Prediction and Testing document

8/10/2019 Prediction and Testing document

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Analyzing, Predictingand Testing the durationvarious paper airplanemodels will stay in theair.

Racer King Fisher 526

Racer 524 Blue Jay

Canard

By: Yana Charoenboonvivat

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Contents

Table of ContentsINTR!"CTIN..................................................................................................................#ANA$%&IN' RAC(R )*+ IN' -I/(R.................................................................................#ANA$%&IN' RAC(R )*0 $"( 2A%........................................................................................3ANA$%&IN' CANAR!........................................................................................................1#CNC$"IN - ANA$%I...............................................................................................13PR(!ICTIN.....................................................................................................................14T(TIN' AN! R("$T....................................................................................................*5CNC$"IN A(! N PR(!ICTIN AN! T(TIN' R("$T.........................................*#T(6P$AT( - 7N PAP(R AIRP$AN( 6!($ !(I'N......................................................*0T(TIN' - 7N8!(I'N(! PAP(R AIRP$AN( 6!($, R("$T AN! CNC$"IN -T(TIN'...........................................................................................................................*)

INTRODUCTIONIn this document, the Racer )*+ ing -isher, Racer )*0 lue 2ay and Canard paperairplane model plane designs will 9e analyzed according to their wing type, dihedral

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angle, !C "ean !erodyna#i$ Chord%, aspe$t ratio, s&rfa$e area of thehori'ontal stabili'erand s&rfa$e area of the verti$al stabili'erto predict which o:the three paper airplane models will stay in the air :or the longest duration. To testagainst the listed aspects, e;uations and :ormulas which were derived 9y scientists will9e used< these e;uations were ta=en :rom sources such as 9oo=s and we9sites. The three

model paper airplane designs will then 9e created and tested to o9serve how long theystay in the air and conclude i: it matches the prediction. ased on the analysis, predictionand testing completed, a paper airplane model which aims to stay in the air longer thanthe three paper airplane models analyzed>tested will 9e designed, created and tested tosee i: it does so. The template as well as the result o: testing o: the designed paperairplane model will also 9e included in this document.

!naly'ing to see whi$h paper glider will stay in the airlongest:

!N!(Y)IN* R!C+R -. /IN* 0I12+R

34ing type

a? wept89ac= wings

Produces less drag

5Dihedral angle

0ig&re 6

ta9ility and !ihedral angle

a? Racer )*+ ing8-isher has a dihedral angle o: 15@see Bgure 1?

7ing position and suita9le dihedral angle

9? 7ing position o: Racer )*+ ing -isher /igh wing see Bgure 1?

c? uita9le dihedral angle :or high wing )@ 8 15@

d? 15@see 5a? is in the range o: )@ 8 15@

D The dihedral angle is in the suita9le range

#

15 15


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7 !C "ean !erodyna#i$ Chord% and Center of gravity

0ig&re -

6AC

a? "sing the :ormula to Bnd 6AC length

i? rc Root Chord rc?0.)cmsee Bgure *?ii? t Taper Ratio t? Tip Chord E Root Chord?*.)cm>0.)cmiii? 6AC rc F *># F 1 G t G t*? E 1 G t??

9? u9stituteH 6AC0.)cm F *># F 1G*.)>0.)?G*.)>0.)? *?E1G*.)>0.)??89.$#rounded to #s.:?

Centre o: gravity

c? "sing the ruleH Center o: gravity must 9e at )5 o: the 6AC :rom the leading edge?:or 9est long duration Jight

i? )5 o: 6AC)5>155 F #.+5cm1.3cm

0ig&re 8

ii? Center o: gravity is not at )5 o: the 6AC :rom the leading edge see Bgure #?

DThe center o: gravity is notat the 9est location :or the 9est long durationJight.

0

$eading edge

Ti chord*.)c

Root

0.)cm

Centre o: gravity that is1.3cm :rom leading

Actual center o:gravity


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;!spe$t ratio

0ig&re < $ength o: wing span

a? $ength o: wing span :or Racer )*+ ing Bsher6.9$# ee Bgure 0?

