Any aircraft or body in motion is subject to Newton’s three laws of motion, which state that:
Most manoeuvres involve changes in direction and speed. Any change of direction and/or speed involves acceleration, which is often evident to the pilots as an apparent change in their weight. During acceleration, the aircraft is not in equilibrium since an out-of-balance force is required to displace the aircraft continuously from a straight line and/or to vary its speed. While an aircraft travels along a curved path, it wants to obey Newton’s first law and travel in a straight line. To keep the aircraft turning, a force is necessary to accelerate it towards the centre of the turn. This force is called the centripetal force. This force has an equal and opposite reaction force called centrifugal force.
The centripetal force can be provided in a number of ways. A good example is a stone on the end of a piece of string. When the stone is swung in a circle, the stone is subjected to centripetal force by the hand pulling the string. If the string is released, the centripetal force is removed and the equal and opposite reaction force (centrifugal reaction) disappears simultaneously. The stone, obeying Newton’s first law, flies off in a straight line at a tangent to the circle.
An aircraft in a turn scribes an arc of a circle. To turn the aircraft, a force will be acting at right angles to the direction of motion (i.e., towards the centre of the arc). This force is generated by banking the aircraft and tilting the lift force (a vector component) into the direction of the turn.
The horizontal component (acting towards the centre of the turn) pulls the aircraft into turn. This is the centripetal force. The reaction force to the horizontal component of lift, or the centrifugal force, is equal in size and opposite in direction to the centripetal force.
For an aircraft to turn, a centripetal force is required to deflect the aircraft towards the centre of the turn. By banking the aircraft and using the horizontal component of the now-inclined lift force, the necessary force is obtained to move the aircraft along the curved path. If the aircraft is banked, the angle of attack is kept constant, and balanced flight is maintained, then the vertical component of lift will be too small to balance the weight, and the aircraft will start to descend. Therefore, as the angle of bank (AoB) increases, the angle of attack must be progressively increased by a backward movement of the control wheel to increase total lift. This is done until the vertical component of lift is large enough to maintain level flight, while the horizontal component is large enough to produce the required centripetal force.
The increased angle of attack brings with it an increase in drag, which must be countered by an increase in power if the airspeed is to be maintained. For angles of bank of 30° or less, a small decrease in speed is accepted and no power is required. Turns steeper than 30° require an increase in power in proportion to the increase in angle of bank.
The load, or loading on an aircraft during a turn, is the force acting on the structure owing to the increased lift generated by the wings to provide the required centripetal force. The loading is usually expressed as a multiple of the weight and is known as the load factor. It acts in the opposite direction of the lift force, to which it is always equal.
Load Factor in Turns
In straight and level flight, lift is equal to weight, and the load is said to be 1g or 1 times the normal acceleration due to gravity (i.e., the pilot feels the same force in the aircraft as the pilot’s weight). In a level turn, the lift force must be greater than the weight so that the VCL is equal to weight and the HCL provides the acceleration required towards the centre of the turn. The opposite reaction to the increase in lift is felt as the load factor—the aircraft has undergone an increase in apparent weight, and the pilot now feels heavier than before.
During a level turn:
(a) At 30° AoB, the load factor is 1.15g; thus, the wings are producing 15% more lift than in straight and level flight, and the pilot feels 15% heavier.
(b) At 45° AoB, the load factor is 1.4g.
(c) At 60° AoB, the load factor is 2g. The wing is required to produce lift equal to twice the weight of the aircraft to maintain altitude, and the pilot feels twice as heavy as normal. The load factor also affects the stalling speed of an aircraft. The stalling speed increases by the square root of the load factor. During a 60° bank turn, the load factor is 2, so the stall speed increases by 1.4.
The questions asked will normally give you the stall speed of the aircraft (VS) and/or the angle of bank (Θ).
Question 1: Determine the stalling speed in a turn.
An aircraft in level flight stalls at 52 knots (VS). What will be the stall speed when the aircraft enters a 55° AoB turn?
