Center of Gravity Position and its effect on stability

 

Center  of  Gravity  Position and its effect on stability

An aircraft’s horizontal tail size and position, and the CG position are the dominant factors controlling the aircraft’s pitch stability, which is the tendency to automatically maintain an angle of attack and airspeed.

The basic effects of moving the CG position are:

Decrease xcg/c    (move CG fwd.):  increased stability; more resistance to α and V changes.

Increase  xcg/c   (move CG back):  decreased stability; less resistance to α and V changes.

There is one particular CG position which gives neutral stability, which is called the Neutral Point (NP). This is shown as xnp in Figure (above). The degree of pitch stability or instability is traditionally specified by the Stability Margin.

S.M= (x_np – x_cg)/c

 

Figure 1 illustrates the natural behaviors of an airplane after a pitch disturbance, for different values of S.M. The unstable behavior occurs when S.M. is negative, i.e. when the CG is behind the NP. Because pitch instability makes the aircraft very difficult or impossible to control, the NP position is considered to be a practical aft  CG  limit.

Figure 1: Natural aircraft responses to a pitch disturbance, for different amounts of pitch stability.

Making the S.M. strongly positive by moving the CG far forward will give plenty of pitch stability and a strong resistance to pitch upsets, but it also has undesirable side effects. One large drawback    of a large S.M. is that it causes large (and annoying) pitch trim changes with changing airspeed. Figure 2 shows the flight paths of airplanes with different nonnegative S.M., immediately after an airspeed increase caused by a power increase. The straight-ahead acceleration of the weakly stable or neutral airplane is more desirable for the pilot.

        Figure 2: Pitch-up behavior from an airspeed increase, for large and small Static Margin.

More specifically, the strongly stable airplane shown in Figure 3 requires a relatively large

elevator angle change commanded by the pilot to restore it to level flight. Figure 4 compares the situation for the strongly and weakly stable airplanes. In effect, a large positive S.M. degrades the pitch trim authority of the elevator, since large trim deflections are needed to

maintain level flight in response to airspeed changes.

Figure 3: Elevator trim adjustment with changing airspeed, for large and small Static Margin

This situation illustrates the benefit of reducing the S.M., by moving the CG closer to the NP. However, if the CG is moved behind the NP, the airplane will now have a negative S.M., and be unstable in pitch to some degree, with the results illustrated in Figure 2. This makes it difficult or even impossible to fly. In general, the small positive S.M. suggested by expression given below  is the ideal situation.

.

SM= xnp-xcg/C  ==== 0.05…..0.15

ASPECT RATIO AND ITS EFFECT

ASPECT RATIO AND ITS EFFECT ON AIRCRAFT

As many early wing were in rectangular shape, the aspect ratio was initially defined as simply the span divided by the chord, for tapper wing it is defined as the span divided by the wing area.

ASPECT RATIO AND WING TIP VORTICES

                                                      When wing is generating lift it has to reduce pressure on the upper surface and an increased pressure on the lower surface , the would like like to escape from the bottom of the wing, moving to the top .

Air escaping around the wing tip lower the pressure difference between the upper and the lower surface , this reduces lift near the tip and also air flowing around the tip flows in a circular path, this reduces the effective angle of attack of the wing airfoil and this phenomenon is called as wing tip vortices .

Now , by keeping the area of the wing constant , tip of high aspect ratio wing is farther apart than low aspect ratio wing its mean the area or part of the wing affected by vortices is less in case oh high aspect ratio wing ,thus high aspect ratio wing does not experienced much loss of lift due wing tip effect as compared to same area low aspect ratio wing.

ASPECT RATIO AND STALING ANGLE

Another effect of changing aspect ratio is change in stalling angle.

Due to reduced effective angle of attack at the tip , a lower aspect ratio wing will stall at higher angle of attack than high aspect ratio wing . this is one reason why tail tends to be lower aspect ratio than wing , delaying the tail stall until well after the wing stall and assures adequate control .

Conversely a canard can be made to stall before the wing by making it a very high aspect ratio surface. This prevent the pilot from stalling the wing .

EFFECT ON STRUCTURE

A long wing has higher bending stress for a given load than a short wing and therefore requires higher structural design specification.

EFFECT ON MAUVERABILITY

A low aspect ratio wing will have a higher roll angular acceleration than one of high aspect ratio because high aspect ratio wing  has higher moment of inertia to overcome.