7ing area

9? ne side o: the wing AC! see Bgure 0?

c? AC! :orm a trapezium 9ecause A>>!C

i? Area o: trapezium AG!C F height

d? u9stitute into c i?H Area o: trapezium0.)cmG*.)cm F 3.5cm *3cm*

e? ince A is the center line, trapezium AC!trapezium (-A

D The wing area* F the area o: trapezium AC! * F *3cm* .$#-

:? "sing :ormulaH Aspect ratio$ength o: wing span?*

i? u9stitute into :?H 1+cm?* *)+cm*


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>1&rfa$e area of the hori'ontal stabili'er

0ig&re

ur:ace area o: the horizontal sta9ilizer

a? ne side o: horizontal sta9ilizerAC! see Bgure )?

9? AC! :orm a trapezium 9ecause A>>!C

c? Area o: trapezium AG!C F height #cmG*cm F #.)cm3.K)cm*

d? ince A is the center line, trapezium AC!trapezium (-A

D The horizontal sta9ilizer area* F the area o: trapezium AC! * F

3.K)cm*:rom >c? 6=9$#-

est sur:ace are o: the horizontal sta9ilizer :or long duration Jight

e? "sing the :ormulaH

est horizontal sur:ace area :or long duration Jight5.+ F t

6ain wing sur:ace area )+cm* :rom Le?

tChord length or 6AC :or any wing shape not rectangular#.+5cm:rom 79?

M/!istance :rom center o: gravity to horizontal sta9ilizer15cmmeasured?

i? u9stitute into e?H 5.+ )+cm*F #.+5cm 6-96$#-rounded to # s.:?

1K.)cm*actual area o: horizontal sta9ilizer8:rom >d?? 1*.1cm* calculated 9est area :orhorizontal sta9ilizer :or long duration Jight8:rom >e i??

DThe horizontal sta9ilizer sur:ace area is not the 9est :or long duration Jight

A9solute diOerence 9etween actual area o: horizontal sta9ilizer and calculated

9est area :or horizontal sta9ilizer :or long duration Jight.

a? "sing :ormulaH l calculated 9est area :or horizontal sta9ilizer :or long duration Jight

8Actual area o: horizontal sta9ilizer l

+

A

-

(

#.)c

*cm

#cm

!

C

**

M/

15c


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i? u9stitute into a?H l 1K.)cm*:rom >d?81*.1cm* :rom >e i?? l 9>!C

c?Area o: trapezium AG!C F height 5.4cmG1.+cm F 1.)cm1.3K)cm*

d? ince trapezium AC!trapezium (-'/ :rom ?a?

D The vertical sta9ilizer sur:ace area* F the area o: trapezium AC! * F

1.3K)cm*:rom?c? 89=$#-

est sur:ace area o: the ertical sta9ilizer


est vertical sta9ilizer areaslightly more than 5.5) F 9

6ain wing sur:ace area)+cm*

:rom Le?

96ain wing span1+cm:rom ;a?

Mv!istance :rom center o: gravity to vertical sta9ilizer11cmmeasured?

i? u9stitute into e?H 5.5) )+cm* F 1+cm


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:? "sing :ormulaH l calculated 9est area :or vertical sta9ilizer :or long 8Actual area o:vertical sta9ilizer l

i? u9stitute into :?H l 0.5Kcm*:rom ?d i??8#.K)cm* ?d? l 98-$#-

!N!(Y)IN* R!C+R -< B(U+ @!Y34ing type

a? Tapered wings

6ore li=ely to stall $ess drag than rectangular wings

5Dihedral angle

0ig&re =

ta9ility and !ihedral angle

a? Racer )*0 lue 2ay has a dihedral angle o: 1)@see Bgure K?

7ing position and suita9le dihedral angle

9? 7ing position o: Racer )*0 lue 2ay /igh wing see Bgure K ?

c? uita9le dihedral angle :or high wing )@ 8 15@

d? 1)@see 5a? is notin the range o: )@ 8 15@

D The dihedral angle is notin the suita9le range

3

1) 1)


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0ig&re A

6AC

a? "sing the :ormula to Bnd 6AC length

i? rc Root Chord rc?)cmsee Bgure 3?ii? t Taper Ratio t? Tip Chord E Root Chord?*.5cm>).5cm5.0iii? 6AC rc F *># F 1 G t G t *? E 1 G t??

