INFLUENCE OF AERODYNAMIC PARAMETERS IN THE DESIGN OF THE AIRCRAFT

Divya.G.S (M.E Aeronautical Engineering)

Madras Institute of Technology,ChennaiAbstract: This study gives the detailed insight on how the aerodynamic parameters influence

the design of the aircraft. The aerodynamic parameters like drag co efficient, lift co

efficient, lift to drag ratio, Aspect ratio, Drag polars etc greatly influence the stability and

structural design of the aircraft so utmost care must be taken to determine these

parameters. These aerodynamic parameters are determined from preliminary weight

estimation and from historic values of certain parameters from the cluster diagram of

similar kind of aircrafts.

Introduction:

Designing of the aircraft is a very interesting and innovative stream in

aeronautical engineering in which all the concepts we have studied like aerodynamics,

propulsion and structures are applied practically. Design of an aircraft consists of three

stages of design like conceptual design, preliminary design and detailed design. Detailed

design is done after the preliminary design is finalized and involves real time testing of

the components. The design of the aircraft is started based on the mission requirements

stated by the customers but bear in mind all the mission requirements cannot be satisfied

without making any compromises in some of the requirements and the designers must be

able to satisfy the customers by bringing the pros and cons of the design such that the

main mission requirement is satisfied. Basically design of the aircraft is an iterative and

laborious process as various requirements has to be satisfied to obtain acceptable values

of aerodynamic and structural parameters.

The design of the aircraft begins with collecting historical values of some

required parameters from similar aircrafts and using these values the weight of the

aircraft is estimated which is followed by the aerodynamic design of the aircraft which

decides the geometrical parameters of the aircraft and includes calculations relating to

aircraft performance and stability.

Aircraft Design:

The first and fore most step involved in the design of the aircraft is the collection

of data about similar kind of aircrafts and plotting cluster diagram from which certain

parameters like gross take off weight(Wto), Aspect ratio (AR), Range (R), Thrust to

weight Ratio (T/W), Wing loading (W/S) and Fineness ratio (l f/df) are obtained. From the

above data collected gross take off weight of the aircraft (Wto) is found by iteration

which is preceded by the second weight estimation in which the weight of the power

plant is taken into account and final gross take off weight of the aircraft is arrived and

immense care must be taken as over estimation or under estimation of these values may

result in unrealistic values in the future aerodynamic calculations involved.

The next step involved in the design of the aircraft is the determination of

geometrical parameters of the wing like wing plan form area (S), placement of the wings,

angle of sweep (Λ), length of the root chord (Cr) and the tip chord (Ct). Span of the wings

(b) etc, followed by the selection of airfoil suitable for the mission specified and high lift

devices. Followed by the determination of fuselage parameters, vertical tail and

horizontal tail parameters.

Each component weight is estimated separately and the balance diagram is

constructed from which the c.g of the aircraft is calculated along with static margin and

the movement of the c.g should be between 5% to 15%. Following the above, landing

gear parameters are calculated followed by drag polar, v-n diagram, performance and

stability calculations which completes the aerodynamic design of the aircraft. Structural

design is carried out following the aerodynamic design as the structural design depends

mostly on the aerodynamic design which was carried before.

Influence of gross take off weight ( Wto):

As the gross take off weight (Wto) increases design lift co efficient also increases

which decides on the selection of the airfoil and this in turn also results in the increase of

the mechanical complexity and the cost of high lift devices as more complicated high lift

devices are required to obtain the required design lift co efficient of the aircraft. As the

gross take off weight (Wto) the size of the tyres required to support the weight of the

aircraft also increases which results in difficulty in accommodating the landing gear when

retracted. This in turns requires a larger plan form area (S) and (t/c)max of the airfoil

which results in the increase of the parasite drag co efficient.

Influence of the wing parameters:

High aspect ratio of the wing results in low induced drag but reduces the Oswald

efficiency factor (e) of the wing. The high AR of the wing also increases the weight of

the wing which in turns increases the operating cost of the aircraft. The change in angle

of attack (ά)to obtain the required Cl also depends upon the Aspect ratio of the wing.

