Chapter 5 Flashcards
What is the assumption made for the first part of chapter 5?
- Gliding flight (no prop)
- Controls fixed (stick-fixed).
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What does stick fixed mean?
The controls are not moved by the pilot throughout the phase of flight being investigated.
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What is the primary understanding/knowledge to be gained by deriving the longitudinal, stick-fixed, equations for static stability?
Moments about the airplanes Y-axis, through the c.g. and their variation with the airplane’s lift coefficient.
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Static stability demands that a _____ moment accompany an increase in lift.
nose down
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Static stability demands that a stalling moment (nose up) accompany a decrease in ________ from equilibrium.
Lift Coefficient
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The aerodynamic center of any subsonic airfoil is located close to _______.
The quarter chord point.
x_ac = c/4
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What do the following symbols mean?
1. i_w
2. i_t
3. \varepsilon
- Incidence angle of the wing in degrees
- Incidence angle of the tail in degrees
- Average angle of downwash behind the wing at the horizontal tail (HT)
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All forces in static stability are usually resolved into ________. Why?
Normal and chordwise forces.
Because it’s easier to take moments about the c.g. if the forces are orthogonal or parallel to each other.
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For equilibrium, the moment about the c.g. must be ____.
Zero
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What is the mathematical definition of tail efficiency?
The dynamic pressure on the tail divided by the dynamic pressure on the wing.
qt/q
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Why is tail efficiency less than unity for power-off flight?
Because of the loss of energy as the air interacts with parts of the wing wake and fuselage boundary layer.
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For the airplane to be stable, the slope of Cm vs CL must be _______.
Negative.
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dCN/dCL is usually ______ for the wing.
Zero.
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The derivative dCM_ac / dCL is______ by definition.
Zero.
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The wing contribution to stability is a function of _______.
The position of the c.g. wrt/ the wing aerodynamic center.
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xa/c is the same as ______.
x_cg - x_ac
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If the c.g. is ahead of the a.c. with respect to the mean geometric wing chord, the aircraft is ________.
Statically stable.
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If the c.g. is behind the a.c. with respect to the mean geometric wing chord, the aircraft is _________.
Statically unstable.
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The x_cg and x _ac values are usually measured _________.
With respect to the mean geometric chord of the wing.
The derivative dCN_tail / dCL is not the same as dCN/dCL for the wing because ______.
The effects of downwash due to the wing wake.
What do the terms a_w and a_t represent? What are their mathematical definitions?
Both are lift curve slopes for the wing and the tail.
a_w =( dCN/dCL)_wing
a_t = (dCN/dCL)_tail
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Describe a wing’s “vortex system.”
A bound vortex is located at the wing quarter chord, and two trailing edge vortices emanating from the wing tips.
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What is the major influence of the downwash behind the wing with respect to the vortex model of lift generation?
The trailing vortices are the dominant factor.
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The strength of the vortex system behind the wing is proportional to the ________.
Lift Coefficient
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Ahead of the wing there is a net ______ due to the ________.
Upwash
bound vortex
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Directly behind the wing quarter chord, the downwash builds up very rapidly because ______.
Of the downward component of the bound vortex.
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What causes the trailing vortices to diminish quickly?
Viscosity in the air.
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What is the theoretical downwash at an infinite length away from the c/4 point?
Two times the downwash at the quarter chord point on the wing.
E_infinity = 2*E_ac
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Actual downwash at the tail can vary considerably from theory. What are the two main divergent factors with respect to design geometry?
- Location of the tail with respect to the wing
- The position of the horizontal tail wrt/t/ wake.
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The usual design of the HT is decided in order to avoid _______.
The wing wake at all lift coefficients.
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Fuselage effects are always ________ wrtt/ static stability of the aircraft.
De-stabilizing.
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If the fuselage is considered to operate at some angle of attack to the free stream in an ideal fluid, the resulting pressure distribution over the fuselage yields only a _______, with the center of pressure being at ______.
Pure couple.
Infinity
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For real fluids, the center of pressure on the fuselage moves to a position _______.
ahead of the nose.
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What did Max Munk demonstrate with respect to bodies of revolution in a freestream?
For a very slender body of revolution, the variation of the pitching moment with the angle of attack is a function of the volume and the dynamic pressure.
