Solutions to the problems:

Task 1: Please refer to spreadsheet, all angles and extra calculations and plottings are ther. ther. Task 2: 2.1 Why do we plot ! p "negati#e$ instead of ! p "positi#e$ upward%

&n the formula of the pressur p ressure e coe'cient:

C p =

p − p∞ 0.5 ρ V ∞

2

( you can see that

when p is smaller than p )( !p will be negati#e* So the plot will also be negati#e* +ence( they use ! p so that the cur#e will be a positi#e cur#e* ,his way you can compare it better with the downward ! p cur#e*

-*-$ a$ the mach number decreases from from .*./0 to .*.0* 2ccording 2ccording to Bernoulli3s law 1

2

1

2

P1+ ρV ρ V 1= P 2+ ρ V 2 2

2

P1 doubles when 4 - 5 416-* b$ 2t 05.* 05.*7( 7( the the 8ow 8ow bec become omes s comp compre ress ssib ible le and and the the follo followi wing ng e9ua e9uati tion on holds: −γ /( γ − 1)

P γ −1 2 =(1 + M ) Pt 2

Which means P is in#ersely proportional to 0-( so the pressure drops 9uadratically with the speed*

2.3) es( es( there is a relation relation between the thic;ness and the pressure pressure distribution of the the airfoil*

2.4: What is the highest value of p that is to !e found in the test and "h#$ %o" do "e call this point$ =ormules used: !p 5 "P>Peff )/(0,5*ρ∞*V∞2) Peff =p∞+(85/135)*(Patm-p∞) Peff is the corrected ip!t press!re "eca!se the ip!t press!re meas!red ma# ot "e acc!rate eo!$h% & tas' 1 #o! ca see that the maim!m p is at a a$e of attac' of 12%5 de$rees% (.(?/@7A??-$ ,he point at maimum !p is called the stagnation point* ,his is when !p 5 1* &n this case it is about 1-*A degrees* 2t a higher angle of attac;( the !p drops again* ,he reason for this is because the pressure under the airfoil is higher than the pressure on the airfoil( because of the diCrence between those pressures( lift is generated* 2t the maimum !p( the wind is in a 8ow that is called attached 8ow* When the angle of attac; is higher dan it would be on the maimum !p it creates a saperate 8ow* Because of this seperate 8ow the pressure under the airfoil drops* ,herefore there is no more lift generated

T&'( 3 3.1: please refer to the spreadsheet attached 3.2 Plot the pressure distribution from the pro#ided data in ecel* Dpper and lower surface ha#e to be plotted in the same graph*

Pressure istri!ution 1*1 .*7 .*/ p

.*@

Dpper Surface

Lower Surface

.*. . >.*-

.*-

.*@

.*/

.*7

1

1*-

>.*@ >.*/ *+

Dse the ,rapeoid Fule to nd the lift coe'cient of the [email protected]@ aerofoil* ,he three column titles are gi#en to point you in the right direction*

pper surface x+c . .(..A.A .([email protected]@? .(.-7.([email protected]/1H

p .(??.? .(A7H11 .(-..H? >.(./7? >.(--?/H

'tep si-e .(..A.A .([email protected]@ .(.1H1 .(.1H?H .(.--1

&verage height .(H7?..(??A .(./[email protected] >.([email protected]/H7 >.(-H?/@

&rea covered .(..[email protected] .(..H17777 .(...?[email protected] >.(..-/H/H >.(../[email protected]

.(./7 .([email protected]@7 .([email protected]@ .(1A7-H .([email protected] .(-A/1 .(-H7A/ .(-?.(H1-7 .(@-.- .(@H. .(A-.?H .(AH1/7 .(/-1?/ .(/H1-H .(H1?..(H/@H? .(7.7@ .([email protected][email protected] .(77/@ .(?1?- .([email protected]? .(?/?H .(?7/-? .(??/A 1

>.(-?/1 >.(7/./ >.(@1-/ >.(@-1./ >.(@1H?>.(@.AA7 >.(7H.1 >.(A?1 >.(-7/? >.(-?AAH >.(-/[email protected] >.(--/?A >.(1?-1? >.(1A?A >.([email protected] >.([email protected] >.(.-7/7 .(.--? .(.7-./ .(1-1./ .(1A/[email protected] .([email protected] .(-1.-H .([email protected]A .(1//. .(??1A-

