1

Design and Manufacturing of a Real Scale Prototype of a Land Sailor

Luís Miguel André Monteiro

luis.miguel.monteiro@tecnico.ulisboa.pt

Instituto Superior Técnico, Lisboa, Portugal

June 2016

The present work documents the mechanical design and the manufacture of a prototype of a land sailor. At first step, the market solutions are studied in order to substantiate a new lighter, low cost, smaller solution that comply with the quality, safety and performance criteria. These criteria result from the analysis performed to the structure (chassis, seat, steering), evaluating diverse load cases (the sail model was approached as an EPPLER profile), designing the structural components according to a Design For Assembly philosophy. Additionally, mechanical design methodologies are applied to evaluate the bolted joints, bearings and welded joints (AWS method and AISC code). A brief cost analysis is performed using the formula SAE cost tables, which result in a production cost of the prototype of 564,32 €, 30 % below the retail price of the reference model (799,01 €). In conclusion, it is presented the built prototype of a land sailor capable of competing in the leisure market that fulfills the proposed goals.

Keywords: Land Sailor; Design For Assembly; Mechanical Design; Structural Design; Drawings; Cost Analysis

INTRODUCTION Land sailors are wind powered vehicles that use a sail or wing as a propulsion system. In the last decades, the land sailors for recreation purposes have been presented with different concepts and solutions. This type of vehicle relies on wind that, combined with an angle of attack, applies an aerodynamic load on the sail. As there couldn’t be found a land sailor manufactured in Portugal, where land sailing is still an undeveloped market, this paper presents the design of a prototype of a land sailor as a product with potential to be built and sold in Portugal. In order to stablish state of the art, a brief literature search was conducted. In [1] is documented the comparison between cloth sails and rigid wing. In [2] is documented the design and analysis of a land sailor. Also, Blokart has developed an electric motor applied to the wheel to improve the driving experience of the land sailor [3]. This work presents the methodology used and fundament choices made in the design of the proposed prototype. The challenge of designing this vehicle is in the expectation that the market of recreation land

sailors catches up to similar markets, such as windsurf and cycling. To ensure the appeal of the prototype, the goals of the design are the following:

Low cost;

Small dimensions;

Low weight;

Simple manufacturing;

Small disassembled dimensions;

Ease of assembly. The main specifications for the designed prototype are presented in the Table 1. For a more detailed description, see [4].

Spec Prototype

Wheel base WB (m) 1.5

Width T (m) 1.2

Height h (m) 5

Sail area A (m2) 5.1

Weight m (kg) 21.5

Table 1 – Main specifications [4].

To ensure the quality and security of this prototype, it was established that the designed vehicle has to fulfil the following requirements [4]:

Disassembled for transportation;

All parts must resist corrosion;

Include steering system;

2

Include a sail control system;

Three or more wheels;

The driver must be sat down;

Must be propelled by a sail or wing. The main constrains that limit the development of this prototype are the following [4]:

Maximum driver’s weight 130 kg;

Manufacturing processes limited to the ones available at the workshop;

Material limited to steel, due to the constrain of the welding equipment.

Production cost limited to 799 €.

METHODOLOGY In the Figure 1 is presented the methodology adopted for this work.

Figure 1 – Methodology.

CONCEPTS In this section are presented the main concepts and solutions eligible for each of the prototype subsystems:

Chassis (Table 2);

Steering (Table 3);

Wheels (for hard ground or sand);

Seat (Table 4);

Sail (Table 5).

Material

Steel;

Aluminum;

Composite.

Geometry

Triangular frame;

Frame in T [4];

Frame in Y [2];

Monocoque).

Reinforce Rear wheels to Mast;

No reinforce.

Connectors Bolts and nuts

Pins.

Table 2 - Chassis solutions.

Controlled with Feet;

Hands.

Front Wheel offset

With offset;

Without offset.

Fork Double arm;

Single arm.

Table 3 - Steering solutions.

Geometry With lumbar support;

Without lumbar support.

Type Steel frame with soft fabric;

Rigid (plastic or composite).

Table 4 - Seat solutions.

Type Boat sail;

Windsurf sail.

Boom Free;

Rotates over the mast.

Mast material

Carbon Fibre;

Aluminum.

Table 5 - Sail Solutions.

PROTOTYPE OF THE CHOSEN CONCEPT In the Figure 2 is shown the CAD model of the designed prototype.

