Internal combustion engines don’t run smoothly, it just seems like they do. Each combustion drives a piston down with force creating a “pulse” in the entire drive train. When this is happening fast and without much resistance, you just feel a mild vibration through the car.
The engine also relies on mechanical advantage to move the vehicle. Low gears give the engine a lot of advantage, so it can turn the wheels easily. Just not very fast. High gears remove that advantage, but allow the engine to turn the wheels fast.
A manual transmission vehicle has a physical link from the engine to the wheels. The gears change how many times the wheels will turn for each turn of the motor, but if the wheels slow down, the engine WILL slow down to match. It is physically connected. And automatic transmission uses fluid pressure to drive the wheels and can spin independently from the engine’s rotations.
Let’s tie all this together. The engine is pulsing with each combustion stroke. It’s in high gear, so the wheels are very hard to turn. The engine is directly connected to the wheels, so it can’t freely turn faster without spinning the wheels faster. This means that when the pulse happens the engine can’t really turn the wheels. Instead, the engine gets shoved by its own power and tries to rotate instead, but it’s held in place by the engine mounts. This is the shake that happens at low speed.
The engine stalls at low speeds because it has very little power at low speed. That means it can’t turn the wheels enough to complete a full stroke and compress another cylinder enough for the engine to fire it and drive the piston down.
Latest Answers