will be perfectly vertical and won't press the piston against the cylinder wall.
Check the animated diagram on Jack's site. See where the piston rubs against the wall? That's energy lost, and power/fuel wasted. The tangential solution saves that energy.
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