1

AN ELECTRIC TRAILER MODELING AND CONCEPTION FOR BICYCLES

Fernando André de Almeida Frescata Correia Pereira

Mechanical Engineering Department, Instituto Superior Técnico, Lisboa, Portugal

ABSTRACT

The aim of this work involved coupling an electric trailer in a bicycle allowing an easier and more comfortable way of

movement of the set cyclist-bicycle-trailer. The electrical and mechanical components that have to be included in the trailer have

considerable weight and volume, being the greater concern in the development of the prototype. To get over these constrains

this work focused in developing a trailer made of lightweight materials to keep the weight of the vehicle at a low range. The

geometry layout is also to be as simple as possible. It was performed a structural analysis taking into account the material

selection of the chassis, the static design and the computational static simulation. The prototype was built at real scale and a

computational dynamic simulation was made to be compared with experimental tests for performance interpretations of the

system and for magnitudes quantification. It was found a satisfactory agreement with the experimental results which reinforce

this prototype as a viable alternative for the current existent mechanisms.

Keywords: Bicycle, Trailer, Chassis, Prototype.

I. INTRODUCTION

Sustainable mobility is increasingly important nowadays as it is

crucial to concretize the European and world goals concern to the

emission of greenhouse gases. Bicycles are still the greener and

healthier means of transport in use and are extremely important for

the sustainable mobility nowadays. These vehicles offer freedom,

comfort and are ecological. However there are still some

limitations that prevent their use in urban areas such as the

difficulty in acquiring high velocities, slopes and the transportation

of load.

The aim of this work involved coupling an electric trailer in a

bicycle allowing an easier and more comfortable way of movement

of the set cyclist-bicycle-trailer. This trailer is a portable system

with some capacity of load. Typically these kinds of systems don’t

have any type of energy recovery ad their move depends only on

the battery charge. Additionally, the motorization of these systems

is made with permanent magnet motors which in case of turning

off by option or by lack of charge in the battery leaves a big drag to

the rider pedaling and consequently produces losses of energy.

The innovation of the present work consists in adding systems

of regenerative braking for energy recovery. Another innovation is

the use of synchronous machines instead of permanent magnet

motors which allows controlling the regenerative braking and

avoiding the electromagnetic drag of the motor when turned off [1].

However this solution involved the use of a heavier and less

compact motor and so the biggest priority for the product feasibility

was the project of the support structure of the trailer (chassis).

II. STRUCTURAL ANALYSIS

It was performed a structural analysis taking into account the

material selection of the chassis, the static design with stress

analysis and the computational static simulation of prototype.

A. MATERIAL SELECTION

Materials always had an important role in human life. The

study development for the materials selection for the structure of

this prototype will be based in knowledge of Engineering Materials.

The choice of the material for the chassis may focus on a light

and resistant material in order to not increase much weight to the

bicycle and the passenger, to minimize the interference with the

dynamics of the system and being resistant to outside conditions

at the same time. The cost of the material must also be taken into

account for market perspectives. The trailer chassis must bear the

weight of the components for proper operation.

The requirements for the material selection are shown in table

1.

2

TABLE 1 – Selecting design requirements for material

Functions Bending beam

Objectives Minimize cost

Minimize cost

Constrains

Strength

Sufficient stiffness

Fracture toughness

Recyclable

Free Variables Material

Thickness

The material selection information is based in the Ashby Maps

that organized the materials through properties groups as these

are the main requirements when choosing the materials for

mechanic projects [2].

In order to minimize the mass, there is the material index:

To acquire satisfactory stiffness, it had into account:

To optimize the costs there is the material index:

Above the lines with slope 1 given by the three indices in

equations 1, 2 and 3 are the desired materials for selection. There

are three possible materials that can be selected for the chassis

which are Aluminum, Carbon Steel and Cast Iron, shown in figure

1. The density itself is an important factor and together with the

cost are important parameters in the choice of the material. The

cost for these three groups of materials is similar. The density of

the Aluminum Alloys is lower when compared with the other

materials. Within the class of Aluminum Alloys it has been pre-

selected the 6063-T6 alloy as it contains the most satisfactory

characteristics for the project as well as the Cast Iron P60-03 and

the Carbon Steel AISI 1030.

FIGURE 1 – Ashby Map: Price*Density versus Flexural Stress (pre-selection) [3]

The properties of the three pre-selected materials are listed in

table 2.

