PATTS COLLEGE OF AERONAUTICSLombos Ave., San Isidro, Parañaque City

AIRPLANE DESIGN

REVEIWER: R.R. RENIGEN

GENERAL PRINCIPLES AND PROCEDURES IN AIRPLANE DESIGN

Two Main Section in the Design of an Airplane:

1. Aerodynamic design2. Structural design

General Design Requirements:

The major items considered by the designer may be summarized as follows:

1. Load required to be carried2. Performance and other aerodynamic requirements3. Type of material, structural and general arrangement4. Weight5. Powerplant

Before a design is commenced, a specification is drawn, up giving the purpose for which the airplane is required, the performance to be provided, and often stating the type of airplane and the powerplant to be used. Thus the specification may fix items (1) and (5) completely and (2) and (3) in part. Of the remaining items, that causing most trouble to designer is (4). The saving of weight is of paramount importance in airplane design, and it is essential that the structure shall be as efficient as possible.

General Procedure:

Once the specification has been received or drawn up, and the type of airplane decided upon, the design proceeds roughly as follows:

1. Aerodynamics Design

a. Preliminary Weight Estimateb. Selection of Airfoil Section for Wing and Determination of Wing Area and Planformc. Estimate of Fuselage Dimensions and General Shaped. Estimate of Sizes of Tail Surfacese. Preliminary Three – View Drawingf. Provisional Personal Checkg. Detailed Weight Estimateh. Balance Diagram and Determination of C.G. Positioni. Revision of Wing Areaj. Final Three View Drawingk. Performance Estimate and Stability Calculation

2. Structural Design

a. Determination of Design Loadsb. Layout and Stress Analysis of Structure

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3. Preliminary Weight Estimate

In the absence of information on the weights of previous airplanes of similar types one method commonly adapted in forming a preliminary estimate of the weight, is to determine the non-structural weight – I.e., power plant, fuel and oil, passengers and crew, baggage, instruments, etc. For most conventional airplanes the structural weight is between 30% and 35% of the total weight, so that it is possible to assume the non-structural weight as between 65% and 70% of the total weight.

4. Airfoil Selection for Wing and Determination of Wing Area and Planform

In selecting an airfoil for an airplanes’ lifting surface (wing, tail or canard) the following considerations are important:

1. Drag (for example to obtain the highest possible cruise speed)2. Lift-to-drag ratio at values of Cg important to airplane performance3. Thickness (to obtain the lowest possible structural weight)4. Thickness distribution (to obtain favorable span loading and/or high fuel volume)5. Stick characteristics (to obtain gentle stall characteristics)6. Drag-rise behavior (associated with item 1)

The wing area can be calculated as:

390WS = CLmax Vs = f (CLmax)

or

W Clmax

= S 390

where: S = gross area (ft²)

Vg = stall speed (mph)

W = maximum design weight (lb)

Cl = maximum coefficient of lift for the wing

W/S = loading (lb/ft)

Typical values for Clmax range from 1.4 for an unflapped wing to 2.0 for a wing with a simple fap. Typical values for stalling speed are 40 mph for conventional tourer/training aircraft and 50 mph for high speed (racer) types. A survey of the wing loadings of several ultra light airplane show a variation from 5 to 16 lb/ft²) with 7.5 and 10 being average values for unflapped and simple flapped wings, respectively. The airplane weight can be assumed to be three times the useful load (i.e., occupant, baggage, fuel and oil)

Aspect Ratio is defined as:

b b² SA = ― = ― = ―

c S c²

where: b = wing span c = mean chordA = 5-8 for ultra-light airplane

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Positioning of the wing along the fuselage is concerned with longitudinal stability and control and as such involves some detailed calculation. In the early stage when many factors are still undecided it is sufficient to position the wing so that the airplane center of gravity (position of which at this stage will have to be approximate) and the wing quarter chord position lie in the same sectional plane. The vertical position of the wing on the fuselage affects many factors:

A high wing allows a continuous structural path for the wing spar or box, provides for a good downward visibility, and offers the highest aerodynamic efficiency. On the other hand, it increases the overall dept of the fuselage cross section, increases the length of the main undercarriage (if it is wing mounted), and makes the cockpit less accessible.

A low wing position generally allows a continuous wing structural path through the fuselage, provides easy entry to the cockpit, and is more convenient for wing maintenance and inspection.

A mid-wing arrangement has minimum interference drag but causes a discontinuity in the wing structural path at the body side.

The wing is normally set at a small angle (1° to 3°) to the longitudinal axis of the fuselage to ensure minimum drag for the whole airplane during cruising flight.

The ailerons usually occupy approximately 9% of the total wing area and have a width of about 25% of the wing chord, which for constant chord means that they occupy the outer 35% of the span.

The wing planform can be selected as:

From theoretical considerations and from pressure distribution tests, it can be demonstrated that the ideal wing form is the elliptical because it has the smallest induced drag. But using the same theory and tests, it was found that a rectangular wing of aspect ratio 6 has only 5 percent greater induced drag than that of an elliptical.

Between these two wing planforms, there is the tapered, which has roughly one percent more induced drag than the elliptical.

Both the elliptical and tapered wings allow a lighter spar construction, but these advantages are of a small importance when compared with the better stalling characteristics and simplified construction of a rectangular wing. The rectangular planform has the best stall characteristics. The stall begins at the root of the wing progressing toward the tips, thus the ailerons remains effective while the center part of the wing is already stalled.

Estimate of Fuselage Dimensions and General Shapes

The shape of the fuselage is largely dictated by the ergonomic considerations – this involves arranging the fuselage lines to provide a comfortable but minimum volume around the pilot and the passenger seats. Unless the designer is the only person to fly the airplane it is necessary to arrange these values to suit the “standard man”. A cardboard scale model of the standard man shown below with pivoting parts will be found to be very useful during layout of the cockpit.

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The positioning of the instrument panel, controls, seat and cockpit floor involves personal preferences, but there are several references available which may be helpful. These are quoted below adjacent to a layout which has been used in the design of certain ultra- light airplane.

The dimensions of the cockpit layout can be varied but it is always advisable to arrange for the

floor to be lower than the pilot’s compressed seat to avoid leg tiring.

The standard man is 20 in. across shoulder, so that, allowing 2 in. each side for clearance and structure, the minimum fuselage width is 24 in. for single seat and 44 in wide for side by side arrangements. Two large people in a 44 in. wide cockpit would find the space rather cramped, or as the sales brochures describe it – “friendly”.

The rear fuselage lines are dependent on the type of undercarriage used, and the structure required to support the tail, together with the requirement for modest taper to avoid high drag. The position of the tail surfaces is decided mainly by the control and stability requirements of the airplane, but as a rough guide the position of the tail quarter chord is a distance of 2.5 to 3.0 times the mean wing chord behind the wing quarter chord. At a later stage this may have to be adjusted to suit the results of the detailed stability and control analysis. For tail-wheel undercarriages, the tail down angle must be sufficient to allow flight at high wing incidence during landing; 15o is representative value.

