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Theory of Flight
Topic Started: Aug 31 2017, 11:46 PM (279 Views)
Kevdyvin
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Calm Winds and Blue Skies
Root Administrator
Factors Affecting Stall Speed

1. Weight - We know that for any level flight (not climbing), the amount of lift must be equal to the weight of the aircraft, thus if the weight is lower/higher, then the amount of lift required is less/more too.
Code:
 
Vs(New) = Vs (old weight) x √(new weight / old weight)

2. Turning & Load Factor - Stall speed increases as load factor increases.
Code:
 
Vs(New) = Vs x √Load factor

4. Climbing/Descending Turns - In a climbing turn, the raised wing (with the greatest rate of turn/faster velocity) has the highest angle of attack and will stall before the lowered wing. As a result, the airplane will therefore roll level. When the airplane descents, the lower wing has the highest angle of attack and at the stall, that wing will drop increasing the bank angle even more.

5. Altitude - Altitude is set by 1/2ρ. So when the aircraft climbs, the factor '1/2ρ' decreases and Cl (AoA) remains the same, true airspeed (TAS) must increase to obtain the same indicated airspeed (IAS). And as stall speed is directly related to AoA it also remains the same; but the TAS, where the stall occurs, increases due to lower air density at higher altitudes.

Quote:
 
So basically, with a constant AoA, the true airspeed will increase (due to decreased drag at high altitudes) which compensates and maintains the same IAS. But because of that, the airplane is now flying at a lower IAS than the actual, and the airplane will stall at a higher (indicated) airspeed.

6. Vortex Generators - The effect they have is that the airflow is energized during high angles of attack and therefore sticks better to the wing surface, so that the separation of the airflow is delayed even more and stall speed is lower with a higher AoA.

7. Power and Climb - Stall speed is lower with engine power applied. Added to this is the fact that the slipstream from the propeller over the inner part of the wing and tail section improves effectiveness and delays the separation of the airflow near the wing root.

8. Flaps or Slats - Stall speed decreases as the wing camber (curvature) increases.

9. Wing Contamination - Wings covered with rime, ice, remains of bugs, and other dirt will cause an early separation of the boundary layer (airflow) and the stall speed will increase. Remember that the same applies to the propeller, but then a decrease in thrust will be the result.

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Kevdyvin
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Calm Winds and Blue Skies
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Straight and Level/Steady Unaccelerated Flight

• All 4 forces acting on an airplane are in equilibrium.
• If the airplane is in a state of equilibrium, it will fly in a straight line with steady airspeed.
• In steady flight, the sum of these opposing forces is always zero which is based on Newton's 3rd law:

Code:
 
L = W
T = D

ΣF = 0

Weight gradually decreases as fuel is burned off, meaning that the lift required will also decrease. Thrust and Drag will vary depending on the Angle of Attack and Airspeed.

Code:
 
Lift/Drag Ratio = 10:1

Example:

L/W = 2000 lbs
T/D = 200 lbs


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Kevdyvin
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Q: Why is it that the propeller blades are showing in a horizontal/vertical position when you take a photo of it?

• Propeller Image Aliasing
• Slow scanning cameras
• When capturing an image, they do not expose all the pixels at the same time. Rather they expose and capture one row of the sensor before moving onto the next.
• It means the different rows (or columns, depending on the orientation of the sensor) of the image are captured at different times.
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Kevdyvin
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Calm Winds and Blue Skies
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Categories of Airplane (C-152)

1. Normal = -1.52 G's / 3.8 G's (75° AoB)
2. Utility = -1.76 G's / 4.4 G's (77° AoB)
3. Acrobatic = 6.0 G's (80° AoB)

Code:
 
Load factor = 1/cosθ
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Kevdyvin
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Calm Winds and Blue Skies
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Aspect Ratio VS Wing Area

Aspect Ratio - it is the ratio between the wingspan (length) and average chord (width).
Quote:
 
33.4 ft / 4.6 ft = 7.2

Wing Area - it is the product of wingspan (length) and average chord (width).
Quote:
 
33.4 ft x 4.6 ft = 153.64 sq ft or 160 sq ft


Code:
 
Average chord = root chord + tip chord / 2
Code:
 
Root chord = 5'4"
Tip chord = 3'8"



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Kevdyvin
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Power Loading VS Wing Loading

Power Loading - the weight per horsepower of an airplane.
Quote:
 
Weight (1670 lbs) / Horsepower (110 HP) = 15.2 lbs/HP

Wing Loading - the amount of weight that each unit area of the wing must support with lift.
Quote:
 
Weight (1670 lbs) / Wing Area (160 sq ft) = 10.4 lbs/sq ft or 10.5 lbs/sq ft (on POH)

Code:
 
As bank angle increases, wing loading also increases.

Example: @60° AoB, load factor is 2 G's.