TABLE 2 – Properties of pre-selected materials

Aluminum

Alloy Carbon Steel

Cast Iron

6063-T6 AISI 1030 P 60-03

ρ [kg/m3] 2,7 x 10

3 7,9 x 10

3 7,2 x 10

3

KIC [MPa.m

1/2]

34 45 44

σy [MPa] 210,5 580 483

Unitary Cost [€/kg]

1,8 0,5 0,4

E [GPa] 71,3 212 164,5

It was made an analysis of the performance indices through a

table of weighted indices (table 3). This revealed that the

Aluminum has the bigger performance index, given by:

In which β is the weighted index and α is the weight of the

property [4].

TABLE 3 – Weighted indices of material properties

β1 β2 β3 β4 β5

γ (%)

Aluminum Alloy 100 76 36 22 34 72,80

6063-T6

Carbon Steel 34 100 100 80 100 72,60

AISI 1030

Cast Iron 38 98 83 100 78 70,10

P 60-03

αi 2/5 3/10 1/5 1/20 1/20

The material used in the construction of the chassis was

Aluminum 6063-T5 which presents similarities with T6 and so has

satisfactory properties for the project. They have the similarities

composition but different thermal treatments. The T5 corresponds

to an artificial aging and the T6 to a solubilization and artificial

aging.

The material properties and the profile used are shown in

tables 4 and 5.

TABLE 4 – Mechanical Properties of Aluminum Alloy 6063-T5 [5]

TABLE 5 – Dimensions of used profile

Yield

Stres

[HB]

Strain

2,7A lumí nio 6063-T 5 120 167,5 68,9 25,8 0,33 5,5 52,5

H ardness

B rinell

[%]

D ensity

[MPa]

T ensile

[MPa]

P o isso n's

rat io

Yo ung's

Strength M o dulus

E [GPa]

Shear

M o dulus

G [GPa] ]

(

) (1)

(

) (2)

(

) (3)

∑ (4)

Width (b)

40 x 20 x 3 324 18892 60812

Area Height (h)Perfil

Thickness (e)

[mm]

40 20 3

[mm] [mm] ]

]

]

Profile

3

B. STATIC DESIGN

The chassis was modeled with the correct electric and

mechanical components that provide the appropriate system

operation in the software Solidworks® (figure 2).

FIGURE 2 – Scheme of chassis components [6]

As a first approach to the static project a study of forces and

reactions involved in the system is made with the aim to

understand the actuating efforts in the prototype. To do this it was

sketch a diagram of free body to the chassis (figure 3).

FIGURE 3 – Free body diagram (red sections)

The involved forces are:

Where: PT/2 = total weight of structure / 2 ; PB/2 = battery

weight / 2 ; PM/4 = motor weight / 4 ; Pc/2 = controller weight / 2.

The maximum efforts given by the transverse effort diagram

and the bending moment diagram results in:

These values correspond to a critical section in chassis hole

making which corresponds to the fit of the wheel shaft of the trailer

(Section 2,B of figure 3).

The concerned stresses are given by:

Finally it was obtain the equivalent stress, given by the Von

Mises criteria:

Through the transfer stress of the utilized material

(table 4), it is obtained the safety coefficient of the project:

The chassis can stand the imposed load and is full safe, the

prototype is oversized and the material supports the imposed

solicitations with ease.

C. COMPUTACIONAL STATIC SIMULATION

The numeric modulation is commonly used in Science,

Engineering and Industry as a way for problem verification without

apparent analytic solution, complex project problems and critical

phenomena. In this case, this static simulation serves to ensure

the reliability of the chassis project and at the same time to verify

and reinforce the analytic calculations of the static project already

carried out [7].

The numeric method utilized was the Finite Elements Method

(FEM) and for this it was used the Solidworks® Simulation

software. The mesh creation is a crucial step for results collection

because these can vary with the mesh type, element type and

density. In order to refine the mesh to obtain a stable standard of

stress values there were prepared a several iterations until it

reaching to a fine mesh of 3D tetrahedral solids, with maximum

spacing of 14mm between them (figure 4).

FIGURE 4 – Representation of mesh and loading [6]

It was found through this simulation that the critical section

was in the chassis hole making corresponding to the wheel shaft fit

of the trailer (figure 5).