Estimate of Sizes of Tall Surfaces (Empennage)

The tail surfaces basically ensure stability and provide control. Determination of their sizes involves a detailed study of many factors (i.e. wing and tail section choice, interference effects, flap system, downwash, c.g. and weight variations, and required response). A study of existing airplane can give some guidance in the study stages before these details are known. Such a study will reveal that the fin and rudder area is approximately 0.010S and that the tail plane and elevator area is approximately 0.20S for airplane with flaps and 0.14S without flaps. A better parameter to use is the tail volume coefficient, defined as:

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__Horizontal Tail Volume Coefficient, VH

__ SH x lH

VH = _ = 0.35 -0.40 (unflapped wing) S x c

__Vertical Tail Volume Coefficient, VV

__ SV x lH

VV = = 0.035 – 0.04 S x b

Where:

SH x lH = horizontal volume

SV x lV = vertical tail volume

SH = horizontal tail area

SV = vertical tail area _c = wing MAC

b = wing span

Tail airfoil section are usually symmetrical and for aesthetic reasons the plan of the tailplane is often chosen to be similar to that of the wing.

Estimate of Landing Gear Dimensions

The choice of a landing gear is just field by the following reasons:

1. A leveled position is more comfortable when entering or leaving the cockpit.2. There is an improved forward vision from the cabin during ground runs.3. The tricycle landing eliminates the ground loop; it gives better ground stability and permits

full braking which in turn reduces the landing distance.4. The small wing incidence permits a faster acceleration, thus a reduction in take-off distance.5. With a leveled taxiing, position the chances of damaging the tail with stones blown up by the

propeller are reduced.

5

The propeller ground clearance is

Seven inches (for airplane equipped with nose wheel type landing gears) of 9 inches (for airplanes equipped with tail wheel type landing gears) with landing gear statically deflected and the airplane in the level, normal take-off, or taxiing attitude, whichever is most critical.

Some General Considerations on Landing Gear Design

(a) Tail Wheel Type (Figure 5)

For tail wheel configurations the wheels are positioned in the side elevation such that:

1. The propeller, flaps, rear fuselage, and elevator have adequate ground clearance in the most adverse conditions which will include a fully flat tire, or where possible a collapsed shock absorber units.

2. At the aircraft landing the main wheels touch down first. This attitude will depend upon choice of section, wing planform, wing or body setting, and flap system, but will no be larger than about 15o

3. The aircraft will not nose-over when brakes are applied.

The overturning coefficient is defined as:

Fhk = , a = h tan Ө

Wa

F k =

W tan Ө

The braking force (F) will be about 0.25W and for good design k should be less than 0.8

Substituting given values in equation above yields;

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There is some latitude in these figures but an angle less than 16o is considered dangerous.

4. The tail load required to rotate the aircraft on take –off is not too large.

5. The tail wheel or skid is attached to the strong rear fuselage structure members required to react the tail surface loads.

6. The c.g. should be located as shown in the front view (Figure 6).

(b) Nose Wheel Type (Figure 7)

The Main wheels position with respect to the C.G. is determined as follows:

1. Calculate the angle of attack α at CLmax with flaps –up

2. Locate the maximum aft C.G.

3. Draw a convenient scale side view of the airplane with the wing at the angle of attack α at CLmax

4. From the C.G. draw a vertical line, and from the tail skid a horizontal line.

5. At the intersection point “A” locate the center point of the tire contact area

6. Draw the landing gear with the tire and shock absorber completely deflected.

7. After the shock absorber deflection is calculated, the extended (unloaded) gear can be drawn.

8. See figure 8 for clearance requirements

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The track and wheel base should be determined next. The relationship between the track and the wheel base is dictated by the Turnover Angle which is determined as follows:

1. Draw a top view showing the desired nose wheel and tail wheel positions. Also the C.G. location.

2. Draw a side view showing the landing gear with shock absorbers and tires statically deflected and the C.G. position.

3. Established line AB Extend the line to a point “C”.

4. Through point “C” draw a line perpendicular to line AB.

5. Through the C.G. (in the plan view) draw a line parallel to AB and obtain point “D”

6. From point”D” measure the height of the C.G. (h) obtained from the side view and obtain point “E”.

7. Trace line EC and measure angle “β”. This is the turnover angle and should be less than 60o

If the turnover angle is more than 60o, increase the track or base and try again.

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The track of the main wheels may be set by arranging the leg mounting to be at a convenient position. For the wheel arrangements, if the track is too small the aircraft will be sensitive to lateral loads on the tail wheel and will be difficult to steer using differential main wheel braking. For tricycle arrangements a small track may cause the aircraft to roll over during braking about a line joining the nose wheel and the braked main wheel ground contract areas.

Representative values for track of tail wheel layout range from 40 to 45% of the fuselage length. For nose wheel arrangements 25 to 30% of the span. The actual value used should provide an angle of at least 15o between the normal ground line and a line from the main wheel to the wing tip (to cover the case of rocking while moving near the ground)

Detailed Weight Estimate

I. Weight of the Wing

0.25 _----- + (0.0004b + 0.001c) Dmax

Ww W/S ----- = ---------------------------------------------------- W 1 + (0.0004b + 0.001c) Dmax

Where: Ww = wing flight (lb)

W = all –up weight (lb)

W/S = wing loading (lb/ft2)

b = span (ft)_c = mean chord (ft)

nmax = maximum load factor multiplied by the ultimate factor (normally 1.5)

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Notes:

Wing weight (a) reduces as wing loading is increased (b) reduces as span loading is increased. (c) reduces as aspects ratio is reduced.(d) reduces as section thickness, sweepback of the structural members, and discontinuities of the structure are reduced.(e) reduces as the taper ratio is increased since the center of pressure of each semi-span is moved closer to the body side.

II. Weight of Fuselage

Fuselage weight = f (SF. W)

WF = 0.4SF + 0.04W

Where: Sp = surface area of fine fuselage (ft2)

III. Weight of Undercarriage

Suggested value is 25 lb/tire plus 10% for accessories

IV. Engine Weight

WEngine Weight = f (------)

P

Where: W/P = Power loading

V. Weight of Propeller and Spinner

= 0.03Do + 0.4 (lb)

Where: D is the propeller diameter in ft. which can be initially assumed to be:

= 4 + 0.01P (where P = the engine horsepower)

VI. Weight of Fuel Tankage and Supply

= 10% W

VII. Weight of Elevator, Rudder, aileron, and flap operating system, together with wheel brake operating mechanism.

= 2% W

VIII. Weight of Instruments and their Mounting

11 1b/ instrument (minimum number of instruments allowed is 5)

IX. Battery Mounting LigthingSeat belts and harnesses = f (typed to be used) = 25 lb typical Cushion and trim

X. Radio – optional equipment

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XI. Weight of Pilot and Passengers = f (seat arrangement)

Acceptable Weight

(a) Single seat types 100 – 225 lb

(b) More than one seat types 120 – 200 lb

XII. Baggage

- 10 lb / ft3

XIII. Fuel and Oil

= f (range and endurance)

Example: An aircraft less than 2, 000 lb AUW will give approximately 25 miles per galloon. For 50 hp engines consumption is about 3 galloons/hour.