Induced drag which is produced as the result of finite wing span can be reduced by

increasing the Aspect ratio of the wing which is given by the relation

Cdi = Cl2/ Π AR

The lift curve slope produced by the wing also depends upon the Aspect ratio in addition

to the lift curve slope of the airfoil (a0 ).

Clά = a0/ [1+(57.3*a0/Π eAR)

The weight of the wing (Wwing) increases with increase in the sweep angle and the plan

form area (S) and it also depends upon the zero fuel weight of the aircraft

Wwing = 0.0017 WMZF [ b/cos L1/2]0.75 [1+ { 6.3 cos L1/2/b}0.5 * (nult)0.55

[bS/trWMZF cos L1/2] where WMZF is the weight of the aircraft without fuel

Influence of aerodynamic parameters in performance:

While calculating the velocity required minimum power(VPr), it should be noted that VPr

minimum increases with increase in the wing loading (W/S) and decreases with increase

in parasite drag co efficient which in turn implies that with increase in parasite drag co

efficient (Cd0)and this Cd0 again depends upon the plan form area of the wing more

powerful engine is required for the operation of aircraft to overcome the drag.

V min power = [ (2/ρ)*(W/S)*(K/3*Cdo)^0.5]^0.5

K = 1/(Π e AR)

Stalling speed (Vs) increases as Cl max decreases and there is a upper limit to the stalling

speed of the aircraft.

Vs = [{2*(W/S)}/ρ*Cl max]

So importance should be given in calculating the maximum lift co efficient.

Thrust required (Tr) by the aircraft is inversely proportional to the C l/Cd and as the drag

increases the thrust required by the aircraft increases so the fuel consumption required

also increases which in turns affects the operating cost of aircraft.

Tr = (Wto)/(Cl/Cd)

Maximum velocity at which the aircraft can be flown increases with increase in thrust to

weight ratio (T/W) and the wing loading (W/S) and these values should be such that the

Vmax becomes very large and goes into transonic and supersonic regime which becomes

unrealistic at times.

Maximum climbing angle (θmax) depends on T/W and it is inversely proportional and it

depends upon K and Cdo which in turn again depends upon Aspect ratio and the plan form

area(S).

Sin θmax = T/W – (4*Cdo*K)^0.5

The velocity required to achieve the θmax depends upon the wing loading (W/S) of the

aircraft and the maximum angle to climb

V θmax = [2/ρ*(k/Cdo)^0.5*(W/S)*cos θmax ]^0.5

The maximum rate of climb (R/C)max increases with (L/D)max increases and with Z

decreases.

(R/C)max = [(W/S)*Z/3*ρ*Cdo]^0.5 * (T/W)^1.5*[1- (Z/6) – (1.5/(T/W)2(L/D)2Z ]

Z = 1+[1+{3/(L/D)2*(T/W)2}]

For gliding unpowered flight , the minimum gliding angle (θmin) depends on (L/D)max

which in turn determines the maximum range to be covered during descent.

Tan θmin = 1/(L/D)max

h/R max = tan θmin

The velocity required to obtain maximum lift to drag ratio depends again on the

geometric parameters given by

V(L/D)max = [2/ρ*{(K/Cd0)^0.5}*(W/S)]^0.5

When calculating the range and endurance again we note it depends upon the (L/D) ratio

and the gross take off weight .

R = 2/c *[(2/ρ*S)]^0.5* (Cl 0.5/Cd)*(Wto 0.5 – Wf 0.5)

Where Wf is the final weight of the aircraft

From the above relation it can be seen that Cl0.5/ Cd depends upon K and Cdo

(Cl0.5/Cd)max = ¾*(1/3*K*Cdo3)1/4

E = 1/c*(L/D)*ln (Wto/Wf)

(L/D)max = (1/4*K*Cdo)^0.5

While calculating the take off distance and landing distance again the parameters (W/S),

Lift, Drag plays an important role in obtaining a realistic values for the above.

