A helicopter does have two propellers: one to get the helicopter in the air and the other one to counteract the torque produced by the first propeller so the helicopter doesn't start to spin. Why aren't the two propellers in the same plane? The bigger propeller does have angular momentum pointing in the positive z-direction, the smaller propeller has angular momentum pointing in the direction of the positive y-axis (if the helicopter is situated at the origin). Isn't angular momentum conserved in every component of the (pseudo)-vector that is representing it? What am I overlooking?
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$\begingroup$ Big helicopters do have two horizontal propellers rotating in opposite directions. It's probably cheaper to have the standard arrangement of one main propeller and some method to counteract the torque. The Wikipedia artcile on helicopters goes into some detail. $\endgroup$– NickDCommented May 26, 2017 at 15:29
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1$\begingroup$ The thing to understand is that a small single-rotor helicopter (so not something like a Chinook) doesn't conserve angular momentum considered as an isolated system: the rotor is continually dumping angular momentum into the air. So it would no be enough to have a small counter-rotating rotor: the helicopter would still spin as it dumped angular momentum into the air. $\endgroup$– user107153Commented May 26, 2017 at 15:39
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2 Answers
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The tail rotor doesn't generate torque along the y-axis. It generates a force along the y-axis. If you take the torque of this force at the origin, you'll see it goes along the z-axis, counteracting the torque of the main rotor.
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$\begingroup$ This might be better if you talked about the pitch, yaw and roll axes, rather than an assumed coordinate system. Or at least defined the coordinate system you are using. $\endgroup$ Commented May 26, 2017 at 17:20
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$\begingroup$ He mentioned Z-axis and Y-axis in a context that makes it clear what coordinate system he's using. $\endgroup$– SteveCommented May 26, 2017 at 17:46
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1$\begingroup$ The tail rotor does generate a torque along that y-axis. It's just both smaller and besides the point (as you mentioned in the rest of your answer). Since it is present, it also has to be countered.... and that is done by the main rotor's cyclic pitch! $\endgroup$– MrBrushyCommented May 29, 2017 at 12:35
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Let's start with the helicopter just having the main propeller. If it had just one, the device would start rotating around xy plane's vertical axis due to conservation of angular momentum. A smaller tail rotor is placed in the helicopter (which rotates around an horizontal axis), to prevent helicopter from spinning.
The Both main and tail rotor generate torque due to frictional force
Why are not the two propellers in the same plane? Actually, you could construct it. It will work if you are able to counteract the torque generated by the main helix. That aim can be claimed if both propellers spin in opposite directions.
