02-4 - Neutral Point, 02-5 - Power Effects

7/23/2019 02-4 - Neutral Point, 02-5 - Power Effects

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Flight Dynamics

AAE 1760

Lesson 02-4

Neutral Point



Total Pitching Moment

=

+

+

+

+ = + + + + +

=

+

+

= + +



Recap

= +

−

=

−

=

+ −

=−

1 −



Total Pitching Moment

= + +

= +

−

+ +

+ −

= + +

= − + − 1 −



Total Effects

On their own nacelles and pylons produce a small destabilizing moment

when mounted on the wing and a small stabilizing moment when mounted

on the aft fuselage



Movement of CG

Longitudinal static stability depends strongly on the location of cg



= +

−

+ +

+ −

= − + − 1 −



Stick-Fixed Neutral Point

• Let denote the cg location when

= 0 =

or where the airplane becomes neutrally stable

•

is called the stick-fixed neutral point• Stick-fixed implies that elevator was held fixed

during angle of attack disturbance



Influence of CG



Stick-Fixed Neutral Point

=

− +

− 1 −

=

= −

+

1 −

Setting equal to zero and solving for the center of

gravity position yields:



Static Margin

= − + − 1 −

= −

+

−

1 −

= −

−

+

1 −

=

−

+

1 −

−

= = −

= −

= −



Aerodynamic Center

=

−

ℎ: =

−

Neutral point is in essence the aerodynamic center of the entire aircraft

= −

For most aircraft designs, it is desirable to have a stick-fixed static margin

between 5% and 15% of the mean chord



Static Margin

Low Static Margin gives less static

stability but greater elevator

authority, whereas a higher StaticMargin results in greater static

stability but reduces elevator

authority.

Too much Static Margin makes the

aircraft nose-heavy, which may result

in elevator stall at take-off and/orlanding.

Whereas a low Static Margin makes

the aircraft tail-heavy and susceptible

to stall at low speed, e. g. during the

landing approach.



Static Margin for Canard Configuration

For a better longitudinal stability, the canard should have higher lift coefficient

and stall at lower geometric Angle of Attack than the main wing.



CG Movement

During flight the CG can move substantially:• As CG moves forward the aircraft becomes more stable

– The forward limit to CG position is limited by the moment that the tail

can produce

– This is a function of tail lift and the tail volume

• While stability improves with forward CG movement

– Drag increases, this increase is known as Trim Drag

– Aircraft maneuverability can suffer, larger control movements are required,

and response becomes sluggish

•When CG moves backwards – Aircraft eventually becomes unstable

– Trim drag reduces



CG Limits

• The absolute limit for forward CG position is

determined by aircraft handling being too

sluggish to control effectively

• The absolute limit for rear CG position is the

onset of instability, and aircraft handling being

too sensitive to control

• Aircraft Designers and Regulatory Authorities

impose a more restricted CG range in practice



CG Limits



Example (Nelson 2.1)

If the slope of the versus curve is -0.15 and the pitching moment at zero lift isequal to 0.08, determine the trim lift coefficient. If the center of gravity of the

airplane is located at =0.3, determine the stick fixed neutral point.



= +

= + = +

= +

0 = 0.08 − 0.15

= −0.08−0.15 = 0.53



− = = −

= −

−

= −

−0.3=0.15

= 0.45




For the data shown in Figure, determine the following:(a) The stick-fixed neutral point.

(b) If we wish to fly the airplane at a velocity of 125 ft/sec at sea level, what would

be the trim lift coefficient and what would be the elevator angle for trim?




Analyze the canard-wing combination shown in the Figure. The canard and wingare geometrically similar and are made from the same airfoil section.

= = 0.2 = 0.45

a) Develop an expression for the moment coefficient about the center of gravity.

You may simplify the problem by neglecting the upwash (downwash) effects

between the lifting surfaces and the drag contribution to the moment. Alsoassume small angle approximations.

b) Find the neutral point for this airplane.



SolutionSame airfoil section

+

=

=

=

=

= − − = +

=

− −

= +

= + = +

= + = + 0.09

Neglecting drag and using small angle approximation

= 0.2 = 0.45



= + 0.09 = − −

+0.09 +0.09

= −

−

+0.09 +0.2

= − + −

+0.09 + 0.2 +

− + = ∴ = + −

= − + −

+0.09 + 0.2 + + −

= 1.09 − −

+ 0.2 + −

= −

−

+0.2

= −

−1.2

= 0 = − −1.2 For Np: ∴ = 1.2 = 0.833



H.W. Assignment # 2

Solve problems 2.2 to 2.3 from Nelson’s book

Submission date: 7 Apr. 2015

Submit at the start of class on due date (even if

you plan to be absent). No credit afterwards.

Do not copy any assignment.



Flight Dynamics

AAE 1760

Lesson 02-5

Power Effects



Effect on Static Long. Stability

• Direct Effects:

Caused by forces developed by propulsion

units

• Indirect Effects:

Caused by propeller slipstream passing over

wing or tail surfaces



Direct Effects

• Thrust Effect: Effect on stability from the thrust

acting along the propeller axis.

• Normal Force Effect: Effect on stability from a

force normal to the thrust line and in the plane

of the propeller.

Conclusion: The direct power effects are destabilizing if

the power plant is ahead and below the cg



Indirect Effects• Downwash Effect: Downwash caused by the

jet/propeller makes the tail trim contribution to be

less negative or less stable than the power-off

situation

• Slipstream Effect: Increased speed of slipstream

impacting tail increases the tail contribution to

stability

F-4 Phantom

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Remarks

• The indirect effects mentioned may be

reduced by locating the horizontal stabilizer

high on the tail and out of the slipstream at

operating angles of attack.

Documents

02-4 - Neutral Point, 02-5 - Power Effects