(a) First, we must find the load factor on this aircraft:
(b) Then, we must put the load factor into the VSM formula:
Therefore, the stall speed in this manoeuvre is going to be 69 knots.
Question 2: Determine the loading during a turn.
An aircraft in level flight stalls at 50 knots (VS). During recovery from a high speed dive, the aircraft will stall at 100 knots IAS. What is the load factor experienced by the airframe and the pilot?
We have been given the stall speed of 50 knots. We also have the stall speed in the manoeuvre of 100 knots. Therefore, we must work backwards by using the triangle:
(a) So we can get the new formula:
(b) This has only given us the square root of the load factor, so we must square this figure to get the load factor.
This is just the same if we get a question relating to an aircraft stalling at a certain speed at a certain angle of bank. Just use the triangle to work out what the question is asking. Make sure you write what information you have been given and what information you require.
Rate of Turn
Rate of turn is the rate of change of the aircraft heading. Rate of turn is defined by the number of degrees the aircraft has turned through in one second. A rate number between 1 and 4 is normally used. A rate one turn (ROT) is an aircraft turning through 3° per second; thus, it will take 2 minutes for the aircraft to turn through 360°. The angle of bank required to achieve a rate one turn is determined by the aircraft’s airspeed. The formula below can be used to calculate the required AOB:
For example, an aircraft travelling at 85 kt would require an angle of bank of 15° to maintain a rate one turn.
Radius of Turn
Radius of turn is the ‘tightness’ of the turn. For a given angle of bank, the radius of the turn is determined by the airspeed. A low airspeed results in a small radius, and a large airspeed results in a large radius.
There are two factors determining the turning performance of an aircraft: angle of bank and TAS. Remember, load factor is associated with angle of bank. For example, at 60° AOB, the pilot knows the load factor experienced will be 2g regardless of the aircraft weight and speed. We can, therefore, say that the turning performance is determined by angle of bank and airspeed.
For a given airspeed, as the AOB is increased, the rate of turn increases, and the radius of turn decreases. A small AOB (15°) requires a small centripetal force (the turning force), which gives a low rate of turn and a large radius. A large AOB (45°) requires a large centripetal force, which results in a high rate of turn and a smaller radius.
For a given angle of bank, as the airspeed increases, the radius of turn increases, and the rate of turn decreases. A low airspeed results in a small radius and a high rate of turn; a high airspeed results in a low rate of turn.
The tighter the turn at a given IAS (the greater the rate of turn), the greater the value of the HCL and angle of bank, weight remaining unchanged. The tightest turn for each IAS is obtained when the wings are producing the greatest amount of lift (CL MAX) on the fringes of the stall. At this point, the angle of attack and induced drag are so high that full power is usually necessary to keep the speed constant. To achieve maximum rate and minimum radius of turn, the aircraft must be as slow as possible (i.e., the stall) and at the largest angle of bank as possible.
The minimum radius will be achieved at the design manoeuvring speed (VA). In aviation, the design manoeuvering speed (VA) of an aircraft is an airspeed limitation selected by the designer of the aircraft. At speeds above the maneuvering speed, full or abrupt movement of any control surface should not be attempted because of the risk of damage to the aircraft. If the aircraft is operated below the VA speed, full control surface deflection will lead to the aircraft stalling, not over stressing the aircraft. As a pilot this is more favourable, as control can be regained following a stall, whereas a damaged aircraft may not. The maneuvering speed of an aircraft is usually shown on a cockpit placard and in the aircraft’s flight manual, but is not commonly shown on the aircraft’s airspeed indicator. This speed also decreases with a decreasing aircraft weight as the aircraft has less inertia, and therefore is more responsive to control inputs.
Remember that stall speed increases when the aircraft is banked (VSM). So, we must bank the aircraft until it is pulling as much g as it is approved for. This is the steepest we can go! Any steeper, and we will be overstressing the airframe. Because Va is the highest speed we can fly at and operate the aircraft at CL MAX, it therefore dictates our max. rate / min. radius of turn.
