performance for students

8/13/2019 Performance for Students

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SMFSMF 45124512AIRCRAFT DESIGN IAIRCRAFT DESIGN I

PART 3:AIRCRAFT PERFORMANCEPART 3:AIRCRAFT PERFORMANCE

6 Basic Mission Se ments

Takeoff Climb Cruise Loiter Descend Land

The performance analysis SHOULD cover at least:

.

2. Power required

3. Power available

4. Rate of climb

5. Maximum velocity and maximum rate of climb

6. Absolute & service ceilings

7. Range & Endurance8. Take-off performance

9. Landing performance

10.Turning flight

11.V-n diagram

Jabatan Kejuruteraan AeronautikFakulti Kejuruteraan Mekanikal

Universiti Teknologi Malaysia1


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AIRCRAFT PERFORMANCE

REMARKS:

As this is a design class not a theoretical class, the lecturesand notes that are going to be delivered are only served as abasic guidance. Students should use knowledge and skill from

aircraft design project.




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The complete drag coefficient of aircraft is:

.[1]

eAR

CCC LeDD

2

, +=

where CL = Total lift coefficient, including the small contributions from the horizontal tail and fuselage

CD,e

= Parasite drag coefficient, which contains not only the profile drag of the wing, but also the

friction and pressure drag of the tail surfaces, fuselage, engine nacelles, landing gear and

CD,e can be presented as :

CD,e = CD,o + r CL2

where CD,o = Parasite drag coefficient at zero liftr = An empirically determined constant




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Thus Eq. 1 can be rewritten as:

. 221

CrCC ++= ,

eAR where e = Span Efficiency Factor

Now we redefine e such that it also includes the effect of the variation of parasite drag with lift, let Eq. 2 becomes:

eAR

C

CC L

oDD

2

, += .[3]

where e which is now include the effect ofr. Now e is known asOswald Efficiency Factor(e = 1 for elliptical wing, the

others are normally between 0.80 to 0.95).

Equation [3] can also be rewritten as:2

LoDD CCC += .[4]

Therefore two parameters that students should determine:

1. Parasite drag coefficient at zero lift, CD,o2. Oswald Efficiency Factor, e




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Before estimating the aircraft performance, aircrafts drag polar must be determined first. Such a plot of CD Versus CL is

called a drag polar. A drag polar curve is essential to the design process as much of the basic aerodynamics of an

airplane is reflected in the drag polar.




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Normally the airfoil of the wing has a positive camber. That means when CL = 0, has a negative value. Atthis condition, the airplane is slightly pitched down and therefore, the corresponding drag coefficient is not

the minimum:

CD,o

> CDmin

The minimum drag coefficient occurs when the airplane ismore aligned with the relative wind.




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Thrust Require, TR

Consider an airplane in steady and level flight at a given altitude and a given velocity. Forces

T = D = qSCD [5]

W = L = qSCL [6]

Dividing Eq. 5 by Eq. 6 :

L

D

SCq

SCq

W

T

=

L

D

C

C

W

T=

Thus the thrust required for an airplane to fly at a given velocity in level, unaccelerated flight is:

DL

W

C

WCT

L

DR

/== .[7]




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AIRCRAFT PERFORMANCE ..

And knowing that :

The total dra = Zero-lift dra + Dra due to lift

TR = D = qSCD = qS(CD,o + CD,i)In other word,

= - + -

.[8]

Zero-lift TR = Thrust required to balance zero-lift drag

Lift-induced TR = Thrust required to balance drag due to lift




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..

At minimum TR, CD,o = CD,iero- rag = rag ue o

This yields an interesting aerodynamic result that at minimum thrust required, zero-lift dragequals drag due to lift.

Exercise:

Given an airplane with the following characteristics:Win s an = 35.8 ft

Wing Area = 174 ft2

Normal gross weight = 2950 Ib

Parasite drag coefficient, CD,o= 0.025

Oswald efficiency factor, e = 0.8

a cu ate Rat t e g t spee o t s(Assume the airplane is flying in level flight wi th air density, 0.002377 slugs/ft3 & gravitational acceleration, g=3.28 ft/s2)




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Power Required, PR

Power = Ener / Time

= (Force x Distance) / Time

= Force x (Distance/Time)

Power = FV

ons er an a rp ane n eve , unacce era e g a a g ven a u e an w ve oc y . e power requ re :

PR = TR V

But as TR = D (for an unaccelerated flight)

PR = qS ( CD,o + CD,i) V

Or in other word,

R - -




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..

1

Remarks:

iDoD ,, 3=1. At minimum power required,

o e: ease g-ou e reason w y s a so

2. The maximum flight velocity is determined by the intersection of the maximum PA and the PR curves (for a propeller-

, .


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..

1 hp = 550 ft .Ib/s = 746 W




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..

The propeller efficiency is depending on type of propeller used and the advance ratio. The

following diagram depicts an example for three-bladed propeller with Clark-Y sections.