.(.-/17 .(.../ .(.H .(.H1 .([email protected] .([email protected]?A .([email protected]/ .([email protected]/ .([email protected]?A .(.A..H .(.A./H .(.A.H1 .(.A.-7 .([email protected]?1 .([email protected] .([email protected] .([email protected]AA .([email protected] .(.H.(.-7? .(.-H?/ .(.--A1 .(.1/A? .([email protected] .(..@H >1

>.(AH7A >.(?? >.(@1/7 >.(@[email protected]? >.(@11HA >.(?/-?A >.(H.AA >.(@7?A >.(1-1 >.(-H7.-A >.([email protected]H1A >.(-.?AH >.(1H.H >.(1[email protected] >.(.??-.A >.([email protected] .(..17.A .(.AH1HA .(1.1A/ .(17AA .(1H.HA .(1?H7A .(-1H1 .(1?A1? .(AH7HHA .(@?AH/

>.(..?/71>.(.1-..7/ >.([email protected]?/H/ >.(.1AAHA//@ >.(.1/AA/@/7 >.(.1H.-.7H >.(.1/?-1HHA >.(.1/-7/7/H >.(.1A-H7H/@ >.(.1?-.H1>.(.1-@?.? >.(.1./-H-?A >.(..7H.1?/ >.(../H.@@7 >.([email protected]H.? >.([email protected]?H7?7 H(7/.HHE>.A .(..-[email protected] .(..HH7..([email protected]/?1 .([email protected]HA1 .([email protected]@A/[email protected] .(../.A1H .([email protected]/ .(..-..7@? >.(@?AH/

o"er surface x+c . .(...-.(../A .(.17 .(.@/@ .(.AA??

p .(??.? .([email protected]/? >.(1--H >.(--1?7 >.(-HH- >.(11-/

'tep si-e .(...-.(../1 .(.11/A .(.1//@ .(.-1A .(.-A7

&verage height .(/H71 .(.7.H1 >.(1H-/-A >.([email protected]?/.A >.([email protected]@A >.(1?7

&rea covered .([email protected]17 .([email protected][email protected]>.(..-.11.71 >.([email protected]@-H >.(../-7-11 >.([email protected]

.(.71H? .(1117 .([email protected]/..([email protected] .(--A7A .(-H.7A .(17/.(/7/ .(@-.A .(@H-1 .(A-/AH .(AH?7.(/--? .(/7A .(H-A .(HH7H.(7-17H .(7/1-? .(7?/A .(?-H./ .(?A-A? .(?H-HH .([email protected] .(??/H 1

>.(-7@ >.(-7>.(-???A >.(-/?/7 >.(-//1 >.(-.AA>.(1H7/H >.(1A-A>.([email protected] >.(1.7.? >.(.7717 >.(.H-A >.(.AHAA >.([email protected]/.7 >.(.@H >.(.-/H>.(.1H1A >.(.11. >.(..-H.(...-.(..A1 >.(.. .(.1?? .(.AH/1 .(??1A-

.(.[email protected] .(.@1? .(.7.? .([email protected]@ .([email protected] .([email protected] .(.A..1 .(.A1H.(.A-7/ .(.A/ .(.A-A .([email protected] .(.A1./ .([email protected]? .([email protected]/H .([email protected]1A .(.[email protected](.A-1 .(..A/ .(.-AA .(.-.17 .([email protected]// .(..?-H .(.. >1

>.(-/.7 >.(1177A >.([email protected] >.(-A[email protected] >.(--1./A >.(1?-.?A >.(1/AA?A >.([email protected] >.(117?1A >.(.?71A >.(.7.-/A >.(./@?A >.(.A171A >.([email protected]@.A >.(..H-A >.(.-1?A >.([email protected]? >.(../7HA >.(..1-A .(..17/A .(...-AA .([email protected]/A .(.7HH .([email protected]/A .(@?AH/

>.([email protected]@ >.(.1.//@7 >.([email protected]/. >.(.1.A//-H>.([email protected]?-A >.(..?1H/H7 >.([email protected]/ >.([email protected]@ >.(../[email protected] >.(..A-/@[email protected] >.([email protected]@111 >.(..@.H?-H >.(..-/@A/[email protected] >.([email protected] >.([email protected]@H17 >.([email protected]/@?A >.([email protected] >.([email protected]/? >.(....[email protected](H/1AE>.A A([email protected]?E>./ .([email protected]?H .(...A??7 .(..1H1./@ >.(@?AH/

