design of human powered vehicle

5/25/2018 Design of Human Powered Vehicle

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Department of Mechanical Engineering

Group Design Project MEC307

Group Report for3

rdYear Design Project 2007 for

Motorsports Engineering Managementand Sports Engineering

The Design o f a Human

Powered Vehic le for

A t tempt ing the World

One-Hou r Distance

Record

Ryan Benson,James Froggett,

Nik Kamarudin,Tim Lewis,

James Melia,Kamal Zaman

18th

May 2007


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Summary

A team was formed under the name Glide by Icycle with the intention of breaking the Dempsey MacCready hourrecord which currently stands at 53.43 miles travelled in an hour. In order to do this, we had to brainstorm ideas forthe most efficient high speed human powered vehicle which ended up being the recumbent bike. Following thisdecision, we had to research current designs and the history of the vehicle in order to evaluate which changes were the

most influential, and which areas could be improved. The section that was seen to be the most influential was reducingfrontal area so this criterion was given the main priority. Sections, including aerodynamics, frame design and powertransmissions were then assigned to individual members of the group who then went on to study these areas in greatdetail. After months of study we finalised the ideal components and features that we hoped to implement in ourrecumbent bike. After numerous meetings, we came up with a design that was able to include all these featureswithout impairing the priority sections. The final design was seen to be a teardrop shape with an elongated rear. Thiswas to house large wheels with high pressure, smooth tyres rotating on hardened steel ball bearings with a UHMWPEcase. The power transmission was decided to be a torque converter system. The method of braking was decided to berim brakes. The frame was crated to be as light as possible using aluminium alloy tubes but to also house a traditionalseat to allow the rider to sit in the supine position and include an under seat steering system. The finalised design wasthen modelled on Pro/Desktop and ANSYS and the calculated forces applied. These programs showed no problems orfaults with our design so all we now have to do is build and test our recumbent bike design.


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Contents

Summary

1.0 Introduction1.1 Aims and Objectives1.2 Project Statement

2.0 Human Powered Vehicle Selection3.0 Analysis of the forces on a recumbent

3.1 Effects of design changes on performance4.0 Recumbent bike components

4.1 Tyres and Wheels4.2 Bearings

4.2.1 Bearings in a recumbent bike4.2.2 Bearing Conclusion

4.3 Powertrain4.3.1 Options for the powertrain4.3.2 Gear ratio selection4.3.3 Powertrain Conclusion

4.4 Bicycle brakes4.4.1 Rim brake4.4.2 Selection of brake for recumbent bike4.4.3 Brake balance

4.5 Breathing4.6 Riders position4.7 Seating4.8 Steering4.9 Frame Design4.10 Aerodynamics

4.10.1 Drag5.0 Conclusion

6.0 References7.0 Appendix


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Nomenclature

a/A Dimensions of contact m2

b Wheel base m

CRRS Static coefficient of rolling resistance

CRRD Dynamic coefficient of rolling resistance

D Deceleration ms-2

D1 Diameter of rolling element mD2 Diameter of axle m Steer angle radsmax Maximum deflection m Load distribution factorE Youngs modulus PaE* Reduced modulus PaF Applied load NFmax Maximum applied load NFN Applied normal contact load Ng Acceleration due to gravitational force ms-2h/HtCG Height of the centre of gravity m

I Moment of inertia kgm

2

k Stiffness N/mK Radial stiffness N/ml Wheel radius mmi Momentm Mass kgP Applied load Npo Maximum contact pressure MPaq Quality factorQ Rolling element load NQ0 Load of a maximum loaded rolling element Nr Radius mR Relative radius of curvature mt Torsional deflection mT Applied torque Nmur Clearance value mmv/V Vehicle velocity m/s PoissonsratioWdf Front dynamic weight, sum of the moment about the front tyre to the road contact point NmWfs Static Front Weight NWt Total weight of recumbent bike NWb Wheelbase mx Deflection mZ Number of rolling elements per row Angle of incline Tilt angle rads


