POF - Principles of flight Quiz 1

Assuming all bodies have the same cross-sectional area and are in motion, which body will have the lowest pressure drag?

• A. Rectangle.

• B. Semi Circle.

• C. Circle.

• D. Oval.

Answer explanation

The lowest drag will be experienced by Oval body because its form drag is reduced significantly by its streamlined shape. The next lowest drag will be experienced by Circle body. Although Semi Circle and Rectangle bodies might appear to experience the same significant value of drag, the Semi Circle body will be subject to a lower drag than Rectangle body – this is because the airflow behind Rectangle body will be more turbulent than behind Semi Circle body.

In summary, if we were to sort the bodies in order from the least to the highest values of drag experienced, the order would be:

Oval, Circle, Semi Circle, Rectangle

And if the question asks for the order from the highest to the least, it would be:

Rectangle, Semi Circle, Circle, Oval

Note that the Semi Circle body is closed. If it would be open, its drag would be higher than the drag of Rectangle body.

Choose the combination of correct statements:

(1) The airfoil's shape in front and back affect the form drag.
(2) Profile drag arises due to tip vortices.
(3) Skin friction and pressure drag constitute profile drag.
(4) Skin friction doesn't affect form drag.
(5) With increasing forward speed, profile drag decreases slightly.

• A. (2), (4) and (5)

• B. (1). (3) and (4)

• C. (3), (4) and (5)

• D. (1), (2) and (3)

Answer explanation

Refer to figure 2380.
Rotor profile drag results from those components acting on the opposite direction of the blade velocities (i.e. the sum of all the profile drags from each blade element). When molecules that have been trapped for a moment on the surface of the blade are released, they collide with passing molecules and slow them down, producing the boundary layer and profile drag, which is for the blades only as it is present even in the hover. At low speeds it is almost constant, but increases slightly when forward speed is gained, while during hover it has the lowest value. It consists of form (or pressure) drag and skin friction drag.

• Pressure drag, also known as form drag, is a type of drag force experienced by objects moving through a fluid, such as air. In the context of helicopter blades, pressure (form) drag occurs due to the difference in pressure on the front and back surfaces of the blade as it moves through the air. When a helicopter blade moves forward, it encounters air resistance. The air pressure on the front (leading edge) surface of the blade is higher than on the back (trailing edge) surface. This pressure differential creates a force that acts opposite to the direction of motion, known as pressure (form) drag. The lowest pressure (form) drag will be experienced by a body with a streamlined shape. The best shape is round at the front and sharp at the end, so the airflow to separate slowly. A flat plate placed at right angles (90°) to the airflow will produce extreme values of pressure (form) drag.

• Skin friction drag is a type of drag force experienced by objects moving through a fluid, such as air. In the context of helicopter blades, skin friction drag occurs due to the frictional resistance between the surface of the blade and the air molecules surrounding it. As a helicopter blade moves through the air, the molecules of air in contact with the surface of the blade slow down due to viscosity, creating a thin layer of slower-moving air adjacent to the blade surface. This layer of slower-moving air exerts a drag force on the blade, which is known as skin friction drag. Skin friction drag is influenced by factors such as the smoothness of the blade surface, the viscosity of the air, and the relative velocity between the blade and the air. Minimizing skin friction drag is important for optimizing the efficiency and performance of helicopter blades. This can be achieved through surface treatments and aerodynamic design techniques aimed at reducing surface roughness and turbulence, thereby minimizing the resistance encountered as the blade moves through the air.

For a subsonic flow the continuity equation states that if the cross-sectional area of a tube increases, the speed of the flow:

• A. does not change.

• B. increases.

• C. first increases then decreases.

• D. Decreases

Answer explanation

In fluid dynamics, the continuity equation is a mathematical statement saying that, in any steady state process, the rate at which mass enters a system is equal to the rate at which mass leaves the system. In fluid dynamics, the continuity equation is analogous to Kirchhoff’s Current Law in electric circuits. The equation of continuity says that “A × ρ × V = constant” in a stationary flow, where:

• A = cross-sectional area,

• ρ (rho) = air density,

• V = airflow velocity.

