why do most airplanes use two spool engines?
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Because it’s more efficient in terms of power vs fuel.
Smaller stages want to run at higher speeds. Having the second spool lets you use a bigger, slower, fan, which means you can push against more air, and consequently accelerate that air less to get the same force.
It helps to think about it in terms of momentum vs kinetic energy. The thrust is proportional to how much momentum the air gets, and this is Mass * Velocity. The energy you have to spend accelerating the air is 1/2 * Mass * Velocity^2 So if you double the amount of air you’re pushing against, and accelerate it half as much, you get the same force but spend half as much energy accelerating the air. If you are able to push against something with extremely high mass, like the earth, you spend energy accelerating yourself, but you don’t really spend anything significant accelerating the earth, because you change its velocity(and energy) by a negligible amount.
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