Quadrotor drones with fixed pitch propellers are cheap to manufacture and light enough that electric power is viable
Such designs only work with electric or hydraulic power – a traditional engine cannot spin up or down fast enough to make a quadrotor work.
By contrast, things like variable pitch propellers are very expensive for drone sized platforms….. So you really only want 1 or 2 if you are doing that, which means helicopter….
Electric power doesn’t scale up – the weight of batteries and multiple motors quickly becomes too heavy for efficient flight.
Also full sized aircraft aren’t as cost constrained as hobby drones.
So when you are doing a full size aircraft it’s easier to use variable pitch constant speed rotors…. And since you aren’t trying to use differential thrust for control you only need 1 or 2 of them, and when you do that you have a helicopter.
Larger rotors are much more efficient, and therefore helicopters are much more efficient than multi rotors. Small drones are multi rotors because they’re much simpler mechanically, they don’t need swash plates and variable pitched blades, anti torque rotors, etc. So multi rotors make sense for small cheap drones. Also multi rotors are inherently unstable and need a flight controller to stabilize them, whereas helicopters are stable without a flight controller.
Lots of good points made already but I think there’s one really crucial aspect missing from the answers thus far.
Mainly a quadcopter configuration requires very very precise and responsive RPM control of each of the four rotors. It is these RPM adjustments that allows it to control itself. This level of RPM control you can get with electric motors but you can’t get with an internal combustion engine.
This works really well on a small scale with a battery-powered drone but we don’t have battery technology with a high enough power to weight ratio to make battery-powered helicopters that can fly for any reasonable time.
Quadrotors don’t scale up well because of how they are controlled.
A traditional helicopter has the blades spinning at a more or less constant speed. Control comes from altering the pitch of the blades, either one at a time at a certain part of the rotor disc for pitch and bank (cyclic) or all at once to increase and decrease overall lift (collective).
A quadrotor, on the other hand, uses blades with a fixed pitch. It is controlled by varying the speeds of the blades. This means that the speed of control inputs is limited by how rapidly the speed of the blades can be changed.
With small plastic blades a few inches long, the torque required to rapidly increase or decrease the speed at which the blades are spinning is manageable.
On a quadrotor the size of a large helicopter, on the other hand, this would require massive amounts of torque applied very rapidly. You’d need to use heavy, hugely overbuilt electric motors, stronger, thicker blades, and a power system that can buffer that kind of sudden shift in power delivery. All of this would add a good deal of weight, and simply wouldn’t be practical.
Airplane = able to land even with complete turbine failure.
Helicopter = still has autorotation after engine failure, at least sometimes.
Quadrocopter = boom.
Not even starting with the technical complexcity.
There are multiple solutions nearly ready for use though. E.g. https://europe.autonews.com/article/20170927/ANE/170929826/dubai-tests-german-built-volocopter-drone-taxi
You can also take a look into hybrid variants (VTOL) and its pros/cons, like the V22 Osprey and yes, it did crash often.
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