In steady roll the longer wing will gives a higher roll moment because of large moment arm of aileron,

low aspect ratio wing usually used on fighter jet , not only for the higher roll rate but especially for longer chord and thinner airfoil involved in supersonic flight

EFFECT ON INDUCED DRAG

only the one relation will tell everything in this section ,that is the induce drag coefficient (C_Di) :-

C_Di= C_L²/∏ e A.R

C_L= coefficient of lift

_e = span efficiency factor

A.R= aspect ratio

 

 

DIHEDRAL EFFECT

When an aircraft is disturbed from an upright position, it will sideslip toward the down-going Wing, increasing airflow along the length of the wing from tip to root. The dihedral angle increases angle of attack to this lateral flow, generating additional lift to restore the aircraft to a level attitude If the center of gravity is below the wing, the weight tends to restore the upright position.This is known as pendulum stability or the keel effect. If the CG is above the wing, the weight is destabilizing.

Sweepback of the wing, especially the leading edge, causes greater drag and greater lift on the wing panel that is rotated forward into the relative wind, increasing the roll still further – three to ten degrees of sweepback is approximately equivalent to one degree of dihedral for most model aircraft.

Dihedral bestows stability at the expense of lift. Only the vertical component of lift in level flight actually supports the airplane. It is proportional to the cosine of the dihedral angle. The horizontal component of wing lift, proportional to the square of the sine of the dihedral angle, is wasted. But the effect is small if the angle is small. A wing of 3 degrees dihedral, for example, wastes only 0.137% of its total lift (cosine 0° – cosine 3° = 0.00137). That may be insignificant in most models, but important in a competition sailplane or the long-term fuel costs of an airliner.

• Dihedral in a multi-engine airplane adds to undesirable roll when one engine quits.

•  Dihedral reduces stability in inverted flight and varies roll rate during the inverted part of a slow roll. Rolls become corkscrew shaped instead of axial.

• Dihedral makes an airplane more vulnerable to turbulence, Especially side gusts.

Where?

Rudder only-(aircraft without aileron)- radio controlled airplanes need lots of dihedral. Their only means of turning is by yawing with the rudder. The wing panel that swings forward presents a greater angle-of-attack to the relative wind, increasing lift. The greater lift banks and turns the airplane.

For efficiency, this method of turning is best implemented by adding extra dihedral to the wingtips, reducing the total dihedral.

The three or four-panel wing, typical of free-flight and rudder-only airplanes, is known as polyhedral. When the nose pulls up, the angle of attack of the outer panels increases at a slower rate than the inner panels. The inner panels stall first. Polyhedral wings do not require the negative twist known as washout.

The gull-wing variant is typically used to increase pendulum stability by raising the wing without the drag of cabane struts. The inverted gull-wing of the F4U Corsair was used to shorten the landing gear struts and lower the height of the airplane for below-deck storage.

Dihedral Sizing Criteria – Spiral Stability

 The dihedral angle of the wing, denoted by Υ in above Figure, provides some degree of natural spiral stability. A spirally-unstable aircraft tends to constantly increase its bank angle at some rate, and therefore requires constant attention by the pilot.Conversely, a spirally-stable aircraft will tend to roll upright with no control input from the pilot, and thus make the aircraft easier to fly. Figure 6 compares the two types of behavior.

Whether an aircraft is spirally stable or unstable can be determined via the spiral parameter B (named after its originator Blaine Rawdon, from Douglas Aircraft):

    B = L_F*Y/b*C_L            (Y in degree) 

B > 5	spirally stable
B=5	spirally neutral
B < 5	spirally unstable

 

The main parameter which is used to adjust B in the design phase is the dihedral angle Υ.

Spiral stability is not a hard requirement, and most aircraft are in fact spirally unstable. Level flight is then ensured either by the pilot, or by a wing-levelling autopilot, provided the instability is slow enough. RC aircraft which can fly stably hands-off must be spirally stable, although a small amount of instability (B=3…4, say) does not cause major difficulties for an experienced pilot.

Dihedral Sizing – Roll Control

On rudder/elevator aircraft, the rudder acts to generate a sideslip angle β, which then combines with dihedral to generate a roll moment and thus provide roll control.

A criterion for adequate roll authority is obtained by the product of Vf and B:

Vf *B =0.10 … 0.20

 

The 0.10 value will likely give marginal roll control, while 0.20 will give very effective control.

For practical reference the value of Vf*B of well famous RC uav SKYLARK by ELBIT SYSTEM Israel is 0.38

 

 

 

SIZING OF AIRCRAFT ACCORDING TO STALL   SPEEED REQUIREMENT 

For some aircraft the mission task demand a stall speed not more than some minimum values. In such cases, the mission specification will includes a requirement for a minimum stall speed.

The stall speed of aircraft may be determined from equation:-

V_s=(2*(W/S) /ρ C_LMAX)^1/2               ————————–(1)

By specifying a maximum allowable stall speed at some altitude equation (1) defines a maximum allowable wing loading(W/S) for given value of C_LMAX.

C_LMAX strongly influenced by factor such as,

a)  Wing and airfoil design

b) Flap type and flap size.

c)  Centre of gravity location.