RB

PB/2 PB/2 PT/2 PM/4 PM/4

RA

PC/2

1 2,B 3 4 5 6 A

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

√( ) ( ) (13)

(14)

4

a)

b)

FIGURE 5 – Critical section a) Detail of wheel hole b) Graph of Von

Mises stress versus parametric distance of nodes [6]

The values obtained by the computational static simulation

were:

These values prove that the theoretical validation (static

design – chapter II.B) serves and proves the numerical static

modulation. The external loads result in a critical section of the

structure which is in full safety, being all the chassis inside the

elastic regime.

III. MANUFACTURING METHODOLOGIES

The chassis structure was thought to be resistant enough to

support interaction between passenger, motor, batteries, wheels,

controllers and flooring. In terms of safety, the stiffness to torsion

and the stiffness to bending are important factors. That means the

chassis shouldn’t deform owing to these loads in a way to

guarantee gentleness in movements and provide a reliable and

precise driving. Thus, even deforming a little, the chassis doesn’t

change its driving characteristics and in cases of impact the

structure will deform in an adequate way to absorb the impact

energies and protect the components. The final cost was taking

into account when constructing and installing the chassis.

After experiencing different types of structures to the chassis it

was reached the final geometry exhibit in figure 6. In this structure

was chosen structural simplicity, using simple forms with 40x20x3

profile of Aluminum proposed before.

FIGURE 6 – Rectangular tubular frame a) Front view b) Side view c)

Isometric view [6]

This chassis meets a set of specifications and demands which

are:

Functionality

Light Material

Low fabrication cost

Simple Construction

Easy installation

Easy dismantling technique to enable the maintenance

Structure with enough stiffness and strength to bear all

the loads

The manufacturing process starts with plans that describe

each element as shown in figure 7.

FIGURE 7 – Chassis sketch for construction, dimensions in [mm]

In the manufactory was developed and constructed the

chassis trailer for bicycles. To do this were carried out pre-tests of

the structure (figure 8) and were used machines such as the

circular saw, drilling machine, a vertical axis milling machine, a

press brake machine and a welding with TIG process to bond the

set.

(15)

(16)

(17)

(18)

a) b)

c)

5

FIGURE 8 – Chassis pre-test

The process of construction and the installation was

concluded (figure 9) and were inserted the two power

controllers, the batteries and their accelerometers to make

experimental tests.

FIGURE 9 – Mounted chassis for experimental tests

IV. RESULTS

This chapter exposes results from computational dynamic

simulation. The results of experimental tests are also showed and

were made an approach to real performance of cyclist-bicycle-

trailer system.

A. COMPUTACIONAL DYNAMIC SIMULATION

It was made a dynamic simulation to the set bicycle-trailer with

their components and cyclist. For this, it was used software

Solidworks® Motion. The study consisted on travelling through a

straight line and passing through a bump which has 50 mm of

radius, as can be seen in figure 10.

FIGURE 10 – Computational dynamic simulation in a straight line with bump [6]

The model has 90 rpm applied to the trailer wheel in straight

line. It is known the radius of trailer wheel (r = 0.216 m) and linear

velocity of motor (v ≈ 2m / s). The value of angular velocity ω is:

The computational dynamic analysis was useful to evaluate

the behavior of the set bicycle-trailer.

The results of dynamic computer simulation for linear

acceleration (vertical direction z) along the time are showed in

figure 11.

FIGURE 11 – Computational Test: Linear acceleration (z) versus Time

The graphical analysis helps to interpret and describe the

different moments of computer dynamic simulation. Initially, the

system describes a straight line motion driven by motor rotation,

until to 7s. At 7s the bicycle front wheel passes through bump,

then at 8s the rear wheel passes and about 9s the trailer wheel

passes through the bump (visible for substantial peaks).

Thereafter, the system continues its movement in a straight line

through the rotation given by motor until the end of simulation, at

15s.

Generally linear acceleration values in figure 11 are located

around the 10m/s2, which approximately corresponds to

gravitational acceleration imposed to the system. We can see that

the trailer has the largest fluctuation in 9s with 25m/s2 peak. This

moment is explained by the trailer wheel passing through bump.

Greater acceleration implies more velocity variation and

consequently more variation of displacement along the time. For

this simulation it is shown in figures 12 and 13 the linear velocity

and vertical displacement of trailer along time.

