Why do piston engine airplanes have no gearboxes?

Why don't airplanes have a manual gearbox?

Have planes fixed Gears (if they even have gears)! However, in a sense, a variable pitch propeller can be thought of as analogous to the gearbox in a car, and it was manual on some airplanes.

The power transmitted by the propeller is proportional to its speed within a reasonable range. And so the power generated by the engine is again in a reasonable range. For slow planes, a fixed pitch propeller does a good job. When you open the throttle, the engine speed increases, as does the propeller, and that is exactly what it has to do to transfer the power. Simpler aircraft have no gears at all and the propeller is mounted directly on the motor shaft. Higher power motors often have a 2: 1 reduction gear because the motor speed would be too high for a propeller.

At higher speeds, the apparent pitch of the propeller is reduced, as the air is already moving, making it turn faster and faster and ultimately too fast for the motor to run. To counteract this, faster propeller aircraft have a propeller with a variable pitch. With increasing speed, a higher angle of attack (coarser) is set so that the performance continues without increasing the speed.

Early variable pitch propellers had manual pitch control, but constant speed propellers were developed fairly quickly (many WWII aircraft already had them) in which a weight on the spring controls the pitch of the propeller so that a constant speed is maintained . The manually controlled units required a lot of attention and the constant speed system is quite simple so manual pitch control was quickly abandoned.

And that roughly corresponds to a perfect variable transmission. The pilot still has a throttle and a propeller pitch lever and selects power and speed independently of each other. Higher speeds enable higher performance, but do not require it. Therefore, the landing is usually done at low power but at maximum RPM so the engine responds quickly when power is added (does not need to be ramped up). A more moderate value is selected while driving (as recommended by the manufacturer) in order to reduce engine wear.

Turboprop engines always have propellers with constant speed, because with a turbine engine the difference between the turbine speed at idle and at full power is not so great. Again, RPM limits the maximum power so the landing is low power but high RPM and the engine reacts quickly when power is added.

Finally, the turbojet / turbofan engines turn the turbines and compressors as required. It is not that different from the fixed propeller, although the jet engines now usually have variable guide vanes in the stator (which are only related to speed).