Operating at CL MAX incurs a large increase in drag. To overcome the drag, power (sometimes full power) must be used to maintain level flight. Many light aircraft have airframes strong enough to sustain up to 6g or even greater. It so happens that there is seldom sufficient power to support the sort of drag one encounters during a 6g turn! As a result, the airspeed settles much lower than Va and a larger radius / lower rate results. It could be said that the power has limited the angle of bank to much less than the airframe is structurally capable of. It is also important to remember that we are considering only level turns here.
Effect of Altitude
An increase in altitude decreases the manoeuvrability of all aircraft, since all aerodynamic forces are governed by the ½ rV2 factor. At the absolute ceiling, all aircraft are limited by the amount of g that can be applied without stalling.
The main reasons for the reduction in manoeuvrability at high altitude are:
(a) The IAS/TAS relationship due to the reduction in air density
(b) The reduction of thrust with altitude
If an aircraft is flying in standard conditions at an IAS of 100 knots at sea level, the TAS will also be 100 knots. If altitude is increased and the IAS is maintained at 100 knots, the TAS must increase due to the reduction of density with an increase of altitude. For the same IAS and angle of bank (and thus HCL), at a high altitude, the rate of turn decreases and the radius of turn increases.
(1) What happens to the rate and radius of turn at a given AOB if you increase the aircraft’s airspeed?
Answer: The rate of turn will decrease and the radius of turn will increase.
(2) What happens to the rate and radius of turn at a given airspeed if you increase the load factor?
Answer: The rate of turn will increase and the radius of turn will decrease.
If a racetrack pattern is flown, the path flown by the aircraft through the air mass may be different to that over the ground. This can be misleading for a pilot, who must always fly the aircraft in balance and at a good airspeed through the air mass. Remember, wind is simply movement of the air mass in relation to the surface. When flying close to the surface, it is easy to be tricked into thinking the aircraft is slipping or skidding (flying out of balance) through the air. If a balanced turn is maintained, the aircraft will slip/skid in relation to the ground. It is merely the pilot’s inability to differentiate between the two that can provide confusion. When flying into wind, the lower groundspeed could prompt the pilot to increase power; the IAS, of course, may not have changed. The opposite happens when flying downwind. This is the slightly more concerning of the two, as it could result in a decrease in IAS. Here, a slow unbalanced turn back into wind again could spell disaster this close to the ground.
Remember, an aircraft ‘skids out’ of a turn and ‘slips’ into a turn.
For a nil wind situation, an aircraft that is established in a constant angle of bank and airspeed will have a constant radius of turn. If there is wind blowing, the radius is no longer circular with reference to the ground. If the angle of bank is maintained, the ground radius of the turn will change, becoming greatest where the groundspeed is highest (i.e., heading downwind), and lowest where the groundspeed is lowest (i.e., heading headwind). To maintain a constant radius turn around a ground feature, the centripetal force must be adjusted to allow for the difference in groundspeed as the aircraft flies around the turn. This means that the higher the groundspeed, the higher the centripetal force required, and vice versa. Therefore, the angle of bank needs to be least when directly into wind and greatest when directly out of wind. However, when we are turning downwind, the wind is assisting us into the turn; therefore, the angle of bank is going to be less than when we are turning upwind.
Tendency to Overbank in Level and Climbing Turns
To commence a level turn, a pilot needs to bank the aircraft by applying ailerons. Once the aircraft starts turning, the outer wing travels faster than the inner wing and so generates more lift. Once this starts, the tendency is for the bank angle to continue to increase. To overcome this tendency, when established in a turn, you may have to hold off bank, i.e., hold opposite aileron.
Note that in the above image, the arc distance of B is greater than that of A, with both arcs taking the same amount of time to create. With this in mind, the outer wing travels faster and produces more lift than the inner wing in a climbing turn. There is a second effect to consider. As the inner and outer wings climb through the same amount of height, the outer wing travels a greater horizontal distance due to being on the outside of the turn. The angle of attack of the outer wing is, therefore, greater than the angle of attack of the inner wing (as can be seen in the below image). Therefore, the lift produced by the outer wing in a climbing turn will be even greater. When established in a climbing turn, you may need to hold off bank to prevent the turn becoming steep. There is no need for a pilot to plan for this. The pilot must just observe what is happening and maintain the desired bank angle with aileron.