FIGURE 12 – Computational Test: Linear velocity (y) versus Time

(19)

-30

-10

10

30

0 2 4 6 8 10 12 14Bicicleta (Motion)Atrelado (Motion)

Computational Test – Linear acceleration (z axis) versus Time

t [s]

az [m/s2]

0

1

2

3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Computatuonal test - Linear velocity (y) versus Time

vy [m/s]

t [s]

6

There is an initial increase on system velocity to achieve the

constant linear velocity given by the motor. As the system passes

through the bump the velocity values have three main peaks at 7,

8 and 9s. These moments correspond to the bump passage of the

bicycle front wheel, bicycle rear wheel and trailer wheel,

respectively. Then, there is a stabilization zone and system

retrieving the impact of bump and reaching its real velocity of 2

m/s.

FIGURE 13 – Computational Test: Vertical trailer displacement versus

Time

The system moves in a straight line to the first contact with the

bump approximately at 8s. There is expected a maximum vertical

displacement about 190 mm, following 21mm and 10 mm (figure

13). Considering that the height of the bump is 50 mm, the

approximate vertical trailer displacement (given by the

computational dynamic simulation) is 140 mm.

The computational dynamic simulation is an approximation of

reality with some limitations. The system is treated as a rigid body,

which in reality does not occur. The suspensions and damping are

negligible or nonexistent which doesn’t happen in real cases. At

the beginning of computational analysis it was forced the system to

fall down to make sure that it recognized all the contacts. These

factors may show values of acceleration, velocity and

displacement with some discrepancies.

The computational dynamic simulation shouldn’t be used

exclusively, being also the experimental tests an important way to

achieve and verify results.

B. EXPERIMENTAL RESULTS

Four experiments were simulated, in straight line (with and

without motor rotation) and in straight line with bump (with and

without motor rotation), to obtain acceleration levels of bicycle and

trailer along the time. To do these experiments it was used the IST

football field and a bump with 50 mm radius. For this purpose, two

accelerometers were placed in the system, an accelerometer on

the bicycle (at the bicycle frame and under seat) and the other

accelerometer on the trailer (at the upper end of the vertical tube).

The respective accelerations for bicycle and trailer were quantified.

Before being converted into G's, the acceleration value in mV

had to be corrected fix on 0 G's using an offset. This happened

because of the different accelerometers locations that instilled

electromagnetic interference in the respective cables which vary

with the proximity to the motor and its electronics. The results from

accelerometers, described above, naturally present some errors

compared to reality. There is always some variation in data

parameters characteristics because of environmental variations or

variations in manufacturing process. For a more accurate and

appropriate use in order to acquire more precise information is

necessary to carry out a calibration test [8].

For the results of each test were applied low-pass filters, in

order to eliminate almost all disturbances due external

environment, without losing the evolution of linear acceleration

along time. For this it was used Matlab® and its subprogram

Simulink. These filters were used taking into account

accelerometers characteristics and the instrumentation system

where they were inserted (table 6).

TABLE 6 – Data to use of low-pass filter

Not all the results from experimental tests will be presented

because of their great extension, only will be considered the most

important tests.

For the tests in straight line with and without the actuation of

the motor, the evolution of linear acceleration for transverse

direction (x axis) along the time, is visible in figure 14.

FIGURE 14 – Straight line test with and without motor: Linear

acceleration (x) versus Time

For the trailer to carry out a route in a straight line, with or

without actuation of the motor, there are no significant differences

between them. We can see through an examination of figure 14

that transverse acceleration (x axis) remains almost constant at a

level range from -1m/s2 to 1 m/s

2.

It is visible in figure 15 a zoom of linear transverse acceleration

(x axis) along the time for initial zone of bump test with motor

actuation. Between 2s and 3s the test begins with the

corresponding pedal of bicycle. It is expected a peak response of

lateral acceleration because of pedaling bicycle.

-202468

10

0 1 2 3 4 5 6 7 8

Atrelado s/ motor

Atrelado c/ motor

Straight line with and without motor (x axis) ax [m/s2]

t [s]

Test Cut

frequency Sampling frequency

Sampling time

[Hz] [Hz] [s]

IST football field 20 714 0,0014

050

100150200

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Computational test - Vertical trailer displacement (z) versus Time

ZCM

[mm]

t [s]

7

FIGURE 15 – Bump test with motor: Linear acceleration (x) versus

Time [0s to 3s]

Bump test was divided into three phases:

▪ Phase 1: initial zone (bicycle pedal and motor ignition)

▪ Phase 2: bump zone (bicycle front wheel, bicycle rear wheel

trailer wheel)

▪ Phase 3: end zone (stops / turns off motor)

In figures 16, 17 and 18 we can see the three phases of bump

test for vertical acceleration (z axis).

