Unless the helicopter is in the middle of the turntable, wouldn't the rotation paths of the upper rotor in relation to the turntable (and relation to the ground) create some sort of unusual repeat like the patterns of a spirograph?

No opinion on the question otherwise, just the first thing that left me wondering.

Arguably, all helicopters take off a (giant) turntable (spinning at about a thousand miles per hour).

I think for any turntable that didn't move the atmosphere with it, though, there'd probably be a problem with air resistance - it could be like trying to take off in a tornado.

No, it does not take off. If you measure the speed of the rotors with respect to the ground/atmosphere, it would equal zero.

This is assuming that each body would be spinning on the same axis and the directions were exact opposites.

The picture in my head would be the helicopter body spinning and the rotors would not be moving, as if you were standing on the ground.

Assuming the turntable matches the main rotor, all will depend on the undercarriage:

NO:
If the heli in question has skids instead of wheels. In the best case, it will probably subject everybody inside to some serious G's. In the worst case, it will topple over and crash.

YES:
If the heli has wheels, they would have to be able to free wheel independently from each other. If that is the case, it should be possible to take off safely. The tail rotor should be able to overcome the wheel friction and keep the heli from rotating together with the turntable. In other words, it would remain stable in place, and the main rotor should be able to create enough lift to safely takeoff.

If, for sake of experiment, you take the helicopter out of it and replace it with just a rotor (no engine) resting on a small pole, it's easy. If the speed of the turntable is the same as a "normal" helicopter, and depending the angle of the rotor and the direction of the turntable the rotor will take off. (It will subsequently crash and shatter while causing a lot of damage but that's not important for now.)

If you replace the rotor with a normal helicopter you can see that, when its engines are not running, it will also take off. The speed of the turntable has to be a bit higher to account for drag and the increased weight but for the rest I see no problem.

Of course, because the engine isn't running it will just take off, spinning wildly and, because it will immediately slow down due to wind resistance it will not fly very high.

Now we turn on the engine and it gets a bit more complicated, mainly because of the tail rotor. The tail rotor have to be turned off, otherwise the helicopter will slide off the turntable. If the main rotor is rotating in the same direction as the turntable the running engine will just add to the lift and it will take off even earlier. (If it turns in the other direction, or the angle of the rotor blades is wrong it will be pushed towards the ground, and not take off.)
The moment it takes off and loses contact with the ground/turntable, it will act just as the situation above and the helicopter will not fly very high. However, if the tail rotor is turned on at that moment and is running at very high speed it might theoretically be possible to stop the spinning of the helicopter and after that it'll just fly as it would normally.

So to summarize, yes it will take off, but will probably crash after that.

Agreed, it doesn't take off, so long as the turntable spins relative to the ground in the opposite direction from the rotors relative to the helicopter body, as the rotor speed relative to the ground (and, we assume, the atmosphere) is then zero.

If the turntable is spinning the other way, obviously the rotors will be going twice as fast as normal wrt the atmosphere, and it takes off at least as quickly as normal.

I don't think this is one that mythbusters will be trying IRL...

If the turntable spins opposite to the rotors then no.

If the turntable spins and the rotors are fixed then, theoretically it should take off momentarily. Probably before falling over, if it hasn't already broken into lots of little pieces from the centrifugal force,.

If the turntable spins with the rotors then theoretically the helicopter should be able to, momentarily, lift with half the normal rotor speed (relative to its body).

This is ignoring the drag from spinning the helicopter round very fast, or the effects of the tail rotor.

I can tell you it's pretty likely to crash if it does take off.

If the direction of the rotor and the turntable are the SAME: Yes, since the rotor is moving through the atmosphere at the same rpm as the turntable.

If the direction of the rotor and the turntable are OPPOSITE: No, since the engine torque and the rotation of the turntable would (ideally) cancel each other out, leaving the rotor stationary relative to the ground.

This, however, assumes that the torque of the rotor is not transmitted at all to the turntable, which is not something easily ignored (helicopters have anti-torque devices in the form of tail rotors to counteract the torque of the main rotor applied to the fuselage).

In the same-direction scenario, maintaining a constant relative RPM would be difficult, since the rotor's torque would be transmitted back down to the turntable, making the rotor speed up marginally relative to the turntable. In the opposite-direction scenario, the rotor would also speed up slightly (in the opposite direction) relative to the turntable.

This also assumes that the helicopter is not equipped with gearing to maintain a semi-constant rpm, as many are.... which complicates things even further. Argh.

As long as the Helicopter still has a working tail rotor it will take off.