Figure 2 – Perspective of the prototype without

the sail. In the Table 6 are presented the solutions adopted for the designed prototype.

Prototype

Chassis Triangular, Steel (6.71 kg)

Steering Controlled with feet, double arm,

no offset (3.48 kg)

Seat Kart bacquet (3.74 kg)

Sail WindSurf sail, free boom (5 kg)

Wheels Metallic rims with pneumatic tires

(2.35 kg)

Table 6 – Solutions and weights of the subsystems [4].

Requirements and goals

Benchmarking

Comparison between solutions

Load cases

Structural and mechanical design

Drawings

Manufacturing

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AERODYNAMIC LOADS In the Figure 3 are represented the angles and the vectors of the velocities and forces considered in the calculations of the maximum aerodynamic load. In the Table 7 it is presented the main dimensions and weight of the prototype and driver, used in the calculation of the loads.

Figure 3 - Wind velocities, angles and forces

(adapted from [5]).

Data Value

Total Weight (kg) 146.5

Centre of gravity coordinates

(467,0,304)

Height of the pressure centre (mm)

2000

Radius of the pressure centre (mm)

800

Width (mm) 1200

Wheel Base (mm) 1500

Table 7 - Dimensions and Weight of the prototype [4].

Methodology for load calculations To better explain the methodology used to calculate the aerodynamic loads, the Figure 4 illustrates the steps.

Figure 4 - Methodology for the loads

calculations.

Apparent wind speed

In order to calculate the loads in the different directions, it is necessary to calculate the speed triangle. This triangle consists of the vehicle speed 𝑉𝑘, wind speed 𝑉𝑉 and the apparent wind speed 𝑉𝐴. The wind speed is estimated, using the equation (1),

𝑉𝑉2 = [𝑧2

𝑧1

]𝑎

𝑉𝑉1, (1)

where 𝑉𝑉1 is the known wind speed at a certain

height 𝑧1, 𝑧2 is the height corresponding to the vehicle and 𝑎 is a parameter discriminating the

type of terrain (𝑎 =1

9 for open terrain) [1].

In order to calculate the apparent wind speed, it is presented the correlations based on the speed triangle, equations (2), (3) and (4) [5].

𝛽 = arctg (𝑉𝑉 sin 𝜙

𝑉𝑉 cos 𝜙 + 𝑉𝐾

) , 𝛽 ≤𝜋

2 (2)

𝛽 = arctg (𝑉𝑉 sin (𝜙 −

𝜋2

) − 𝑉𝐾

𝑉𝑉 cos (𝜙 −𝜋2

)) +

𝜋

2 , 𝛽 >

𝜋

2 (3)

𝑉𝐴 = √𝑉𝑉2 + 𝑉𝐾

2 + 2𝑉𝑉𝑉𝐾 cos 𝜙 (4)

The maximum of 𝑉𝐴 (when 𝜙 =𝜋

2) is calculated

using the following equation (5) [4].

𝑉𝐴 =𝑉𝑉

sin 𝛽

(5)

Aerodynamic coefficients

In order to calculate the aerodynamic loads, the sail was approached as an EPPLER 472 airfoil [6]. To estimate the lift coefficient 𝐶𝐿 for the finite wing, using the equation (6), is used the lifting-line theory [7].

𝐶𝐿 =Λ

Λ + 2 𝐶𝑙 𝑚𝑎𝑥

𝛼𝑝𝑒𝑟𝑑𝑎

𝛼, (6)

where Λ = 𝑏/𝑐 = 6.27 is the aspect ratio, 𝑏 =8 𝑚 is the lenght and 𝑐 = 1.275 𝑚 is the chord

of the wing. 𝐶𝑙 𝑚𝑎𝑥 = 1.4 is the maximum infinite

lift coefficient at an angle of attack 𝛼𝑝𝑒𝑟𝑑𝑎 =

15.5° [6].

Maximum aerodynamic load for each β

Lateral load of equilibrium

Aerodynamic load equivalent to Lateral load for each β

Choose the smaller between the Aerodynamic equilibrium load with

the maximum aerodynamic load

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The finite drag coefficient 𝐶𝐷 (7) results from the

adding of the infinite drag coefficient 𝐶𝑑 and the

induced drag coefficient 𝐶𝐷𝑖 =𝐶𝐿

2

𝜋Λ [7], i. e.