9? u9stituteH 6AC)cm F *># F 1G5.0G5.0?*?E1G5.0?89=6$#rounded to # s.:?

Center o: gravity

c? "sing the ruleH Center o: gravity must 9e at )5 o: the 6AC :rom the leading edge?:or 9est long duration Jight

i? )5 o: 6AC)5>155 F #.K1cm1.3+rounded to #s.:?

0ig&re

ii? Center o: gravity is not at )5 o: the 6AC :rom the leading edge see Bgure 4?


4

$eading

Root Ti chord*cm

)cm

Centre o: gravity that is1.3+ cm :rom leading



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;!spe$t ratio

0ig&re 6 $ength o: wing span

a? $ength o: wing span :or Racer )*0 lue 2ay-$#see Bgure 15?

7ing area

9? ne side o: the wingAC! see Bgure 15?

c? AC! :orm a trapezium 9ecause A>>!C

i? Area o: trapezium AG!C F height

d? u9stitute into c i?H )cmG*cm F 15cm8$#-

e? ince A is the center line, trapezium AC!trapezium (-A

D The wing area* F the area o: trapezium AC! * F #)cm* =$#-


i? u9stitute into :?H *5cm?* 055cm* 9=6rounded to # s.:?

K5cm* K5cm*

15

A

7ing span

-

(

15cm

*cm)cm

C

!

*

*

7ing area


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0ig&re 66


a? ne side o: horizontal sta9ilizerAC! see Bgure 11?

9? AC! :orm a trapezium 9ecause A>>!C

c? Area o: trapezium AG!C F height 0cmG*cm F ).*)cm1).K)cm*

d? ince A is the center line, trapezium AC!trapezium (-A

D The horizontal sta9ilizer area* F the area o: trapezium AC! * F1).K)cm*:rom >c? 869$#-

est sur:ace are o: the horizontal sta9ilizer :or long duration Jight


est horizontal sur:ace area :or long duration Jight5.+ F t

6ain wing sur:ace area K5cm* :rom Le?

tChord length or 6AC :or any wing shape not rectangular#.K1cm:rom 79?

M/!istance :rom center o: gravity to horizontal sta9ilizer1#cmmeasured?

i? u9stitute into e?H 5.+ K5cm*F #.K1cm 6-9$#-rounded to # s.:?

#1.)cm*actual area o: horizontal sta9ilizer8:rom >d?? 1*.5cm* calculated 9est area :orhorizontal sta9ilizer :or long duration Jight8:rom >e i??

DThe horizontal sta9ilizer sur:ace area is not the 9est :or long duration Jight

A9solute diOerence 9etween actual area o: horizontal sta9ilizer and calculated

9est area :or horizontal sta9ilizer :or long duration Jight.

11

A

*cm

0cm

).*)c

-

( !

C

**

M/

1#c


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:? "sing :ormulaH l calculated 9est area :or horizontal sta9ilizer :or long duration Jight


i? u9stitute into :?H l #1.)cm*:rom >d?81*.5cm* >e i?? l 69$#-

?1&rfa$e area of verti$al stabili'er

0ig&re 6-

ur:ace area o: the ertical sta9ilizer

a? ertical sta9ilizer AC! see Bgure 1*?

9? AC! :orm a trapezium 9ecause A!>>C

c?

Area o: trapezium A!GC F height

i? u9stitute into c?H 1.)cmG0.)cm F #.)cm15.)cm*

D The vertical sta9ilizer sur:ace area 69$#-


d? "sing the :ormulaH


6ain wing sur:ace areaK5cm* :rom Le?

96ain wing span*5cm:rom ;a?


i? u9stitute into e?H 5.5) K5cm* F *5cm .98.$#-rounded to # s.:?

15.)cm*actual area o: vertical sta9ilizer8:rom ?c i?? is slightly more than+.#+cm*calculated 9est area :or the vertical sta9ilizer8:rom ?d i??

DThe vertical sta9ilizer sur:ace area is the 9est

1*

A

#.)c

1.)c

0.)c

!

C

*

*

Mv

1


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0ig&re 6155 F #.#1cm1.++rounded to #s.:?