Fuel Weight = 6 lb/galloonRatio, 25 galloons of fuel: 1 galloon of oil

Oil Weight = 75 lb / galloon

XIV. Empennage

= 25%Ww

Balance Diagram and Determination of C.G. Position

The C.G. position is calculated simply by calculating the moments of each component with respect to reference lines. The following procedure is recommended: (See Table 1)

1. Draw a side view of the airplane at a convenient scale (1/10 is adequate). Indicate the C.G. of each component by a small circle. It requires some practice to estimate by “eye ball” the position of the C.G. of some components. As a general guide, the C.G. of wings lies at 40% of the Mean Aerodynamic Chord. The C.G. of Vertical and Horizontal Tails can be located at 50% of the fuselage length measured between the firewall and the tail cone.

2. Enter the weight of each component in column of Table 1

3. Draw a vertical reference line at the spinner vertice and horizontal reference line in ground level. (See figure 10)

4. Measure the horizontal and vertical distance of each component C.G. from their reference lines. Enter these values in columns and of Table 1.

5. Multiply the weight of each component by its horizontal distance (column x column and enter the result in column

6. Multiply the weight the weight of each component by its vertical distance (column x And enter the result in column

7. Add column to obtain the sum of weights. Add column to obtain the sum of horizontal moments. Add column to obtain the sum of vertical moments

8. Divide the sum of horizontal moments by the sum of weights to obtain the horizontal location of the C.G.

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3

4 5

3

4 5

3 3

5

3 5

7

9. Divide the sum of vertical moments by the sum of weights to obtain the vertical location of the C.G.

Table 1

Item Designation WWeight

XHorzArm

WxHorzMom

yHorzArm

WyVertMom

1234567891011

Engine and Propeller FuelNose gearInstrument Pilot Wing Main GearFuselage Baggage Tailplane Fin

ΣW ΣWx ΣWy

__ ΣWx _ ΣWyx = -------- ; y = ----------

ΣW ΣW

The most Rearward C.G. Position is the most critical for stability, therefore, this will be calculated first. The most rearward C.G. position will occur under the following assumption:

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1 2 3 4 5 6 7

N in the engine task Baggage overload Pilot and Passenger (heavy) = 170 lb each Airplane in climb, assume ½ fuel in tanks pilled up in the rear half of the tanks

Notes: It is desirable to keep the C.G. at any condition ahead of the 30% of the Mean Aerodynamic Chord.

The most Forward C.G. position should be calculated next. This condition is critical for elevator dimensioning.

The Most Forward C.G. occurs under the following assumption:

No baggage No passenger No fuel Very light pilot = 120 lbMaximum oil in the engine tank

Notes; For preliminary design purposes, the Most Forward C.G. position should be kept behind 15% of the Mean aerodynamic Chord.

And finally the C.G. position for airplane Gross Weight (All-Up Weight) is calculated. Obviously, it must fall between the two extremes (Most Rearward C.G. & Most Forward C.G.)

MOST REARWARD C.G. POSITION

Item Description W x Wx y Wy

Empty weight Pilot Passenger Baggage No. of galloons of fuel in the Rear of tanks

170170

ΣW ΣWx ΣWy

__ ΣWx _ ΣWyx = -------- ; y = ----------

ΣW ΣW

Table 3 MOST FORWARD C.G. POSITION

Item Description W x Wx y Wy

Empty weight Pilot Oil (max. in the engine tank)

120

ΣW ΣWx ΣWy

13

__ ΣWx _ ΣWyx = -------- ; y = ----------

ΣW ΣW

Table 4ALL –UP WEIGHT C.G. POSITION

Item Description W x Wx y Wy

Empty weight Pilot Passenger Baggage (full)Fuel (full)Oil (full)

170170

ΣW ΣWx ΣWy

__ ΣWx _ ΣWyx = -------- ; y = ----------

ΣW ΣW

REVISION OF WING AREA, ETC.

DESIGN OF THE WING

General Considerations

The first three-view, the preliminary weight estimate, and the arrangement of the balance diagram are necessary steps in furnishing the data for the type of wing for the position relative to the fuselage, and for its size. The preliminary three – view has more or less set the shape of the wing and determined whether it is to be a monoplane, a full cantilever or an externally braced wing or, for example, a biplane with wings of different proportions.

The preliminary weight is instrumental in determining the approximate wing area needed, so that with at least this established it becomes a comparatively easy matter to select a suitable aspects ratio and thus be able to fix the governing dimensions of span, chord, and taper.

The balance diagram is necessary to locate the wing relative to the center of gravity; otherwise, difficulty might be experienced later in obtaining suitable static longitudinal stability.

The wing planform may be changed considerably owing to certain requirements of landing gear retraction, flap attachments, and the like. Suppose it is desired to retract the landing gear straight inboard towards the fusel age without the necessity of swinging it back first and then inboard in order to retract the gear fully into the wing without interfering with the front spar? Such retraction requires that the root portion of the wing be somewhat forward of the leading edge of the mean geometric chord; or in other words, the wing should have the leading edge swept back so that there are two original conditions that must be met by the wing and the landing gear. The wing, for example, should be placed so that the 25 percent point of the mean geometric chords falls directly under the center of gravity the landing gear, on the other hand, must be placed at a certain angle ahead of the center of gravity to prevent nosing over. These conditions for the wing and landing gear must be kept, and unfortunately, these conditions may play havoc with original ideas of wing planform and simple landing gear retraction.

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The incorporation of flaps and ailerons often affects wing planform. For simpler operating mechanisms, it may be desirable to have the hinge lines perpendicular to the plane symmetry of the airplane, or perhaps it may be desirable to have a constant chord flap whose spanwise axis is perpendicular to the plane of symmetry. Both of these more or less arbitrary conditions will affect ultimate planform of the wing. It is a good plan, therefore, to list at first all the various ideas that the designer wants to incorporate, and then make preliminary sketches of possible solutions to determine whether the various ideas are compatible.

With this general picture in mind, the new designer should now consider the following features of wing design.

Before the design of the wing may be begun it in necessary to study various features which affects its final design. The more important features are considered here although it is impossible to point of all possible effects of miscellaneous items such as landing lights, engine nacelles, landing gear, and fuel tanks.

DETERMINATION OF THE MEANAERODYNAMIC CHORD (M.A.C)

a). RECTANGULAR WING

The M.A.C. will be equal to theChord (c)

If the wing tips are rounded as shown in Figure 11, the M.A.C. still be assumed equal to c.

b) TAPERED WING

The M.A.C. could be determined graphically as shown in Figure 12 and described next:

1. Locate point “A” at the middle of cr

(root chord)2. Locate point “B” at the middle of ct

(tip chord)3. Locate point “C” at a distance equal to

ct behind the trailing edge. 4. Locate point “D” at a distance equal to

c forward of the leading edge. 5. Track lines A-B and obtain point “E”.