𝐶𝐷 = 𝐶𝑑 + 𝐶𝐷𝑖 (7)

The equation (7) can be written as shown in the equation (8),

𝐶𝐷 = 𝑐1 + 𝑐2 𝛼2 +𝐶𝐿

2

𝜋Λ,

(8)

where 𝑐1 = 0.0096 and 𝑐2 = 8.99 × 10−5 [4].

Equations for aerodynamic loads

The lift and drag equations [7]:

𝐹𝐿 =1

2𝜌𝑉𝐴

2𝐶𝐿𝐴 (9)

𝐹𝐷 =

1

2𝜌𝑉𝐴

2𝐶𝐷𝐴 (10)

where 𝜌 = 1.22 𝑘𝑔/𝑚3 is the air density [8], and

𝐴 = 5.1 𝑚2 is the area of the sail. From this, results the aerodynamic load (11).

𝐹𝐴 = √𝐹𝐿2 + 𝐹𝐷

2 (11)

Lateral load at equilibrium

The lateral load at equilibrium, 𝐹𝑌, results from

the momentum equilibrium around the axle 𝑄, that links the front wheel to one of the rear wheels depending on the direction of the force. In the Figure 5 are presented the parameters necessary to calculate 𝐹𝑌.

Figure 5 - Parameters used in the calculation

of 𝑭𝒀 (adapted from [5]).

The equilibrium of momentum around 𝑄 defines

𝐹𝑌′, i. e. ∑ 𝑀𝑄 = 𝐹𝑌

′ × ℎ − 𝑃 × 𝑁 = 0, (12)

𝐹𝑌

′ = 𝑃 ×𝑁

ℎ,

(13)

where 𝑁 = 383.6 𝑚𝑚 and 𝜆 = 21.8°. the lateral load of equilibrium 𝐹𝐴 𝑒 is calculated using the equation (14).

𝐹𝐴 𝑒 =𝐹𝑌 𝑚á𝑥

cos(𝜔 − 90° + 𝛽)

(14)

Aerodynamic loads

Now, the aerodynamic load is limited by two conditions, the maximum aerodynamic load from the sail 𝐹𝐴 𝑚𝑎𝑥 (𝛼 = 𝛼𝑝𝑒𝑟𝑑𝑎) and the

aerodynamic load equivalent to the lateral equilibrium load 𝐹𝐴 𝑒. Both of this conditions limit

the magnitude of the aerodynamic load 𝐹𝐴 for

each 𝛽 (15). 𝐹𝐴(𝛽) = min(𝐹𝐴 𝑒 , 𝐹𝐴 𝑚á𝑥) (15)

STRUCTURAL ANALISYS To enforce the safety and quality of the prototype, it was required a factor of safety (FOS) 𝑛 = 2.

Chassis

With the purpose of choosing a solution for this work, different chassis geometries are analysed (Figure 6). For this analysis it was used the finite element method, to run a static linear analysis

Figure 6 - Different chassis geometries.

The geometries are evaluated according to the

results 𝜎𝑚𝑎𝑥/𝑚𝑎𝑠𝑠 and 𝑈𝑚𝑎𝑥/𝑚𝑎𝑠𝑠, as well as

the design goals presented earlier. The material used was steel AISI 1045. Some of the material properties are presented in the Table 8 [9].

𝑬

(𝑮𝑷𝒂)

𝝈𝒄𝒆𝒅

(𝑴𝑷𝒂)

𝝈𝒖𝒍𝒕

(𝑴𝑷𝒂)

𝝂 𝝆

(𝒌𝒈/𝒎𝟑)

𝟐𝟎𝟔 530 625 0.29 7.85

Table 8 - Some properties of the steel AISI 1045 [9].

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It was used circular tube, the section is illustrated in the Figure 7.

Figure 7 - Tube sections for the chassis.

For this analysis, it was applied a moment load 𝑀𝑥 = 613.4 𝑁. 𝑚 and the total weight 𝑃 = 1484.7 𝑁, see [4]. The 3 wheels were constrained (Figure 8). In the Table 9 is presented the finite element size for each geometry. As an example, the Figure 9 presents the displacement for different elements size for the 3rd geometry. In the Figure 8 are presented the mesh, loads and constrains used in this analysis.

1 – T reinforced

2 – T 3 - Triangle 4 – Y

𝟏𝟎 𝒎𝒎 5 𝑚𝑚 10 𝑚𝑚 7.5 𝑚𝑚

Table 9 - Element size for the different chassis geometries [4].

