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I have limited experience with flight simulators but I have never bumped into a plane with manual transmission while, on the contrary, it's very common for other means of transportation (like cars and bikes) that rely on engine with some form of transmission control.
First of all, I'd like to know if it's actually true that no airplane have (or had) manual transmission and, secondly, why that is so.
Aircraft have fixed gears (when they have gears at all)! However in a sense a variable-pitch propeller can be considered analogous to transmission in a car and it was manual in some aircraft.
The power transmitted by propeller is, within some reasonable range, proportional to its rotation rate. And so is, again within some reasonable range, the power produced by the engine. So for slow planes a fixed pitch propeller with connected by fixed gear does a decent job. As you open the throttle, the engine speed increases, so does the propeller and that's exactly what it needs to do to transmit the power. Simpler aircraft have no gears at all and propeller is mounted directly on the engine shaft, higher power engines often have 2:1 reduction gear as the engine rpm would be too high for a propeller.
Now at higher speed, the apparent propeller pitch is reduced as the air is already moving, so it would spin faster and faster and eventually too fast for the engine. To counter this, faster propeller-driven aircraft have variable pitch propeller. As speed increases, it is set to higher angle of attack (coarser) so it keeps delivering power without increasing rpm.
Early variable pitch propellers had manually controlled pitch, but quite quickly constant speed propellers were developed (many WWII aircraft had them already) where a weight-on-spring controls the propeller pitch so that constant rpm is maintained. The manually controlled units required a lot of attention and the constant-speed system is rather simple, so manual pitch control was quickly abandoned.
And that is kind of equivalent to perfect variable gear transmission. The pilot still has a throttle lever and a propeller pitch lever and selects power and rpm independently. Higher rpm allow higher power, but don't require it, so landing is usually done with low power, but max rpm so the engine reacts quickly if power is added (does not need to spin up). During cruise some more moderate value is selected (according to manufacturer recommendation) to reduce wear of the engine.
Turboprop engines always have constant-speed propellers, because in a turbine engine the difference between turbine speed at idle and at full power is not actually that big. Again the rpm limits maximum power, so landing is done with low power, but high rpm and the engine reacts quickly when power is added.
Last the turbojet/turbofan engines just turn the turbines and compressors as they need. It's not much different from the fixed propeller really, though the jet engines now usually have variable guide vanes in the stator (that are just linked to rpm).
Because most aircraft engines do not have geared transmission at all:
Image from wiki
The power is directly transmitted from the turbine to the compressor with a rigid shaft.
It is true, though, that some engines have it, in particular, propeller engines:
Image from ATSB
but you have to realize that this a fixed gear ratio, no gear shifting is involved and thus, no manual nor automatic "transmission" is required.
What you might have, in "old style" propeller engines, is different levers/knobs for manifold pressure/throttle, propeller pitch and mixture.
I suspect that the real answer involves torque.
Aircraft engines don't have or need multiple gears because the engine doesn't move the aircraft from standstill by applying torque to wheels. Instead an aircraft engine can run at full RPM while the aircraft is stationary at the start of a runway.
If you put your car in top gear (6th?), ran it at maximum RPM (8000?) and dropped the clutch, something would break - at the very least you'd burn the clutch and crawl away slowly. Aircraft engines don't have or need a clutch, ultimately because they are pushing air, not turning wheels on tarmac.
Variable ratio gearing in road vehicles (cars, bicycles, etc.) is required to match the speed and torque capabilities of the prime mover (gas engine, human leg power, etc.) to the speed and torque requirements of the road wheels over varying conditions of vehicle speed, road grade, etc. Basically, there is a need (or at least benefit) to vary the mechanical advantage between prime mover and driving wheel(s).
