This is where it gets interesting. /me grins.

As you probably know, helicopters fly and move horizontally using one or more sets of spinning rotor blades. Each of these blades are an aerofoil shape which, when moving through the air, force air downwards and in doing so are themselves forced upwards. Fair enough so far.

Rewind about 350 years to Newton and his third law of motion: for every action there is an equal and opposite reaction. A helicopter creates lift by spinning its main rotor blade(s) in one direction; this action has an equal and opposite effect on the helicopter fuselage, making it 'want' to spin in the opposite direction. This is no problem on the ground but when the helicopter lifts off, something has to counteract the force or a ridiculous spinning top-type situation would result.

There are a number of ways that this torque force is counteracted in rotor design: they follow in rough order of fame.

Tail rotor

Most will be familiar with this design - pioneered by Igor Sikorsky in 1941 - as the vast majority of modern helicopters use it for yaw control. Since the torque acting on the fuselage is known, an equal and opposite force can be applied to cancel it out.

This force is applied by a second, smaller rotor fitted to a tail boom. It provides "sideways lift", resisting the torque that is being applied to the fuselage by the main rotor, as indicated by this incredibly not to scale plan view:

     Blade Rotation <--- \
                            \
                               \
                _____            \
               /     \            \
               |     |             |
              /       \            |
 _____________|__ _ __|_____________
|________________|_|________________|
              |       |
 |            \       /
 |             \     /
  \             \   /
   \             | |
     \           | |
        \ --->   | |
                 | |  || ---->
                 | | _||  
                 | ||_|           Tail Rotor "lift"
                 |_|  ||
                      || ---->
                  |
 Main Rotor       |
Torque Force <----|

This allows the helicopter to hover without its fuselage spinning wildly.

Controlling Yaw

The tail rotor can also rotate the helicopter about its rotor mast and provide limited rudder-like control during forward flight (I will come back to this later). This is achieved by altering the collective pitch of the tail rotor blades to increase or decrease their anti-torque effect. With the made-up helicopter above, the fuselage would rotate clockwise if the collective pitch on the tail rotor were decreased, counter-clockwise if it were increased.

Although this is the most common method of providing helicopter yaw control, it is one of the most complex. A commonly-cited flaw is that the lift generated by the tail rotor is "wasted" because it is not keeping the helicopter aloft (a tail rotor may require anything from 5-30% of power output to operate). Furthermore, the components used to drive and control the tail rotor add weight to the rear of the helicopter at a detriment to its manoeuvrability. A helicopter with a tail rotor requires more storage and manoeuvring space due to the tail boom length, and the clearance for the tail rotor when it is operating. Finally, exposed and operating tail rotors are a proven hazard to people near them: there are many documented incidents of people being killed or dismembered by a strike from a spinning tail rotor.

Counter-Rotating Rotors

This is a reasonably common configuration whereby a helicopter has two sets of rotor blades and no tail rotor. It is used in heavy lifting applications as the twin rotors create more lift between them and spread the weight of the load. Seen most frequently on Boeing's Chinook and variants, there are several more exotic craft such as the Mil Mi-12 with a rigid rotor blade mounted on a frame structure on either side of the fuselage and the V-22 Osprey which is more like an aircraft with oversized, variable geometry rotors fitted to the end of each wing. The Kaman K-MAX uses the most interesting variation of the twin-rotor design: it has twin rotor masts side by side on the top of the fuselage, but each one is angled outwards approximately 15-20° from the vertical centre of the fuselage. The result is two sets of angled, intersecting rotor blades; a timing system prevents the rotors from colliding. Helicopters of this type are called synchrocopters.

Controlling Yaw

As different as they can be, all counter-rotating rotor systems use similar means for controlling yaw in flight or hover. Since there are two rotor blades, the simplest way to counteract the torque produced by one set of rotor blades is to spin the other set in the opposite direction. This can easily be seen watching a twin-rotor helicopter in flight.

Fair enough, but my question that triggered what became this writeup was:

"A helicopter with twin, counter-rotating rotors balances out any rotational forces by design. How does the pilot rotate the helicopter when there is no tail rotor to apply additional rotating force?".

The answer is dependent upon rotor configuration, but will benefit from a brief description of a helicopter's cyclic control (skip the next paragraph if you have read Helicopter pitch control or know how cyclic control works anyway).