Figure 8 - Mesh and boundary conditions of

the chassis.

Figure 9 - Displacement vs. element size for

the 3rd chassis geometry. In the Table 10 are presented the results of this analysis for the 4 different geometry.

1 2 3 4

𝝈𝒎𝒂𝒙 (𝑴𝑷𝒂) 394.4 611.8 484.4 714.7

𝑼𝒎𝒂𝒙 (𝒎𝒎) 17.5 23.4 27.9 35.6 𝝈𝒎𝒂𝒙

𝒎𝒂𝒔𝒔

(𝑴𝑷𝒂/𝒌𝒈) 70.4 218.5 110.1 264.7

𝑼𝒎𝒂𝒙

𝒎𝒂𝒔𝒔

(𝒎𝒎/𝒌𝒈) 3.13 8.26 6.34 13.19

𝒎𝒂𝒔𝒔 (𝒌𝒈) 5.6 2.8 4.4 2.7

Table 10 - Results of the different chassis geometries [4].

To better fulfil the design goals, the adopted geometry is the triangular, number 3, due to its advantage in assembly and disassembly.

Steering fork In this analysis are compared 4 different geometries for the steering fork (Figure 10). These geometries differ from each other in the type of arm (single or double) and the offset between the steering axle and the wheel axle (w/ offset or w/o offset). In the Figure 11 are presented the section of the tubes used in this analysis.

Figure 10 - Steering fork geometries.

Figure 11 - Tube section: a) double arm; b)

single arm (mm).

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This static linear analysis was conducted using the finite element method. The material of the models is the same used in the chassis analysis (Table 8). In the Figure 12 is presented the displacement for different finite element sizes for the 2nd steering fork geometry. In the Table 11 are presented the results of this analysis, in the conditions indicated at Figure 13.

Figure 12 - Displacement vs. element size for

the 2nd steering fork geometry.

Figure 13 - Mesh and boundary conditions of

the steering fork.

Geometry nº 1 2 3 4

𝑼𝒎á𝒙

(𝒎𝒎) 0.772 0.624 1.363 1.463

𝝈𝒎𝒂𝒙

(𝑴𝑷𝒂) 121.4 127.4 149.7 153.2

𝝈𝒎𝒂𝒙

𝒎𝒂𝒔𝒔

(𝑴𝑷𝒂/𝒌𝒈) 0.572 0.439 1.065 1.117

𝑼𝒎𝒂𝒙

𝒎𝒂𝒔𝒔

(𝒎𝒎/𝒌𝒈) 89.9 89.7 117.0 116.9

𝒎𝒂𝒔𝒔 (𝒌𝒈) 1.35 1.42 1.28 1.31 Table 11 - Results of the different steering

forks geometries [4].

Based on the results 𝜎𝑚𝑎𝑥/𝑚𝑎𝑠𝑠, the chosen geometry is the 2nd (double arm without offset).

Analysis of the set chassis/seat/steering

In this section it is briefly analysed the static behaviour of the set chassis/seat/steering. The material used is the steel AISI 1045 presented in the Table 8. The aerodynamic loads were applied to the centre of the sail (Table 1). Two different load cases were applied. The Load Case 1 (LC1) is assuming that the 3 wheels are in contact with the ground, and using the maximum value of the aerodynamic loads. For the Load Case 2 (LC2) it is assumed that only the front wheel and rear (right) wheel are in contact with the ground, and that the wind speed considered is the double of the wind speed considered for LC1. The load cases are presented in the Table 12. In the Figure 14 are illustrated the boundary conditions for the LC1. The results are presented in the Table 13, including the factor

of safety 𝑛 =𝜎𝑐𝑒𝑑

𝜎𝑉𝑀.

In the Table 14 and Table 15 are presented the reaction forces for the LC1 and LC2, respectively.

