Prediction and Testing

Calculating which paper glider will stay in the air longest:

RACER 526 KING FISHER

①Wing typea)Swept-back wings

Produces less drag ②Dihedral angle

Figure 1 Stability and Dihedral angle

a)Racer 526 King-Fisher has a dihedral angle of 10◦(see figure 1) Wing position and suitable dihedral angle

b)Wing position of Racer 526 King Fisher= High wing(see figure 1)c)Suitable dihedral angle for high wing= 5◦ - 10◦d)10◦(see ②a) is in the range of 5◦ - 10◦

∴ The dihedral angle is in the suitable range

1

10◦10◦

③MAC(Mean Aerodynamic Chord)and Center of gravity

Figure 2 MAC

a)Using the formula to find MAC lengthi)rc = Root Chord=4.5cm(see figure 2)ii)t = Taper Ratio = (Tip Chord ÷ Root Chord)=2.5cm/4.5cmiii)MAC = rc x 2/3 x (( 1 + t + t2 ) ÷ ( 1 + t )) b) Substitute: MAC=4.5cm x 2/3 x ((1+(2.5/4.5))+(2.5/4.5)2)÷(1+(2.5/4.5))=3.60cm( rounded to 3 s.f)

Centre of gravity c) Using the rule: Center of gravity must be at 50% of the MAC(from the leading edge) for best long duration flight

i) 50% of MAC=50/100 x 3.60cm=1.8cm

Figure 3ii)Center of gravity is not at 50% of the MAC from the leading edge(see figure 3)

∴The center of gravity is not at the best location for the best long duration flight.

2

4.5cm

2.5cm

Root chord

Tip chord

Leading edge

Centre of gravity that is 1.8cm from leading edge of MAC.

Actual centre of gravity

④Aspect ratio

Figure 4 Length of wing span

a)Length of wing span for Racer 526 King fisher=16cm (See figure 4) Wing area

b) One side of the wing ABCD (see figure 4)c)ABCD form a trapezium because AB//DC

i)Area of trapezium=AB+DC x height d) Substitute into c(i): Area of trapezium=4.5cm+2.5cm x 8cm=28cm2e)Since AB is the center line, trapezium ABCD=trapezium EFBA

∴ The wing area=2 x the area of trapezium ABCD= 2 x 28cm2 = 56cm2f)Using formula: Aspect ratio=(Length of wing span)2

i) Substitute into f): (16cm)2= 256cm2= 4.57(rounded to 3 s.f) 56cm2 56cm2

3

Wing span= 16cm

4.5cm

B

C

D

2.5cm

E

F

8.0cm

2

2

A

Wing area

⑤Surface area of the horizontal stabilizer

Figure 5 Surface area of the horizontal stabilizer

a)One side of horizontal stabilizer=ABCD(see figure 5)b)ABCD form a trapezium because AB//DCc)Area of trapezium= AB+DC x height = 3.0cm+2.0cm x 3.5cm=8.75cm2d) Since AB is the center line, trapezium ABCD=trapezium EFBA

∴ The horizontal stabilizer area=2 x the area of trapezium ABCD= 2 x 8.75cm2(from ⑤c) = 17.5cm2 Best surface are of the horizontal stabilizer for long duration flight

e)Using the formula: Best horizontal surface area for long duration flight=0.6 S x tS=Main wing surface area= 56cm2 (from ④e)t=Chord length or MAC for any wing shape not rectangular=3.60cm(from ③b)ℓH=Distance from center of gravity to horizontal stabilizer=10cm(measured)

(i) Substitute into e): 0.6 56cm2 x 3.60cm = 12.1cm2(rounded to 3 s.f)17.5cm2(actual area of horizontal stabilizer-from ⑤d))≠12.1cm2(calculated best area for horizontal stabilizer for long duration flight-from ⑤e(i))

∴The horizontal stabilizer surface area is not the best for long duration flight Absolute difference between actual area of horizontal stabilizer and calculated best area for horizontal stabilizer for long duration flight.

a) Using formula: l calculated best area for horizontal stabilizer for long duration flight -Actual area of horizontal stabilizer l(i)Substitute into a): l 17.5cm2 (from ⑤d)-12.1cm2 (⑤e(i)) l =5.4cm2

4

A

BC

D

3.0cm2.0cm

3.5cm

E

F

2 2

ℓH

10cm

⑥Surface area of vertical stabilizer

Figure 6 Surface area of the Vertical stabilizer

a)Half of vertical stabilizer ABCD=EFGH(see figure 6)b)ABCD form a trapezium because AB//DCc) Area of trapezium= AB+DC x height = 0.9cm+1.6cm x 1.5cm=1.875cm2d) Since trapezium ABCD=trapezium EFGH(from ⑥a)