The M.A.C. is the chord line traced at point “E”.

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c) RECTANGULAR CENTER PANEL AND TRAPEZOIDAL OUTER PANEL

If the wing has a rectangular centersection and tampered outer panels, the procedure is as follows:

1. Determine the M.A.C. of the rectangular and tapered panels separately (c1 and c2)

2. Determine the areas of the rectangular and tapered section as follows:

Area Rectangle = A1 = a1cr cr + ct

Area Trapezoid = A2 = a2 -----------------

2

3. The M.A.C. of the entire wing will be :

c1A1 + c2A2

M.A.C. = ----------------------- A1 + A2

4. The distance from the Airplane Center Line to the M.A.C.

y1A1 + y2A2 a1

y = -------------------- y1 = ----- A1 + A2 2

5. The distance from a spanwise reference line to the M.A.C.

x1A1 + x2A2

x = -----------------------A1 + A2

6. The distance from a Reference Plane to the M.A.C. (See figure 13 – Front View)

z1A1 + z2A2

z = ----------------------- A1 + A2

d) ELLIPTICZL WING 1. Divide the wing in “n” stripe of equalwith h (Δy).

2. Measure the mean aerodynamic chord of the strip (ci) and the distance form the airplane center line to the strip mean chord (yi)

3. Prepare Table 1.

16 2 3 5

4. Add columns , , and

5. The M.A.C. of the wing will be:

ΣM.A.C. = ------------

Σ

Table 1

Strip Number

Strip chord x

Distance to Line

xDistance to Ref Line x

12--N

ct

c2

--

cn3

ct2

c22

--

cn3

y2

--yn

c1y1 c3y3

--

cnyn

x1

x2

--xn

c1x1

c2x2

--

cnxn

THE LANDING GEAR

The landing gear consists of the wheels, tires, brakes, shocks absorbers, struts, cowlings and, if rectractable, the retracting mechanisms.

General Considerations

The landing gear must, of count, take the shocks when landing or when going over an obstruction, and so it incorporated two means of absorbing shocks loads-the tire which absorbs minor shocks. Not only must the landing gear be able to take these shocks, but also it must be so placed that the airplane will be prevented from nosing over when landing. In order to accomplish this, the front wheels of the conventional landing gear are placed somewhat ahead of the center of gravity of the airplane.

While it may be desirable to have the landing gear reasonably far enough ahead of the center of gravity of the airplane if placed too far forward there would be difficulty in taking of. In taking off the of the airplane must be raised until the longitudinal axis of the airplane is practically horizontal. In this position, the airplane accelerates quickly until it reaches climbing speed and is ready to take off. But, in order to reach this horizontal attitude, there must be a lift on the horizontal tail surfaces produced by the relative wind on these tail surfaces caused by the propeller slipstream and forward acceleration of the cratt. The lift multiplied by the distance from the center of pressure on the horizontal tail surfaces to the point of contact of the wheel with the ground, is the moment which must be equal to the moment produced by the weight of the airplane times the distance from the center of gravity of the airplane to the point of wheel and ground contact. When these moments are equal, the airplane starts to accelerate, the elevation, which have been depressed up to this time, are gradually neutralized. Otherwise, too much lift would be created and the airplane would nose over.

If the front wheels were quite far ahead of the center of gravity of the airplane, a greater moment would have to be produced by the horizontal tail surfaces. Since the lift on the tail surfaces is proportional to the square speed, it would be necessary to increase the speed to obtain the necessary lift. However, it takes time to start at zero speed and accelerate up to a particular speed, and the longer it takes to accelerate, the longer will be the take-off run.

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7

3

2

1 2 3 4 5 6 7

1 1 2

4 1 1

Brakes are used to reduce the landing run. If the brakes were used immediately upon level landing, the inertia of the airplane might be sufficient to nose over. It is necessary, therefore, to put the wheels farther forward for a landing gear employing brakes than one without brakes.

Landing introduces another problem in the disposition of the wheels. If the tail wheel is too close to the front wheels, or the front wheels are too close together in relation to the span of the wings, the airplane may groundloop, a phenomenon in which the airplane may pivot on the wheel, meanwhile dragging a wing tip along the ground.

THE TRICYCLE GEAR

The present interest is the so-called tricycle landing gear. This reverses the location of the single wheel, which in the conventional landing gear is the tail wheel and new becomes the nose wheel for the new type.

Whereas the center of gravity was slightly behind two wheels, it is now slightly ahead of the two wheels and the nose wheel is placed as far as the particular design will permit.

Various test have been made by the army, by the National Advisory Committee for Aeronautics, and by a few commercial companies. The results of these test and investigation may be summarized as follows.

1. There should be greater passenger comfort since passengers are sitting in a cabin, which is level not only when flying but also on the take-off.

2. There is better vision both for the pilot and for the passengers not only in landing but also on take-off.

3. The tricycle landing gear gives greater ground stability since the three wheels are likely to be more evenly loaded at all times.

4. There should be no tendency to nose over since the nose wheel, being ahead of the center of gravity of the airplane, would resist any nosing over. The nose wheel is therefore a definite nosing over preventive.

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5. Since the airplane cannot nose over, there is the possibility of landing at almost any angle of attack. For the private flyer who may be a “dub” pilot, this is a very good feature since the landing technique need not be well-high letter perfect. For transport airplanes, the possibility of landing at almost any angle is advantageous in blind flying when the ground is not visible.

6. Also, because nosing over is unlikely, it is possible to have a shorter landing run since the brakes can be applied to have a shorter landing run since the brakes can be applied as soon as contact with ground is made. Moreover since the lift on the wings is less at the moment of landing due to the smaller angle of attack, the load on the wheels will be greater, and the width brakes on all three wheels, the braking will become more effective.

7. The smaller angle of incidence of the airplane with the ground will permit the airplane to accelerate up to take-off speed and practically “automobile” take-offs are possible and in much shorter time than for the conventional landing gear.

8. The quicker take-offs and the shorter landing runs permit a shorter black-to-black speed which is an important factor in economical commercial air transportation.

9. The airplane rests or wheels with the wings at a small angle of attack than the conventional landing gear. The lift coefficient of the wings at small angles of attacks is small so that even at relatively large wind speeds, the lift on the wings is not likely to be great enough to blow the airplane over.

Against these very favorable advantages of the tricycle landing gear, there should be balance these possible disadvantages which may entirely or at least partially overcome by proper design.

1. If the two main wheels in the rear of the center of gravity are too far back, the load on the nose wheel will be increased. This will necessitate a heavier nose wheel.

2. If the two main wheels are to near the center of gravity, the nose wheel will not have enough load on it and will therefore tend to bounce more easily when taxiing.

3. If the front wheel is located to close to the two main wheels, one of the following may occur. (a) A sudden swerve of the airplane may be followed by turning over, at about a line

connecting the nose wheel with one of the two main wheels (b) The front nose wheel may shinny unless there is friction damping. (c) The airplane may have tendency to buck.