Subsonic flow is considered incompressible and in an incompressible flow the density ρ (rho) is constant. Therefore, any change in the area has no effect on density, but only on the velocity. The velocity (V) must decrease if the area (A) is increasing and vice versa.

Refer to a tilt-rotor aircraft. What is the purpose of the shaft connecting both rotors?

• A. Maintaining roll equilibrium OEI in a hover.

• B. Keeping RPM of both engines constant.

• C. Keeping both engines at constant delivered torque.

• D. Decreasing the power which is necessary for a hover.

Answer explanation

Side by side rotor helicopters (or transverse rotor helicopters) have two large horizontal rotor assemblies mounted side by side (like a kind of an aeroplane with rotors on each end of the wing). Single rotor helicopters need a tail rotor to neutralize the twisting moment produced by the single large rotor. Side by side rotor helicopters, however, use counter-rotating rotors, with each cancelling out the other's torque. Also, all of the power from the engines can be used for lift, whereas a single rotor helicopter uses power to counter the torque. Older types of side by side rotor helicopters or transverse-mounted helicopters use fixed engines (example: Mil V-12), modern types are called transverse-mounted tilt-rotors, because the rotors can be tilted (an example for a civil tilt-rotor aircraft is the AgustaWestland AW609, which is still under development but already passed several test flights. A famous military tilt-rotor aircraft, which is already in service, is the Bell Boeing V-22 Osprey), so they are more a kind of a mixture of an aeroplane and a helicopter which can take off and land vertically.

In a tilt-rotor aircraft both rotors are connected via gears and transmission interconnect shafts (located within wings and fuselage), so that in case of an engine failure both rotors can be driven by the remaining operating engine and maintain the same thrust and roll equilibrium.

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OEI = One Engine Inoperative

Induced drag may be reduced by:

• A. an increase in the taper ratio of the blade.

• B. the use of a blade tip with a much thinner aerofoil.

• C. an increase in aspect ratio.

• D. a decrease of the aspect ratio.

Answer explanation

Refer to figure 2337.
The aspect ratio of a helicopter blade is defined as the ratio between blade span and the average chord. The average chord is the same as the mean geometric chord. Blade area is blade span multiplied by average chord and therefore average chord is the blade area divided by the blade span. Informally, a high aspect ratio indicates long, narrow blades, whereas a low aspect ratio indicates short, stubby blades.

• Aspect Ratio = (blade span)² ÷ blade area, or

• Aspect Ratio = blade span ÷ mean chord.

For a given airspeed, to generate a given value of lift, a blade with long span (high aspect ratio) does not need to generate so much downwash, which is the reaction of lift. Generally, two aerofoils can have equal surface areas (and therefore equal lift production), but different aspect ratios, making their aerodynamic reaction different. The higher aspect ratio, the higher lift to drag ratio, the less induced drag you get because there is a lower amount of lift per unit span and less of the surface is exposed to tip losses from vortices.

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In aerodynamics, the induced drag (also referred to as the "lift-induced drag", "vortex drag", or sometimes "drag due to lift"), is a drag force that occurs whenever a moving object redirects the airflow coming at it. This drag force occurs in helicopters due to blade rotation. With other parameters remaining the same, as the angle of attack increases, induced drag increases. Induced drag is a by-product of lift and exists only if lift exists.

When producing lift, air below the blade is generally at a higher than atmospheric pressure, while air above blade is generally at a lower than atmospheric pressure. This pressure difference causes air to flow from the lower surface blade root, around the blade tip, towards the upper surface blade root. This spanwise flow of air combines with otherwise flowing air, causing a change in speed and direction, which twists the airflow and produces vortices along the blade’s trailing edge. The vortices created are unstable, and they quickly combine to produce blade tip vortices. The resulting vortices change the speed and direction of the airflow behind the trailing edge, deflecting it downwards, and thus inducing downwash behind the blade. Blade tip vortices also modify the airflow around the blade, reducing the effectiveness of the blade to generate lift, thus requiring a higher angle of attack to compensate, and tilting the total aerodynamic force rearwards. The angular deflection is small and has little effect on the lift. However, there is an increase in drag equal to the product of the lift force and the angle through which it is deflected. Since the deflection is itself a function of lift, the additional drag is proportional to the square of the lift.