NOW,

Take a example so that it’ll get clear to everyone,

EXAMPLE:-  A mission demanding stall speed of 50m/s with full flap                  down (i.e landing flaps) and of 60 m/s with flap up (neutral).

For this case, first take value of C_L which is typically 1.6 for neutral flap condition and 2.0 for flap down condition.

With the help of eq-(1),

to meet flap down requirement (W/S) is:-

W/S=(50²/2*1.2256*2)  = 509.954 N/m² = 51.98 kg/m²

The obtained value is maximum value ,so practical value is less than this i.e W/S < 51.98 kg/m²

Similarly,

To meet flap up requirement:-  W/S < 93.5693 kg/m²

So, to meet both requirement the take off wing loading mush be less than  51.98 kg/m² at take off.

Like that we can predict the size of aircraft wing on the basis of stall speed requirement.

MORE EXITING STUFF IS COMING SOON ………SO , STAY TUNE……….:-)

 AIRCRAFT TAIL DESIGN

The empennage or tail assembly provides stability and control for the aircraft. The empennage is composed of two main parts: the vertical stabilizer (fin) to which the rudder is attached; and the horizontal stabilizer to which the elevators are attached.

The major difference between the tail and wing is that, the wing is designed to carry substantial amount of lift ,and tail is designed for provide stability and control to the aircraft.

Tail assembly generally having low aspect ratio than wing to delay the stall at tail and which make aircraft under control while after wing stall.

Tail assembly (specially horizontal stabilizer) should always placed above or below the plane of wing to avoid the effect of downwash on tail.  high tail assembly is most favorable .

TYPES OF TAIL CONFIGURATION

There are many different forms an aircraft tail can take in meeting these dual requirements of stability and control, that are stated below :-

1)  Conventional Tail 

a)   The conventional tail design is the most common form.

b)   It has one vertical stabilizer placed at the tapered tail section of the  fuselage and one horizontal stabilizer divided into two parts, one on each side of the vertical stabilizer .

c)  For many airplanes, the conventional arrangement provides adequate stability and control with the lowest structural weight.

2) T- TAIL

a) T-tail is inherently heavier than a conventional tail because the vertical tail must be strengthened to support the horizontal tail.

b)   due to end plate effect, the T-tail allow smaller vertical tail. The T-tail lifts the horizontal tail clear of the wing wake (downwash) and propwash, which make it more efficient and hence allow reducing its size and also allows high performance aerodynamics and excellent glide ratio as the horizontal tail empennage is less affected by wing slipstream. This also reduce the buffet on the horizontal tail, which reduce fatigue for both the structure and the pilot.

c) The disadvantages of this arrangement include higher vertical fin loads, potential flutter difficulties, and problems associated with deep-stall.

Here question may arise that why T-tail prone to suffer dangerous deep stall condition?

,the region is, At the stall, lift is significantly reduced, drag is significantly increased and the airflow across, and behind, the wing becomes turbulent. , this turbulent air in the wake of a stalled mainplane can affect the horizontal stabilizer, substantially reducing the effectiveness of the elevators and potentially negating the ability to recover from the stall by using pitch controls to reduce the mainplane angle of attack.

3) CRUCIFORM TAIL

a) cruciform tail is compromise between the T-tail and conventional tail arrangement.

b) The cruciform tail gives the benefit of clearing the aerodynamics of the tail away from the wake of the engine and wing’s wake, while not requiring the same amount of strengthening of the vertical tail section in comparison with a T-tail design.

4) H-TAIL OR TWIN TAIL

 

a)   H-tails use the vertical surfaces as endplates for the horizontal tail, increasing its effective aspect ratio.

b)   H-tail is heavier than conventional tail but its end plate effect allow a smaller horizontal tail.

c)    On multi-engine propeller designs H-tails are sometimes used to reduce the yawing moment associated with propeller slipstream impingment on the vertical tail. .

d)   A special case of H- tail is twin boom tail or double tail where the aft airframe consists of two separate fuselages, “tail booms”, which each have a rudder but are usually connected by a single horizontal stabilizer.

e)   Disadvantages of H-tail includes complex control linkages and reduced ground clearance.

5) V- TAIL

a)   V-tails combine functions of horizontal and vertical tails. They are sometimes chosen because of their increased ground clearance, reduced number of surface intersections.

b)    the V-tail is lighter, has less wetted surface area.

c)    Sometimes called ruddervators, combine the tasks of the elevators and rudder.

d)   V- Tail offer reduced interference drag but at some penalty in control actuation complexity ,as the rudder and elevator control inputs must be blended in a mixer to provide the proper movement of V-Tail.

6) Y –TAIL

 

a)   Y tail is similar to V-tail, except that the dihedral angle is reduced and a third surface is mounted vertically beneath the V. this third surface contains the rudder whereas the V surface only provide pitch control.

b)   This tail arrangement reduce the complexity of ruddervators while reducing interference drag when compared to a conventional tail.