Step sie is the diCerence between the 6cn and 6cnI1

2#erage height 5

C pn+ C pn +1 2

2rea co#ered 5 step sie J area co#ered* Where !L is the lift coefficient( K is the angle of attac; and ! a is the aial force coefficient* &n 2nderson "-..7$ it is stated that for small angles of attac; "K AM$ you can assume that ! L ≈ !n*

∫ C

=∑ Area coveredlower=−0,12155

∫ C

=∑ Area covered upper=−0.66495

p ,l

p ,u

C l ≈ C n=∫ C p , l −∫ C p ,u = 0,543401

3.3 !alculate the lift coe'cient*

( ) ( )) ( ( ) ( )) ( ) ( ))−(¿¿)=[( )− ( ) ] −([( )− ( ) ] +[− ( )+ ( ) ] ( − ) ( ) =∫ ¿ 0.13

∫ 0

(

x x d 1− 0.84 c c

(

2

x 1−200 c

x c

x 0.42 c

1

x d c

2

+ ∫ −2.47 +2.63 x d x

1

x c

0

C p ,l

c

0,13

C p , u

200 x 3

x d c

3

c

0.13

0

c

x 2.47 c

x 1.315 c

2

1

1

0

1

∫¿

C l=C n=

0

,2SN @ O2!2 ..-. "Wind tunnel$

C l =0

.

α

DC l / dα C l

@*@HA/ 2bout 1* at 1H

max

C l =0

•

,he point where

•

,his is logical as it is a symmetric airfoil* DC l / dα is the gradient of the graph( which was calculated to be about

•

α

is when the graph crosses the ais* ,his is .*

@*@HA/ "calculations shown in the spreadsheet$ C l is the point where the graph stops increasing "its maimum$* We do max

not ha#e enough angles to determinate this accurately* +owe#er( we got while in the lab that the stall angle was about 1H>17 degrees* =rom this information( we linearied the

C l

max

to be around 1* at 1H degres*

+owe#er this is not accurate as the gradient actually starts decreasing before reaching the maimum point of the cur#e*

,2SN A

)

0.13

=1.453

A*1 O2!2 ..-. has a lift cur#e that is going through the origin( because this aerofoil is symmetrical( and symmetrical aerofoils "non>cambered$ ha#e ero lift at an angle of attac; of ero( whereas cambered aerofoils ma;e for a lower pressure at the top of the wing and thus creating a pressure diCerence* ,his results in a lift coe'cient at an angle of attac; of ero* A*When the angle of attac; gets too high( attached 8ow turns into separated 8ow on the upper surface of the aerofoil( which causes the pressure diCerence to drop signicantly and !L drops precipitously* 2t this stage( the airplane is in a stall*

A* ,he formula for !l( when the aircraft has a stationary( le#el 8ight( is m∗g 1 2

2 ρ V S * Gi#en is that S( 4 and m constants are when comparing 0ars to

Earth* ,he difference is thus g6( therefore the ratio is "gmars6mars$6 "gearth6earth$( which gi#es a ratio of *1 A*@ 2ccording to the ,hin 2erofoil ,heory the slope of the Lift cur#e !L( K 5 -Q*

/* 2t steady horiontal 8ight: Weight5Lift and Rrag5,hrust

05-*A ;g G5*H-m6s5.*1--AH? ;g6m 45Am6s S5.*HHm!L5 0JG6"*A4-JS$ !L51*@?

,2SN / Build the ecel sheet capable of calculating the total lift force in Oewton* See ecel sheet !alculate E using E9uation 1-* 1

A ellipse = a! 2

A 1 2

= ellipse

1 4

a!

A rectangular =a

"=

A rectangular A 1 2

ellipse

=

1 1 4

= 4

!

!

=or tas; H( 7 and ? see the ecel sheet* Teroen U Turian Bart and Louis Tin Vian U 0a Tonathas la'ta Loedy

-*1( *-( *( ,as; H( 7( ? -*-( ,as; A U / -*-( tas; A( tas; / ,as;1( ,as;@ -*@( and helped in all( assisting with data calculation and more

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