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One factor that determines the magnitude of the blade tip vortices is the aspect ratio of the blade, which is the relationship between its length and width. A high aspect ratio blade will produce less induced drag than a blade of a low aspect ratio because the size of the blade vortices will be much reduced on a longer, thinner blade. The magnitude of the blade tip vortices can therefore be said to be inversely proportional to the aspect ratio.

Induced drag depends on the angle of attack, and with a constant IAS in level flight the angle of attack is constant. However, if the weight changes, lift must change correspondingly by adjusting the angle of attack (e.g. if weight decreases as the fuel in cruise is burned off, angle of attack must be decreased and thus induced drag decreases). The speed of the flight also affects the angle of attack => a lower speed requires a higher angle of attack and thus more induced drag is created. The induced drag coefficient C_Di is equal to CL²/πAR, where AR is the aspect ratio and C_L is influenced by the angle of attack. Increased C_L means increased C_Di and thus induced drag. Increased aspect ratio means less induced drag.

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Summary:

• Higher aspect ratio = lower induced drag

• Higher angle of attack = higher induced drag

• Higher weight = higher angle of attack = higher induced drag

Which of the following defines lift/drag ratio?

• A. The maximum lifting effort compared with the drag obtained at the same angle of attack

• B. The greatest value of lift that can be obtained against the value of induced drag.

• C. The maximum value of drag that can be obtained against lift at a specific angle of attack

• D. The maximum lifting effort obtained at any angle of attack.

Answer explanation

Refer to figure 1163.
The best lift to drag ratio is when the highest lift is obtained with the minimum amount of drag. This is only relevant when considering the same angle of attack for the obtained lift and drag. In general, the optimum angle of attack for the best lift to drag ratio is at about 4°. Increasing the angle of attack above this value will decrease the lift to drag ratio as the generated drag would become increasingly higher. This is not a problem as when flying at higher angle of attacks, the goal is to fly slower (as during approach for example) and to have the most efficient L/D ratio.

Which of these statements with regard to a tandem rotor helicopter are correct or incorrect?

(1) The two rotors rotate in opposite directions.
(2) The aft rotor is positioned higher than the forward rotor.

• A. 1) is correct, 2) is incorrect.

• B. 1) is correct, 2) is correct.

• C. 1) is incorrect, 2) is correct.

• D. 1) is incorrect, 2) is incorrect.

Answer explanation

Refer to figure 1047.
Side by side rotor helicopters (or transverse rotor helicopters) have two large horizontal rotor assemblies mounted side by side (like a kind of an aeroplane with rotors on each end of the wing). Single rotor helicopters need a tail rotor to neutralize the twisting moment produced by the single large rotor. Tandem rotor helicopters, however, use counter-rotating rotors, with each cancelling out the other’s torque. Counter-rotating rotor blades won’t collide with and destroy each other if they flex into the other rotor’s pathway. This configuration also has the advantage of being able to hold more weight with shorter blades, since there are two sets. Also, all of the power from the engines can be used for lift, whereas a single rotor helicopter uses power to counter the torque. Older types of side by side rotor helicopters or transverse-mounted helicopters use fixed engines (example: Mil V-12), modern types are called transverse-mounted tiltrotors, because the rotors can be tilted (an example for a civil tilt-rotor aircraft is the Bell Boeing V-22 Osprey), so they are more a kind of a mixture of an aeroplane and a helicopter.