∴ The vertical stabilizer surface area=2 x the area of trapezium ABCD= 2 x 1.875cm2(from⑥ c) = 3.75cm2 Best surface area of the Vertical stabilizer

e)Using the formula:Best vertical stabilizer area=slightly more than 0.05 S x bS=Main wing surface area=56cm2 (from ④e)b=Main wing span=16cm(from ④a)ℓv=Distance from center of gravity to vertical stabilizer=11cm(measured)

(i) Substitute into e): 0.05 56cm2 x 16cm = 4.07cm23.75cm2(actual area of vertical stabilizer-from ⑥d)) is not slightly more than 4.07cm2(calculated best area for the vertical stabilizer-from ⑥e(i))

∴The vertical stabilizer surface area is not the best Absolute difference between actual area of the vertical stabilizer and calculated best area for the vertical stabilizer

f) Using formula: l calculated best area for vertical stabilizer for long -Actual area of vertical stabilizer l5

A

BC

D E

FG

H

2 2

1.6cm

0.9cm

1.5cm

ℓv

11

(i)Substitute into f): l 4.07cm2 (from ⑥d(i))-3.75cm2 (⑥d) l =0.32cm2


RACER 524 BLUE JAY

①Wing typea)Tapered wings

More likely to stall Less drag than rectangular wings

②Dihedral angle


a)Racer 524 Blue Jay has a dihedral angle of 15◦(see figure 7 ) Wing position and suitable dihedral angle

b)Wing position of Racer 524 Blue Jay= High wing(see figure 7 )c)Suitable dihedral angle for high wing= 5◦ - 10◦d)15◦(see ②a) is not in the range of 5◦ - 10◦

∴ The dihedral angle is not in the suitable range

6

15◦15◦


Figure 8 MAC

a)Using the formula to find MAC lengthi)rc = Root Chord=5.0cm(see figure 8)ii)t = Taper Ratio = (Tip Chord ÷ Root Chord)=2.0cm/5.0cm=0.4iii)MAC = rc x 2/3 x (( 1 + t + t2 ) ÷ ( 1 + t )) = b)Substitute: MAC=5.0cm x 2/3 x ((1+(0.4))+(0.4)2)÷(1+(0.4))=3.71cm( rounded to 3 s.f)

Center of gravity c) Using the rule: Center of gravity must be at 50% of the MAC(from the leading edge) for best long duration flight

i) 50% of MAC=50/100 x 3.71cm=1.86(rounded to 3s.f)


∴The center of gravity is not at the best location for the best long duration flight.

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Leading edge

5.0cm

2.0cm

Tip chordRoot chord

Centre of gravity that is 1.86 cm from leading edge of MAC.

Actual centre of gravity

④Aspect ratio


a)Length of wing span for Racer 524 Blue Jay=20.0cm(see figure 10) Wing area

b) One side of the wing=ABCD (see figure 10)c)ABCD form a trapezium because AB//DC

i) Area of trapezium=AB+DC x heightd) Substitute into c(i): 5.0cm+2.0cm x 10cm=35cm2e)Since AB is the center line, trapezium ABCD=trapezium EFBA

∴ The wing area=2 x the area of trapezium ABCD= 2 x 35cm2 = 70cm2f)Using formula: Aspect ratio=(Length of wing span)2

(i) Substitute into f): (20cm)2 = 400cm2= 5.71(rounded to 3 s.f) 70cm2 70cm2

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2

2

A

B

C

D5.0cm 2.0cm

10.0cm

E

F

Wing span= 20.0cm

Wing area


Figure 11 Surface area of the horizontal stabilizer

a)One side of horizontal stabilizer=ABCD (see figure 11)b)ABCD form a trapezium because AB//DCc)Area of trapezium= AB+DC x height = 4.00cm+2.00cm x 5.25cm=15.75cm2d) Since AB is the center line, trapezium ABCD=trapezium EFBA

∴ The horizontal stabilizer area=2 x the area of trapezium ABCD= 2 x 15.75cm2(from ⑤c) = 31.5cm2

Best surface are of the horizontal stabilizer for long duration flight e)Using the formula: Best horizontal surface area for long duration flight=0.6 S x tS=Main wing surface area= 70cm2 (from ④e)t=Chord length or MAC for any wing shape not rectangular=3.71cm(from ③b)ℓH=Distance from center of gravity to horizontal stabilizer=13cm(measured)

