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APPENDIX B

DESIGN AND CALCULATIONS OF THE FLYGUY’S FRAMEWORK

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Appendix B

Design and calculations of flyguy’s framework 1. Technical requirements.

Use only MayTec aluminum profiles.

Fixed and rigid structure.

Easy to assemble and flexible in case of modifications.

Support the weight of one person (ranging from children to elders) plus the weight of

hanging equipment.

Enough space for the person to try any movement freely when “flying”.

2. Given data.

Mass of an average adult = 90 kg

Mass of hanging equipment = 10 kg

Total mass to be supported = 100 kg

Weight (force) applied to the bar = 1000 N (approx.; W = 100 kg*9.81 m/s = 981 N)

Safety factor = 2

Maximum weight to be supported = 2000 N

Figure B.1 shows the dimensions of an individual with height 1.85 m lying in

horizontal position. That was just to have an idea of the approximate ground space

needed and the approximate required size of the assembled framework.

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Figure B.1 Dimensions of a person in “flying” position

The height of the structure was defined taking into account an appropriate vertical

space of minimum 750 mm between the ground and the individual plus the unstretched

length of the hanging ropes 750 mm. That makes a total of 1500 mm.

The final sizes of the framework are shown in the CAD drawing.

3. Calculations.

From the catalogs I chose a profile size of 40 x 40 mm (moment of inertia = 12

cm4). The bar which is directly supporting the weight has a length of 1250 mm. Now I

substituted all data into formula no. 5 from the bending strength chart to obtain the

maximum deflection (in case that maximum weight was applied):

f = F l3 48 E J 104 f = (2000 N) (1250 mm)3 48 (70000 N/mm2) (12 cm4) 104

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f = 9.688 mm (approx. 1 cm; it is ok for the purpose of the frame which is mainly to

experiment positions and it does not need to be extremely rigid but also not so much

flexible that overcomes the action of the elastic hanging ropes).

4. Finite element truss analysis.

An analysis of the framework as a simple truss was simulated in Algor under the

same force conditions, using similar material (Aluminum 6061-T6, E = 68000 N/mm2) to

the MayTec profile’s one, and having the same area properties (fig. B.2). The

displacement and strength results are shown in figures B.3 and B.4.

Figure B.2 Forces applied to the frame

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Figure B.3 Finite element analysis of displacements

Figure B.4 Finite element analysis of stresses

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The most relevant data in the analysis of the structure is the displacement having a

maximum of 0.0679 mm which confirmed the correct selection of the MayTec profile

size (remember that its maximum deflection was almost 10 mm) and the correct

configuration of the frame design.

5. Selection of materials (standards).

From the MayTec catalog’s web page I selected the necessary materials (profiles

and connectors) and I generated the following order list:

PROFILES 40x40, 4E: 1. Six pieces, 1250 mm length, two connector bores (left and right, 1 each) 1.11.040040.43-AA1AA1/1250 2. Four pieces, 1750 mm length, two connector bores (left and right, 1 each) 1.11.040040.43-AA1AA1/1750 3. Six pieces, 2000 mm length, two connector bores (left and right, 1 each) 1.11.040040.43-AA1AA1/2000 4. Four pieces, 1768 mm length, saw cut 45 degrees on both extremes (left and right in direction 2), 2 connector bores (left and right, 1 each, in direction 1) 1.11.040040.43-EA1EA1/1768 Additional description: Bores must be on the perpendicular direction than from the saw cut (e.g., If saw cut is made on direction 2, the bores must be made on direction 1). CONNECTORS: 1. Thirty standard connectors 1.21.4E1 2. Ten oblique connectors (left-right) 1.21.4EK1 V

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6. Drawings.

Figure B.5 represents the 3D assembly of the framework (made in AutoCAD) and

shows the position of a person hanging there. It shows in general the configuration of the

experiments done in October during the second face to face meeting and how the frame

was tested. The 2D plot of the framework design is shown separately at the back cover of

this thesis. Additionals\framework2D.dwg. Following the illustrations, figures B.6 (a to

d) represent a three-dimensional view of how the two elements used on this frame

(profiles and connectors) are joined together. For a test report and summary of activities

on the prototype test task, please refer to chapter 5.5.2.

Figure B.5 Flyguy’s framework 3D model

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Figure B.6 (a) Connection elements

Figure B.6 (b) Profile and connector assembly

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Figure B.6 (c) Profile and connector assembly

Figure B.6 (d) Looking inside the assembly

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7. Catalogs.

Extruded profile as per DIN 17615

Aluminum alloy: Al Mg Si 0,5 F25 Material No. 3.320672 (low temperature annealed)

Mechanical Data Profile tolerance Flatness of profiles surfaceTopics : Straightness tolerance of the edge Parallelism tolerance

Mechanical Data (Values give in the direction of the press flow) Tensile strength in RM min 250 N/mm2 Elongation min 200 N/mm2 Stress point A5 min 10 % Stress point A10 min 8 % E-Module about 70.000 N/mm2 Brinell hardness HB 25/187,5 = 75 Coefficient of elongation 23,8 x 10-6/K

Surface as per DIN 17611: E6/EV1-dull finish and anodized colors Coat thickness ca. 10 micron Coat hardness 250-350 HV Special colors upon request The surface area - subject to technical procedure - can show optical changes.

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Bending strength

For the computation of deflection use formulas on this page.

For the computation of deflection by the profiles own weight apply "Type of load" 4, 7 or 10.

f = Deflection in mm F = Type of load in N I = Profile length in mm J = Moment of inertia in cm4 E = Module of elasticity in N/mm2 EAL = 70.000 N/mm2

The moments of inertia of a certain profile are listed on the respective profile page.

Type of load

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Detail der Profilgruppe 40 , E3-Nut Schwer

Bezeichnung Profil 40 x 40, 4E Stange (6 m) Packeinheit (6 m Stangen)

1.11.040040.43.60 1.11.040040.43.61 (8 Stg.)

Trägheitsmoment cm4 Widerstandsmoment cm3 Gewicht kg/m

lx = 12,0 ly = 12,0 Wx = 6,5 Wy = 6,5 2,0

CAD-Zeichnungen zum Download: DWG: - Vorderansicht - Linke Seite / Rechte Seite - Draufsicht / Unteransicht - Rückansicht DXF: - Vorderansicht - Linke Seite / Rechte Seite - Draufsicht / Unteransicht - Rückansicht

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Connector component parts As an alternative to the complete connectors it is also possible to order the component parts

Because of the extensive combination possibilities, storage of the complete connectors will reduced by 80 %.

Design Article-number. Technical Data

Standard-connectors 1.21.2E0 Material

: 9 S Mn Pb 28K

Strength : 460-710 N/mm2

Surface : galvanized