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4. Unless the airplane can assume a greater angle of attack at take-off, the take –off run on muddy ground may be long. The propeller thrust and the higher ground drag due to the mud seem to cause the nose wheel to dig in at slow angles of attack. By raising the nose of the airplane the load on t he nose wheel is relieved.

5. With increase in propeller thrust, the load on the nose wheel increases since the propeller thrust line is above the nose wheel. Unless the nose wheel is equipped with a larger “oleo” travel and a stronger structure, for the sever shock load are likely to be transmitted to airplane structure, for the “oleo” or shock absorber may be compressed long before any serious loads imposed.

6. Difficulty may be encountered with the nose wheel in riding over obstacles. The tail wheel to behave better under such circumstances.

7. The tail wheel has the advantage of protecting the tail surfaces. Unless a skid or special crash pad is provided for the rear portion of the fuselage when the nose wheel type of the landing gear is used, the rear portion of the fuselage may be damaged in case of unusual “tail low” landing.

8. The nose wheel causes more difficulty in retraction because of its location on the forward portion of the fuselage and because of its longer shock absorber travel.

Wheel and Tire Sizes

The size of the wheels and tires in the conventional landing gear is determined by the static weight equal of half the gross weight of the airplane per wheel. It is not necessary determine the load factors and loads imposed by various landing conditions since the wheels and tires are originally designed with ample margins of safety.

The size of the wheels for a tricycle landing gear depends upon their position relative to the center of gravity. The two rear wheels may have from 85 to almost 100 percent of the load while the front wheel may have from 10 to 25 percent of the gross weight of the airplane as the static load. Refer to Figure 15 and 18.

Size of Tail or Nose Wheel

The weight of the tail wheel for preliminary weight estimate and balance determination can be estimated by assuming a static load of about one-fifth to one –twelfth the gross weight of the airplane and then choosing the required nose or tail wheel, with the larger fraction for the nose wheel.

After the center of gravity has been found, the weight and size of the nose wheel or tail wheel may be corrected by finding the correct static load on the wheel as follows:

a Static load R1 = ------------- gross weight

a + b

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Wheel Position

Examination of the landing gears that the wheel without any load on it, as incorporated in the normal landing gear, may toe-in; or the vertical centerline when viewed from the front is at the angle of several degrees from the vertical, commonly known as the camber. These two features are of course accentuated when the landing gear is in fully extended position due to the configuration of the particular members of the level-landing position or the three –point landing position.

The wheels are given no toe-in for the normal conditions unless the configurations of the landing gear should such as to cause an appreciable toeing –out in the fully contracted position.

The camber given the wheels may be 1 and 2 degrees outward unless, again, the configuration of the landing gear is such as to give an undesirable camber when in the fully contracted position.

Too much leeway either way may cause the tire to roll off when landing. The position of the wheels with relation to the center of gravity is shown in the illustration for

conventional landing gear and the tricycle landing gear.

Tail Surfaces

The tail surfaces serve two functions. The fixed portions of the tail surfaces, together with the movable, provide stability while the movable portion in conjunction with the fixed portion, provides for control.

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General Requirements

It is very important that these tail surfaces be so located that they are not blanketed by the fuselage. If the fuselage has a relatively large cross section for the greater part of its length and then tapers suddenly near the tail post, it is very likely that the horizontal tail surfaces will be blanketed unless the aspects ratio of these surfaces is high.

The vertical tail surfaces are most likely to be blanketed not only by the fuselage but also by the horizontal tail surfaces, especially when the airplane is at high angle of attack. In order to minimize this effect, it would be desirable to get some of the vertical tail surfaces below the horizontal tail surfaces.

Aerodynamically, it would be nice to have a large aspect ratio for both the vertical and horizontal tail surfaces, but unfortunately the greater the aspect ratio the more difficult it becomes to get an efficient structure that will be rigid. Since the movable surfaces are a reasonably large proportion of the total area, the fixed portion, which supports the movable surfaces, must contain all the necessary structure. If the aspect ratio is too great for the area, there is relatively little depth with the result that fixed surfaces may deflect so much under a load that the hinges of the movable surfaces bind.

The proportion of the movable surfaces to the whole depends upon the degree of control desired. A large movable surface, for example, needs less angular deflection than smaller-sized surfaces. If the airplane is to very maneuverable, it is desirable to have relatively large movable surfaces. In any case it is necessary to have sufficient control at the lowest and at the highest speeds the airplane will attain.

The elevator should be able to trim the airplane at the lowest, or stall speed, at which time the elevator will usually have its maximum angular deflection upward. The elevator should also be able to trim the airplane practically at zero lift, at which time the elevator may have its maximum angular deflection downward.

Control, however, is not measured only by the change in angle of trim of the airplane caused by a definite angular deflection of the elevator (and the discussion here applies equally to the vertical tail surfaces) but also by the hinge moments produced. If for the same angular deflection of the movable surface one has a greater hinge moments than another, it should be obvious that the one with the smaller hinge moments can be actuated far more quickly, and the response of the entire airplane will be quicker therefore.

The magnitude of these hinge moment is becoming an increasingly important problem. There are several solutions available. In some cases, (for example, the aileron) it helps materially in reducing the hinge moments to have a smaller chord so that the ratio of the chord of the movable surfaces to that of the entire surfaces is 15 to 20 percent. This necessitates a large span in order to get the same total control but, unfortunately, the rudder or elevator seldom has the ratio of its chord to the chord of the complete surfaces less than 45 to 50 percent. In order to reduce the hinge moments, the surfaces may be partially aerodynamically balanced either by having the hinge line of the movable surfaces somewhat in rear of its leading edge, or by having the hinge line of the movable surface or tab attached near the trailing edge of the main movable surface. This small surfaces has an angular deflection opposite to that required fir the main movable surfaces.

If the tab is small or its setting fixed and changed only when the load conditions change the center of gravity, then its purpose is for trim only, and is known as trimming tab. It takes the place of the adjustable stabilizer.

If the tab can be controlled from the cockpit, it may be used to operate the larger surfaces and is then called a control tab or a servo tab. Aerodynamic balance is generally used, even if trailing-edge tabs are present. The design of this balance is very critical and is still the subject of much experimental work. For greater effectiveness, a slot in front of the leading edge of the balance is provided. Although this slot helps to increase the effectiveness of the movable surfaces, yet, more often than not, the relatively large gap caused by the slot increases the parasite drag.

Great care should be taken in designing the leading edge of the aerodynamic balance so that it is not too sharp and does not project too far above the upper contour of the fixed surface when the movable surface is deflected. Such projections collect ice very quickly under icing conditions and may lead to unbalance of the control surfaces, or jamming of the controls.

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Airfoil Sections

Symmetrical airfoils are usually used for tail surfaces so that equal effectiveness per degree of deflection may be obtained for both up and down movements.

The airfoil section used should have a thickness ratio of at least 8 or 9 percent and not more than 12 percent. Unless the tail surfaces are exceptionally large, the same airfoil is used from tip to root. The NACA 0009 and 0012 are recommended.