An aircraft wi th 2 reciprocating engines propeller, fl ies at 238 mile/hr. The propeller is a three-

bladed propeller with Clark Y sections w ith a diameter of 6.27 ft. If each engine produce 285 hp at

2000 rpm, calculate the horsepower generated by the propeller if the blade angle is 45 deg?




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..




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..




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..

And for the maximum R/C:

Question :

As alt itude increases, the excess power wi ll be the same, or changing to become bigger or

smaller?




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At this case , you should be at enough high altitude!!!




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Effect of altitude on PA_max, PRand Vmax(Propeller-driven airplane)




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Jabatan Kejuruteraan Aeronautik

Fakulti Kejuruteraan Mekanikal



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..





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2/3

C

Breguet Endurance Formula (for reciprocating engine, propeller-driven airplane)

12 = o

D

WWSCc

E

where Ein seconds.

To maximize the endurance, we want :

1.The largest possible propeller efficiency,

. ,

3.The highest fuel weight Wf

4.Flight at maximum CL3/2/CD. This confirms our argument that for maximum endurance, we must fly at maximum CL

3/2/CD

5.Flight at sea levelbecause is the largest at sea level.

It is interesting to note that endurance depends on altitude, whereas range is independent of altitude.





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Exercise:

Estimatethemaximumrangeandmaximumenduranceforapropellerdrivenairplaneif:

Wo =2950Ib c=2.27x107 ft1

Wf =367

Ib S

=174

ft2

= 0.8





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The running length along the ground required by an airplane, starting from zero velocity to gain flight

speed and lift from the ground is defined as theground roll, orliftoffdistance, sLG





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..

44.1 2

LO

Ws

=

For the ground roll,

7.0max LOVrL

To ensure a margin of safety during takeoff, the liftoff velocity is typically 20 percent higher than the stalling velocity. Hence;

max

22.12.1

L

stallLOSC

WVV

==

, ,

(measured along the ground) to clear a 35-ft height (for jet-powered civilian transports) or a 50-ft height (for all other airplanes).





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Landing Performance

To minimize the distance required to come to a complete stop, the pilot needs to decrease the thrust to zero at touchdown.

, .

D -r(W L) = m dV/dt

Landing ground roll,

( )TVrL

LLWDSCg

Ws

7.0max

2

][

69.1

+=

To maintain a factor of safety,

VT = 1.3 Vstall

where VT = Touchdown velocity





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..

However some aircrafts utilize thrust reversal during the landing ground roll. Thus :

- R - r

And then the landing ground roll becomes :

69.1 2W

( ) }][{ 7.0max TVrRLL

LWDTSCg ++

Exercise:

Estimate the landing ground roll distance at sea level for this aircraft. No thrust reversal is

used, however, spoilers are employed such that L = 0. The spoilers increase the zero lift drag

coefficient b 10 ercent. The fuel tanks are essentiall em t , so ne lect the fuel wei ht,

take W1= 12352 Ib. The maximum lift coefficient, with flaps fully employed at touchdown, is2.5 .

GivenC =0.02, =32.2 t/s2, =0.002377slu / t3,S=318 t2and =0.4Jabatan Kejuruteraan Aeronautik


Universiti Teknologi Malaysia

,

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Turning Flight

Lets consider curved flight paths. A level turn is illustrated in Figure 1 below.

Figure 1. An airplane in a level turn



Universiti Teknologi Malaysia

e w ngs o e a rp ane are an e roug ang e , ence e vec or s nc ne a ang e o e ver ca .

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The bank angle and the lift L are such that the component of the lift in the vertical direction exactlyequals to the weight: L cos = W

And therefore the air lane maintains a constant altitude movin in the same horizontal lane.

Turning Flight (Cont..)

However, the resultant ofL and W leads to a resultant force Fr, which acts in the horizontal plane.

This resultant force is perpendicular to the flight path, causing the airplane to turn in a circular path

with a radius of curvature equal to R.

From the force diagram in Figure 1, the magnitude of the resultant force is:

Introducing a new term, the load factor n, defined as:

The load factor is usually quoted in terms of gs , for example an airplane with lift equal to 5 times

the weight, is said to be experiencing a load factor of 5 gs. Hence Fr can be rewritten as:





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urn ng g on ..

The airplane is moving in a circular path at velocity V. Therefore the radial acceleration is given

by V2/R. From Newtons second law:

,

The angular velocity, denoted by

is called the turn rate and is given by V/R

,

Thus to obtain both a small turn radius and a large turn rate, we want:


Fakulti Kejuruteraan MekanikalUniversiti Teknologi Malaysia

. .

Thelowest possible velocity

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AIRCRAFT PERFORMANCEV-n Diagram (Cont)

The V-n diagram shown in the previous slides is for maneuver envelope. Practicallywe must consider as well the extreme condition i.e. the gust envelope. Therefore

students are required to plot :

.

2. Gust Envelope

3. Combined Envelope

Please refer FAR 23_ Flight Loads for further detai ls.



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END OF PERFORM NCE P RTNotes:

t i erent a titu es, i erent grap swill be obtained. Graphs at cruisingaltitude and sea level are compulsory in

student report. Use the STANDARD airens ty or respect ve a t tu e.

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