The most important thing to consider is the speed of the rotors with respect to a fixed reference frame on the ground. As long as the blades/rotors are spinning with respect to that fixed reference frame, then the blades are cutting through the air and therefore generating lift and the helicopter will take off.

The different reference points get a bit confusing.

Let's assume that the central axis of the record player and the central axis the chopper's rotor are the same.

Let's start with 1 scenario: Clockwise spinning blades and clockwise spinning turntable. As the problem is defined, when the rotors start to spin, the turntable will begin to spin in the same direction, causing the body of the chopper to also spin in the same direction. Thus the turntable will serve to increase the angular velocity of the blades. This scenario should actually make it easier, in a sense, for the chopper to lift off.

Scenario 2: Counter-clockwise spinning blades and clockwise spinning turntable. I think this is what Dennis G is describing and I agree with his conclusion. Although this conclusion makes an assumption on air speeds. It realistic to assume that if the turntable and body of the helicopter were to be spinning quite fast, that this movement would move the around around it.. That air would also move past the blades, which would generate lift in the same manner as if the blades were moving through the air. It is somewhat plausible that the swirling air could move fast enough to cause liftoff.

If the turntable is spun in the opposite direction of the rotors, the helicopter will say "Paul is Dead."

Oh please God let's not go through all of this again.

I like how a sheet that was supposed to drag an airplane the opposite way ripped as one of the guys ran on it... Maybe that's the real myth, that a sheet that a 180 pound man ripped trough can drag an aircraft across a tarmac.

Yeah, that sheet was definitely keeping the plane stationary relative to the ground- flawless execution there Mythbusters!

As with the original "airplane on conveyor belt" scenario, this problem is underspecified. What matters as far as lift is the net speed of the rotor with respect to the air. (yes, there is the angle of attack of the rotor but none of the special characteristics of this scenario impinge on that.)

The components to figure that out that are missing are: 1) speed of air relative to the ground; and 2) speed of helicopter body relative to turntable. Reasonable assumptions would be that 1) is 0, i.e. still air, and that 2) is also 0, i.e. the helicopter is on skids and thus the body rotates with the turntable. Therefore, in one direction the turntable would counteract the rotor thus leaving the rotor motionless with respect to the air and in the other the helicopter would achieve lift at half the shaft speed required when the helicopter was directly on the ground.

(There are of course practical problems introduced by the fact that 2) means that the turntable is imparting force on the helicopter. In the direction where lift is achievable, when the helicopter hits half the normal lift-off shaft speed the helicopter will start losing contact with the turntable and therefore no longer have enough net rotor speed to lift the helicopter. It will start skipping across the turntable. In addition, you have the fact that the body is spinning madly at the point just before lift-off and is probably unpleasant for the pilot, to say the least.)

As mentioned above, there is a second reasonable assumption for 2), that is a helicopter with wheeled landing gear which could then use the rotor to maintain orientation (or some other type of landing dear that could skid across the turntable before lift-off). In this case the speed of the helicopter wrt the turntable is always equal and opposite to the speed of the turntable wrt to the ground and wil always cancel out. Therefore in this case the turntable has no net effect and lift-off occurs the same as for a helicopter resting directly on the ground.

whereas an airplane on a treadmill is moving in a direction and a speed the fuselage and systems (fuel, lubrication, hydrolics, etc.) was designed for. A helicopter's frame and particularly the engine systems spinning at 1000rpm would have MASSIVE issues dealing with the centifugal force.

so i don't think it matters. if the helicopter frame somehow magically holds together either the fuel will never reach the cylinders, the oil will never reach the friction points, or the coolant would pool to one side of the system. all of which pretty much end in failure.

Don't know if it'll take off, but I'm very sure that the pilot(s) WILL get sick! :P

I thought "Helicopters on a Turntable" was the name of an indie band.

YES, aside from crashing, I don't see how the turntable has any bearing on the ability of the rotors to turn. Regardless of the direction of spin, the helicoptor will still have the aerodynamic ability to achieve lift.

Just thinking about this makes me dizzy.

If the rotors are powered by jet or rocket engines mounted on the blades, it'll take off. And then crash spectacularly unless the engines are perfectly balanced and synchronized.

If it's a conventional copter, with the rotors powered by an engine mounted to the body of the copter, it won't -- it would be the equivalent of a plane powered by engine turning wheels to achieve lift.

