# Stability

This article discusses helicopter stability.  Stability refers to a helicopter's behavior after being disturbed from a steady flight condition.  For example, what happens after a hovering helicopter is hit by a gust of wind.  Such disturbances change the helicopter’s speed and cause pitch, roll and/or yaw motion.  Stability characteristics will tell us what happens afterward, without pilot control inputs.

## Static Vs. Dynamic Stability

Stability can be subdivided into two types: static and dynamic.  Something is statically stable if, after being disturbed from an initial state, it “pushes” back to the initial state.  For example, a pendulum at the lowest position is statically stable.  If moved away from this position gravity pulls it back to the lowest position.  A soccer ball at the bottom of a valley is statically stable: kick it any direction and it tends to roll back to the bottom.  This ball is unstable, however, at the peak of a nearby hill.  A slight kick will cause gravity to pull it down, further away from the initial position.

If something is statically stable, then we can talk about dynamic stability.  Dynamic stability is about how a system returns to the initial state, and what happens after that.  After disturbing the statically stable pendulum, for example, it swings back and forth around the initial, statically stable state.  Likewise, a statically stable aircraft will not “directly” settle back to the initial state after a disturbance, but will typically pass through the initial state and “overcorrect.”  Since it’s statically stable, it will push back against this overcorrection as well.  When the pendulum is displaced right it swings back left of the initial state, but eventually this overcorrection is also corrected and it swings right again .  Helicopters, like the pendulum, often oscillate about the initial state for some time.  The behavior of these oscillations is what dynamic stability measures.  If the helicopter eventually settles back into the initial state (i.e. the oscillations die out) it’s said to be dynamically stable.  If the amplitude of oscillations increase, it’s said to be dynamically unstable.  If, as is the case with the pendulum, the oscillation continues at the same amplitude, it’s called neutrally stable.

Stability behavior can depend on the type of disturbance and the initial state.  For example, a helicopter flying at 50 knots may be dynamically stable to a gust of headwind, but not at 100 knots.  Of course, the stability behavior also depends on the type of disturbance.  For example, different types of disturbances may change roll, pitch, yaw or any combination thereof.  The level of stability will depend on this.  Below we will simplify the subject by considering a single axis at a time, e.g. roll stability.  Unfortunately, there is often a tight coupling between axes.  Useful analysis often requires e.g. roll, yaw and lateral speed to all be considered together (called lateral-directional stability).

## Helicopter Static Stability

A helicopter is statically stable.  If “nudged” in velocity, pitch, roll and/or yaw the rotors will naturally push back towards the initial condition.  Notice we included velocity, and this means speed in any direction.  Push a helicopter to the right, it will push back to the left.  Push it up it will push back down.  Below we explain more about how the rotors produce this stability.

### Pitch, roll and airspeed

Static stability in pitch, roll and horizontal velocity are all due to the same concept – a phenomenon called flap back or blowback.  This is simplest to explain via an airspeed disturbance.  Assume a helicopter is flying forward at 70 knots.  If a 20 knot gust of headwind hits the helicopter, the airspeed jumps to 90 knots.  While this changes a few things, let’s focus on the main rotor.  A blade on the advancing side of the rotor experiences increased airspeed while a blade on the retreating side of the rotor experiences decreased airspeed (the gust reduces the speed it obtains from rotor rotation).  This creates additional lift on the advancing side and less on the retreating side, an imbalance that leads the rotor to flap up over the nose.  (Peak flapping lags peak lift by about 90 degrees of rotor rotation, see this for more detail.)  This flapping back of the main rotor tilts the main rotor thrust aft, which pitches the nose up and reduces airspeed.  The rotor therefore provides static stability.

So how does this flap back phenomenon explain roll and pitch stability?  Rolling or pitching will cause the helicopter to accelerate in the direction of roll/pitch.  This increases the airspeed in the associated direction which induces the opposing flapping response described above.  We’ll consider a roll disturbance below.