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From Multhropp, the variation of the fuselage longitudinal pitching moment with angle of attack is primarily affected by ______.
The upwash in front of the wing and the downwash behind it.
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What is Multhopp’s method concerned with?
Finding how the pitching moment of the fuselage varies with wing interference.
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The beta term in Multhopp’s equation is the sum of what two components?
- The angle of attack in the free stream
- The induced angle of attack
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Ahead of the wing the absolute value of dbeta/dalpha is ______ than unity.
Greater
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Behind the wing dbeta/dalpha is _____, and becomes _______.
Less than unity
1-depsilon/dalpha
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In the region between the wing leading and trailing edge, dbeta/dalpha is considered ________.
Zero.
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For sections immediately ahead of the wing leading edge, the magnitude of dbeta/dalpha ______.
Rises abruptly.
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For segments aft of the wing, it is assumed that dbeta/dalpha __________________.
Rises linearly from zero at the tailing edge to (1- depsilon/dalpha) at the tail.
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True or False
For any given airplane, the stability equation is fixed except for the movement of the center of gravity, which affects the wing term through the variation of xa.
True
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True or False
A shift in the c.g. has very little effect on the tail’s contribution to stability, a negligible contribution to the fuselage term, and a large contribution to the wing term.
True
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As the c.g. is moved aft, the slope of the pitching moment curve for the airplane becomes ______.
More positive.
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When dCm/dCL = 0, the airplane is ______.
Neutrally stable.
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In stick-fixed analysis, the location at which the c.g. can be placed, such that dCm/dCL = 0, is called the ______.
Stick fixed neutral point.
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What are the two main contributions of a running propeller to the airplane’s equilibrium and static longitudinal stability?
- The forces generated by the prop (thrust and normal force)
- The propeller slipstream and its interactions with the wing and tail surfaces.
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Propeller efficiency _______ with increasing lift coefficient.
decreases
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What is the average value of dC_thrust/dCL?
0.5
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How does a high vs low thrust line affect the static stability of a typical airplane?
A high thrust line is stabilizing.
A low thrust line is de-stabilizing.
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The angle of attack of the propeller is slightly higher than the angle of attack of the wing due to _____.
The props location in the up-wash field ahead of the wing (recall the bound vortex).
alpha_prop = alpha_wing + epsilon (5.46)
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How does the position of the prop wrt/ the c.g. affect the airplane’s static stability?
For a prop ahead of the c.g. –> De-stabilizing
For a prop behind the c.g. –> Stabilizing
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True or False
The normal force generated by the prop still has a large effect even when the thrust on the prop is zero.
True
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What are the four major contributors to the indirect effects (slipstream) of running propellers on static longitudinal stability?
The effect of the slipstream on…
1. Wing-fuselage moments.
2. Lift Coefficient
3. Downwash at the horizontal tail
4. Increased dynamic pressure on the tail
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True or False
The change in pitching moments introduced by the interaction of the prop slipstream on the wing and fuselage are major factors.
False, these terms are quite small in comparison to other slip-stream effects.
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List the three reasons why slipstream effects from a propeller generating thrust, can change the contribution of the HT to static stability.
- The wing angle of attack will be altered and therefore so will the angle of attack on the horizontal tail.
- The angle of attack of the horizontal tail will be changed due to the downwash from the propeller
- The velocity over the HT will change when the propeller is generating thrust.
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The velocity of the slipstream (prop created flow) is mainly a function of ______.
The thrust coefficient.
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When the prop is considered, the downwash characteristics at the tail are primarily influenced by what two factors associated with the prop?
- The normal force
- Thrust force
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What does a “windmilling” prop imply?
The prop is spinning but is not generating any thrust.
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If the tail is carrying an upload (CL_t >0), the stability contribution will be ___________.
Stabilizing.
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If the tail is carrying a download (CL_t <0), the stability contribution will be ___________.
De-Stabilizing
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If the c.g. is moved aft, CL_t must _______ for longitudinal static stability to be maintained.
Increase
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If the c.g. is moved forward, CL_t can be _______ to maintain longitudinal static stability.
Reduced
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At a thrust of zero (windmilling), what two contributions to stability remain wrtt/ prop?