Horizontal Tail SurfacesLocation

The horizontal tail surfaces should be so located that any blanketing by the wing or the fuselage is avoided. Partial blanketing usually exists, however, but certain features may be incorporated to limit the effect of blanketing.

In some cases, the location of the horizontal tail surfaces is determined by clearance requirements for the elevator, as shown in Figure 10, when the elevator is deflected downward through its total angular range and with the tail-wheel assembly fully deflected.

Conventional airplanes of today located the tail surfaces about 2 ½ to 3 chord length (mean aerodynamic chord of the wing) behind the center of gravity so that the observance of this rule will assure reasonable static longitudinal stability.

Movement

Elevator are designed to have an equal angular movement up and down from neutral. About 30-degree movement is considered maximum and, with efficient design, a 25-degree deflection down should be sufficient.

The stabilizer may be adjusted through a small angular displacement either on the ground or in the air from the cockpit (usually the later, if at all; since trimming tabs are displacing adjustable stabilizer)

If an adjustable stabilizer is used, a total of 6 to 8 degree movement (about 5 degrees up and 3 degrees down) is usually used.

Aspect Ratio

The aspect ratio of the tail surfaces should be as high as possible in order to avoid blanketing of the structure to which they are attached. Aspect ratios greater than 6 are seldom used unless they can be braced adequately.

In proportioning the tail surfaces, it is not desirable to start with the aspect ratio because the fuselage section increases the span of the tail surfaces seemingly beyond the desirable limit.

For correcting airfoil data from the given aspect ratio to that of the tail surfaces, the aspect ratio is calculated on the basis of the square of the span length from tip to tip divided by the area including that covered by the fuselage. In other words, exactly the same procedure is followed as in calculating the aspect ratio of the wing.

Angle of Incidence

The incidence of the horizontal tail surfaces is determined by the amount of downwash from the wing, its relative location with respect to the wing, and the moment required to obtain the required trim angle.

On small airplanes it has been customary to make the stabilizer adjustable through a limited angular range, about 3 degrees up and 3 degrees down. The adjustment has been possible either on the ground or in the air by means of a control located in pilot’s cockpit. The adjustment in the air preferable. On the large transport airplanes. Variations in trim (the object of the adjustable stabilizer) are obtained by means of trailing-edge tabs.

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Dihedral

Normally horizontal tail surfaces are not given any dihedral, but is has been found that the effectiveness of the horizontal tail surfaces can be increased considerably, particularly at high angles of attack, by incorporating some dihedral in the horizontal tail surfaces. How large the dihedral angle should be depends upon the downwash of the wing; for purposes of symmetry, the span line of the tail surfaces maybe made parallel to the span line of the wings.

Area

Examination of airplane of all sizes reveals that the ratio of the horizontal tail surfaces to the effective wing area varies from 15 to 20 percent. The greater the tail length is, in terms of the wing chord, the smaller percentage area is required. Wings equipped with lift –increase device usually require that the percentage area of the horizontal tail surface be greater than if the wings were not so equipped.

The elevator area varies from 35 to 45 percent of the horizontal tail surface area.

Construction

For ease in assembly and disassembly, the horizontal tail surfaces are attached to the top of the fuselage, especially if tubular steel construction is used for both the tail surfaces and the fuselage. When reinforced metal monocoque construction is used, the horizontal tail surfaces may be located nearer the longitudinal centerline of the rear portion of the fuselage and still obtain the necessary rigidity.

Vertical Tail Surfaces

Location

The vertical tail surfaces are, almost without exception, located above the horizontal tail surfaces in order to centralize control systems and simplify the supporting structure contained in the fuselage.

It is desirable to locate about half of the rudder below the axis of symmetry of the fuselage but this may not be possible because of required clearance with the ground.

Aspect Ratio

The aspect ratio of the vertical tail surfaces should be between 2 and 3. It is difficult to state exactly what the aspect ratio of the vertical tail surfaces may be, because the rear portion of the fuselage influences the vertical tail-surface effectiveness.

Figure 20. The distance A for conventional airplanes should be from 2 ½ to 2 time the mean aerodynamic chord of the wing. The angle B, corresponding tot eh maximum deflection of the elevator, should permit the trailing edge of the elevator to clear the ground comfortably.

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Trailing-edge Tabs

Trailing –edge tabs on movable surfaces are popular at the present time. A tab on the airleron is used to overcome engine torque. It may be used with the rudder for the same purpose as the offset fin and on the elevator for the same purpose as the adjustable stabilizer.

Trimming tabs have a chord varying from 5 to 10 percent of the movable surfaces chord and approaching 25 percent of the chord if used as servo control tabs. The aspect ratio should be as high as possible, varying usually from as low as 5 to as high as 20.

Static Stability

Stability is the property of a body which, when the body is disturbed from a condition of equilibrium, causes forces or moments which acts to restore it to its original condition.

Stability of an airplane means that the airplane tends to remain at the same attitude with respect the relative wind.

A plane is statically equilibrium if, when in flight, the sum of all forces acting in all directions equals zero and the sum of when the sum of the vertical forces is zero and sum of the horizontal forces is zero.

ΣV = 0ΣH = 0ΣM = 0

As there are three axes of rotation, so there are three classes of stability-longitudinal or fore and aft stability, lateral stability, and directional stability.

Longitudinal stability – stability with reference to disturbances in the plane of symmetry, i.e. disturbances involving pitching and variation of the longitudinal and normal velocities.

Longitudinal Balance

In level flight the forces, which must be considered, are the weight, acting downward; the propeller thrust, acting forward; the lift, acting upward; the total drag, acting backward; and the tail load, which may be either upward or downward.

ΣM c.g. = 0

(D x b) - (L x e) + (T x a) ± (P x d) = 0

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+

ΣM c.g. = 0

(-D x b) - (L x e) + (T x a) ± (P x d) = 0

In the conventional high wing monoplane shown in Fig. 21a, the thrust and drag both act to produce stalling or positive pitching moment. The lift produces a negative or diving moment. The moment of the tail load must be such as to be equal in magnitude to the difference of the plus minus moments and of the same sign as the smaller. In order to ensure that the lift always produces a diving moment, the center of gravity must be ahead of the most forward position of the center of pressure of the airplane. At high angles of attack, for some airfoils the center of pressure moves forward to a position 25 percent of the chord back of the leading edge, so that the center of gravity must be in front

Whether the airplane is high-wing or low wing, the distribution of weights should be such that the center of gravity will be on or close as possible to the thrust line. The purpose of this is to make the moment due to the thrust, T x a, in Eqn. [ (D x b) – (L x e) + (T x a) + (P x d) = 0 ] either zero or a small as possible. Changes in thrust or complete engine failure will then cause little or no change in the longitudinal balance.

If the center of gravity of a low –wing monoplane is located as shown below the thrust line and above the line of action of the total drag, both thrust drag will cause a diving or negative moment. It is necessary then that the horizontal tail surface have downward force acting on it as to produce a stalling moment.

