This has been puzzling for quite a long time.
Every action movie or military documentary features helicopters with no door or with open doors and yet people inside look like they couldn't care less. Apparently they're not falling out...
Why is it so?
Aircraft, fixed-wing or rotorcraft, have limited capability to produce a sideways force, so they simply can't throw you out.
It is a matter of physics. Inertial forces (gravity and centrifugal force) act on you and the aircraft the same, so they won't make you move relative to the aircraft. The only force between you and the seat is caused by the aerodynamic forces. And the wing or rotor can only produce significant force vertically, and some torque with help of control surfaces. But for lateral force there is only drag of the fuselage and the vertical stabilizer and, in most helicopters, anti-torque rotor, which don't produce that much force unless there is really bad turbulence or in some cases if the handling is really bad.
When aircraft turns, it banks to be able to produce the necessary side force, so the resulting force is still mostly straight to the floor.
Of course the other reason is that all aircraft and helicopters have seat-belts and the people sitting by open door usually have them on—except for skydivers, who have the parachute on already, and rescue divers who are tied to the winch instead.
The reason that the occupants are so calm about being in an open helicopter are because they are strapped in. There are many configurations that open helicopters can have, some with seats and some not. The seats are generally removable, connecting to points on the floor. Occupants in the back have 2 options for strapping in, the first is your typical seat belt, the other is known as a "monkey harness", which is a harness that goes around your shoulders and waist and can be clipped to points in the floor. Door gunners usually preferred harnesses because it allowed much more freedom of movement so they could fire at more angles.
Remember also that these people were used to it as well. I'm sure most of them were bricking it big-time their first few trips no matter how well they were strapped in. Also, I suppose when you're about to be shot at falling out may frighten you less than it may otherwise.
I taught sport skydiving for 10 years, and I have sat half-out of the open door of an aircraft, no seatbelt, hundreds of times while the aircraft makes 45 degree banks toward the open door side. It's a bit odd seeing the airport above the wingtip.
Unless the plane is in a spin or otherwise spectacularly out of control, the forces are largely perpendicular to the floor of the aircraft. At no time have I ever felt like I was going to fall out, and actually getting out is difficult enough that we spend an hour or more practicing it on the ground.
You asked about helicopters specifically - they are less able to produce cross-fuselage forces than fixed-wing planes. Look at the rotor, then the thin post connecting the rotor hub to the fuselage. It's not that thick and thus cannot produce enough force to toss someone out the door.
Heavy turbulence could bounce you around to the point where falling out is possible. Not guaranteed, just possible if you bounce in that direction. But at low speeds and clear weather it's unlikely to the point where sitting down is adequate. Standing and moving around with an open door is common, but the 1 inch strap that is plenty strong enough to hold you up is very hard to see, especially on TV.
Consider for a moment what would have to happen for you to fall out. That would have to happen either through gravity, or inertia.
Some rough over-the-thumb rationalizing (and keep in mind that I'm not a pilot, let alone a helicopter pilot -- just some basic physics applying here):
Gravity. The helicopter would have bank at a significant angle, and at the same time not have enough centripetal force (which would press you into your seat via inertia, as during a "normal" bank). For example, if the pilot forces the copter into a bank and then zeroes out on the collective. However, that same gravity will act on the chopper as well... uncomfortable low-g conditions, yes, and you probably would want to grab hold of something, but you don't get ripped out of your seat immediately.
Inertia. The helicopter would have to make a sudden lateral movement, so you get jerked out of your seat. However, as others have pointed out already, a helicopter does not have a way to induce sudden lateral movements of that magnitude. So, no dice.
Once we start considering outside forces -- turbulence, high winds, blasts from ordonance fired at you -- you probably had enough sense to strap yourself in.
Many of the movies you've been seeing will be picturing helicopters operating in Vietnam, Iraq, Afghanistan, Somalia... see a pattern here? Those are hot climates we're talking about. So, given that the usual chopper ride is unlikely to toss you out of the door, why shouldn't people enjoy a bit of a breeze? ;-)
I don't fly helicopters, but I can tell you that in fixed wing aircraft you always strap in. I assume helicopters are the same.
If a plane has no doors and you are not strapped in, you will have an excellent chance of falling out. I would assume the same is true for helicopters. Some of the other answerers have talked about centrifugal forces or whatever. In reality what happens is that gusts hit you and knock you around all the time. You don't notice the gusts in big aircraft like Airbuses, but in a small aircraft it can be like being inside of a barrel rolling down a mountain. You definitely do not want to be unsecured at any time in flight, especially with a door open.