(i) Substitute into e): 0.6 70cm2 x 3.71cm = 12.0cm2(rounded to 3 s.f)31.5cm2(actual area of horizontal stabilizer-from ⑤d))≠12.0cm2(calculated best area for horizontal stabilizer for long duration flight-from ⑤e(i))


9

A

B C

DE

F

5.25cm

4.00cm

2.00cm

2 2

ℓH

13cm

f) Using formula: l calculated best area for horizontal stabilizer for long duration flight -Actual area of horizontal stabilizer l(i)Substitute into f): l 31.5cm2 (from ⑤d)-12.0cm2 (⑤e(i)) l =19.5cm2



a) Vertical stabilizer ABCD(see figure 12)b)ABCD form a trapezium because AD//BCc) Area of trapezium= AD+BC x height

(i) Substitute into c): 1.5cm+4.5cm x 3.5cm=10.5cm2∴ The vertical stabilizer surface area = 10.5cm2

Best surface area of the Vertical stabilizer d)Using the formula:Best vertical stabilizer area=slightly more than 0.05 S x bS=Main wing surface area=70cm2 (from ④e)b=Main wing span=20cm(from ④a)ℓv=Distance from center of gravity to vertical stabilizer=11cm(measured)

(i) Substitute into e): 0.05 70cm2 x 20cm = 6.36cm210.5cm2(actual area of vertical stabilizer-from ⑥c(i)) is slightly more than 6.36cm2(calculated best area for the vertical stabilizer-from ⑥d(i))

∴The vertical stabilizer surface area is the best 10

A

B

C

D

4.5cm

1.5cm

2

2

ℓv

11

3.5cm


CANARD

①Wing typea)Tapered wings

More likely to stall Less drag than rectangular wings

②Dihedral angle


a) Canard has a dihedral angle of 13◦(see figure 13) Wing position and suitable dihedral angle

b)Wing position of Canard= High wing(see figure 13)c)Suitable dihedral angle for high wing= 5◦ - 10◦d)13◦(see ②a) is not in the range of 5◦ - 10◦

∴ The dihedral angle is not in the suitable range11

13◦ 13◦


Figure 14 MAC

a)Using the formula to find MAC lengthi)rc = Root Chord=4.0cm(see figure 14)ii)t = Taper Ratio = (Tip Chord ÷ Root Chord)=2.5cm/4.0cm=0.625iii)MAC = rc x 2/3 x (( 1 + t + t2 ) ÷ ( 1 + t )) = b)Substitute: MAC=4.0cm x 2/3 x ((1+(0.625))+(0.625)2)÷(1+(0.625))=3.31cm( rounded to 3 s.f)

Center of gravity c) Using the rule: Center of gravity must be at 50% of the MAC(from the leading edge) for best long duration flight

i) 50% of MAC=50/100 x 3.31cm=1.66(rounded to 3s.f)


∴The center of gravity is not at the best location for the best long duration flight.12

Leading edge

Tip chordRoot chord

4.0cm

2.5cm

Actual centre of gravity Centre of gravity that is 1.66cm from leading edge of MAC.

④Aspect ratio


a)Length of wing span for Racer 524 Blue Jay=17cm(see figure 16) Wing area

b) One side of the wing=ABDE=FGBA (see figure 16)c)ABCE forms a trapezium and CED forms a right angle triangle

(i)ABCE form a trapezium because AB//CE(ii) Area of trapezium ABCE=AB+CE x height(iii)Substitute into c(ii): 4.0cm+2.5cm x 8cm=26.0cm2(iv)Area of right angle triangle CED=Base x Height= CD x ED(v) Substitute into c(iv): 0.5 x 2.3=0.575cm2

d)ABCE+CED=ABDE (see figure 16)∴The area of ABDE=ABCE+CED=26.0cm2(from ④c(iii))+0.575cm2(from

④c(v))=26.575cm2e)Since AB is the center line, ABDE=FGBA(see figure 16)

∴ The wing area=2 x the area of ABDE= 2 x 26.575.cm2 = 53.15cm2

13

A

2

2

B

C D

EF

G

Wing span= 17.0cm

2 2

4.0cm2.3cm2.5cm

0.5cm

8.0cm

2

f)Using formula: Aspect ratio=(Length of wing span)2 (i) Substitute into f): (17cm)2 = 289cm2= 5.44(rounded to 3 s.f)