Tandem rotor helicopters (example: Boeing Vertol CH-46 Sea Knight, Chinook) have two large horizontal rotor assemblies mounted one in front of the other. Currently this configuration is mainly used for large cargo helicopters. Single rotor helicopters need a mechanism to neutralize the yawing movement produced by the single large rotor. This is commonly accomplished by a tail rotor, coaxial rotors, and recently the NOTAR systems. Tandem rotor helicopters, however, use counter-rotating rotors, with each cancelling out the other’s torque. Therefore all of the power from the engines can be used for lift, whereas a single rotor helicopter uses some of the engine power to counter the torque. Advantages of the tandem-rotor system are a larger centre-of-gravity range and good longitudinal stability. Disadvantages of the tandem-rotor system are a complex transmission, and the need for two large rotors. The two rotors are linked by a transmission that ensures the rotors are synchronized and do not hit each other, even during an engine failure (in case of an engine failure on a twin-engine type, the power available decreases equally on the two rotors and the remaining engine drives both rotors). Tandem rotor designs achieve yaw by applying opposite left and right cyclic to each rotor, effectively pulling both ends of the helicopter in opposite directions. To achieve pitch, opposite collective is applied to each rotor; decreasing the lift produced at one end, while increasing lift at the opposite end, effectively tilting the helicopter forward or back.

Tandem rotor helicopters have the advantage of being able to hold more weight with shorter blades, since there are two sets. However, the rear rotor works in the aerodynamic shadow of the front rotor, which reduces its efficiency. This loss can be minimized by increasing the distance between the two rotor hubs, and by elevating the aft hub over the other. Tandem rotor helicopters tend to be used for bulk loading rather than single rotor helicopters. Tandem rotor helicopters typically require less power to hover and achieve low speed flight as compared to single rotor helicopters. Both configurations typically require the same power to achieve high speed flight.

A streamline flow approaches an aerofoil and pauses at the stagnation point. At this point, the static pressure:

• A. decreases.

• B. increases.

• C. reaches a minimum value.

• D. reaches a maximum value.

Answer explanation

Refer to figure 830.
The stagnation point on an aerofoil (or any object in a fluid flow) is where the fluid velocity is zero relative to the object. At this point, the fluid is brought to rest, and all its kinetic energy is converted into pressure energy. Because of the shape of the aerofoil profile and the resulting upwash ahead of the leading edge, the stagnation point is situated slightly below the chord line on the leading edge of the airfoil. There is also a stagnation point at the trailing edge of the airfoil, where the airflows from the upper and lower surfaces meet.

To understand why the pressure reaches a maximum at the stagnation point, one can use Bernoulli’s equation for incompressible flow:

Total Pressure = Static Pressure + Dynamic Pressure = constant, or
Total Pressure = Static Pressure + 1/2ρV² = constant, where ρ is the fluid density and V is the fluid velocity.

• Away from the stagnation point: The fluid has some velocity (V) and a corresponding static pressure (P_static).

• At the stagnation point: The fluid velocity (V) is zero (since the fluid is at rest at this point). According to Bernoulli’s equation, all the dynamic pressure 1/2ρV² is converted into static pressure.

Therefore, the static pressure at the stagnation point (P_static) is higher than the static pressure at any other point along the streamline where the fluid is in motion.

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Why the other answer options are incorrect:

• “decreases”: This is incorrect because, at the stagnation point, the fluid velocity decreases to zero, which causes the dynamic pressure to convert to static pressure, thus increasing the static pressure.

• “reaches a minimum value”: This is incorrect because the static pressure reaches a maximum value at the stagnation point due to the conversion of kinetic energy into pressure energy.

• “increases”: This statement is partially true as the static pressure indeed increases compared to the free-stream static pressure. However, it is not as precise as the correct option, which correctly states that the static pressure reaches its maximum value at the stagnation point. Simply stating that it “increases” does not convey the full extent that it reaches the highest possible pressure in the flow field.

The lift coefficient CL versus angle of attack curve of a symmetrical aerofoil section intersects the vertical axis of the graph:

• A. above the origin.

• B. nowhere.

• C. below the origin.

• D. at the origin.