Once I was getting towed in a glider and my harness popped open. In about 2 seconds my left foot was sticking straight up, wedged against the bubble canopy and my right knee was in my face. I was upside down. Meanwhile, the glider is moving around like Pirates of the Caribbean and the tow pilot is wondering, "What the hell is he doing?" I had to wedge myself against the sides of the glider and instrument panel like Jackie Chan to get the harness buckled again.
Of course, the knuckleball motion of a gusted aircraft can be an advantage sometimes, such as when you need to deal with an unruly passenger. Just unbuckle his harness when he isn't looking, kick his door open and he will be singing "Free Falling" by Tom Petty in no time :-) Just kidding, of course, don't do that.
You don't fall, even in the turns because of the the direction of the body acceleration is toward the helicopter floor, including when the pilot turns. So the body is maintained with a force towards the floor, never towards the open door.
On my first ride out to the jungle (Vietnam), I looked for a seat. There weren't any. I was instructed to just sit on the side with feet hanging out. The first ride was interesting, but they soon became routine. The pilot could turn sideways and this force would hold you in. Sometimes we flew so low I thought my feet were touching the treetops.
I think about this 40 some years later. Would I sit on the side again without being strapped in ? I don't think so.
To fall out of a helicopter, your center of gravity would have to lie outside of the aircraft. Because helicopters tend to bank smoothly when they accelerate, your center of gravity stays within the aircraft. Unless the aircraft were struck by another object, it is unlikely you would ever experience a significant lateral force while flying in a helicopter.
The helicopter is basically suspended from its main rotor, so you are sitting in the equivalent of a large swing/ride and pulled towards its floor. Suspended monorails with the ability to lean into curves can likewise look precariously wobbly from the outside while appearing perfectly stable for the inside passengers who don't feel the outside forces exactly because the craft is able to follow them, compensating their effect on the load.
The amount of jerk you can put on a heli by controlling the main blades is limited. You'll probably cause more problems by switching on and off auxiliary means of propulsion. However, those don't make for the dramatic dives, banks and turns in movies.
If you mean when the helicopter banks then all the people are either strapped into their seats like your car seat belt as all the people above have mentioned or because the have a cord attached to their jacket. (The cord part is what I saw in a documentary on the Discovery Channel).
Are you expecting them to fly out of the helicopter because in movies, when the plane/spaceship/whatever door is opened, people get sucked out?
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If so, that effect is real (though perhaps exaggerated), but it's not caused by the craft's movement. It's caused by the depressurization of the room.
The inside has high pressure, while the outside has low pressure. When a door opens, the high pressure inside-air moves towards the outside, exerting a force on anything it meets (in the same way that the wind pulls you during a nasty storm). However, the effect dies down quickly as the pressure equalizes.
In a helicopter with open sides, that pressurization never happens to begin with, so there is no depressurization to pull the passengers out.
Might not be relevant but here in the UK, I have been in helicopters on Search and Rescue training and missions in the mountains and you will always be belted in, whether it is by ground entry or winched up. The winchman will be attached by leash and harness as he is usually hanging around or out of the door.
Actually seat belts in helicopters and airplanes aren't really to keep you in the plane, rather, they are to keep you from losing control if turbulence happens to throw you against the ceiling and/or knock you out. Helicopters usually avoid negative G forces as it does bad things to the rotor system, so becoming airborne is less likely, but still possible. These forces could cause you to levitate and if the turbulence is also of a sidewards component, the helicopter could travel sideways while you are airborne. Guess what?
As an "Airmobile" infantryman (101st), I rode in Blackhawks countless times, sometimes in a seat belted in, but usually not. Maybe because we were only in the Blackhawk to get out of it -- rappelling, fast-roping, helocasting. I don't know if we ever had the doors closed -- can't think of a time, anyway. I have thought of this before, looking back, and wondered why we never seemed concerned about sitting in the door with our legs dangling out. I'm guessing that the scientific explanations offered above are the reason why. But I can tell you, it's not just Hollywood. We really did sit in or around the open door and never seemed to think twice about it.
People aren't falling because the cabin isn't pressurised. If you would try to open the door in mid-air of your average passenger æroplane cruising in the upper troposphere, you would be not amused. People would be sucked out. But helicopters usually don't fly at altitudes where pressure is a problem, so there is no cabin pressurisation, so there is no outward force due to an open door.
Take a bucket of water with a handle. Start swinging it in a pendulum motion until it has enough swing to actually go around at the same constant speed. Not a drop of water will be spilled. #Pendulumeffect