LC Loads Constrains

1

𝐹𝐿 = 326.2 𝑁

𝐹𝐷 = 26.2 𝑁 𝛽 = 25°

𝑊𝑒𝑖𝑔ℎ𝑡 = 1275.3 𝑁

Front wheel, 𝑈𝑟𝑎𝑑 e

𝑈𝑎𝑥𝑖𝑎𝑙

Rear wheels, 𝑈𝑟𝑎𝑑 e

𝑈𝑎𝑥𝑖𝑎𝑙

2

𝐹𝐿 = 416.3 𝑁

𝐹𝐷 = 34.7 𝑁

𝛽 = 50° 𝑊𝑒𝑖𝑔ℎ𝑡 = 1275.3 𝑁

Front wheel, 𝑈𝑟𝑎𝑑 e

𝑈𝑎𝑥𝑖𝑎𝑙

Right rear wheel,

𝑈𝑟𝑎𝑑 e 𝑈𝑎𝑥𝑖𝑎𝑙

Table 12 - Load cases for the set chassis/seat/steering.

Figure 14 - Boundary conditions for the set

chassis/seat/steering.

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Load Case 1 2

𝑼𝒎á𝒙

(𝒎𝒎) 0.778 1.50

𝝈𝒎𝒂𝒙 (𝑴𝑷𝒂)

258 276

𝒏 2.05 1.92

Table 13 - Results of the set chassis/seat/steering [4].

Right Rear Wheel

Left Rear Wheel

Front Wheel

𝑹𝒙 (𝑵) 340.8 47.6 −535

𝑹𝒚 (𝑵) 104.9 87.3 −23.5

𝑹𝒛 (𝑵) 248.7 149.3 692

Table 14 - Reactions for the LC1 [4].

Right Rear

Wheel Front Wheel

𝑹𝒙 (𝑵) 716.2 −916

𝑹𝒚 (𝑵) 400.2 60.9

𝑹𝒛 (𝑵) 412.3 1220

Table 15 - Reactions for the LC2 [4].

DETAILS ANALISYS

Connectors In order to choose the type of connectors, a comparison between pins and bolt connectors is presented. In this comparison the mechanical resistance and safety of the connection is analysed. The Grade of the bolt connector is 8.8, which means the Proof Strength is 𝜎𝑝 = 600 𝑀𝑃𝑎 [10].

The pre-load assumed on the bolt due to tightening, for non-permanent connections is calculated using equation (16) [10]. 𝐹𝑖 = 0.75𝐹𝑝, (16)

where the proof load is 𝐹𝑝 = 𝐴𝑡𝜎𝑝 = 34800 𝑁,

with the tensile stress area 𝐴𝑡 = 58 𝑚𝑚2 for M10 bolts [10]. The pre-load applied in the M10 bolt is 𝐹𝑖 = 26100 𝑁. Considering the friction coefficient between the parts is 𝜇 = 0.2 [10], the maximum friction load supported by the bolted connections is given by equation (17). 𝐹𝜇 = 𝜇 𝐹𝑖 = 5220 𝑁 (17)

So, when the shear load in the bolted connections is bigger than 𝐹𝜇 = 5220 𝑁, the

connection is in failure. The resulting von Mises stress 𝜎𝑉𝑀 = 115.11 𝑀𝑃𝑎 is lower than the yield stress 𝜎𝑐𝑒𝑑 = 530 𝑀𝑃𝑎 of the material AISI 1045, so the pin connector has a better strength compared with the bolt connector. Although the pin connector has a better strength compared with the bolt connector, due to the level of tolerances needed to avoid free play and the fact that pins doesn’t resist axial loads, the type of connector used in this work was the bolted connectors.

Bolts strength The resulting stresses in the bolts are calculated based on the resulting loads on the bolts (see detail in [4]). The bolt stress is calculated using equation (18) [10].

𝜎𝑏 =𝐹𝑏

𝐴𝑡

=𝐶𝐹 + 𝐹𝑖

𝐴𝑡

, (18)

where 𝐶 is the fraction of load 𝐹 supported by the bolt (19). The bolts used in this work were M10x65 and M10x90, with respectively, 𝐶 = 0.153 and 𝐶 = 0.106. The three factors of safety (FOS) analysed in this work were regarding the separation of the parts (19), the slip between the parts (20), and the bolt tension (21) [10].

𝑛𝑠 =𝐹𝑖

𝐹𝑠

=𝐹𝑖

𝐹(1 − 𝐶)

(19)

𝑛𝑒 =

𝐹𝜇

𝐹𝑒

=𝑝 𝜇 (𝐹𝑖 − 𝐹(1 − 𝐶))

𝐹𝑒

(20)

𝑛𝑏 =

𝜎𝑝𝐴𝑡

𝐶𝐹 + 𝐹𝑖

(21)

To summarize the results, in the Table 16 are presented the minimum for each factor of safety for the LC1.