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1.0 IntroductionThe traditional cycling hour record is the most famous world record in cycling. Records have been kept since 1876, in

which the first record was recorded to be 25.506 km travelled in one hour. The cycling hour record is now known as

the Dempsey-MacCready hour record. The Dempsey-MacCready hour record was created to inspire and promote

light, pollution free, human powered transportation. Originally, the $25,000 Dempsey-MacCready hour prize was

awarded to the first team that is able to travel more than 90 km in an hour. The distance, has not, thus far, been

exceeded and the prize has expired so the prize was awarded to the team that had travelled the furthest distance in onehour. The rider of this team was Fred Markham who travelled 85.991 km in an hour which is currently the Dempsey-

MacCready hour record. This is the distance which our team, Glide by Icycles, hope to exceeded using a human

powered vehicle.

During the history of the record, the vehicles have adopted a more aerodynamic shape as the years have

progressed and the distance has increased. From this we know aerodynamics are paramount so Glide by Icycles,will

be focussing on getting the right balance between aerodynamics and power. Having a human powered vehicle with

good aerodynamic properties hampers the power the driver is able to provide due to the awkward position of the driver

and so it is essential we get this perfect if Glide by Icycles is going to break the Dempsey-MacCready hour record.

There are also many other features which will contribute to the success of the human powered vehicle such as weight,

power train, etc. However, like all world record attempts, there are also many regulations that we have to abide to,

such as the vehicle must fit into a box 1.5 m high, 1 m wide and 3.1 m long, all vehicles must have a safe means of

stopping aswell as numerous others.

1.1 Aims and Objectives

To design a human-powered vehicle to break the current Dempsey-MacCready Hour Record (85.991km).

To improve upon the current design.

2.0 Human Powered Vehicle Selection

In order to decide which type of human powered vehicle we will used to break the Dempsey-MacCready hour record,we performed a general brainstorm of ideas. Of the designs that were proposed, they then had to be evaluated todetermine which will be the most effective design.

We decided that amongst the factors that affect the performance of the human powered vehicle, some were ofgreater importance than others. To allow for this to be taken into account whilst evaluating the designs we came upwith a way of weighting the criteria. As a group, it was decided that aerodynamics was of greatest importance to thedesign, as this gives the greatest opposing force due to drag. Power is second most important, as the more power thatcan be delivered, the faster the vehicle is able to travel. The lowest scoring criterion was ease of manufacture, as thereis no price limit for the design since we are producing a one-off model to break the one-hour record.

The most important of the criteria was given a power weighting of 8, meaning that the scores given to thedifferent designs for this criteria are multiplied by 8. The power weightings are given in order with lowest order beingmultiplied by 1.

Each type of human powered vehicle that was proposed was then scored out of 5 against each of these criteria, asshown in the performance matrix (Table 1). These scores were multiplied by the weighting factor and then totalled tofind the most effective design.

Criteria Type of human powered vehicle


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Table 1: Performance of human powered vehicles matrix

From the evaluation using table 1, we can see that the upright bike and the recumbent bike were clearly the leadingdesigns. Of these, the recumbent bike scored highest, so this is the type of design that we will develop to break theDempsey-MacCready one hour record.

3.0 Analysis of the forces on a recumbent

In order to design our recumbent bicycle to be of optimum performance, we need to analyse the make-up of thevarious opposing forces on the vehicle.

The general formula for the losses of a recumbent;

RIDRRDRRSDOPP FVCmgCvACF 04.0)2(2

1 2 (1)

The total opposing force is made up of the aerodynamic drag, the rolling resistance and the transmission losses.Rolling resistance is affected by a static coefficient, and a dynamic coefficient which varies with vehicle velocity. The

tyres can be assumed to have a static and dynamic rolling resistance coefficient of 0.002 and 0.05 respectively [1]. Themass of the recumbent and rider has been approximated as 75kg.