For a helicopter to produce lateral motion, it is necessary for its entire rotor disc to be tilted in the required direction of movement. To move forward for example, the rotor disc must be tilted forwards; however, actually tilting the rotor disc on its mast is impractical. Instead, a tilting effect is produced by varying the pitch of each rotor blade (and thus the lift it generates) as it rotates. For forward movement, pitch control is such that rotor blades generate the most lift when they are pointing behind the helicopter and the least lift when they are pointing to the front. This has the same effect as actually tilting the rotor disc forwards (the front of the rotor disc will drop and the rear will rise) and creates forward lift. This 'tilt-effect' control is called 'cyclic' and is operated by the pilot with the main control stick.

Now, how cyclic is used to control yaw:

Where the two sets rotors are in a tandem configuration (i.e. one set is in front of the other, as with the Chinook), a left-right cyclic differential is used to produce rotation or approximation of rudder control. To rotate clockwise for example, right cyclic is applied to the front rotor disc and left cyclic is applied to the rear.
In a side-by-side configuration, (i.e. one rotor blade is on either side of the fuselage, as with the V-22 Osprey) a forward-aft cyclic differential is used. To rotate clockwise for example, forward cyclic is applied to the left-hand set of rotors and aft cyclic is applied to the right-hand set.

Contra-Rotating Coaxial Rotors

During the late 1940s, Soviet helicopter manufacturer Kamov pioneered a twin-rotor system called a "twin coaxial" configuration, where two sets of contra-rotating rotor blades are stacked on the same drive shaft. Virtually all helicopters from Kamov use this system and furthermore, most coaxial twin-rotor helicopters are Kamovs.

The main benefit of this rotor system is helicopters using it require less horizontal space for storage or manoeuvre than those with a tail rotor. Although some helicopters with coaxial rotors have similar dimensions to more conventional helicopters (such as the Ka-50 Hokum), it is possible to build them with greatly shortened tail booms and such designs are well-suited to shipboard operations (Kamov's Ka-28 is a perfect example of this; it operates from ships, performing ASW duties). Although the rotor mast in coaxial systems is taller than that of other helicopter types this rarely proves to be an issue. The main drawback of the configuration is larger cross section of the twin rotors, which adds to drag and limits cruising speed. This clearance between the rotors is necessary because without it, the rotors would smash each other to pieces as they flexed up and down. More recent designs use more rigid rotor blades which can be installed closer together, reducing the drag effect.

Controlling Yaw

Yaw control in twin-rotor coaxial systems is an interesting affair, operated by the collective system. In hover, the two sets of rotor blades rotate at the same speed and cancel out each other's torque effect on the helicopter fuselage. Using cyclic differential would give no yaw effect since both rotor discs rotate about the same axis, so the only way to produce it is to decrease the lift produced by one set of rotor blades and/or increase the lift produced by the other.

This is done by altering the collective pitch of both sets of the rotor blades, such that the force already acting to spin the helicopter in the required direction is under-compensated for by one set of rotors (the set acting to spin the helicopter in the opposite direction) and applied more strongly by the other set. Whereas a contra-rotating non-coaxial system uses cyclic differential, contra-rotating coaxial systems use collective differential. This is rather difficult to describe and I'm not going to kill myself trying to ASCII-ize it, so please bear with my inevitably convoluted explanation.

The easiest way to explain and understand this is to ignore the rotation of the rotor blades and concentrate on their effects on the helicopter itself. To recap, the following is true for the abstract helicopter for which this example applies:

Rotor disc 1 has a counter-clockwise torque effect on the fuselage: it tries to rotate the helicopter counter-clockwise.
Rotor disc 2 has a clockwise torque effect on the fuselage: it tries to rotate the helicopter clockwise.
The torque effects of the two rotor discs cancel each other out when they are both pitched equally. Thus, the helicopter does not rotate in either direction.

Now, let's say our fictional helicopter is hovering and we want to rotate it clockwise. The following are all possible ways of doing it:

Increasing the collective pitch of rotor disc 2, which would overcompensate for the counter-clockwise force produced by rotor disc 1.
Decreasing the collective pitch of rotor disc 1, which would under-compensate for the clockwise force produced by rotor disc 2.
Both of the above.

All will result in the helicopter fuselage rotating clockwise, so the question is which method is preferable? Increasing the collective on a set of rotor blades increases their angle of attack and thus their torque, their drag and thus the stress on the powerplant(s). Reducing collective does nothing but reduce energy requirements and fuel expenditure, but has the same effect of producing the rotation we want. However it must be remembered that both sets of rotors run from the same powerplant(s), so their rotation speeds are inextricably linked. Increasing the collective on only one set of rotors will therefore reduce the speed of both (at least temporarily), resulting in either:

A loss of altitude, or
an increase in stress on the engine as it throttles up to maintain rotor speed, and a subsequent increase of altitude.

As one can see, either will result in a change of altitude, which we don't want. We're just trying to rotate the helicopter on the spot.