Problem: A monoplane weighing 3, 000 lb, having a rectangular wing of 30 ft. span and 4.0 ft chord is flying at 100 mph at standard sea level conditions. The lift drag relation is C.Do = 0.015 + 0.050CL2. The center of gravity of the airplane is 1.0ft back of the leading edge of the wing, 0.98 ft above the thrust line, and 0.66ft below line of action of total drag. It is 9 ft from the center of gravity of the airplane to the center of pressure of the tail. The center of pressure of the wing is 40% of the chord from the leading edge. What should be the tail load?

Location of Center of Gravity Experimentally This point is quite often the rear face of the propeller hub.

The center of gravity of an airplane is the point where the entire weight may be considered to be acting. The determination of its location may be made in following manner. The front wheels are placed on scales as is the tail wheel, as shown in Fig. 22. The sum of the weights on the front wheel is W1, the weight on the rear wheel is W2. The distance b is the horizontal distance, parallel to the longitudinal axis, form of the line connecting the contact points of the two front wheels to the point of contact of the tail wheel. If the tail is elevated, as in Figure 22b, measurement is made to the vertical projection of the point of contact of

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+

the rear wheel. The distance a is the horizontal distance from the line connecting the points of contact of the two front wheels to the vertical projection of some convenient point of reference on the airplane.

Figure 22. Location of C.G.

Datum line – the datum is an imaginary vertical plane from which all horizontal measurement are taken for balance purposes with the airplane in level flight.

Note:

W1 = Weight on the front wheel W2 = Weight on the rear wheel W = W1 + W2

+ ΣMD.L. = W (c cosθ + d sinθ) – W1a – W2 (a+b) = 0

W(c cosθ + d sinθ) = W1a+W2 (a+b) W(c cosθ + d sinθ) = (W1+W3) a+W2b[W(c cosθ + d sinθ) = (Wa+W2b)] 1/Wcosθ

Problems:

1. From the following date, find the location of the center of gravity.

Tail is down Tail is up

θ = 12o 0o

a = 12o 2.7o

b = 19.1o 18.2o

W1=1812lb 1876lbW2 =188lb 124lb

2. Find the location of the center of gravity, if, when θ = 2o, a is 7.0 ft, b is 35.2 ft, weight on the front wheels is 13, 246 lb, weight on rear wheel is 1, 022 lb, and when θ = 13o, a is 6.3ft, b is 35.9 ft, weight on front wheels is 12, 490 lb, and the weight on rear wheel is 1, 778 lb.

3. Find location of the center of gravity, if, when θ = 0o, a is 5.2ft, b is 47.1 ft, W1 is 10, 520 lb, and W2 is 1360 lb and when θ = 10o, a is 48.3 ft, W1 is 10, 510 lb, and W2 is 1, 370 lb.

Structural Design

Principal causes of airplane accidents:

(1) Forced landlines in unsuitable locations, caused by motor failure, fuel exhaustion, or bad weather;

(2) Unskillful landings; unusual skill maneuvering for landing is necessary because of gusty air or small or obstructed airports;

(3) “ Ground loops” caused by a. Down-wind or cross-wind landings b. Faulty arrangement of wheels or landing gearc. Insufficient rudder control while taxiing.

(4) Unnecessarily violent maneuvers (dive, loops, rolls, spin, etc)

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(5) Unusual strong gusts of air, up – gusts, which break the wings or down-gusts, which break the tail surfaces or throw the airplane against the ground.

In order to minimize the number of airplane accidents, promote a public inherent in flying, and encourage defense industries related to aircraft or missiles, the various governments of the world have evolved

1. Rules in flying 2. Rules for the design of aircraft

The government agency in the U.S.A. which devices and enforces such rules is the Federal Aviation Administration.

The U.S. Federal Regulation of the Federal Aviation Administration of primary importance on airplane airworthiness are given in FAR 23: Normal, Utility, Acrobatic categories.

Procedure in Design

The design of an aircraft is an engineering problem solving:

1) The location of the various structural members in each part so that the loads can be carried by the structure without structural disintegration.

2) An estimate of the loads to which the various parts of the aircraft are likely to be subjected when it is used as intended.

3) A knowledge of the properties (strength and stiffness) of the material of which the airplane is to be made and

4) Calculations to show that the design loads will not cause failure of the materials (“stress analysis”).

DEFINITION OF PRIMARY IMPORATANCE IN STRUCTURAL DESIGN

LIMIT LOAD. The maximum load anticipated in service.ULTIMATE LOAD. The maximum load, which a part of structure must be capable of supporting. FACTOR OF SAFETY. The factor by which the limit load must be multiplied to establish the ultimate load (normally 1.5 “unless otherwise specified”) LIMIT LOAD FACTOR. The limit load factor is the load factor corresponding to limit loads. ULTIMATE LOAD FACTOR. The ultimate load factor is the load factor corresponding to ultimate load. LOAD FACTOR. The load factor is ratio of specified load to the total weight of the aircraft. The specified load may be expressed in terms of the following; aerodynamics forces, inertia forces or ground or water reaction.

Flight Envelope or V-n Diagram

Condition I: Maneuvering Load Factors(a) The positive limit maneuvering load factor “n” may not be less than the following

values. 24, 000

n = 2.1 + -------------------, Normal category W + 10, 000

except that “n” not be greater than 3.8 and shall not be less than 2.5

n

(b) The negative limit maneuvering load factor “n” may not less be less than

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Design Maneuvering Speed, VA

VA = VS √ + n

Where:

Vs = stall speed with flaps up +n = positive limit maneuvering load factor

(a) Formula for + CNA maximum curve:

nW nW+CAN = ------------ -------------------- ; n = positive limit maneuvering

qAS ( 1/2 ) pVA2S load factor

CAN ½ pVA2

+n = --------------------W--- S

(b) Formula for CN A maximum curve

-CNA = -nW = -nW -n = negative limit maneuvering load qAS ½ pVA2S factor

-CNA ½ pV A2S

-n = ----------------------------W/S

Condition II: Load Factor due to Gust

Design Cruising Speed, Vc des

Vcdes = 0.9 VmaxVc may not be less than the following condition Vc (in knots) </33 √ W/S (for normal and utility category) Vc (in knots) </33 √ W/S (for acrobatic category)

Where: W/S is in lb/ft2

Limit Gust Load

n = 1 + Δn

n = 1 + KUVa 575 (W/S)

Where:

K = ½ (W/S) ¼ (for W/S < 10 lb/ft2)

U = nominal gust velocity (= ±30 fps)

V = airplane speed up to Vc, mph

a = slope of lift curve per radian = CL a-ao

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Design Drive speed, Vp

For V D, the following apply

VD < 1.4V cmin (for normal category)

VD < 1.5V cmin (for utility category)

VD < 1.55V cmin (for acrobatic category)

Limit Gust Load Factor

n = 1 ± Δn

KUVan = 1 ± -----------------------------

W575(-----) S

Where:

U = nominal gust velocity ( = ± 15 fps) V = airplane speed up to VD, mph

Example: Determine the limit factors at sea level required by FAR 23 and construct a V-n Diagram for an

airplane assuming the following data; gross weight = 2000 lbs., Bhpmax = 150, span, b = 38 ft., design the wing area = 210 sq. ft., CLmax = 1.5, estimated level high speed = 160mph, slope of lift curve = 4.25 per radian, utility category.