- The prop normal force
- Effect of the wake from the propeller on the horizontal tail
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The effects of a jet’s propulsive system on static stability are easier to analyze as opposed to a propeller-driven aircraft because ______.
There are no slipstream effects.
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What are the three major contributors of a jet unit to the equilibrium and static longitudinal stability of the airplane?
- Direct thrust effects
- Direct normal force effects at the air duct (if any)
- Induced flow effects at the tail due to the hot exhaust gases.
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For a jet, describe how the location of the thrust line affects the static stability.
Thrust line above the c.g. –> Stabilizing
A thrust line below the c.g. –> De-stabilizing
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True or False
For unaccelerated flight in a jet, the thrust will contribute nothing to the stability of the airplane.
True
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What creates the normal force on a jet inlet?
The normal force is created as a result of the momentum change incurred as the free stream is bent to flow along the duct axis.
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Jet exhaust can create an _______ on the horizontal tail due to turbulent mixing.
Up-flow.
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The c.g. should never be _____ of the neutral point if the aircraft is required to have some static stability.
Aft.
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For static stability, the most aft position of the c.g. must lie _____ the stick fixed neutral point.
in front of.
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What three factors can be used to control the trim lift coefficient. Which is the most effective?
- CM_ac
- xa/c
- Angle of attack of the tail (most effective)
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As the c.g. is moved forward, the equilibrium CL is ______.
Reduced
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For the most powerful control available in terms of a horizontal tail, what configuration design option should be used?
A stabilator is the best option if large pitching moments are required.
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A trailing edge up elevator deflection is considered _______.
Negative
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A trailing edge down elevator deflection is considered ______.
Positive.
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Define “elevator power.”
The magnitude of the aircraft pitching moment coefficient obtained per degree of deflection of the elevator.
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The derivative dalpha_tail/ ddelta_e is a function of what geometric design property?
Note: delta _e is the deflection of the elevator.
The ratio of the elevator area to the total horizontal tail area (Se/St)
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The term dalpha_tail /ddelta_e is referred to as _________, and usually given the symbol ______.
The elevator effectiveness parameter
Lowercase tau
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True or False
The elevator effectiveness parameter (tau) is independent of the lift coefficient.
True
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True or False
The elevator angle required to vary the equilibrium lift coefficient varies inversely with the elevator power derivative.
True
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As the c.g. moves more forward, the airplane becomes more ______ and more elevator is required to trim out ________.
Stable
CL_Max
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With respect to stick fixed analysis, what determines the maximum forward c.g.?
The point where the elevator can no longer trim out CL_max.
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Is the airplane more or less stable with the prop windmilling?
More stable.
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In stick-fixed analysis, the maximum allowable stability, and consequently the most forward permissible c.g., vary directly with the ____, and inversely with ______.
Elevator power.
The maximum lift coefficient
(dCm/dCL)_max = (de0 - de_max)*(Cmd/CL_max)
Eq. (5-83)
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The extent of an aircraft’s allowable c.g. “range” depends heavily on ______.
The elevator control power.
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What four parameters determine the magnitude of the elevator control power?
- The slope of the tail lift curve: a_t
- The tail area, S_t
- The distance of the tail from the c.g., l_t
- The elevator effectiveness term, tau
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How do elevator requirements change with a decrease in downwash over the tail?
The decrease in downwash increases the angle of attack on the HT, requiring more up-elevator to maintain trim at a given lift coefficient.
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Ground effect moves the neutral points _____.
Aft.
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What variables are altered by ground effect?
- Wing angle of attack, alpha_w
- The elevator power, C_M_delta_e
- The tail’s lift curve slope
- The downwash angle
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Of the variables that are influenced by ground effect, which one is affected the most?
The downwash angle (epsilon)
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True or False
Close to the ground, the reduction in downwash at the tail is large, therefore requiring considerably more up elevator to achieve CL_max during landings.
True
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What approximation should be used for the downwash angle while in ground effect?
Half of the downwash angle in free flight.
epsilon_GE = 0.5*epsilon_normal flight
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True or False
The larger the c.g. range required, the less the magnitude of the elevator power.
False, the elevator power must increase with increasing c.g. range.
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