A formula can be set up, as in table 2, using this equation to calculate the power requirements to overcome eachof these losses. The resulting data has been plotted on figure 1, to highlight the contribution of the different dragforces to the total drag, and how they vary with vehicle velocity.

Velocity(m/s)

Aerodynamicloss

RollingResistance,

FR

Transmissionloss

Required riderpower (W)

0 0 0 0 0

10 15.104 24.715 1.59276 41.41176

20 120.832 69.43 7.61048 197.87248

30 407.808 134.145 21.67812 563.6311240 966.656 218.86 47.42064 1232.93664

50 1888 323.575 88.463 2300.038

Table 2: Data of forces on a recumbent

Jumpingpowered

Hoppingpowered

Walkingpowered

Zorbball

Uprightbike

Recumbentbike

Aerodynamics (8) 2 2 2 1 3 5

Weight (5) 4 5 1 3 4 3

Power (7) 2 1 1 2 5 4

Tyre friction (4) 5 5 5 1 4 4

Reliability (2) 2 2 1 4 4 4Safety (3) 1 1 3 2 3 5

Ease of manufacture(1)

1 1 1 5 4 3

Ease of use over 1hour period (6)

1 1 4 3 4 5

Totals with weighting 84 82 84 78 140 155


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0

500

1000

1500

2000

2500

0 10 20 30 40 50 60

Velocity (m/s)

Power(W)

Total power req.

Aerodynamic

Rolling Resistance

Transmission

Figure 1 shows the losses and power required for a recumbent bicycle. As vehicle velocity increases, the lossesthrough rolling resistance and transmission increase fairly linearly. However, the aerodynamic losses increaseproportionally as the velocity is increased, and this loss is the main contributor to the drag force on the vehicle.

The total power required to achieve a given speed is shown, and it can be seen that the relationship betweenvelocity and required power is not a linear one. To achieve 50m/s, the power required is around 2300W, which dropssignificantly at 30m/s to around 550W. This means that for each m/s increase in velocity we are to achieve with ourrecumbent, we must take into account that the power requirements will be increasing more and more.

As figure 1 shows, the aerodynamic drag is the greatest contributor to overall drag, reducing it is of greatimportance. A good recumbent design with a fairing can help to reduce this loss by minimising the frontal area. In our

design, we need to reduce this loss further, through a more aerodynamic fairing which would result in less separationand pressure drag at the rear of the recumbent.

Figure 1 also shows that the rolling resistance loss has a fairly significant effect on performance, with around300W of the rider power needed to overcome this at 50m/s. This is an area which must be analysed in our design inorder to reduce this loss.

Transmission loss is the other main area where energy loss occurs; this refers to energy lost largely in the chainand gear mechanism. This will be reduced by investigating into the most efficient bearings that can be fitted, and alsoa more efficient system of power delivery, using a shorter chain, in our recumbent.

3.1 Effects of design changes on performance

The current one-hour record is 53.43 miles (85.987km). If we assume that the acceleration from rest up to thecruising speed will take approximately 30 seconds, the cruising speed for the current design can be approximated as55mph. Our design has been based on achieving a steady speed of 60mph. This will comfortably break the hour-record even if the losses have been slightly under-estimated in our calculations.

To see the effect that the implemented changes will have on the performance of the recumbent, a formula hasbeen set up so that the changes are easily visible. For the calculations, the effects will be analysed at the cruisingvelocity since this is the speed the recumbent will be travelling at for the majority of the one-hour record attempt. Thiscruising velocity is assumed to be 60mph, which correlates to 26.82m/s.

