# Turn Performance

## Introduction:

• When an aircraft banks, the resultant lift splits between a vertical and horizontal component, providing the horizontal forces necessary to turn
• lift is a key principle of flight, essential to flight and therefore turn performance
• When an aircraft is placed in a bank, the lift vector of an aircraft rotates with it, producing a vertical and horizontal component
• The relationship between the aircraft's speed and bank angle determines the rate and radius of turns
• The bank angle, in conjunction with aircraft speed, form a relationship between the rate of turn and radius of turn
• The equal and opposite reaction to this side-ward force is centrifugal force, which is merely an apparent force as a result of inertia
• Pilots endeavor to maintain coordination throughout turns to avoid slipping/skidding
• Understanding the rate, radius, and performance in a turn, aircraft performance while turning is easier to understand
• Pilots must be careful to not 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:

• 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 component, 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 &divide; by 10 + 5 = 14°)

• 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

## 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 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 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:

2. Yaw against the direction of turn (lift)
3. Diving tendency
4. Over-banking tendency
5. Increased stall speed

• 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
• 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:

• 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 60° angle of bank, the level turn equation becomes highly non-linear
• Minor changes in 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 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 in 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

## Conclusion:

• Rate and radius of turn are directly/indirectly related to bank angle respectively
• Any time ailerons are used, adverse yaw results
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