FOS Value Bolt

Separation

𝒏𝒔 297.9

Rear seat support / chassis

Slip 𝒏𝒆 160.84 Rear seat support /

chassis

Bolt 𝒏𝒃 1.33 -

Table 16 - Minimum FOS for the bolted connection [4].

Due to the pre-load applied to a tightened bolt and the resultant forces are significantly smaller

8

than the pre-load, the bolt’s factor of safety in this work is always 𝑛𝑏 ≈ 1.33.

Bearing selection To select the bearing for each application, the following methodology was used [10]: 1. Choose an initial 𝑌 from the table;

2. Calculate 𝐶10; 3. Choose a bearing and save the value of 𝐶0;

4. From 𝐹𝑎/𝐶0; choose a new 𝑌;

5. Calculate 𝐶10; 6. If equal, stop; 7. If not, return to step 4. In the Table 17 are presented the reactions of the LC1 used to select the bearings. Based on the presented methodology and the reaction loads, the chosen bearings are presented Table 18.

𝑭𝒓 (𝑵) 𝑭𝒓 (𝑵)

Upper steering 166.7 258.7

Lower steering 260.6 607.8

Right rear wheel 421.9 104.9

Left rear wheel 156.7 87.3

Front wheel 874.7 23.5

Table 17 – Loads on the bearings [4].

𝑪𝟏𝟎 (𝒌𝑵) Bearing

Upper steering 3.45 𝑑 = 10 𝑚𝑚 𝐷 = 30 𝑚𝑚

Lower steering 5.82 𝑑 = 12 𝑚𝑚

𝐷 = 32 𝑚𝑚

Right rear wheel 9.71 𝑑 = 20 𝑚𝑚 𝐷 = 47 𝑚𝑚

Left rear wheel 4.84 𝑑 = 10 𝑚𝑚

𝐷 = 30 𝑚𝑚

Front wheel 13.42 𝑑 = 25 𝑚𝑚

𝐷 = 52 𝑚𝑚

Table 18 - Selected bearings [4].

Welded joints To analyse the welded joints, the resulting von Mises stress from the FEM analyses are considered to calculate the factor of safety 𝑛. Using the AISC code for welded metals, the minimum FOS are established for each type of loads, tension (22) and shear (23) [10]. 𝑛𝐴 𝑚í𝑛𝑖𝑚𝑜 =

𝜎𝑐𝑒𝑑

0.6 𝜎𝑐𝑒𝑑

= 1.67 (22)

𝑛𝜏 𝑚í𝑛𝑖𝑚𝑜 =

𝜏/0.4

√3𝜏= 1.44

(23)

In this work, it was considered the more conservative FOS of 𝑛 = 2. There are 4 parts analysed with welded connections in this work. In the Table 19 are presented the minimum values for each part and the respective welded joints.

𝒏 Welded joint

Mast support 3.93 Upper steering

Lateral member

2.70 Connection to Mast

support

Rear member 2.41 Insert 3

Seat supports 2.35 Rear right connection

to chassis

Table 19 - Minimum FOS for each part [4].

MANUFACTURING DETAILS In order to better control the dimensions and geometry of the prototype, a Jig was built to place the components to weld (Figure 15). In the Figure 16 and Figure 17 are presented some welding details. The manufactured prototype is presented in the Figure 18.

Figure 15 - Jig.

Figure 16 - Details: a) Insert; b) Lateral

Member; c) Steering.

9

Figure 17 - Details: a) Lathing of an insert; b)

Hole drilling.

Figure 18 - Prototype.

DRAWINGS

Regulations and Norms In this work, the norm ISO 7200 was used on the title block of technical drawings and the European type projections were used [11]. In the Figure 19 is presented the technical drawing of the designed prototype.

Figure 19 - Technical drawing of the prototype.

Tolerances and surface finish For the fitting between holes and shafts, in this work the class H8-f7 was chosen. This gives a rotational tight fit [11]. The overall geometric and dimensional tolerance applied in this work complies with the norm ISO 2768-cL [11]. This norm gives a rough dimensional (c) and geometric (L) tolerance.

Regarding the surface finish, the chosen average roughness was 𝑅𝑎 = 3.2 μm corresponding to the characteristic roughness of lathing and milling [11].