Figure 1: Forces on a recumbent


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Velocity(m/s)

AerodynamicDrag, FD

Rolling Resistance,FRR

Riderforce,FRID

Transmissionloss ()

Requiredrider power

(W)

Traditionalhigh-speedrecumbent

26.82 10.86 4.15 15.02 0.60 418.89

10% Lessfrontal area

26.82 9.78 4.15 13.93 0.56 388.59

Reduce CRRS,CRRD10%

26.82 10.86 3.74 14.60 0.58 407.31

Reduce Mass10% 26.82 10.86 4.01 14.87 0.59 414.79

ReduceTransmission

loss 10%

26.82 10.86 4.15 15.02 0.54 417.28

Implement all 26.82 9.78 3.61 13.38 0.48 371.87

Table 3: A table showing which features are the most critical to increasing the efficiency of the recumbent bike

Table 3 shows that reducing the frontal area of our recumbent has the greatest effect on lowering the required riderpower. At the cruising velocity, the drag force is the largest opposing force, so reducing this has the biggest effect onperformance. A more streamlined rider position will enable us to have a smaller frontal area. This will be achieved bymaking the riders seat position angled closer to the horizontal, so that the fairing to encompass him will be smaller.

It can be seen that reducing the rolling resistance coefficients has a significant effect on the power requirementsof the recumbent. They can be reduced by ensuring that the wheels are as low friction as possible, through usingsmoother, high pressure tyres.

The mass reduction appears to have a small effect on the power required to maintain the speed of the recumbent.In actual fact, the effect of mass will be greater since there is an inertia force produced during acceleration whichaffects the performance. Since the inertial loss has also been reduced, this will reduce the time taken for the recumbentto accelerate up to the cruising speed. Reducing the mass of the vehicle therefore has the combined effect of reducingthe rolling resistance as well as reducing the inertial loss

The transmission efficiency for a bicycle is already very high, around 96%, so the transmission loss is very smallin comparison to the other forces involved. Bicycle gears and bearings are highly efficient, so increasing theirefficiency only has a small effect on performance.

Implementing all of these changes reduces the required power to maintain the cruising velocity by 12.6%, whichwill have a significant effect on our performance, and will possibly enable us to break the record. The required powerof 371.87 W is realistic, as it has been found that a top athlete can achieve a maximum power of around 400W. Itwould therefore be possible for an elite athlete to achieve the cruising velocity stated for the duration of the attempt.

4.0 Recumbent bike components

4.1 Tyres and wheels

An important feature of the recumbent bike is the wheels. They provide alarge resistive force in terms of rolling resistance, and also contribute to theaerodynamic drag. Rolling resistance is one of the major factors contributingto the losses of a recumbent, making up around 15% of the losses at highspeeds.

2

2

1vACD

RRDRRS VCmgC 2 RIDF04.0RRD FF )( RIDFV

RFRR

mg

F

Figure 2: Diagram to show the forces exertedon the wheels


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This force must therefore be minimised in our design if we are to break the one-hour record, so the different optionsavailable to the team must be analysed. Figure 2 shows a simplified version of the forces on the wheels;

Rolling resistanceThe rolling resistance is the mechanical friction generated between the tyre and the road as it rolls. This force opposesthat of the propelling force produced by the rider. In order to achieve optimum speeds, this rolling resistance must bereduced as much as possible.

The fundamental equation for rolling resistance is defined as;

RRDRRSRR VCmgCF 2 (2)

The equation shows that the rolling resistance is influenced by vehicle velocity, weight and coefficients of rollingresistance. The static coefficient,CRRS, is based on the tyre pressure and smoothness, and the dynamic coefficient, CRRD, is based on the speed. If our team is to achieve optimum speeds, the weight and the frictional coefficientstherefore need to be lowered.This can be achieved in our design by utilising;

Smooth high pressure tyres

Big wheels Latex inner tubes

Good quality road surface

Tyres

Theoretically, the highest tyre pressure that can be attained is desirable. This would give virtually no deformation ofthe tyres as they are supporting the weight of the rider and recumbent. Tyres are cyclically loaded each time thewheels turn through one rotation, as they bear the weight of the rider and the recumbent. Energy loss occurs as thetyres are deformed, as transformation of mechanical into thermal energy occurs. However, this high desired tyrepressure must be traded-off with the need for safety, so that the tyres will not suffer a blow out during the hour inwhich the recumbent is being ridden. Track racing tires can typically be inflated up to c.14 bar [2].The tyre properties should also be as consistent as possible, and hence be predictable to the rider.

