The main difference between them is one of technology.
A drone has multiples fans, which are (almost always) fixed fans, and its controlled by varying the speed of those fans. So to go forward, the fans on the frontend slows slightly, while the back speeds up slightly, tipping it forward, and moving it on a now vectored thrust. And to keep stable, the fans are run in paired directions, clockwise and anticlockwise, so to rotate, you adjust the speed based on the fan direction, to keep overall thrust up, but rotate by gyroscopic procession.
A helicopter works very very differently. instead of ‘fans’ just blowing air down, it has rotors, which are wing-shaped, and on a movable mounting. A helicopter moves by the helicopter wing generating lift like an aircraft. The aircraft is steered by altering the angle of the rotor, generating more or less lift at certain points of the sweep. [this link](https://www.explainthatstuff.com/helicopter.html) explains the method much better than I can.
So the BIG difference is that drones work by blowing air down and using that as thrust, while a copter generates lift on the rotor. This makes a HUGE difference in one area – loss of power. If your drone runs out of power, the fans are no longer being spun, and no thrust is being generated, and as it drops the wind force will back-spin the props. When a helicopter runs out of power, the wind force also spins the blades, but because they’re wings, that produces ‘some’ lift, this is called ‘autorotate’, and is a way to not have everyone immediately die. It’s also how autogyro/gyrocopters ‘fly’. The world record for helicopter altitude is 40,000ft, and its record is when the engine flamed out and died, and it only survived because of autorotation. No autorotation, no passenger safety certification.
And then we come to design. a drone needs an even number of rotors, all of equal size, and for controlability they need to be spread around it. That means you’ve now got 4 (or more) large rotors spread around a large aircraft which means a lot of shafts to drive it, and then a lot of really complex gearing to adjust the speed on each of them. Its pretty much impractical to do it with ICE, so it has to be electric. And because motors get less efficient in a power/size ratio the larger they get – the motors needed for an equivilent of a light utility helicopter (a Robinson R22 for instance) would be 50lb each, plus expensive power controllers, thick cables for power plus all the batteries, and you’re getting to the same problem as the rocket equation, more motor power means more weight, which means more battery for the same flight time, etc. ICE doesn’t scale the same way. For instance the R22 has a [Lycoming O-320](https://en.wikipedia.org/wiki/Lycoming_O-320#Specifications_(O-320-A1A))engine, which develops 160hp, and its 244lb. Its big brother, the R66 uses a [Rolls Royce RR300](https://en.wikipedia.org/wiki/Rolls-Royce_RR300#Specifications_(RR300)) turbine engine, which develops 300hp from 200lb of engine, but being a turbine it drinks a bit more fuel, and has a more complex transmission. The medium size Augusta AW109 (best known from the best TV show ever, 1990s Interceptor featuring the black Interceptor copter G-MEAN started with a 300hp Allison model250 turboshaft, but now has a PW206 turbine making 500hp, for a similar weight and size (they’re retrofitable). Plus, if you upgrade the engine in a copter, you just need to adjust your throttle, controls the same, while an upgrade to drone motors needs everything redone because a 1 % difference in the motors is now far greater.
Basically, quadrotors are ok for small, short flights not carrying people. for anything people-sized they’d be huge, heavy, and poorly performing, with no safety. For small light stuff it’s cheaper to do than the complex mechanical controls of a helicopter, and more physically robust too.
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