Underbank/Overbank in a Descending Turn
In a descending turn, the outer wing travels faster and wants to produce more lift than the inner wing, creating an overbanking scenario. But, due to the descent, the inner wing travels a smaller horizontal distance for the same height loss when compared with the outer wing; thus, the inner wing has a larger angle of attack. In effect, the inner wing is descending on a steeper spiral path than the outer wing. Therefore, the inner wing tends to produce more lift, meaning the inner wing wants to create an underbank scenario. As a result, the two effects more or less cancel each other out. In a descending turn, you may have to hold bank on (or off), depending on the aircraft. There is no need for a pilot to plan for this. The pilots just need to keep their eyes open and maintain the desired bank angle with aileron.
A loop is a 360° ‘turn’ in the vertical plane. If an aircraft is accelerated by 3g while diving vertically, an accelerometer in the cockpit would show a loading of 3g, as the wings are producing lift equal to 3 times the aircraft weight. If the aircraft is looped, at the bottom of the dive, still at an acceleration of 3g, the accelerometer would show 4g, i.e., the loading on the aircraft has increased since in level flight the wings must produce extra lift (1g) to balance the weight. While climbing vertically, the accelerometer will read the loading to be 3g, but at the top of the loop, still at an acceleration of 3g, the accelerometer will read 2g, since gravity, acting vertically downwards, supplies the additional g unit to make up the total acceleration, while the accelerometer reading shows only the loading on the wings. The radius of the looping manoeuvre is proportional to TAS / load factor. Therefore, the speed, load factor, and radius of a loop will be greatest at the bottom of the loop and smallest at the top of the loop.
The operating flight strength limitations of an aircraft are presented in the form of a Vn or Vg diagram. The Vn diagram here represents the general characteristics of any aircraft and gives a graphical representation of the aircraft’s manoeuvring envelope and its speed and load factor limitations. The horizontal scale is airspeed (V) and the vertical scale is load factor. The diagram is valid for one known aircraft weight and configuration. The upper and lower curved lines represent lines of maximum lift capability (i.e., positive and negative stall regions). Flight in these areas is not possible because the aircraft will be stalled. In this case, the aircraft is capable of developing no more than positive 1g at the wings’ level stall speed of the aircraft. The positive limit load factor is +3.8g and the negative limit load factor is −1.5g. If the aircraft is flown at a positive load factor greater than the positive limit load factor of +3.8g, it is possible to cause structural damage to the aircraft. The limit airspeed (or red line, VNE) is a design reference point for the aircraft. If flight is attempted beyond the limit speed, structural damage or structural failure may result. A single large stress will cause structural failure. Less severe stress over time will cause fatigue. As well as possible structural damage or failure, the aircraft may encounter critical gust, destructive flutter, and aileron reversal or surface divergence.
VS : Basic stall speed.
VA : Design manoeuvering speed – (from previous) is an airspeed limitation selected by the designer of the aircraft. At speeds above the maneuvering speed, full or abrupt movement of any control surface should not be attempted because of the risk of damage to the aircraft. If the aircraft is operated below the VA speed, full control surface deflection will lead to the aircraft stalling, not over stressing the aircraft. As a pilot this is more favourable, as control can be regained following a stall, whereas a damaged aircraft may not. The maneuvering speed of an aircraft is usually shown on a cockpit placard and in the aircraft’s flight manual, but is not commonly shown on the aircraft’s airspeed indicator. This speed also decreases with a decreasing aircraft weight as the aircraft has less inertia, and therefore is more responsive to control inputs.
In severe trubulence the aircraft should be slowed to VA speed or below, this will help preserve load factor limits and avoid over stressing the aircraft which could lead to structural damage.
VNO : Normal Operations: Maximum structural cruising speed – do not exceed this speed except in smooth air, and then only with caution.
VNE : Never Exceed – do not exceed this speed in any operation.
Discuss the following questions in class now.