Tubular tyres should be used. They give a greater weight reduction compared to thetraditional clincher type. The tyres are required to be very firm, so less energy is dissipated asheat in deforming the tyre. Smooth tread on the tyres will reduce the rolling resistance withthe road. Using a laser machining technique to produce the tyres for our recumbent couldproduce an extremely smooth surface down to a molecular level.

Clincher and tubular rims

The tubular and clincher rims are shown in figures 4 and 5. It illustrates the advantage of the tubular design, which hasavery simple lightweight box-section rim, rather than the heavier U-shaped clincher rim.

Figure 3: A tubular tyre

Figure 4:Clincher rim Figure 5: Tubular rim


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The wheelbase of our recumbent is important to its performance. Short or long wheelbase designs differ in theposition of the front wheel in relation to the cranks. Our design will use a short-wheelbase, where the pedals are outahead of the front wheel. The high foot position provides an aerodynamic shape, and due to the position of the pedals,more power is transferred through the drive train.

This rider position, with the pedals located as shown, will enable us to make our design front wheel driven. Thisis advantageous, since traditional designs have been rear wheel driven, leading to the need for a long, heavy chain.This has been explored in the section on gears.

Figure 6: Short wheelbase design

A 10% reduction in the rolling resistance leads to a 10% longer braking distance on a wet road. This increase inbraking distance can be ignored in our design, however, since we are only attempting the record once, and there is along distance for the recumbent to slow and come to rest in.

Size of the wheel

It is clear that larger wheels will increase the performance of the recumbent, as the same effort from the cranks willresult in a longer distance covered per rotation of the wheel. Making the wheels as large as possible however wouldnot optimize performance, since increasing the wheel size has negative consequences of increased apparent area andweight. A balance must therefore be struck. The higher the weight of the wheel, the harder the rider has to work toturn the wheel. Typical racing tyres are 700mm in diameter, since this size provides an optimum balance. This is thewheel size we will use in our design.Rolling resistance increases in near proportion as wheel diameter is decreased for a given constant inflation pressure[3]

Wheel mass

The mass of our wheels is important, since the rider must provide more power to ride a bike with heavier wheels. Theadditional power required is proportional to the additional weight during accelerations. Heavier wheels also have anincreased rolling resistance. Weight reduction in our wheels could be achieved through;

Straight pull, high tension spokes, enabling reduced spoke counts Lightweight rims sections and materials Lightweight spokes Half-discs on wheelsonly on the outermost exposed section

Rotational inertia

A rider must provide more power for wheels with a greater moment of inertia (MOI). The moment of inertia applies tothe wheels, since they rotate as well as tranlate as the recumbent moves. Lowering the MOI means the wheels willaccelerate more quickly and with less effort.

Mass situated a large distance from the axis of rotation of the wheel increases the rotating inertia. Since the rims arethe outermost section of the wheels, it is these that have the greatest effect on rotational inertia. The wheel rim musttherefore be of reduced weight. Tubular tyres could achieve this in our recument, as they use a very lightweight simple

box-section rim, thus helping to reduce rotational inertia.Other features, such as the half-discs we use, and the spoke nipples must be as lightweight as possible to reduce theMOI. Locating the spoke nipples at the hub rather than at the rims could also reduce the MOI in our design.