Given:

W = 7000lb. Bhpmax = 150b = 38 ft. s = 210ft3

CLmax = 1.5 Vmax = 160 mph a = 4.25/radian utility category

Required:

Limit load factors and V-n diagram

Solution: For positive limit maneuvering load factor; n:

24, 000n = 2.1 + ---------------

W + 10, 000

24, 000 = 2.1 + ----------------------

2, 000 + 10, 000

= 4.10

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W 2 1Vs = (----- ) ( ------) ( -------)

S P CLmax

2, 0000 2 1Vs = (----------- ) ( ------------) ( ----------)

210 0.002377 1.5

Vs = 73.09ft/s = 49.83 mph ____

VA = Vs √ +n ____ = 49.83 √ 4.10

VA = 100.90mph

WVcmin(in mph) = 38 -----

S

2, 000= 38 -------------

210

VCmin = 117.27 mph VD = 1.50 VCmin = (1.50) (117.27)VD = 175.90 mph

Since the level high speed is estimated to be 160 mph and it may be desired to cruise at 90% of this figure, the actual design cruising speed may well be made, higher than the minimum, permitted by FAR 23. Accordingly at is proposed to make.

Vdes = 0.9 Vmax = (0.9) (160)

Vdes = 144 mph

For negative limit maneuvering load factor, n: -n = -0.4n = (-0.4) (4.1) -n = -1.64

Gust Load Factor

KUVa n = 1 ± -------------

W 575 ( -----)

S

For this airplane;

W 2, 000--- = ----------- = 9.52lb/ft2

S 210

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1 W ¼ K = ----- ( -------)

2 S

= (0.5) (9.52) ¼ K = 0.88

The regulation specify that the airplane must stand U = ± 30 fps up to speed Vc and U ± 15 fps up to speed VD.

at Vc = 144 mph

(0.88) (30) (144) (4.25)n = 1 ± ---------------------------------- = 3.95 or 1.95

575 (9.52)

at VD = 175.90 mph

(0.88) (15) (175.90) (4.25)n = 1 ± ---------------------------------- = 2.8 or -0.80

575 (9.52)

VF = 1.4 Vs which is greater VF = 1.8VsF

Vs = the computed stalling speed with flaps retracted at the design weight.

Lose Factors, n

Positive High Angle of Attack (PHAA)

n = 1 + Δn

32, 000 3.25 Δn = 0.77 + ----------------------- ------------------- maneuvering

Use the W + 9, 200 W load factor higher (---) 0.435 increment value KUVa S

Δn = ------------ W

575( ------) gust load factor increment S

Where:

W = gross weight, lb W/P = power loading, lb/hp V = max level speed, mph U = gust velocity (= 30fp) W/S = wing loading, lb/ft2 a = slope of lift-curve per radian K = (1/2) (W/S)1/4 , for W/S, 16 lb/ft2

2.67

= 1.33 - ---------- , for W/S > 16 lb/ft2

W ¾ (-----) S

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Positive Low Angle of Attack (PLAA)

n = 1 + Δn

32, 000 3.25 Δn = 0.77 + ----------------------- -------------------

Use the W + 9, 200 W higher (---) 0.435 value KUVa S

Δn = ------------ W

575( ------) S

Where:

U = gust velocity ( = 15 fps) V = airplane speed at gliding Vg, mph Vg = ≥ Vc + Kg (Vm + Vc) Vg = ≤ Vc + 100mph or 1.5 Vc Use the lower value

1, 850Kg = 0.08 + ----------------

W +3, 000

Vm = terminal speed (power off)

W 2 1 _= (----) (----) (----) sin y

S P CDo

CDo = Zero-lift drag coefficient _Y = 90o

Vc = cruising

Negative High Angle of Attack (NHAA)

n = 1 + Δn

KUVaΔn = ------------

W575 (----) S

Where:

U = - 15 fps V = airplane speed at gliding, mph

Airplane Categories are defined as:

1. Normal Category – Airplanes in this category are intended for non-acrobatic non-scheduled passenger, and non-scheduled cargo operation.

2. Utility – Airplanes in this category are intended for normal operation and limited acrobatic maneuvers. These airplanes are not suited for use in snap or inverted maneuvers.

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Limited Acrobatic Maneuvers is interpreted to include steep turns, spins, stall (except whip stalls), lazy eights, and chandelles.

Steep Turns – A flight maneuver in which the degree of back varies from 45o to about 75o

Spin – A flight maneuvers if done intentionally and a flight condition if it occurs otherwise, which is the result of a complete stall after which the airplane, still in stalled attitude, loses altitude rapidly, and travels downward in a vertical helical or spiral path.

Stall – The condition of an airfoil or airplane in which it is operating at an angle of attack greater than the angle of attack of maximum lift. It is a loss of flying speed and in many cases temporary loss of lift and control of the airplane. A complete stall in normal flying is to be avoided at all times, but it sometimes occurs unintentionally, because of inexperience piloting, and is sometimes done inadvertently by the experienced pilot.

Whip stall – A flight maneuver or condition, which is the result of a complete stall in which the nose of the airplane whips violently and suddenly downward. In some cases the airplane slides backward a short distance before the nose of the plane drops. Whip stalls cause severe strains on the engine mounts, and all surfaces.

Lazy Eight; Flight – An advanced flight –training maneuver, which combines the dive, turn and the climb. It is a maneuver in which the nose of the airplane describes a horizontal figure eight lying on its side upon the horizon. An object on the horizon is selected and used as an axis for the maneuver, i.e the horizon divides the halves and the selected object is the intersection of the two halves of the eight.

Chandelle – A flight training maneuver of the composite type, composite type, combining the climb and turn, approach to a stall and recovery back to normal flight. The simple chandelle is really an exaggerated 180o climbing turn in which the bank and climb are gradually increased until a maximum is reached, approximately at the 90o point during the 180o turn. After reaching this point, recovery is started by gradually reducing the climb and shallowing the bank until at the time of arriving at the 180o point of the turn, the plane is flying straight and level at a speed just above the stalling point. The advanced “chandelle” is started by doing a slight forward slip and pulling up and around; the initial bank remaining constant. The vertical flight path of the airplane up to 90o point of the turn is on bias to the vertical plane and as the turn increased the bank only seems to increase. At the 90o point of the turn, recovery to normal flight (180o change of initial direction) is executed the same as with the simple “chandelle”. The main objective of this maneuver is to gain altitude at the same time that the direction of flight is changed.

3. Acrobatic Category – Airplanes in this category will have no specific restrictions as to type of maneuver permitted unless the necessity therefore is disclosed by the required flight test.

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