1,670 lbs x 2 = 3,340 lbs

So,

Wing Loading = 3,340 lbs / 160 sq ft
Wing Loading (New) = 20.88 sq ft


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Kevdyvin
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Excess Thrust VS Excess Power

Excess Power

• During a steady climb, the Rate of Climb (Vy) depends on the excess power.
• Power increases significantly with speed.
• Since power available increases with airspeed, Vy occurs at a higher speed than minimum power required (60 kts).

Excess Thrust

• During a steady climb, the Angle of Climb (Vx) depends on the excess thrust.
• Thrust reduces with speed.
• Since thrust available decreases with airspeed, Vx occurs at a lower speed than minimum thrust required (60 kts).

Quote:
 
When throttle is set to full, with wheel brakes applied, and the airplane is stationary on ground, the propeller is producing thrust but no power yet.

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Kevdyvin
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What is a Zero Lift Line?

• It is a line through an airfoil, along which the relative airflow produces zero/no lift.

For a Symmetrical Airfoil, it is at zero angle.

For a Cambered Airfoil, it would need a negative angle to have a zero lift line.

Quote:
 
Posted Image          Posted Image
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Kevdyvin
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Left Turning Tendencies

1. Torque Reaction - This is basically Newton's Third Law of Motion. Due to the propeller that is turning clockwise, there is also an equal force that is trying to rotate the airplane in the opposite direction (counter-clockwise).
Quote:
 
In flight, the propeller is rotating to the right which reacts the airplane to roll to the left.

On ground, the left side of the aircraft is being forced down, so more weight is being placed on the left main landing gear. This causes more ground friction on the left wheel, slowing it down, and therefore making the airplane to turn left.

2. Spiraling Slipstream/Corkscrew Effect - At high power setting and low airspeed, the spiraling rotation is very compact and exerts a strong sideward force on its vertical stabilizer. Whereas at high power setting and high airspeed, the spiraling rotation becomes elongated that it tends to miss the vertical stabilizer and making this effect inapparent.

3. Gyroscopic Precession - It is one of the two characteristics of a gyroscope. It states that when a force is applied to a spinning rotor/wheel, the force will act 90 deg ahead of the direction of rotation from the point of application. This is more prominent in a conventional-type of landing gear (taildragger), and it occurs when the tail is being raised during take-off roll.
Quote:
 
Rigidity in Space - Once the gyroscope starts spinning, it tends to remain in its position and resists being moved. If forced to change, precession results.

4. P-factor/Asymmetric thrust/Asymmetric loading - When the airplane is flying at high AoA and high power setting, the bite of the downward moving blade is greater (more density and velocity) than the bite of the upward moving blade. This makes the airplane to yaw to the left.

In level flight, it is not apparent since both blades of the propeller meet the relative wind equally (same AoA), and therefore, producing same amount of thrust.
Quote:
 
P-factor is short for Propeller factor.

Code:
 
In general, left turning tendencies are greatest in flight with high power setting, high angle of attack, and low airspeed. Correct these tendencies by proper use of rudder during take-off roll and climbing.
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Kevdyvin
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Calm Winds and Blue Skies
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Stability around the Airplane Axes

Longitudinal Stability

• Stability around the lateral axis (also known as Pitch Stability)
Position of the C.G. & Horizontal Stabilizer/Tailplane - they tend to balance each other out.
Quote:
 
If there is a sudden disturbance (wind) that is coming from below, because of its nose heavy characteristics, it will pitch the nose back down. On the other hand, if there is a sudden disturbance (wind) that is coming from above, the horizontal stabilizer will meet with the relative wind which will bring the tail down, therefore the nose up.

• If the C.G. is too far forward, the airplane will have a longer take-off run and higher stalling speed because it is too stable and too nose heavy. Also, the more stable the aircraft, the more it is harder to maneuver the controls, which is very tiring.
• If the C.G. is too far aft, the airplane will be unstable, making the control surface (elevator) to be more difficult to control. In addition, recovering from a stall will be harder in an aft C.G.

Lateral Stability

• Stability around the longitudinal axis (also known as Roll Stability)
Dihedral & Keel Effect/Pendulum Effect
• High wing airplane will have a better roll stability due to its Center of Gravity located under the wing compared to a low wing airplane wherein the Center of Gravity is located above the wing.
Quote:
 
So if the C.G. is below the wing, the weight tends to restore the upright position. This is known as the Pendulum Stability. If the C.G. is above the wing, the weight is destabilizing or disrupted.
Quote:
 
Dihedral - an upward angle of the wing in relation to the horizontal plane. For C-152, it's 1 deg dihedral.

Directional Stability

• Stability around the vertical axis (known as the Yaw Stability)
Sweep-back/Swept back Wing & Vertical Stabilizer/Fin
Quote:
 
Swept back wing is also one factor to determine the airplane's lateral stability.
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