FIGURE 16 – Initial zone: Linear acceleration (z) versus Time

All base line for initial zone is around 1G because of the

imposed gravity. Between 0s and 2s the vehicle is stationary,

being the moment which we turn on the acquisition box data of

accelerometers. At 3s is registered the first relevant cycle which

corresponds to a 6 m/s2 peak followed by a 12.7 m/s

2 peak. At this

time it was observed the moment of bicycle pedal. Hundredths

seconds later, the bicycle pedal is felt by trailer, which is observed

with a 11.5 m/s2 peak (in red). Then there is an area of noise and

acceleration stabilization. Approximately at 5.2s the motor is

turned on and the first to feel this effect is trailer, as expected. It

records its highest peak of 12.5 m/s2.At 5.7s the motor ignition is

sensed by the bicycle indicating a substantial peak of 13.7m/s2

(figure 16).

Between initial zone and bump zone (6 to 12 seconds), the

bicycle goes driven by the motor with constant linear acceleration

along z axis about 1G.

FIGURE 17 – Bump zone: Linear acceleration (z) versus Time

Bump zone is visible in figure 17 (12s until 14s) pointing out

three moments, the passage bicycle front wheel, bicycle rear

wheel and the passage trailer wheel. The passage of the front

wheel is felt first by the bicycle (green) as expected evidencing the

cycle peaks at approximately 5 m/s2 and 15.8 m/s

2. This effect is

felt by trailer after, but having little effect because of the large

distance between bicycle front wheel and its respective

accelerometer. This effect is felt at about 12,5s test. The second

moment, the passage of bicycle rear wheel through the bump, is

felt in the first place by the bicycle, because the position of the

accelerometer is closer than bicycle frame, being closer to the rear

wheel. On the bicycle and in this region two peaks are recorded

approximately 26 m/s2 and -5 m/s

2. The response of the trailer

comes immediately with 19m/s2 peak. Then at 13.17s, when the

trailer wheel passes through the bump, there is the greatest peak

acceleration at about 35 m/s2

and -25 m/s2. The response of the

bicycle under acceleration is not so affected in this area it is

observed a little oscillation.

FIGURE 18 – Final zone: Linear acceleration (z) versus Time

There were observed approximately at 16.25s, relevant peaks

of trailer acceleration (about 3.5 m/s2 and 25 m/s

2), and

respectively peaks in bicycle (about 7 m/s2 and 14 m/s

2). This

moment corresponds to bicycle immobilization and motor stopping

(figure 18).

In figure 19 is compared the evolution of linear acceleration (z

axis) along the time for bump tests with and without actuation

motor.

FIGURE 19 – Bump test with and without motor: Linear acceleration (z)

versus Time

Trailer acceleration driven by motor is slightly higher when

compared with test without motor action. But generally, there are

no significant differences in z axis when compared bump tests with

and without motor.

Taking into account bump tests, it is made a linear velocity

analysis in longitudinal direction y along the time. This is visible in

figure 20 that shows the test restricted to initial area (0s to 7.5 s),

-2-1012

0 1 2 3Bicicleta

Atrelado

Bump test with motor (x axis) [0s to 3s] ax [m/s2]

t [s]

57,510

12,5

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6

Bicicleta

Atrelado

Bump test with motor (z axis) [initial zone] az [m/s2]

t [s]

-35-20

-5102540

12 12,5 13 13,5 14

BicicletaAtrelado

t [s]

Bump test (eixo z) [bump zone] az [m/s^2]

-30-20-10

010203040

0 2,5 5 7,5 10 12,5 15

Atrelado - s/ motor

Atrelado c/ motor

Bump test - with and without motor (z axis) az [m/s2]

t [s]

05

10152025

15,5 16 16,5BicicletaAtrelado

Bump test with motor (z axis) [final zone]

az [m/s2]

t [s]

8

which reveals to be essential for understanding constant level of

linear velocity reached by the motor.

FIGURE 20 – Bump test with motor: Linear velocity (y) versus Time [0s

to 7,5s]

In initial moments and approximately until 2.5s, it is noticed

that vehicle has not yet begun their march, it is stationary and with

zero linear velocity. At 3s system is affected for bicycle pedal by

cyclist, this being evidenced by an increase velocity until 4.5 m/s.

And then at 5s it is visible a constant level of linear velocity in 2m/s

which corresponds to speed imposed by motor. At this instant

occurs motor ignition.