53.15cm2 53.15cm2


Figure 17*The horizontal stabilizer for the canard is its front wing

Surface area of the horizontal stabilizer a)Canard horizontal stabilizer Semi-circle ABC(see figure 17)b) Area of a semicircle= r2

(i)Substitute into b): (3)2 =9=14.1(rounded to 3 s.f) Best surface are of the horizontal stabilizer for long duration flight

c)Using the formula: Best horizontal surface area for long duration flight=0.6 S x tS=Main wing surface area= 53.15cm2 (from ④e)t=Chord length or MAC for any wing shape not rectangular=3.31cm(from ③b)ℓH=Distance from center of gravity to horizontal stabilizer=7cm(measured)

(i) Substitute into c): 0.6 53.15cm2 x 3.31cm = 15.1cm2(rounded to 3 s.f)14.1cm2(actual area of horizontal stabilizer-from ⑤b(i))≠15.1cm2(calculated best area for horizontal stabilizer for long duration flight-from ⑤c(i))

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Wing area

A

B

C

2

r=3cm

r=3cm

2 2

ℓH

7cm


f) Using formula: l calculated best area for horizontal stabilizer for long duration flight -Actual area of horizontal stabilizer l(i)Substitute into f): l 15.1cm2 (from ⑤c(i))-14.1cm2 (⑤b)) l =1cm2



a) Vertical stabilizer=ABDEF(see figure 18)b)ABCF forms a trapezium and FCDE forms a rectangle

(i)ABCF forms a trapezium because AB//FC(ii)Area of trapezium ABCF=AB+CF x height(iii)Substitute into b(ii): 1.5cm+5.0cm x 3.0cm=9.75cm2(iv)Area of rectangle FCDE=Length x Width=FC x CD (v) Substitute into c(iv): 5cm x 1.5cm =7.50cm2

c)ABCF+FCDE=ABDEF (see figure 18)∴The area of ABDEF=ABCF+CED=9.75cm2(from ⑥b(iii))+7.50cm2(from

⑥b(v))=17.25cm 2 Best surface area of the Vertical stabilizer

d)Using the formula:Best vertical stabilizer area=slightly more than 0.05 S x bS=Main wing surface area=53.15cm2 (from ④e)b=Main wing span=17cm(from ④a)

15

A

B C D

EF

G1.5cm

3.0cm

5.0cm

1.5cm

2

2

ℓv

ℓv=Distance from center of gravity to vertical stabilizer=8cm(measured)(i) Substitute into e): 0.05 53.15cm2 x 17cm = 5.65cm2(Rounded to 3 s.f)

17.25cm2(actual area of vertical stabilizer-from ⑥c) is not slightly more than 5.65cm2(calculated best area for the vertical stabilizer-from ⑥d(i)), it is a lot more. ∴The vertical stabilizer surface area is the not best

Absolute difference between actual area of the vertical stabilizer and calculated best area for the vertical stabilizer e) Using formula: l calculated best area for vertical stabilizer for long -Actual area of vertical stabilizer l

(i)Substitute into e): l 5.65cm2 (from ⑥d(i))-17.25cm2 (⑥c) l =11.6cm2CONCLUSION

Each design is ranked 1-3 for each criteria based on the mathematical/physics prediction, 1 being the best and 3 being the worst. The design with the lowest sum of rank will be predicted to stay in the air the longest. ①Wing typeDesign Wing type Rank(1-3)Racer King-Fisher 526 Swept-back 2Racer Blue Jay 524 Tapered 1Canard Tapered 1

②Dihedral angle Stability

Design Dihedral angle(˚) Rank(1-3)Racer King-Fisher 526 10 3Racer Blue Jay 524 15 1Canard 13 2*The more the dihedral, the higher the ranking Suitable dihedral angle for wing position

Design In suitable range for wing position?(Yes/No) Rank (1-2)Racer King-Fisher 526 Yes 1Racer Blue Jay 524 No 3Canard No 3*If the dihedral is in the suitable range, the higher the rank

③MAC(Mean Aerodynamic Chord)and Center of gravityDesign Is the center of gravity at 50% of the MAC from the leading edge?(Yes/No) Rank(1-3)Racer King-Fisher 526 No 3Racer Blue Jay 524 No 3Canard No 3*If the center of gravity is at 50% of the MAC from the leading edge, the higher the rank

④Aspect ratio16

8cm

Design Aspect ratio Rank(1-3)Racer King-Fisher 526 4.57 3Racer Blue Jay 524 5.71 1Canard 5.44 2*The higher the aspect ratio, the higher the rank⑤Surface area of the horizontal stabilizerDesign Is the actual surface area the same as the calculated best surface area of the horizontal stabilizer for long duration flight? (Yes/No)