Mark, "Helicopters on a Turntable" used to be an indie band before they sold out to the Man. ;)

*prints up 'Heli Yeah The Chopper Takes Off' t-shirts*

I'd hardly call the airplane-conveyor-belt question "settled." A scientific study of the issue would use reproducible results based upon acceleration limits for both the airplane and the conveyor belt. The Mythbusters solution was to have both Jamie and the Pilot "gun it", so to speak, and let chance take care of the rest. Moreover, they used speed (for takeoff) as the essential measurement. Not helpful if both the airplane and belt are both increasing in speed at different rates. Of course a lightweight airplane accelerated faster than a *huge truck* pulling the fabric underneath (what are both of their 0-60mph times?).

of course it will take off. the rpm of the rotor is far greater than that of any turntable. you also forgot about the antiorque device that is the tail rotor.

it will crash within half a second of reaching Vo though.

First, let's clarify what we're looking at. I'm visualizing one of those cartoons where something that is supposed to spin is stuck or blocked, and the thing that is supposed to be stationary begins spinning instead. (I think this happened twice in Wallace & Gromit shorts, once with a drill and once with an airplane propeller.)

So if I understand this experiment correctly, an outside observer will see the body of the helicopter spinning furiously on the turntable, while the rotor blades remain motionless, as if held in place by an invisible giant.

You need the blades to be spinning through the air to generate lift, so if they are motionless, then the helicopter won't take off.

The airplane question is tricky because it's easy to forget that airplanes and cars are propelled differently, even while on the ground. The question is worded to take advantage of that confusion by introducing the conveyor belt as if it would be effective in slowing down a plane, when in reality it would be like using a conveyor belt to keep something from rolling downhill.

The helicopter question doesn't have any tricks in it though, as far as I can tell. Spinning the helicopter on a turntable would have the intuitive effect of canceling out the blade rotation, so the blades would remain motionless, and the helicopter would not take off.

Nothing tricky about the airplane question- if the conveyer belt is going fast enough to create enough drag on the wheels (doesn't matter how little drag there is, since we apparently have a conveyor belt capable of keeping the plane still) it won't take off.

Same deal with the rotating helicopter- if the rotation speed is matched by the turntable it won't take off.

Neither case can be tested in the real world, but I think the answers are pretty obvious.

How is the airplane thing possibly not settled? There is no question - the issue was settled as soon as it was posed. The only confusion is why there was continued controversy (though I think Adam@12.40 is right: people forget that airplanes aren't powered by their wheels).

This question likewise has a clear and unambiguous answer: if the blades move relative to the air, it'll take off. If they don't, it won't.

The turntable is basically freewheeling. Looks closely, folks, there's a slipmat on it. Ergo the helicopter takes off completely normally.

Of course, if you spun it around quickly enough in the direction that will cause the blades to traverse the air more slowly (maybe even bringing them to a halt relative to the ground or even making them go backwards), you'd keep the craft down. But this scenario has hidden depths: maybe the tail rotor would act as a windmill? Don't forget it's linked to the main rotor! Would any significant interaction occur?

This question is even more pointless than the airplane on a conveyor one.

It's trivial to design a helicopter so that it could take off from a turntable like this, and for exactly the same reason planes can take off from conveyors: Merely replace the skids with a giant lazy susan that makes it impossible for the turntable to impart a torque to the helicopter (hey, if you can build a silly turntable, I can build an even sillier lazy susan... it's a much easier engineering problem).

On the flip side, no existing helicopter would survive being rotated at even 1/10th the speed of the rotors, and it's unlikely that a helicopter that was torn apart (or even just had an engine starved of fuel by the centrifugal "force") could fly.

Light on details, indeed. At least Kottke set out some ground rules.

I'm going to state a few more of my own assumptions. I assume that the helicopter sits firm on whatever turntable I place it on (it cannot roll or rotate freely at its base). I'm also going to assume that the turntable is spinning to counteract the rotation of the blades, similar to the notion of the conveyor belt moving opposite of the direction of plane take-off. Lastly, I'm going to assume (again, similar to the plane on a conveyor question), that the turntable spins at the same magnitude of speed, just with the opposite direction of rotation.

Under these assumptions, no, the helicopter cannot lift off. The plane on a conveyor belt had wheels to isolate the external forces applied by the conveyor on it. The mechanism of forward motion (the prop) was able to still pull the craft forward in order to create lift.

Unless there are helicopters commonly outfitted with some sort of rotational bearing beneath them in order to isolate the craft from the ground, we do not have lift. the turn-table spins the craft at an equal and opposite rotation of the blades, therefore making the blades essentially motionless WRT the surrounding air and ground.

This all of course ignores whatever craziness the stabilizing rotor would throw into the mix. Without one, a helicopter might very well look as though it were on a turn-table...

If the turntable rotates in the same direction as the copter's blades, the blades are still rotating and generating lift.

If the turntable rotates in the opposite direction of the copter's blades, the blades are still rotating and generating lift.

The copter always lifts off.