Stability

In short, stability refers to an aircraft’s behavior after being disturbed from a steady flight condition.  For example, a hovering helicopter’s reaction to a gust of wind.  This gust will change the helicopter’s speed and cause pitch, roll and/or yaw motion.  Hover 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.  E.g. pendulum at the lowest position (if moved away from this position gravity pulls it back to the lowest position) or a ball at the bottom of a hill.  A pendulum is unstable, however, at its highest point (any disturbance will cause gravity to pull it down, further away from the top position) and a ball is unstable at the peak of a hill. 

If something is statically stable, then we can talk about dynamic stability – how it returns to the initial state and what happens after that.  Typically, a statically stable aircraft will not “directly” settle back to the initial state but will pass through the initial state and “overcorrect.”  In the pendulum analogy, if you move it left from center it will return to center and then swing right (overcorrect).  Since it’s statically stable, it will push back against this overcorrection as well.  This overcorrection will itself often be over corrected, … so that the aircraft (or pendulum) oscillates 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 damp out) it’s dynamically stable.  If the amplitude of oscillations increases, it’s 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 (e.g. something maybe stable at one airspeed but not another).  The reaction will be different if the disturbance was to roll, pitch or yaw.  We try to 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 considered statically stable.  If “nudged” into a pitch, roll or yaw motion the helicopter’s rotors will naturally push back towards the initial condition.  This is even true for speed – after a sudden increase in headwind, causing an increased airspeed, a helicopter main rotor will “flap back” and slow it down.  We’ll explain more about how this stability occurs below.

Pitch, roll and airspeed

Static stability in pitch, roll and airspeed 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 70kts airspeed.  If a 20kt gust of headwind hits the helicopter, it’s airspeed jumps to 90kts.  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 obtain 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 (flapping lags peak lift by about 90 degrees of rotor rotation, see this for details).  This flapping back of the main rotor tilts the main rotor thrust aft, which pitches the nose up and reduces the airspeed.

So how does this flap back phenomenon explain roll and pitch stability?  Either 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 resistive 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 (again, see this to understand why).  This flapping orients the main rotor thrust more to the left, which rolls the helicopter back (left wing down) to the original position.   (There are other considerations like fin and fuselage aerodynamics, but typically the main rotor is dominant.) 

Lateral flapping after rolling

Yaw

If a disturbance changes the helicopter’s yaw rate, it will change the flow of air through the tail rotor.  E.g. 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 stabilizes yaw but is normally supplemented with an additional effect at higher speeds – the vertical fin on the helicopter tail.  At high speeds, a yaw disturbance creates sideslip - a lateral airspeed that pushes on the tail fin.  

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 (see components) provides further help – aerodynamic forces push it down (nose up) when the AOA decreases and vice versa.  A horizontal stabilizer’s effect increases the further aft it is placed and the larger it is.  However, a designer must be careful that the main rotor wash effect on the stabilizer is not too awkward or destabilizing (the wash will decrease from hover to cruise and move aft).  Now we’ll discuss the longitudinal oscillations.

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 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 generally 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.