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# Turn Performance

## Introduction:

• By referencing the lift discussion, lift is perpendicular to the relative wind
• When an aircraft is placed in a bank the resultant lift (the lift we talk about being perpendicular) is split between a vertical and horizontal component
• The equal and opposite reaction to this side-ward force is centrifugal force, which is merely an apparent force as a result of inertia
• The relationship between the aircraft's speed and bank angle determine the rate and radius of turns
• Any time ailerons are used, adverse yaw is produced Instrument Flying Handbook,Forces In a Turn

## 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:
• 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:
• 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, must 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 7
• 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 + 7 = 16°)

## Radius of Turn:

• The radius of turn varies with changes in either speed or bank [Figure 2:]
• Speed:
• If the speed is increased without changing the bank angle, the radius of turn increases
• If the speed is decreased without changing the bank angle, the radius of turn decreases
• Bank Angle:
• 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
• This means that 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:

• In a slipping turn, the aircraft is not turning at the rate appropriate to the bank being used, and the aircraft falls to the inside of the turn
• 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 excess of centrifugal force over the horizontal lift component, pulling the aircraft toward the outside of the turn
• 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 of center on the side toward the turn, the aircraft is slipping and rudder pressure should be added on that side to increase the rate of turn or the bank angle should be reduced
• If the ball is off of center on the side away from the turn, the aircraft is skidding and rudder pressure toward the turn should be relaxed or the bank angle should be increased
• If the aircraft is properly rigged, 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 angle of attack necessary to maintain altitude) results in a minor loss of airspeed if the power setting is not changed

## 5 Undesired Side Effects of a Turn:

1. Adverse Yaw (drag)
2. Yaw against the direction of turn (lift)
3. Diving tendency
4. Over-banking tendency
5. Increase in stall speed

• Load factor is a measure of what is supported by the wings
• In level flight, the amount of vertical lift required must equal weight
• Note that 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 a stress on its structure; the amount of this force is termed load factor
• A load factor is the 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 load factors that can be expected in normal operation under various operational situations
• 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, the aircraft must be designed to withstand certain maximum load factors without any structural damage
• The specified load may be expected in terms of aerodynamic forces, as in turns
• 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 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
• We can't blindly pull back on the stick or yoke because we may fly the aircraft right into an accelerated stall
• Accelerated stall speed is found by simultaneously solving lift equations for 1-g and accelerated flight with the lift coefficient set to CL max

## Overbanking:

• Turn Performance:
• Making a level turn is relatively easy at mild bank angles however, above 60° AOB, the level turn equation becomes highly non-linear
• Minor changes in AOB 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
• The overbank equation has three variables (a z , n and φ) making it difficult to visualize
• The overbank equation requires a 3-D graph or simplifying assumptions
• 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° AOB
• 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 VSI 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 do a loop, you lose airspeed in the vertical so you need to ease your pull (increase radius) or you will fly an egg