Let’s say a disturbance rolls the helicopter right wing down, as shown in the diagram bellow.  Main rotor thrust no longer counteracts gravity (it’s tilted right), allowing the helicopter to accelerate down and to the right in the picture.  This gives rise to a more right-to-left airflow on the main rotor.  If the main rotor is spinning counter-clockwise when viewed from above (typical for an American helicopter), this flow increases lift in the aft portion of the rotor relative to the front (the aft blade moves into this flow and generates more lift while the front blade sees less airspeed and lift).  This causes the rotor to flap up on the right side.  This flapping orients the main rotor thrust more to the left, which rolls the helicopter left wing down: towards the original position.   (There are other considerations like fin and fuselage aerodynamics, but typically the main rotor is dominant.)

### Yaw

If a disturbance changes a helicopter’s yaw rate, it will change the flow of air through the tail rotor.  For example, if the nose moves right the tail rotor moves left and hence sees and increased left-to-right airflow.  This changes the angle of attack and thrust of the tail rotor so that it pushes back in the opposite direction (tail right).  This effect alone stabilizes yaw, but there's more.  All modern helicopters have a vertical fin on the tail.   At higher speeds, a yaw disturbance creates sideslip, which is a lift-right or right-left flow of air across the helicopter.  This creates aerodynamic forces on the vertical fin: it pushes in the direction of the side-to-side flow.  This counters the motion of the tail and adds to the stability provided by the tail rotor.

### Spiral Stability

We ignored a complication with the example of roll stability given above.  When a helicopter rolls right wing down and moves right its directional (yaw) stability also comes into play.  Directional stability yaws the nose of the helicopter right, which counters the increase in sideslip.  This reduces the (leftward) lateral flow across the rotor, which is what provides the roll-corrective flapping.  With too much directional stability, there will not be enough lateral flow to stabilize the roll angle.   The roll angle and yaw rate can increase leading to a spiral dive.  This phenomenon is called spiral stability.  High directional stability reduces spiral stability.

## Dynamic stability

### Longitudinal - Phugoid

Longitudinal stability refers to pitch and forward airspeed here.  These values are coupled – when a helicopter pitches nose down it will increase airspeed (and descent rate) and when it pitches up it will reduce airspeed (and climb).  As discussed in the static stability section, main rotor flapping will automatically change to resist pitch and airspeed changes.  The horizontal stabilizer provides further help:  aerodynamic forces push it down (nose up) when the AOA decreases and vice versa.  Here we discuss the longer term behavior after a longitudinal disturbance: longitudinal dynamic stability

The long-term mode of oscillation in which the helicopter automatically pitches down, descends, speeds up, pitches up, climbs, slows down, pitches down, descends, … without pilot input is called a phugoid mode.  From discussion above, the frequency and damping of these oscillations is highly dependent on the rotor flapping characteristics and the horizontal stabilizer.  The values are also dependent on the initial flight condition.  A typical period for a helicopter phugoid mode is about 20s.  The mode may or may not be dynamically stable, depending on the model and airspeed.   Automatic flight control systems (AFCS), when employed, will typically damp out this mode quickly.

Click here to see a real phugoid pitch response along with a method for estimating the frequency and damping.

### Lateral-Directional - Dutch Roll

Lateral-directional stability deals with how the helicopter recovers after it’s heading, roll angle and/or lateral speed are disturbed.  These are considered together because they are intimately coupled.  A disturbance to any one of these values will impact the other two (and even pitch to a lesser degree).  A mode of oscillation after such disturbances called Dutch roll is described below.

Let’s say a cruising helicopter has a disturbance in yaw – the nose moves to the right slightly.  Some of its forward airspeed now moves left-to-right across the main rotor (due to sideslip).  The associated flap back phenomenon lifts the left side of the rotor up and rolls the helicopter right wing down.  (It also flaps the front of the rotor down and causes a pitch down movement, but we’ll ignore that axis here – the motion is smaller.)  The tail rotor (and vertical stabilizer with larger speeds) will push the helicopter back to the original sideslip but overcorrect.  In the overcorrection the flap back will occur in the opposite direction, inducing a left wing down roll.   This coupled yaw-roll oscillation will continue and is called Dutch roll.   Like the phugoid mode, this mode may or may not be stable depending on the helicopter model and flight condition.  Of course, an AFCS can improve this behavior significantly.