The prime mover (jet or piston engine, turbofan or propeller) in an aircraft produces thrust largely independent of airspeed, so for many aircraft, variable ratio gearing is not required. For propeller aircraft, it can be beneficial to vary the mechanical advantage between the powerplant and the airstream. It is done, not by variable ratio gearing, but by varying the pitch of the propeller. For one thing, varying the pitch can vary mechanical advantage over a continuous range where a gearbox is limited to a few fixed steps. For another, gearing systems add a lot of weight. Changing gears would mean disconnecting the engine from the propeller as a different gear ratio is selected - that's a big reliability/safety issue, and for a piston engine, couldn't even be workable. Piston engines can't run without a flywheel; in an aircraft, the propeller serves as the flywheel.
So, where the benefits of variable mechanical advantage justify the added cost, weight, and complexity, a variable pitch propeller is fitted.
Some variable pitch systems provide a lever which directly control the pitch - the pilot moves the lever over a range between "fine" (engine gets more mechanical advantage, suitable for take-off) and "coarse" (engine has less mechanical advantage, suitable for cruise).
Other variable pitch systems provide a lever which selects a target engine RPM. The pitch control system continously adjusts the propeller pitch in an attempt to maintain the selected RPM. The pilot uses the throttle to increase or decrease engine thrust, and the pitch control to optimize the engine RPM for the operating conditions (take off, climb, cruise, etc.). On a PA32-300, for example, the pitch control would be fully forward (max RPM) for taxi, take-off, and initial climb-out, but would be adjusted back somewhat for cruise to reduce engine RPM (and fuel consumption).
You could think of the pitch control systems I've described as analogous to a manual and an automatic transmission respectively, but the analogy is a loose one at best.
Slightly different answer to the last one. Air whipping engines don't need a lot of torque to push through viscous friction that resists blade travel. That is why quadrotors work and yet are very light.
Simple comparison, push against a wall and there is a normal force pushing back. Now wave your arm in the air. The only resisting force is a function of your arm speed. It's tiny.
Since they don't need to use gear reduction to increase torque like other applications, they don't need a gear changing transmission. In fact Bernoulli effect works on thrust from air flow over the blade so you want the propellers spinning as many times as possible to get maximum lift. Electric motors for quadrotors spin 10000 RPM for example. They control motor spin speed through throttling air and fuel for turboprops or pulse width modulation for electric motors. Turbines are air and fuel I think as well, but that's not my expertise.
Flight simulators don't have geared transmissions because real planes don't have geared transmissions. The closest thing a plane would have is a variable pitch prop.
With a vehicle with wheels, the engine rpm is easily calculated as a ratio with ground speed and the gearing. There's nothing like that with an aircraft.
Another factor not mentioned is that in land vehicles gears are used for travelling slowly, so the engine can stay in its operating range. But an airplane won't fly below a certain minimum stall speed, so gears are pretty pointless. In a typical small plane, your range of flying speeds (say 65-150 mph) corresponds to an engine speed range of roughly 1700-2500 rpm. If you throttle back to idle (or your engine quits), you basically have to glide, trading altitude for the airspeed needed to stay above stall speed.
A lot of complicated answers... but the simple truth lies in the term itself - transmission!
Power must be transmitted, somehow, from the engine to whatever will push the vehicle forward - the wheels or the propeller. Internal combustion engines have an optimum power transmission rpm range - above or below which the efficiency of the engine drops drastically.
The difference between land vehicles and air or sea vehicles is, as mentioned by others here, that the friction between the wheel & land needs a much greater starting torque to get that wheel moving. Whereas, rotating a propeller through the air or water can be done much more easily & quickly.
In fact, this also ties up with why only land vehicles have (and can have) brakes. Neither air nor sea vehicles can have brakes. Because braking involves that same friction which was overcome to get the vehicle started. Due to lower co-efficients of friction, both sea & air vehicles continue to move even if the engine stops functioning. Obviously, air vehicles never need to be braked to a standstill while still in air. But water vehicles do and that is achieved by reversing the direction of the propellor's rotation.
Because propellers in water and air use the friction to move the object. And this friction is far less than the one between asphalt and tires. In one way, the gas is acting as gearbox. The other side of this coin is that it makes it hard to do fast accelerations from 0.