COST ANALISYS This analysis was conducted using the cost tables from Formula SAE [12] [13]. These tables are used to evaluate the unitary production cost of a series of 1000 formula type vehicles. In the Figure 20 are presented the overall cost for each subsystem, excluding the sail. In the Table 20 are presented the total costs for the different resources (Materials, Processes, Fasteners and Tooling) and subsystems.

Figure 20 - Overall cost of each subsystem.

Table 20 – Estimate total costs for subsystems and resources using [12] and [13].

In the Figure 20 are presented the overall cost for each subsystem, excluding the sail. Note: This work follows a Design For Assembly (DFA) because the goal is to build a single prototype. This results in a higher unitary vehicle cost for a production series of 1000 units assumed in the procedure

Mate

rials

Pro

cess

es

Faste

ners

To

olin

g

To

tal

Chassis 41,56 € 114,42 € 3,99 € 12,63 € 172,59 €

Steering 5,45 € 40,20 € 0,80 € 3,89 € 50,34 €

Seat 128,49 € 15,67 € 4,88 € 4,90 € 153,93 €

Wheels 30,00 € 4,50 € 2,89 € - € 37,39 €

Sail 150,00 € - € - € - € 150,00 €

Total Vehicle

205,50 € 174,78 € 12,55 € 21,41 € 564,25 €

10

ACKNOWLEDGEMENTS First and foremost, I would like to thank Professor Miguel Matos Neves and Professor Luís Reis for the guidance, knowledge, support and the opportunity to develop this project, as well as the supply of means to acquire the parts and materials necessary, and the access granted to the workshop (Laboratório de Técnicas Oficinais do DEM/IST). I would also like to thank André, Manuel, Pedro and Ricardo for the availability, knowledge and review offered at some stages of this work. I thank the workshop technicians for the help and patience offered in the manufacturing of the components, and I specially thank Pedro for the time dispended welding the components and also to Mr. Frade for making the resources necessary to weld available. Lastly, a special thanks to my parents for providing the possibility to fulfill my academic goals, as well as the support given during this journey.

References

[1] F. Dias, “Metodologias de Implementação de uma Asa num Kart à Vela e Previsão de Velocidade,” MSc Dissertation (in portuguese), DEM, Instituto Superior Técnico, Lisboa, 2013.

[2] V. Monteiro, “Desenvolvimento e Análise de um Kart à Vela,” MSc Dissertation (in portuguese), DEM, Instituto Superior Técnico, Lisboa, 2013.

[3] “UKPPG,” Blokart electric motor, 2016. [Online]. Available: http://ukppgwebstore.com/blokart-electric-motor-1567-p.asp.

[4] L. M. A. Monteiro, “Projeto e Fabrico de um Protótipo à Escala Real de um Kart à Vela,” MSc Dissertation (in portuguese), DEM, Instituto Superior Técnico, Lisboa, 2016.

[5] M. Khayyat and M. Rad, “Comparison Final Velocity for Land Yacht With a Rigid Wing and Cloth Sail,” World Congress on Engineering, vol. II, p. 6, 2008.

[6] “EPPLER 472 AIRFOIL,” Airfoil Tools, 2015. [Online]. Available: http://airfoiltools.com/airfoil/details?airfoil=e472-il#polars. [Accessed 27 9 2015].

[7] V. d. Brederode, Fundamentos de Aerodinâmica Incompressível, Lisboa: DEM IST UTL, 1997.

[8] J. Katz, Race Car Aerodynamics: Designing for speed, Cambridge: Bentley Publishers, 1995.

[9] “AISI1045,” MatWeb, 1996. [Online]. Available: http://www.matweb.com/search/DataSheet.aspx?MatGUID=cbe4fd0a73cf4690853935f52d910784. [Accessed 30 9 2015].

[10] Budynas-Nisbett, Shigley's Mechanical Engineering Design, Eight Edition, The McGraw-Gill Companies, 2008.

[11] A. Silva, C. T. Ribeiro, J. Dias and L. Sousa, Desenho Técnico Moderno, Lisboa: Lidel, 2004.

[12] “FSAE Rules,” [Online]. Available: http://students.sae.org/cds/formulaseries/rules/2015-16_fsae_rules.pdf. [Accessed 21 9 2015].

[13] “Cost SAE,” Formula SAE, [Online]. Available: http://www.fsaeonline.com/page.aspx?pageid=5ade9b01-8903-4ae1-89e1-489a8a4f08d9. [Accessed 21 9 2015].