(If "no")Absolute difference between actual surface area and the calculated best surface area for long duration flight(cm2)

Rank(1-3)

Racer King-Fisher 526 No 5.4 2Racer Blue Jay 524 No 19.5 3Canard No 1.0 1*The lower the difference between the absolute difference between actual surface area and the calculated best surface area for long duration flight, the higher the ranking*OR the highest ranking(1) if the actual surface area is the same as the calculated best surface area of the horizontal stabilizer for long duration flight⑥Surface area of vertical stabilizerDesign Is the surface area slightly more than the calculated best surface area for the vertical stabilizer(Yes/No)

(If "no")Absolute difference between actual surface area and the calculated best surface area for the vertical stabilizer (cm2)

Rank(1-3)

Racer King-Fisher 526 No 0.32 2Racer Blue Jay 524 Yes - 1Canard No 11.6 3*The lower the difference between the absolute difference between the actual surface area and the calculated best surface area for the vertical stabilizer, the higher the rank*OR, the highest rank(1) if the actual surface area is slightly more than the calculated best surface area for the vertical stabilizer.

Table to show the sum of ranking

Based on the results of the prediction, I can make a conjecture that:"The Racer Blue Jay 524 will stay in the air for the longest duration followed by the Canard then the Racer King-Fisher 526"

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Design Sum of rankingRacer King-Fisher 526 16Racer Blue Jay 524 13Canard 15

TESTING

Equipment: Protractor, 30cm ruler, Wooden rod, Rubber catapult, Racer 526 King fisher, Canard, Racer 524 Blue Jay, Stop watch.

Controlled variables

Controlled variable How it will be controlledEnvironmental condition

Ensuring the same environmental condition each time(description of what the environmental condition is like)

Angle glider is released at

Released at an angle of 45˚ or 90˚(for the Racer 526 King Fisher) using a protractor to measure the angle

The force the glider is launched with

Using a rubber catapult to release the glider from the same stretched length each time (the most the rubber band can stretch)

RAW DATARacer 526 King Fisher

Controlled variable check:

Controlled variable DescriptionEnvironmental condition Sunny, slight windAngle glider is released at(˚) 90(see diagram 1)Stretched length of the catapult that the glider is released with

The most the rubber band can stretch(see diagram 1)

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Diagram 1Raw data table to show how long Racer 526 King Fisher can stay in the air for 5 trials(seconds)

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5Duration Racer 526 King Fisher stays in the air(seconds)

6.35 5.74 6.85 6.53 6.76

Racer 524 Blue JayControlled variable check:



19

x cm

90˚

Diagram 2

Raw data table to show how long Racer 524 Blue Jay can stay in the air for 5 trials(seconds)

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5Duration Racer 524 Blue Jay stays in the air(seconds)

7.81 7.91 5.75 6.88 5.51

CanardControlled variable check:



20

x cm

45˚

Diagram 3

Raw data table to show how long canard can stay in the air for 5 trials(seconds)

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5Duration Canard stays in the air(seconds) 4.10 4.16 5.46 5.91 4.88

Calculating the average duration the gliders stay in the air(s):

1) Using the formula: Trial 1+Trial 2 +Trial 3+Trial 4+ Trial 5

Racer 526 King Fisher

a)Substitute into 1): 6.35s+5.74s+6.85s+6.53s+6.76s = 6.45s (rounded to 3 s.f.)

Racer 524 Blue Jay

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5

5

x cm

45˚

b) Substitute into 1):7.81s+7.91s+5.75s+6.88s+5.51s =6.77s (rounded to 3 s.f.)

Canard

c) Substitute into 1): 4.10s+4.16s+5.46s+5.91s+4.88s =4.90s(rounded to 3 s.f.)

PROCESSED DATA

Design Average duration it stays in the air(seconds)Racer 526 King-Fisher 6.45Racer 524 Blue Jay 6.77Canard 4.90

CONCLUSION

In conclusion, the conjecture

"The Racer Blue Jay 524 will stay in the air for the longest duration followed by the Canard then the Racer King-Fisher 526"was partially proven through testing. Based on the testing results, it was proven that the Racer 524 Blue Jay stayed in the air longest. However, the test results did not show that the Canard stayed in the air the 2nd longest or that the Racer 526 King-Fisher stayed in the air for shortest amount of time. Instead, the test result showed that the Racer 526 King-Fisher stayed in the air 2nd longest and the canard stayed in the air for the shortest amount of time.

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Prediction and Testing

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