The best method is the third: collective on rotor disc 2 is increased to increase their torque effect on the fuselage, and collective on the rotor disc 1 is reduced equally so this additional torque is not counteracted. The flattening of rotor disc 1 (and the subsequent reduction in drag) balances the extra drag incurred by the increased pitch of rotor disc 2. Moreover, the overall lifting effect of the rotors is the same because as the lifting effect of rotor disc 2 is increased, that of rotor disc 1 is decreased by an equal amount so it requires no more power from the engine(s). Elegant.

In summary, contra-rotating coaxial twin-rotor helicopters control yaw by reducing collective on one set of rotors and increasing it on the other set, such that extra torque effect is produced in the required direction of rotation.

No Tail Rotor (NOTAR)

This is the most recent development in yaw control, developed by McDonnell Douglas in the late 1970s. This system has the same effect as a tail rotor but without the associated risks - those of striking objects with the tail rotor, vulnerability to enemy fire in military applications and danger to people near a spinning tail rotor.

Controlling Yaw

There are two main components to the NOTAR system - the tail boom and a small air jet at the end of it. The tail boom has entry slots at or behind its root, through which downwash from the main rotors can enter. At the root of the tail boom is a compressed air fan. Two sets of outlet slots along the length of the tail boom and about 70° and 140° around the boom cross-section (looking forward from the rear, where top vertical is 0°) allow air blown along the tail boom by the fan to exit.

The coanda effect dictates that air tends to flow over the surface of an object rather than around it, so as this air exits it flows over the surface of the tail boom. Without going into too much depth, the flow of air over the tail boom is such that it mimics a vertically-pointing aerofoil. As the air flows over the boom it generates lift that opposes the majority of the torque generated by the main rotor.

The remaining anti-torque force is provided by the jet at the end of the tail boom. The pitch of the blades on the compressed air fan are controlled indirectly by the pilot's rudder pedals, as are the pitch of the vanes controlling the strength of the air jet. The strength of the air jet can be controlled to provide an increased or reduced anti-torque effect, rotating the helicopter fuselage one direction or the other.

Helicopters that use NOTAR are shaped much the same as those with tail rotors, with a tail boom and one or more vertical stabilisers. The benefits of NOTAR are numerous: not least decreased noise and more efficient operation (the power required to operate the compressed air fan is significantly less than that which would be required to operate a tail rotor), the following is noted by Aerospaceweb.org:

Though the NOTAR arrangement still requires a long tail boom, the need for a spinning tail rotor is eliminated. This reduces the danger to ground crew, and also allows the pilot to maneuver into positions that he or she normally would not even consider. For example, NOTAR allows a pilot to stick the tail boom into a tree. Try that with a standard tail rotor, and it will be time for an unscheduled landing.

In virtually all cases, yaw control systems are operated with a pair of pedals much the same as those that control the rudder in an aircraft. Obviously the anti-torque systems as described are automatic but the pilot can add their own input to this with the pedals.

I mentioned the 'limited' in-flight rudder control that a tail rotor (and NOTAR) provides earlier. To clarify, the yaw can be controlled by a tail rotor or NOTAR while in forward flight, but due to the way air flows over the helicopter fuselage, the higher the airspeed the less effect it has, much as with the rudder on an aircraft. The helicopter will rotate a limited amount, but will be "pushed back" most of the way by the airflow over the fuselage. A tail rotor or NOTAR is more of a trim control at high speed; banking with the cyclic is much more suitable for changing heading.

It is worth noting that were a helicopter to fly fast enough, a vertical stabiliser at the rear would be sufficient to counter the torque exerted by the main rotor. This obviously can't be counted upon when hovering, but many helicopters (mostly single-rotor) do have a vertical stabiliser as a safety measure to help the pilot retain some control if the tail rotor fails.

helicopter	No Tail Rotor	Coanda Effect	CH-47 Chinook
Jane's Fighting Nodes	Dissymmetry of lift	Ka-50 Hokum	cyclic
Helicopter pitch control	Retreating blade stall	How to survive a helicopter mishap	Osprey
Inextricable	A short tale of pilots and helicopters	gyroscopic precession	Translating tendency
Newton's Third Law of Motion	collective	Helicopter lift control	George W. Bush's 2005 State of the Union Address
Sikorsky Skycrane	Helicopter altitude control	Vortex ring state	Dynamic rollover

Helicopter yaw control

Tail rotor

Controlling Yaw

Counter-Rotating Rotors

Controlling Yaw

Contra-Rotating Coaxial Rotors

Controlling Yaw

No Tail Rotor (NOTAR)

Controlling Yaw

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