Construction of the flight envelope also depends upon max lift co efficient, max load

factor and the wing loading of the aircraft to be designed.

Influence of Aerodynamic parameters on stability:

To ensure the longitudinal stability of the aircraft the derivative δCm/δCl must be

negative.

δCm/δ Cl = (Xc.g – X a.c)/ C +(δCm/δCl)fuselage – at*Vht*ŋht/aw (1 – δε/δα)

δε/δα = 2*Cl αw/(Π*AR)

(δCm/δCl)fuselage = Kf*wf2*lf/(Sw*C*Clαw)

Where Kf is the constant (0.012)

which again depicts the importance of carefully evaluating the aerodynamic co efficients.

In evaluating the stick fixed and stick free maneuver point also wing loading, tail arm and

the elevator effectiveness factor comes into play which depends upon the plan form area

of the control surface.

To ensure directional stability of the aircraft the derivative δCn/δψ should be negative and

the contribution to this derivative comes from wing, fuselage and nacelle etc which all

depends upon the aerodynamic parameters of the respective components. For detailed list

of formulae refer to PERKINS AND HAGE and the same thing applies to lateral stability

also.

When considering the dynamic stability of the aircraft the co efficients of the quartic

equation depends on the aerodynamic parameters like lift co efficient, drag co efficient

moment co efficient and similar kinds of derivatives. For detailed list of formulae refer to

PERKINS AND HAGE.

Influence of aerodynamic parameters in structural design:

In identifying the loads acting on the wing and its weight distribution the (t/c)max of the

airfoil selected comes in to play as the weight carried by the wing depends upon the

chord and the thickness of the airfoil. Similarly the fuel weight distribution of the wing

also depends on the same and these are very useful parameters in plotting the shear force

and the bending moment diagram depending upon the spar design is carried out for the

wings. The same principle applies well for the fuselage design of the aircraft.

Conclusion:

From the above discussion it is clearly shown that the aerodynamic parameters must be

calculated with acceptable accuracy and this depends mainly on the gross weight

estimated in the first and foremost which must be done carefully as slight variation may

have significant impact on the aerodynamic parameters calculated which is the basis for

performance, stability and structural design of the aircraft.

References:

1. Jasdeep Singh, Notes on Weight Estimation, 2006.

2. ,Mohamed Sadaraey, Drag force and its Coefficients

3. Daniel P.Raymer, Aircraft Design: A conceptual Approach,AIAA

Education Series,1992

4. Egbert Torenbeek, Synthesis Of Subsonic Aircraft Design, Delft University

Press.1979.

5. Lloyd R.Jenkinson, Civil Jet Aircraft Design, Arnold Publications, 1999.

6. Stansford University Online notes.

7. Online notes by Prof. Tulapurkara.

8. Dr.Jan Roskam, Airplane Design Volume 1-7, Roskam Aviation and

Engineering corporation,1985

9. ,John.D.Anderson Aircraft performance and Design,,Tata Mcgraw Hill

publications

10. Perkins and Hage, Airplane Stability and Control, John Wiley &Sons

publications.

a0 Lift curve slope of the airfoilaw Lift curve slope of the wingat Lift curve slope of the tailB Span of the wingAR Aspect Ratio of the wingC Mean Aerodynamic chord

Cr Length of the root chordCt Length of the tip chordCm Pitching moment co efficientCl Lift co efficientCd Drag co efficientClαw Lift curve slope of the wingCn Yawing moment coefficientCdo Parasite drag co efficientCdi Induced Drag co efficientD DragE Oswald s efficiency factorE Endurance H Height of the aircraft from the groundL Liftlf Length of the fuselagedf Diameter of the fuselagen ult Ultimate load factorS Plan form area of the wing(t/c)max Maximum thickness to chord ratioVs Stalling velocityV VelocityVht Tail volume co efficientwf Width of the fuselageWto Gross take off weightWf Final weight Xc.g Position of centre of gravity of aircraftX ac Position of aerodynamic centre of aircraftε Downwashα Angle of attackρ Density of the airΛ1/2 Angle of sweep at half chord

Nomenclature: