Unit 3 - Practice Quiz

Newton's Third Law states that for every action, there is an equal and opposite reaction. The wing pushes air down (action), and the air pushes the wing up (reaction), creating lift.

Newton's Second Law is fundamentally expressed as Force (F) equals mass (m) times acceleration (a). This principle governs how forces cause an aircraft to accelerate or change its velocity.

An airfoil is a structure with a curved surface designed to produce an aerodynamic force, primarily lift, when it moves through a fluid like air.

The chord line is a reference line drawn straight from the leading edge (front) to the trailing edge (rear) of an airfoil, used for defining angles and dimensions.

Lift is the upward force generated by the wings that directly opposes the downward force of weight, allowing the aircraft to stay airborne.

Thrust is the propulsive force that moves an aircraft through the air. It is generated by engines (e.g., propellers or jets) and opposes the force of drag.

Flaps are trailing-edge devices that increase the camber and surface area of the wing, which generates more lift, allowing for safer flight at slower speeds typical of takeoff and landing.

Slats are located on the leading edge of the wing. When extended, they allow air to flow from below the wing to the upper surface, delaying airflow separation and allowing the wing to be flown at a higher angle of attack before stalling.

For a typical airfoil, lift increases almost linearly with the angle of attack until it reaches the critical angle of attack, after which the wing stalls and lift decreases sharply.

The critical angle of attack (also known as the stall angle) is the point where the airfoil produces the most lift. Increasing the angle beyond this point causes airflow separation (a stall) and a dramatic loss of lift.

Induced drag is an unavoidable consequence of lift generation. It is created by the wingtip vortices that form due to the pressure difference between the upper and lower surfaces of the wing.

Parasite drag is composed of all drag sources not associated with the production of lift. It includes form drag (due to shape), skin friction drag, and interference drag.

Range is the total distance an aircraft can fly between takeoff and landing on a given amount of fuel. It is a measure of how far the aircraft can go.

Endurance is the total amount of time an aircraft can stay in the air on a single load of fuel. It is crucial for missions like surveillance or loitering.

The rate of climb is the speed at which an aircraft is increasing its altitude, typically measured in feet per minute or meters per second.

The absolute ceiling is the maximum density altitude an aircraft can reach and maintain level flight. At this altitude, there is no excess power available to climb any higher, so the rate of climb is zero.

A roll involves rotating the aircraft around its longitudinal (nose-to-tail) axis. Ailerons on the wings are the primary control surfaces used to perform a roll.

Dihedral is the upward angle of the wings relative to the lateral axis. It is designed to provide inherent lateral (roll) stability.

Dihedral provides lateral stability. If a wing drops, the dihedral effect causes the lower wing to generate more lift than the higher wing, creating a rolling moment that tends to return the aircraft to a wings-level attitude.

In a NACA 4-digit series, the first digit represents the maximum camber (curvature) as a percentage of the chord length. For a NACA 2412, the maximum camber is 2% of the chord.

Newton's Third Law states that for every action, there is an equal and opposite reaction. The action is the engine pushing the hot gas mass backward, and the reaction is the gas pushing the engine (and thus the aircraft) forward.

For a NACA 4-digit airfoil, the first digit represents the maximum camber in percent of the chord. Increasing the first digit (e.g., to a NACA 3415) would increase the maximum camber from 2% to 3% of the chord, which generally increases the maximum lift coefficient.

In steady, level flight, the aircraft is not accelerating vertically or horizontally. According to Newton's First Law, the net force in both directions must be zero. Therefore, the upward force (Lift) must balance the downward force (Weight), and the forward force (Thrust) must balance the backward force (Drag).

Exceeding the critical angle of attack causes the smooth airflow over the upper surface of the wing to separate from the surface. This turbulent separation drastically reduces the pressure difference between the upper and lower surfaces, leading to a sharp drop in lift, a condition known as an aerodynamic stall.

Induced drag is a byproduct of lift and is inversely proportional to the square of the velocity (). Parasite drag (due to form, skin friction, etc.) is directly proportional to the square of the velocity (). Therefore, as speed doubles, induced drag is quartered, while parasite drag is quadrupled.

Extending trailing edge flaps increases the curvature (camber) of the airfoil. This change allows the wing to generate more lift at a given angle of attack and also increases the maximum lift coefficient (), enabling the aircraft to fly at lower speeds.

The range equation for a jet aircraft shows that range is directly proportional to the lift-to-drag ratio (L/D). Therefore, to travel the farthest distance for a given amount of fuel, the aircraft must fly at the angle of attack that produces the maximum L/D ratio, often referred to as .

Rate of climb is a vertical velocity, which is determined by the excess power available to the aircraft. Excess power is the difference between the power produced by the engine and the power required to maintain level flight. The climb rate is maximized when this difference is greatest.

When an aircraft with dihedral rolls, the lower wing meets the relative wind at a higher angle of attack than the higher wing due to a sideslip component of airflow. This increased angle of attack on the lower wing generates more lift, creating a rolling moment that tends to lift the lower wing and restore the aircraft to a wings-level attitude.

The load factor in a level, coordinated turn is calculated as , where is the bank angle. For a 30-degree bank, . This means the wings must produce lift equal to 1.15 times the aircraft's weight to maintain level flight.

According to Newton's Second Law, acceleration is the net force divided by mass (). The net force in the direction of motion is Thrust - Drag. So, . The acceleration is .

In the NACA 4-digit series, the first two digits ('00' in NACA 0012) indicate the camber and its location. Zeros in both positions signify zero camber, meaning the airfoil is symmetrical. The NACA 2412 has a maximum camber of 2% of the chord ('2') located at 40% of the chord ('4'), making it a cambered airfoil.

Interference drag is generated when the airflows around different parts of the aircraft (e.g., where the wing joins the fuselage or where struts attach) merge and interact. This interaction creates more turbulence and drag than the sum of the individual parts would produce in isolation.

Deploying flaps increases the airfoil's effective camber. This results in a higher lift coefficient () for any given angle of attack, shifting the lift curve upwards. It also increases the maximum lift coefficient (). However, this increased camber often causes flow separation to occur at a slightly lower angle of attack, thus decreasing the critical angle of attack and shifting the peak of the curve to the left.

Features like a high-mounted swept wing can create excessive lateral (roll) stability, making the aircraft feel sluggish and difficult to maneuver. Designers introduce anhedral to counteract this effect. Anhedral reduces roll stability, making the aircraft more responsive to pilot inputs and increasing its roll rate, which is desirable for aerobatic and combat aircraft.

Endurance is about minimizing the rate of fuel consumption over time. For a propeller aircraft, the rate of fuel flow is roughly proportional to the power produced. Therefore, to stay in the air for the longest possible time, the aircraft must be flown at the speed where the power required to maintain level flight is at its absolute minimum.

Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure. The faster-moving air over the top surface creates a region of lower static pressure compared to the slower-moving air below the wing. This pressure differential creates a net upward force, which is lift.

Leading-edge slats are high-lift devices that, when extended, form a slot between the slat and the wing's leading edge. High-pressure air from beneath the wing is ducted through this slot to the upper surface. This injection of high-energy air into the boundary layer delays airflow separation, allowing the wing to achieve a higher maximum lift coefficient and a higher critical angle of attack.

As an aircraft climbs, the air density decreases, reducing engine performance and thus the excess power available for climbing. The service ceiling is the practical upper limit of flight, defined as the density altitude where the aircraft's maximum rate of climb is only 100 ft/min. The absolute ceiling is the altitude where the rate of climb is zero.

In a steady climb, the flight path is inclined upwards. Lift acts perpendicular to the flight path, while weight acts vertically downwards. A component of weight acts rearward along the flight path, adding to drag. To maintain a constant airspeed climb, Thrust must overcome both Drag and this rearward component of Weight. Consequently, Thrust must be greater than Drag. Also, Lift only needs to balance the component of Weight that is perpendicular to the flight path, so Lift is less than the total Weight of the aircraft.

Newton's second law for a variable mass system is . The net external force is gravity acting on the current mass of the rocket, . However, the total force driving the change in the rocket's momentum is the thrust force plus the external gravitational force. Thus, .

In a level turn, the vertical component of lift balances weight (), and the horizontal component provides the centripetal force (). From the first equation, . Load factor . Substituting into the second equation gives , which simplifies to .

Supercritical airfoils have a flattened upper surface, a large leading-edge radius, and significant aft camber. The flattened top surface reduces the peak supersonic flow velocity, which weakens the resulting shockwave and moves it further aft. This delays the sharp increase in wave drag known as drag divergence, allowing for more efficient flight at high transonic Mach numbers.

In the NACA 6-series nomenclature, the number in parentheses indicates the range of lift coefficients in tenths above and below the design lift coefficient in which favorable (laminar-flow-promoting) pressure gradients exist on both surfaces. Here, '(1)' signifies a range of .

For a cambered airfoil, as increases from zero, the CP moves forward along the chord. This movement makes it a difficult reference point. The Aerodynamic Center (AC), typically near the quarter-chord for subsonic flight, is the point where the pitching moment coefficient () is essentially independent of the angle of attack. This property makes the AC a much more stable and useful reference point for aircraft stability and control analysis.

Skin friction coefficient is inversely related to the Reynolds number (e.g., for turbulent flow). Thus, as decreases at high altitude, increases. This decrease in also thickens the boundary layer, which alters the effective shape of the airfoil and its pressure distribution. For most conventional airfoils, this 'thickening' effect leads to a more negative (nose-down) zero-lift pitching moment.

These devices use different but complementary mechanisms. The Krueger flap increases the airfoil's camber and effective leading-edge radius, preventing early flow separation. The Fowler flap extends aft and down, which increases both the wing's surface area and its camber. The slots in a multi-element Fowler flap allow high-energy air from below to flow to the upper surface, re-energizing the boundary layer and keeping it attached at higher angles of attack. The combination produces a very high .

