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Helicopter Forward Flight

In this article we examine how the state of a helicopter changes with speed in forward flight. We’ll look at the control positions, forces/moments on various components, and some other quantities. We consider trimmed, level flight—the helicopter is not accelerating or climbing/descending.

Torque, Thrust and Induced Velocity

We first look at torque, thrust and induced velocity. These are needed to understand other phenomena like control positions. Although it may be counterintuitive at first, torque actually decreases as airspeed increases up to around 60-80 kts. In short, this is due to the rotor being engulfed in its downwash at lower speeds, as shown in the second plot. To better understand this, read about induced power.

Eventually torque increases with airspeed as the rotor must work to overcome increasing drag on the aircraft. The main rotor tilts forward to counter aircraft drag, in addition to supporting the weight of the helicopter. Hence, there’s a sharp increase in rotor thrust at higher speeds as shown in the third plot below.

Finally, the last plot shows tail rotor thrust. Tail rotor thrust is used to counter the “reaction torque” associated with powering the main rotor—without it, the helicopter would spin in the opposite direction as the main rotor. Hence, tail rotor thrust roughly follows the trends in torque. This can be less true at high speeds where the vertical tail can produce a lateral force, lessening the need for tail rotor thrust.

Plot of helicopter torque vs. airspeed
Plot of main rotor downwash vs. airspeed
Plot of main rotor thrust vs. airspeed
Plot of tail rotor thrust vs. airspeed


The plots below show how control positions change with airspeed. All controls are measured as a percent of full throw here—the collective is 0 when down, the longitudinal cyclic is 0 when full aft and the pedal is zero when the left pedal is fully depressed (they’re 100 when fully pressed in the opposite direction).

The collective decreases as airspeed increases from hover. This is due to the decrease in induced velocity discussed above. At lower speeds/higher induced velocities the blades must be feathered up more to generate the same lift. Of course, as the speed increases beyond a threshold (about 70kts in the example plot), the collective must increase again. This is because the main rotor has the added duty of overcoming drag on the aircraft, which increases roughly with the square of the forward speed. The higher collective results in the larger thrust required.

The longitudinal (fore/aft, or just F/A) cyclic, on the other hand, strictly increases with forward speed. Forward cyclic primarily induces longitudinal (F/A) flapping on the main rotor, tilting the front of the rotor down (aft up). The need for increasing cyclic with speed is two fold: (1) to provide more “forward thrust” to counter drag on the aircraft and (2) to counter the natural tendency of the rotor to flap aft (flapback) with increasing airspeed.

The pedal position roughly mirrors the collective. This is because the pedal is primarily used to counter main rotor torque, which is closely related to collective position. It’s more closely related to the torque plot shown previously, since the pedal is strictly used to counter torque in trimmed flight. Lower pedal positions correspond to higher tail rotor thrust, which is required for higher torque/collective. So as the torque decreases the pedal increases. Like the collective, this is only true up to a certain point. Eventually the torque requirement increases again and the pedal must be reduced. The vertical fin on the tail of the helicopter helps counter torque at high speeds, so that the pedal doesn’t have to decrease as much as it would otherwise.

Plot of collective control vs. airspeed
Plot of cyclic control vs. airspeed
Plot of pedal control vs. airspeed


As alluded to above, the drag increases roughly with the square of the airspeed. This is shown in the plot below.

Plot of helicopter drag force vs. airspeed

Pitch and Longitudinal Flapping

As mentioned already, the main rotor is responsible for overcoming drag on the aircraft, in addition to supporting the weight. In order to do this, the main rotor is tilted forward, allowing it’s thrust to pull the helicopter forward. This tilt can be achieved by (1) pitching the entire helicopter nose down or (2) tilting the main rotor down while the aircraft stays fixed. The latter is called (longitudinal) flapping—blades flap down over the nose of the helicopter and up over the tail so that the “rotor disk” is effectively tilted relative to the helicopter. For more details about cyclic and flapping, see this article.

Pitch and flapping have different effects on the helicopter. A major difference is the (negative/nose down) pitch moment created by forward flapping. Hence flapping can also be used to counter other, positive pitch moments that push the nose up. For example, if the main rotor is forward of the helicopter’s CG, it’s thrust actually creates a positive, nose up pitch moment. Forward rotor flapping can therefore be used to counter this, preventing the helicopter from pitching up. Using flapping and pitch to create the proper forward force/propulsion and pitch moment is like solving two equations with two unknowns. The following two plots show the solution at various airspeeds for an example helicopter.

Plot of helicopter pitch angle vs. airspeed
Plot of main rotor longitudinal flap angle vs. airspeed


Helicopter tail rotors produce lateral thrust, pushing the helicopter left or right. If the helicopter's main rotor spins counterclockwise (viewed from above), the tail rotor pushes it to the right. Hence, if the helicopter's nose is pointed north, it actually flies slightly east of north. In other words, the net air velocity is actually not straight into the nose but slightly "into the pilot's right ear." The angle between the direction the helicopter is facing—it's heading—and the angle it's actually flying—it's track—is called the sideslip angle.

Sideslip is small at high speed because a small sideslip angle produces a large leftward aerodynamic force on the fuselage, countering the right tail rotor thrust. At lower speeds, sideslip can exceed 10 degrees (the air doesn't push the fuselage left as much). To counter this, pilots often fly the helicopter with a small amount of roll (left wing down). This allows gravity to counter tail rotor thrust and keep the chopper flying "straight."

Pitch Moments

As discussed above, a balance of pitch moments is required for trimmed flight. The “big” pitch moments acting on a helicopter are due to aerodynamic forces on (1) the main rotor (forces at the hub and moments about the hub), (2) the fuselage and (3) horizontal stabilizer. All of these are plotted below. The fuselage and main rotor produce substantial negative pitch moments at high speed. The stabilizer on the tail of the helicopter is pushed down aerodynamically with airspeed, providing a large positive (nose up) pitch moment which roughly counters the fuselage and rotor. These plots represent a main rotor with hub restraint—a teetering rotor produces no hub moments.

Plot of main rotor force pitch moment vs. airspeed
Plot of main rotor hub moment pitch moment vs. airspeed
Plot of main rotor hub moment pitch moment vs. airspeed
Plot of main rotor force pitch moment vs. airspeed

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