Pilots must be careful not to over-anticipate or over-compensate, leading to overbanking in a turn
These principles are typically in reference to turns, but they are foundational to several maneuvers, including aerobatics
Lift Review:
Instrument Flying Handbook, Forces In a Turn
The principles of flight show us that lift occurs perpendicular to the relative wind
We usually think of this as an aircraft flying straight and level as producing lift in the upward direction
As an aircraft banks, however, that lift vector rotates with it, which splits the lift vector into a vertical and horizontal component
This means the resultant lift is a combination of the vertical and horizontal component [Figure 1]
Rate of Turn:
The rate depends on a set bank angle at a set speed [Figure 2]
The standard rate of turn is 3° per second
Speed & Rate of Turn:
If the aircraft increases speed without changing the bank angle, the rate of turn decreases
If the aircraft decreases speed without changing the bank angle, the rate of turn increases
Bank Angle & Rate of Turn:
If the aircraft bank angle increases without changing airspeed, the rate of turn increases
If the aircraft bank angle decreases without changing airspeed, the rate of turn decreases
Speed and bank angle, therefore, vary inversely to maintain a standard rate turn
This is important in the instrument environment, such as when holding or on an instrument approach
A rule of thumb for determining the standard rate turn is to divide the airspeed by ten and add 5
Example: an aircraft with an airspeed of 90 knots takes a bank angle of 16° to maintain a standard rate turn (90 ÷ by 10 + 5 = 14°)
Radius of Turn:
The radius of turn varies with changes in either speed or bank [Figure 2]
Speed & Radius of Turn:
If the speed increases without changing the bank angle, the radius of turn increases
If the speed decreases without changing the bank angle, the radius of turn decreases
Bank Angle & Radius of Turn:
If the speed is constant, increasing the bank angle decreases the radius of turn
If the speed is constant, decreasing the bank angle increases the radius of turn
Therefore, intercepting a course at a higher speed requires more distance and, therefore, requires a longer lead
If the speed is slowed considerably in preparation for holding or an approach, a shorter lead is needed than that required for cruise flight
Instrument Flying Handbook, Turns
Instrument Flying Handbook, Turns
Coordination Throughout Turns:
A slipping turn results from the aircraft not turning at the rate appropriate to the bank being used, and the aircraft falls to the inside of the turn [Figure 3]
The aircraft is banked too much for the rate of turn, so the horizontal lift component is greater than the centrifugal force
A skidding turn results from an excess of centrifugal force over the horizontal lift component, pulling the aircraft toward the outside of the turn [Figure 3]
The rate of turn is too great for the angle of bank, so the horizontal lift component is less than the centrifugal force
The ball instrument indicates the quality of the turn and should be centered when the wings are banked
If the ball is off-center on the side toward the turn, the aircraft is slipping, requiring added rudder pressure on that side to increase the rate of turn
Also, reducing the bank angle without changing the rudder pressure will help coordinate the turn
If the ball is off-center on the side away from the turn, the aircraft is skidding, requiring rudder pressure on that side to be relaxed to decrease the rate of turn
Also, increasing the bank angle without changing the rudder pressure will help coordinate the turn
The ball should be in the center when the wings are level; use rudder and/or aileron trim if available
The increase in induced drag (caused by the increase in the angle of attack necessary to maintain altitude) results in a minor loss of airspeed if the power setting is not changed
Aircraft Performance While Turning:
Undesired Side Effects of a Turn:
Adverse Yaw (drag)
Yaw against the direction of turn (lift)
Diving tendency
Over-banking tendency
Increased stall speed
Instrument Flying Handbook, Adverse Yaw
Load Factor:
Load Factor, Vg Diagram
Load factor is a measure of what is supported by the wings and is useful in performance measurements like a Vg diagram [Figure 4]
In level flight, the amount of vertical lift required must equal weight
Note that the load factor required for a level turn is a function of bank angle (φ) only and is airspeed, weight, and altitude independent
Any force applied to an aircraft to deflect its flight from a straight line produces stress on its structure; the amount of this force is the load factor
A load factor is a ratio of the aerodynamic force on the aircraft to the gross weight of the aircraft (e.g., lift/weight)
Example: A load factor of 3 means the total load on an aircraft's structure is three times its gross weight
When designing an aircraft, it is necessary to determine the highest expected load factors under various normal operations
These "highest" load factors are called "limit load factors"
Aircraft are placed in various categories, i.e., normal, utility, and acrobatic, depending upon the load factors they are designed to take
For reasons of safety, aircraft design accounts for certain maximum load factors without any structural damage
In level flight in undisturbed air, the wings are supporting not only the weight of the aircraft but centrifugal force as well
As the bank steepens, the horizontal lift component increases, centrifugal force increases, and the load factor increases
If the load factor becomes so great that an increase in the angle of attack cannot provide enough lift to support the load, the wing stalls
Since the stalling speed increases directly with the square root of the load factor, the pilot should be aware of the flight conditions during which the load factor can become critical
Steep turns at slow airspeed, structural ice accumulation, and vertical gusts in turbulent air can increase the load factor to a critical level
Accelerated Stall Speed:
Accelerated Stall Speed
As discussed above, the load factor makes no mention of stall speed [Figure 5]
We can't blindly pull back on the stick or yoke because we may fly the aircraft right into an accelerated stall
Overbanking in a Turn:
General Turn Performance:
Making a level turn is relatively easy at mild bank angles; however, above a 60° angle of bank, the level turn equation becomes highly non-linear
Minor changes in the angle of bank require fairly large load factor adjustments to maintain a level turn
That's no problem if maintaining a level turn is the only task, but when the pilot becomes task-saturated, precise adjustment of bank angle and load factor may go out the window
High bank angles and low altitude can quickly become a deadly combination
Overbank Acceleration:
Over time, a vertical acceleration turns into a descent rate and altitude loss
Rather than trying to plot it three-dimensionally, it is easier to simplify the equation
If we represent two levels of pilot distraction with 5° and 10° of overbank
Example:
A 2-g level turn requires a 60° angle of bank
What happens if the aircraft is at 2-gs and 65° or 70° of bank angle instead of 60°? The plot below shows the 5° and 10° overbank cases at 1-g increments. Notice that a given bank angle error is worse at high g's
Overbank Vertical Speed and Altitude Loss:
Over time, overbank acceleration causes a steady ramp-up of velocity
Distance traveled builds as a function of time squared
This makes overbank much more dangerous than a constant rate of descent because the initial sink rate may go undetected
By the time the pilot detects the rapidly increasing VSI, the aircraft may already be in extremis
The pilot's last-ditch effort to avoid ground impact may lead to an accelerated stall departure
Aerobatics:
All of the above applies to any plane
Example:
As you make a loop, you lose airspeed in the vertical, so you need to ease your pull (increase radius), or you will fly an egg-shaped loop