Deploying leading-edge slats increases lift on the forward portion of the wing. This forward shift in the center of lift creates a significant nose-down pitching moment. To maintain longitudinal trim, trailing-edge flaps, which create a nose-up pitching moment, are deployed concurrently. This balanced deployment allows for a large increase in lift without a large out-of-trim condition.

Dynamic stall occurs when an airfoil's angle of attack changes rapidly. During a fast pitch-up, flow remains attached past the static stall angle, and a powerful leading-edge vortex (LEV) forms. This vortex enhances lift significantly but is unstable. When it is shed, there is an abrupt loss of lift. Flow reattachment during pitch-down occurs at a lower angle of attack. This entire cycle of delayed separation and delayed reattachment creates the hysteresis loop in the lift curve.

In subsonic flow, the lift curve slope is given by the Prandtl-Glauert rule: , so it increases as M approaches 1. At M=1, linear theory breaks down predicting an infinite slope. Once fully supersonic, the slope is given by Ackeret theory: . This value is finite and smaller than the high subsonic values, and it decreases as M increases further. The transition involves a sharp drop after passing through the transonic region.

The speed for minimum drag () occurs where parasite drag equals induced drag. The formula for this speed is , which shows that is proportional to the square root of the weight (). If the weight increases by 21%, the new weight is . The new speed will be . Therefore, the speed must be increased by a factor of 1.1, which is a 10% increase.

The aerodynamic behavior of a swept wing is largely determined by the component of flow normal to its leading edge. By sweeping the wings, the effective Mach number 'seen' by the airfoil sections () is less than the free-stream Mach number (). This allows the aircraft to fly at a higher before reaches the critical Mach number of the airfoil, thus delaying the formation of strong shockwaves and the associated sharp rise in drag (drag divergence).

The range is proportional to the efficiency parameter . A 5% increase in changes the parameter by a factor of 1.05, resulting in a 5% range increase. A 5% decrease in means the new value is . The range is proportional to , so the parameter changes by a factor of . This corresponds to a 5.26% increase in range, which is slightly greater than the improvement from the L/D increase.

Endurance is maximized by minimizing fuel flow rate. For propeller aircraft (piston or turboprop), fuel flow is nearly proportional to the brake horsepower (power) the engine produces. Thus, they fly at the speed for minimum power required (). For jet engines (turbojet/turbofan), fuel flow is nearly proportional to the thrust produced. To minimize fuel flow, they fly at the speed where thrust required is minimum. In level flight, thrust equals drag, so this is the speed for minimum drag (), which corresponds to the maximum L/D ratio.

An aircraft's rate of climb depends on its excess power. As altitude increases, the excess power available for climbing decreases, approaching zero at the absolute ceiling. The time required to climb a given altitude interval is inversely proportional to the rate of climb. As the rate of climb approaches zero near the ceiling, the time to climb the final distance approaches infinity. Therefore, the absolute ceiling is a mathematical limit that cannot be reached in finite time.

The aircraft's motion is relative to the airmass it is in. If that airmass is moving vertically upwards, the aircraft's velocity vector relative to the ground becomes the vector sum of its velocity in the airmass and the airmass's velocity. Therefore, its rate of climb relative to the ground and its flight path angle relative to the ground will both increase instantaneously by the vertical velocity of the updraft.

A properly executed chandelle is performed in two 90° stages. In the first 90° of turn, the pilot establishes and holds a constant, medium bank angle (e.g., 30°) while continuously increasing pitch to trade airspeed for altitude. Therefore, at the 90° point, the bank is at its maximum value for the maneuver, pitch is still increasing, and airspeed is decreasing. In the second 90°, the pilot begins rolling out of the bank while continuing to increase pitch, timing the rollout to be complete at the 180° heading.

When the engine fails, the rotor RPM will rapidly decay due to drag if the blade angle of attack (AOA) is high. By immediately lowering the collective, the pilot reduces the blade AOA. This allows the upward flow of air from the helicopter's descent to create an aerodynamic force on the blades that has a component in the direction of rotation, which drives the rotor and maintains its RPM. This prevents a catastrophic loss of rotor speed and allows for a controlled descent and landing.

During a sideslip to the right, the relative wind has a vertical component relative to the plane of each wing due to the dihedral angle. This component increases the angle of attack on the right wing and decreases it on the left wing. The resulting differential lift (more lift on the right, less on the left) creates a rolling moment that raises the right wing and lowers the left, correcting the sideslip by rolling the aircraft to the left.

Swept wings naturally provide a strong positive dihedral effect, which promotes roll stability. While some stability is desired, too much can lead to poor handling, including a poorly damped, oscillatory yaw-roll coupling known as Dutch roll. Anhedral (negative dihedral) provides a destabilizing roll moment. Designers use anhedral to cancel out some of the excessive stabilizing dihedral effect from the wing sweep, resulting in a more balanced and controllable aircraft with better damped Dutch roll characteristics.