0ig&re 6

ii? Center o: gravity is not at )5 o: the 6AC :rom the leading edge see Bgure1)?


10

$eading

0.5c

Ti chord*.)c

Root

Centre o: gravity that is1.++cm :rom leading edge



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;!spe$t ratio

0ig&re 6.

$ength o: wing span

a? $ength o: wing span :or Racer )*0 lue 2ay6=$#see Bgure 1+?

7ing area

9? ne side o: the wingA!(-'A see Bgure 1+?

c? AC( :orms a trapezium and C(! :orms a right angle triangle

i? AC( :orm a trapezium 9ecause A>>C(

ii? Area o: trapezium AC(AGC( F height

iii? u9stitute into c ii?H 0cmG*.)cm F 3cm-.$#-

iv? Area o: right angle triangle C(! ase F /eight C! F (!

v? u9stitute into c iv?H 5.) F *.#9=$#-

d? AC(GC(!A!( see Bgure 1+?

DThe area o: A!(AC(GC(!*+cm*:rom ;c iii??G5.)K)cm*:rom ;c v??

-.9=$#-

e? ince A is the center line, A!(-'A see Bgure 1+?

D The wing area* F the area o: A!( * F *+.)K)cm* 896$#-


i? u9stitute into :?H 1Kcm?* *34cm* 9


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)#.1)cm* )#.1)cm*


0ig&re 6=

QThe horizontal sta9ilizer :or the canard is its :ront wing


a? Canard horizontal sta9ilizer emi8circle AC see Bgure 1K?

9? Area o: a semicircle r*

i? u9stitute into 9?H #?*4 6


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:? "sing :ormulaH l calculated 9est area :or horizontal sta9ilizer :or long duration Jight


i? u9stitute into :?H l 1).1cm*:rom >c i??810.1cm* >9?? l 6$#-


0ig&re 6A

ur:ace area o: the ertical sta9ilizer

a? ertical sta9ilizerA!(- see Bgure 13?

9? AC- :orms a trapezium and -C!( :orms a rectangle

i? AC- :orms a trapezium 9ecause A>>-C

ii? Area o: trapezium AC-AGC- F height

iii? u9stitute into 9 ii?H 1.)cmG)cm F #cm9=$#-

iv? Area o: rectangle -C!($ength F 7idth-C F C!

v? u9stitute into c iv?H )cm F 1.)cm =9$#-

c? AC-G-C!(A!(- see Bgure 13?

DThe area o: A!(-AC-GC(!4.K)cm*:rom ?9 iii??GK.)5cm*:rom ?9v??6=9-$#-


d? "sing the :ormulaH


6ain wing sur:ace area)#.1)cm* :rom Le?

96ain wing span1Kcm:rom ;a?


1K

(-

#.cm

)cm

1.)c'

1.)c

!C

A

*

*

Mv


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i? u9stitute into e?H 5.5) )#.1)cm* F 1Kcm 9.$#-Rounded to # s.:?

1K.*)cm*actual area o: vertical sta9ilizer8:rom ?c? is notslightlymore than).+)cm*calculated 9est area :or the vertical sta9ilizer8:rom ?d i??, it is a lot more.

DThe vertical sta9ilizer sur:ace area is the not 9est

A9solute diOerence 9etween actual area o: the vertical sta9ilizer and calculated

9est area :or the vertical sta9ilizer

e? "sing :ormulaH l calculated 9est area :or vertical sta9ilizer :or long 8Actual area o:vertical sta9ilizer l

i? u9stitute into e?H l ).+)cm*:rom ?d i??81K.*)cm* ?c? l 669.$#-

CONC(U1ION O0 !N!(Y1I1(ach design is ran=ed 18# :or each criteria 9ased on the mathematical>physics prediction, 1 9eingthe 9est and # 9eing the worst. The design with the lowest sum o: ran= will 9e predicted to stay in

the air the longest.

