[Ref RPL Instruction Kit (502) 8th Edition P. 91-96, Pilot’s Handbook of Aeronautical Knowledge, FAA-H-8083-25B Page 5-23, 6-4]
4 Forces in a Turning Maneuver
- Lift is titled and which should still be perpendicular to the flight path through the CP.
- Weight acts vertically downwards toward the earth
- Thrust acts forward along the propeller shaft – acts forward and parallel to the flight path
- Drag acts to the rear parallel but opposite to the flight path
In a steady level turn, tilted resultant lift (= apparent weight) is slightly larger than the actual weight !
The tilted resultant lift force include two component – 1) the lift component (“vertical component of lift”) and 2) centripetal force component (“horizontal component of lift”)
The lift component is same magnitude but opposite to the downward weight and
the centripetal force component is the force causing the turning maneuver
In other words, the apparent weight (opposite to the tilted resultant life force) is larger than actual weight.
What if the magnitude tilted lift is not larger than that in steady straight and level?
Again! Tilted resultant lift could be disassembled into two component – 1) the lift component and 2) centripetal force component. If the overall lift don’t increase, the centripetal force is acting as the downward and inward force that could cause the sideslip.
What is involved in a balanced level turn?
By applying backward pressure on control yoke – increasing the AoA, the tilted resultant lift could be increased to the magnitude that the centripetal force component acting sideway while the vertical lift component is equal to the actual weight of the plane. At that moment, the level turn could achieve. Be noticed that the steeper the turn, the more elevator back pressure that is needed.
However, one more factor should be considered in a level turn – the balance of turn – a steady level turn should be coordinated as well. To achieve this, we have to learn use aileron, rudder and power in combination for turning maneuver.
Rudder is used in rolling (banking) to bring the nose back in line with the relative wind. Interestingly, once in the turn, the rudder suppose to be not needed.
As the desired angle of bank is established, aileron and rudder pressures should be relaxed;
Elevator back pressure should be held constant to maintain altitude.
Power (thrust) might be needed to prevent a reduction in airspeed.
As mentioned above, by increasing the AoA, the tilted resultant lift could be increased. However, since the drag of the airfoil is directly proportional to its AoA – induced drag increased as the lift is increased. This, in turn, causes a loss of airspeed in proportion to the angle of bank. So, power might be needed.
“Centripetal force” vis-a-vis “Centrifugal force”
Centripetal force (向心力) is the resultant force refers to one of the components of tilted resultant lift force ;
Centrifugal force (離心力) is the reaction force with equal magnitude but opposite direction to the resultant force
CentriPetal force (向心力)
CentrifUgal force (離心力)
(2) Two ways to measure the turn performance:
Radius of the turn refers to the turn tightness
In practice, we usually make a turn with fixed AOB and so by using different regimes to achieve certain radius of turn
Radius of turn = Speed / AOB
R (in feet) = V² / [11.26 x tan(AoB)]
Radius of turn (R) , is expressed in feet, which is equal to the velocity squared divided by 11.26 times the tangent of the bank angle.
NOTE: the airspeed is True Airspeed (TAS)
Rate of turn is the rate at which the heading changes
The rate of turn at any given airspeed depends upon the amount of Centripetal force;
Meanwhile, at any given airspeed and level turn, original total lift during the bank is divided into vertical and horizontal components. The aircraft loses altitude unless additional lift is created. This is done by increasing the AOA until the vertical component of lift is again equal to the weight. Therefore, AOA is somehow proportional to ROT.
AoA ∝ ROT (constant airspeed and altitude);
ROT = AOB / Speed
The formula denotes that :
- the larger the AoB, the higher rate of turn;
- the higher the speed, the lower rate of turn
The reason why ROT is proportional to AOB is that as the angle of bank is increased (AOB↑), the horizontal component of lift increases (centripetal force↑), thereby increasing the rate of turn (ROT↑). Consequently, at any given airspeed, the ROT can be controlled by adjusting the AOB.
In combination, we have the third formula:
ROT = AOB/Speed = 1/Radius of turn
ROT (rate of turn) [in degrees per second] = [1091 x tan (AoB) ] / Speed in KT
Rate of turn (ROT), is expressed in degrees per second, which is determined by taking the constant of 1,091, multiplying it by the tangent of any bank angle and dividing that product by a given airspeed in knots.
NOTE: the airspeed is True Airspeed (TAS)
In rule of thumb
AoB for standard rate one turn – 3º per second (2 mins for 360 degree turn):
AoB = (Speed in KT /10) + [(Speed in KT /10) * 0.5]
Apart from above mentioned performance, in turning maneuver, we should pay attention on few more factors:
Overbanking is the tendency for the aircraft to bank further into the turn – it is related to spiral instability.
The cause of overbanking tendency is that – as we turn the aircraft, the outer wing will travel forward and faster than the inner wing. This results in extra lift being produced by the outer wing and a tendency for the aircraft to bank further into the turn.
a simply lift formula:
Lift = IAS x AoA
The formula clearly shows that the higher the speed (IAS) in a fixed AoA condition, the more lift would be generated.