TAIL SURFACE SIZING

Horizontal tail

The Neutral Point location x_np is primarily controlled by size of the horizontal tail and its moment .

arm from the CG. A measure of this tail effectiveness is the horizontal tail volume coefficient:

V_h =(S_t*L_t /S_w*mac)

A well-behaved aircraft typically has a Vh which falls in the following range:

0.30………0.60

If Vh is too small, the aircraft’s pitch behavior will be very sensitive to the CG location. It will also show poor tendency to resist gusts or other upsets, and generally “wander” in pitch attitude, making precise pitch control difficult.

Vertical fin

The primary role of the vertical tail is to provide yaw damping, which is the tendency of yaw oscillations of the aircraft to subside. The vertical tail also provides yaw stability, although this will be almost certainly ensured if the yaw damping is sufficient. One measure of the vertical tail’s effectiveness is the vertical tail volume coefficient:

V_F=(S_F*L_F/b_*S_W)

Most well-behaved aircraft typically have a Vf which falls in the following range:

0.02………..0.05

If Vf is too small, the aircraft will tend to oscillate or “wallow” in yaw as the pilot gives rudder or aileron inputs . and   also give poor rudder roll authority in an aircraft which uses only the rudder to turn.

AIRCRAFT WING DESIGN

Aircraft wing designed based upon the aircraft application.

 As we know that aircraft will able to fly only because of wing that produces lift (the upward force) .so before starting to design of an aircraft we should much aware of its kind ,applicability, advantages or disadvantages.

Types of aircraft wing

Below I have listed different wing configuration with detail:-

1)  STRAIGHT WING

straight wing is most basic and simplest kind of wing with no dihedral or anhydral   ,no sweep ,and also having no tapper .we can also called it a rectangular wing.

a)   It can carry a reasonable load and fly at a reasonable speed, but does nothing superbly well.

b)   It is ideal for personal aircraft as it is easy to control in the air as well as inexpensive to build and maintain.

c)   Good stalling characteristics because this wing generally have low aspect ratio.

d)     Greater aileron control.

2)  ELLIPTICAL WING

 

 Elliptical wing as the name suggest elliptical in shape .

a)   This type of wing is ideal for flight at low speeds since it provides a minimum drag. This type of planform is difficult to construct and its stall characteristics  are not as favorable as rectangular wings.

b)   This type of wing have Less drag because of its nearly elliptical in shape the span efficiency factor is unit hence induce drag is comparatively less than other wing planform.

c)   Aileron are less effective due to its shape.

3)  SWEPTBACK WING

 

  a)   They are efficient at high speed. Low speed performance is degraded by this design.

b)   Sweepback of wing helps in roll stability, why? , Sweepback of the wing, especially the leading edge, causes greater drag and greater lift on the wing panel that is rotated forward into the relative wind, increasing the roll still further – three to ten degrees of sweepback is approximately equivalent to one degree of dihedral for most model aircraft.

4)  TAPPER WING

a)   Tapper wing is similar to rectangular wing ,only the difference is the tip chord is less than the root chord.

b)   This type of wing provides increase in lift and decrease in drag which is most effective in high speeds.

c)    A good form of an aircraft is a combination of both rectangular and tapered configurations. These are also cost effective.

5)  DELTA WING

 

a)   The delta wing advances the swept wing concept, pulling the wings even further back and creating even less drag. The downside to this however is that the aircraft has to fly extremely fast for this wing to be efective.

b)    it’s only found on supersonic aircraft (aircraft that fly faster than the speed of sound) such as ighter jets and the Space Shuttle orbiter.

c)   This types of wing s having good stall characteristics because of low aspect ratio.

6)  VARIABLE GEOMETRY WING

 

a)    The wing can change its geometry and sweep, in flight or on the ground and attain deferent characteristics. Mostly used on early supersonic military aircraft it is an easy way to succeed slow takeoff and landing speeds while the aircraft can cruise at mach 2-3-(4) (1 mach= Speed of sound,2 mach twice the speed of sound ).

b)   This wings are able to change its sweep angle from 0 to desired high value for supersonic flight. 0 degree sweep help to increase performance in low speed flight, whereas  sweep will help to cruise to high speed by increasing the critical mach no. in doing so reduces the transition time.

7)  FLYING WING CONFIGURATION

 

a)   Flying wing configuration is one in which the fuselage is laying inside the wing and don’t have any tail control surface.

b)   The absence of fuselage and tail surfaces makes the flying wing aerodynamically and structurally superior to conventional types of aircraft.

c)   Reduces minimum drag due to elimination of empennage assembly.

d)     Elliptic span loading is easily achieved through wing camber and twist.