does upshifting drop RPMs not because its harder to spin the wheel, but rather the opposite? And gears in general

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For example, if you shift to 2nd to 1st, does the rpm jump not because the engine load has decreased and it can spin faster, but rather because it has to work harder than it would in higher gears?

In: Engineering
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The work the engine needs to do is the same. The question is what speed (as in RPM) makes it easier for the engine to do the work. Higher revs have byproducts like more friction, more heat, etc.

The other interesting thing to realize is that, all else being equal, having more weight in the car will need to use more fuel to turn the engine at any given RPM.

When you look at two ends of a shaft, they must both be spinning at the same speed because they are connected.

If you connect two shafts together with gears, then their speeds will be coupled – one will always spin at some multiple of the other. Let’s say double. By changing the gearing ratio, it may change from double to triple or quadruple.

So, if the wheels are spinning at, say, 1000 RPM, and the gears are 1:1, then the engine must be spinning at 1000 RPM. If we shift gears, the shafts are now connected to a 1:2 ratio. The engine must now be spinning at double the speed of the wheels, and any discrepancy is rectified by friction in the clutch.

Ever ridden a 10 speed bike? Same thing. Lower gears allow you to pedal quickly with little resistance but you go slow. That’s 1st gear in a car. 10th speed you can only pedal slowly with a great amount of resistance, but with each turn of your crank, your rear tire starts whipping around fast. That’s 5th gear in your car.

When you downshift the engine speed increases because you’ve changed the gear ratio and now a larger engine RPM corresponds to the same wheel RPM or ground speed. It’s a matter of gear ratios. The load on the engine determines your fuel consumption. You can have super high RPM with minimal load, and super low RPM with very high load, depending on your driving conditions, current speed, and throttle position. The engine RPM is set by your gear ratio and your ground speed (more accurately stated: “Your ground speed is set by your engine RPM and your gear ratio.”)

In a car the engine rate is proportional to the wheel rate and the ratio of the two is determined by the gearing. If you change gears (thereby changing the ratio of wheel to engine rates), either the engine or the wheels need to change rate. If the wheels have grip, they cannot spin at a different rate without slowing or accelerating the very heavy vehicle and so the engine speed must change.

When operating a manual transmission, you will typically use the throttle to adjust the engine RPM before re-engaging the clutch that links the engine and transmission. If you don’t and quickly engage the clutch, the vehicle will decelerate slightly with a jolt as the vehicle’s momentum brings the engine to the appropriate speed. If you have no grip at all, the engine rate will depend almost entirely on the amount of throttle (though there will be some small change due to the momentum of the wheels themselves and the bits that connect it all together).