Answer explanation

Refer to figure 833.
The coefficient of lift of an aerofoil placed in an airflow is a dimensionless quantity that represents the lift generated by the aerofoil and depends on blade’s design and angle of attack. Angle of attack is the angle between the chord line of the aerofoil and the direction of the airflow.

A symmetrical aerofoil has identical upper and lower surfaces when viewed from the side. This means that the camber (curvature) of the upper surface is equal and opposite to that of the lower surface, resulting in zero net camber. The camber line of a symmetrical aerofoil coincides with the chord line. A symmetrical aerofoil section placed at the airflow at zero angle of attack, will have a zero lift coefficient and zero lift production. Therefore, the lift coefficient versus angle of attack curve of a symmetrical aerofoil section intersects both the vertical and horizontal axis of the graph at the origin.

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Positive camber refers to the curvature of an aerofoil where the upper surface is more curved (bulging upwards) than the lower surface. The camber line is found above the chord line. This asymmetry creates a pressure difference between the upper and lower surfaces, generating lift when the aerofoil is placed in an airflow at zero angle of attack. Therefore, the lift coefficient versus angle of attack curve of a positive cambered aerofoil section intersects the vertical axis of the graph above the origin and the horizontal axis left of the origin.

Negative camber refers to the curvature of an aerofoil where the lower surface is more curved (bulging downwards) than the upper surface. The camber line is found below the chord line. A negative cambered aerofoil placed in an airflow at zero angle of attack will generate a negative lift coefficient and a force in the opposite direction of lift. This asymmetry provided by the negative camber aerofoil creates a pressure difference between the upper and lower surfaces, but on the opposite sides of a positively cambered aerofoil; this time the greatest pressure is found on the upper side. In order to eliminate this negative force, the negative cambered aerofoil must be placed in the airflow at a positive angle of attack in order for the lift coefficient to become zero. Above this angle, the coefficient of lift has a positive value and lift starts to be produced. Therefore, the lift coefficient versus angle of attack curve of a negative cambered aerofoil section intersects the vertical axis of the graph below the origin and the horizontal axis right of the origin.

Assuming no flow separation, which of these statements about the flow around an aerofoil as the angle of attack increases are correct or incorrect?

(1) The stagnation point moves up.
(2) The point of lowest static pressure moves forward.

• A. 1) is correct, 2) is correct.

• B. 1) is incorrect, 2) is incorrect.

• C. 1) is correct, 2) is incorrect.

• D. 1) is incorrect, 2) is correct.

Answer explanation

Refer to figures 830 and 2314.
The stagnation point is the exact point on an aerofoil where the airflow splits, with some air moving over the upper surface and some over the lower surface. At this point, the air momentarily comes to a stop, leading to maximum air pressure. Because of the shape of the aerofoil profile and the resulting upwash ahead of the leading edge the stagnation point is situated slightly below the chord line on the leading edge of the airfoil. If the angle of attack is increased the stagnation point will follow the curvature of the profile and thus move downwards (and backwards). Inversely, the location of the stagnation point will be further up and forward if the angle of attack is decreased. There is also a stagnation point at the trailing edge of the airfoil, where the airflows from the upper and lower surfaces meet.

Since the term “stagnation” means “no movement”, the stagnation point is where the air is brought to a standstill and the velocity of the airflow is zero. The pressure at the stagnation point is equal to total pressure, which is static pressure + dynamic pressure. Since dynamic pressure has converted to a static pressure that is equal to the total pressure in the airstream, static pressure at the stagnation point reaches a maximum value.

The point of lowest static pressure on an airfoil on normal flight conditions is typically located near the point of maximum curvature, slightly behind the leading edge on the upper surface. This is because the air accelerates over the upper surface of the airfoil, reaching its highest velocity (and thus lowest static pressure) near the point where the curvature is greatest. When the angle of attack increases, the airflow over the upper surface of the airfoil speeds up even more, and the low-pressure area intensifies and moves forward. The point of lowest static pressure tends to move closer to the leading edge as the angle of attack increases. This forward shift is due to the increased acceleration of airflow over the upper surface, which happens more abruptly near the leading edge at higher angles of attack.