C. VEHICLE PERFORMANCE

In the listed tests above there were inserted into chassis two

batteries (only one was on) located in upper region of structure,

closer to the bicycle. At bottom side there were placed (in battery

supports) the accelerometers box data acquisition and breakers.

Figure 21 shows the different components assembled to carry

out experimental tests.

FIGURE 21 – Components used in experimental testes

In which:

A – Controller

B – Acquisition box data of accelerometers

C – Breakers

D – Lead Acid Battery 12V 36A.h

E – Accelerometer

After experimental tests, it was evaluated chassis assembly

cyclist. Their behavior was inspected in order to understand the

real performance of prototype designed (figure 22).

FIGURE 22 – Cyclist-bicycle-trailer system

Vertical displacement suffered by trailer when it passes on

bump with r = 50 mm can be seen in figure 23. Adding damper on

the trailer wheel, would control movement of suspension, and

improve vertical oscillations. This application maintains a continue

contact with ground and improve its stability.

FIGURE 23 – Vertical displacement of the trailer

There were some lateral oscillations on the trailer, which can

be seen in figure 24.

FIGURE 24 – Lateral oscillations of trailer

Increase cable length and its installation on handlebar would

be a satisfactory possibility to achieve a better functionality (figure

25).

FIGURE 25 – Ignition motor with aid of another person

Some possible solutions for facts observed in the experimental

tests are:

▪ Improve mass distribution of chassis components.

0246

0 1 2 3 4 5 6 7

LOMBA COM MOTOR: Velocidade Linear (y) verus Tempo

t [s]

vy

[m/s]

D

E

A

A

B

C

D

9

▪ Elevation the structure and decrease width to make larger

curves.

▪ Decrease length of linkage mechanism bicycle-trailer, i.e.,

lower brace, reducing torsional stresses.

▪ Improve grips in linkage mechanism bicycle-trailer.

D. CONCLUSIONS

The electric propulsion vehicles have become increasingly

useful and necessary because they are not only an alternative to

limited resources and energy constraints but also because of

environmental impacts associated that are increasing negatively

for the sustainability of the planet.

The developed prototype has proved to be portable and

allows, if desired, the exclusive use of the bicycle without being

affected by motor, operating as a common bicycle. This electric

trailer combines together the functions and benefits of electric

bikes and trailers, only in a single system.

The decision parameters of material selection were density

(more relevant parameter), fracture toughness, yield strength,

unitary cost and stiffness. Through Ashby maps analyses and in

order to select a material to satisfy the requirements of the

chassis, it was selected Aluminum 6063 which was the best

solution.

With static design analysis it was found that critical section

was in chassis hole making which corresponds to the fit of wheel

shaft of the trailer. Maximum efforts totaled an effective Von Mises

stress of 5.4 MPa. The previously material selected confirmed the

prototype safety with safety factor of n = 22.2. The external loads

are low and result in a critical section which is in full safety, with all

chassis in elastic regime. It is also conclude that theoretical

validation made by stresses analysis serve and prove

computational static simulation performed.

The computational dynamic simulation has been validated and

was used to predict the behavior of the system, verifying a

satisfactory agreement with experimental results. Both in dynamic

simulation and in experimental tests we can understand the

behavior of bicycle as well as trailer. Through graphic analysis

some different moments such as bicycle pedal, motor ignition,

passing through bump by bicycle and trailer are perceptible and

also the ending moment of braking or turning off the motor.

REFERENCES

[1] Dário Silva; Electromagnetic braking system for aircraft application,

Prototype design; Dissertação para obtenção do Grau de Mestre em

Engenharia Aeroespacial; IST; 2010.

[2] Ashby, M., Shercliff, H., and Cebon, D.; Materials: engineering, science,

processing and design; Butterworth-Heineman; 2nd

Ed; 2010.

[3] http://www.grantadesign.com/education/edupack2011.htm; Software

CES Edupack 2011.

[4] http://www.dem.ist.utl.pt/~m_mII/Download/Indice_de_desempenho.pdf

[5] http://www.matweb.com/; MatWeb.

[6] http://www.solidworks.com; 3D CAD Design Software Solidworks

[7] http://web.MIT.edu/16.810/www/16.810_L4_CAE.pdf

[8] José Afonso; Projecto e avaliação operacional de uma estrutura;

Dissertação para obtenção do Grau de Mestre em Engenharia

Aeroespacial; IST; 2010.