34ing type

Design 4ing type Ran "68%Racer ing8-isher )*+ wept89ac= *Racer lue 2ay )*0 Tapered 1Canard Tapered 15Dihedral angle

1tability

Design Dihedral angle "E% Ran "68%

Racer ing8-isher )*+ 15 #

Racer lue 2ay )*0 1) 1

Canard 1# *

FThe more the dihedral, the higher the ran=ing

1&itable dihedral angle for wing position

Design In s&itable range for wing positionG"YesHNo%

Ran "6-%

Racer ing8-isher )*+ %es 1Racer lue 2ay )*0 No #Canard No #FI: the dihedral is in the suita9le range, the higher the ran=


Design Is the $enter of gravity at of the !Cfro# the leading edgeG "YesHNo%

Ran "68%

Racer ing8-isher )*+ No #Racer lue 2ay )*0 No #Canard No #

FI: the center o: gravity is at )5 o: the 6AC :rom the leading edge, the higher the ran=

;!spe$t ratio

Design !spe$t ratio Ran "68%Racer ing8-isher )*+ 0.)K #

Racer lue 2ay )*0 ).K1 1Canard ).00 *

QThe higher the aspect ratio, the higher the ran=

13

3c


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Design Is the a$t&al s&rfa$e areathe sa#e as the $al$&latedbest s&rfa$e area of thehori'ontal stabili'er for

long d&ration JightG"YesHNo%

"If KnoL% !bsol&tediMeren$e between a$t&als&rfa$e area and the$al$&lated best s&rfa$e

area for long d&rationJight "$#-%

Ran "68%

Racer ing8-isher)*+

No ).0 *

Racer lue 2ay )*0 No 14.) #Canard No 1.5 1QThe lower the diOerence 9etween the a9solute diOerence 9etween actual sur:ace area and thecalculated 9est sur:ace area :or long duration Jight, the higher the ran=ing

QR the highest ran=ing 1? i: the actual sur:ace area is the same as the calculated 9est sur:ace area o:the horizontal sta9ilizer :or long duration Jight


Design Is the s&rfa$e areaslightly more thanthe $al$&lated bests&rfa$e area for theverti$al stabili'er"YesHNo%

"If KnoL% !bsol&tediMeren$e betweena$t&al s&rfa$e areaand the $al$&latedbest s&rfa$e areafor the verti$alstabili'er "$#-%

Ran "68%

Racer ing8-isher )*+ No 5.#* *Racer lue 2ay )*0 %es 8 1Canard No 11.+ #

QThe lower the diOerence 9etween the a9solute diOerence 9etween the actual sur:ace area and thecalculated 9est sur:ace area :or the vertical sta9ilizer, the higher the ran=

QR, the highest ran= 1? i: the actual sur:ace area is slightly more than the calculated 9est sur:acearea :or the vertical sta9ilizer.

Table to show the s of raning

R+DICTIONased on the results o: the analysis, I can ma=e a prediction>conecture thatH

"The Racer Blue Jay 524 will stay in the air for the longest duration

followed by the Canard then the Racer King-isher 52!"

14

Design 1 of raningRacer ing8-isher )*+ 1+Racer lue 2ay )*0 1#Canard 1)


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45S

F cm

T+1TIN* !ND R+1U(T1(;uipmentH Protractor, #5cm ruler, 7ooden rod, Ru99er catapult, Racer )*+ ing Bsher, Canard, Racer )*0 lue2ay, topwatch.

Controlled varia9les

Controlledvariable

2ow it will be $ontrolled

(nvironmentalcondition

(nsuring the same environmental condition each timedescription o: what the environmental condition is li=e?

Angle glider isreleased at

Released at an angle o: 0)S or 45S:or the Racer )*+ ing-isher? using a protractor to measure the angle

The :orce theglider is launchedwith

"sing a ru99er catapult to release the glider :rom the samestretched length each time the most the ru99er 9and canstretch?

R!4 D!T!Ra$er -. /ing 0isher

Controlled varia9le chec=H

Controlled variable Des$ription(nvironmental condition unny, slight windAngle glider is released at S? 45see diagram 1?8 angle it should 9e

released at :or per:ormance at its :ullpotential.tretched length o: the catapultthat the glider is released with

The most the ru99er 9and canstretch see diagram 1?

Diagra# 6

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Raw data ta9le to show how long Racer )*+ ing -isher can stay in the air:or ) trials seconds?

Trial 6 Trial - Trial8

Trial

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Prediction and Testing document