Moment of inertia, I, is calculated from;

2

ii rmI (3)This gives the power required in terms of the linear velocity and acceleration as;


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var

IP

2 (4)

Equivalent massThe equivalentmass is a combination of the mass and moment of inertia of the wheels. It enables a comparisonbetween weights of rotating and non-rotating bicycle components, such as wheels versus a frame. It also enables abetter comparison between various wheel sets that may have similar masses, but different MOI. The effect ofequivalent mass on performance is that a rider must provide more power to accelerate wheels with a greater equivalentmass. The additional power requirement is proportional to the additional equivalent mass during accelerations [4].

2rImmeq (5)

The stiffness of the wheels is an important property, as large deflections will result in energy losses and reduce theefficiency of the bike. Stiffness can affect our wheels performance by three methodologies; Torsional stiffnessprevents any deflection in the wheels with each fluctuation in the crank torque.

T = kt * q (6)

Lateral stiffnessflexing of the wheel due to side loads from events such as sprinting or cornering.F = kl * x (7)

Radial stiffnesswheels subjected to radial loads due to weight of the rider. Greater radial stiffness will result in aharsher ride, while those with lower radial stiffness will flex more and absorb shock loads better. [5]

K = E*A/L (8)

Materials of the wheels

Moulded carbon fibre rimsRubber tyresThin Kevlar layer between the tyre casting and the outer tread provides excellent puncture resistance.Titanium spokes

Our recumbent design is to be front wheel driven, so as our rear wheel is not driving the recumbent, reduced spokecounts can be used, which will provide less weight. The spokes traditionally must transmit the torque applied to therear hub by the drivechain out to the rim. This is not the case with our rear wheel, and it will be essentially free-wheeling. In order for the wheel to remain true and straight, the spoke tension must be equal and appropriate to givethe wheel enough strength.

3.2 BearingsBearings are extremely common devices used to reduce the level of friction between two surfaces. The motion

between the two surfaces is usually rotary or linear. Bearings are broadly classed by their shape or by the type of

motion they allow and in this section, Glide by Icicle will consider all the available options and materials to try and

make the recumbent bike parts rotate as freely as possible.

There are numerous places where the recumbent bike which will need a bearing type device to reduce friction

between the surfaces. These places in the front and rear hubs, the bottom bracket, the pedals and we may also need to

consider the fork tube and the freewheel [6]. This will depend on our steering mechanism and whether we will need to

incorporate a freewheel as this allows the pedal cranks to turn independent of the wheels. But if we are going for a

world record, will they be constant pedal power applied? If so then is there any need for a freewheel?

There are four commonly used, feasible shapes for bearings. Each shape has its own advantages and

disadvantages. The four variations of bearing are the ball bearing, the roller bearing, the tapered roller bearing and the

spherical roller bearing [7].


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3.2.1 Bearings in a recumbent bike

The front and rear hubs are situated by the points indicated in

figure 7 as A and B along with the significant loads.

To calculate the maximum force upon the bearings

present in the front and rear hub we need to consider the

external load. The mass of the rider can be assumed to be 80kg and the mass of the bike to be 18 kg giving a total mass of

98 kg. Therefore the applied load is;

NmgF 96181.998 (9)

Using 0 we get;

NmgF 19220cos961961cosFmax (10)

The way these forces interact with the bearings can be seen in

figure 8. Since there are two tyres, and two sets of bearings per

tyre, the force on each set of bearing is 480.1N.This load isdistributed amongst the bearings within the bearing case. Theway the load is distributed depends on a number of factors.

One factor is the centrifugal force, Glide by Icycles is

expecting to make the recumbent bike travel at around 90

km/h which will create such force upon the bearings, values of which can be seen in table A13.

From table A13, it can be seen that the largest centrifugal

force we calculate is slightly above 1 N. This is tiny compared

to the overall forces so we can safely neglect the effects of

gyroscopic motion and centrifugal force from our load

distribution calculation.

Next, Glide by Icicle has to decide on the clearance value to

use. Clearance present in roller bearings allows for somemanufacturing imperfections, a small amount of deflection under

load and thermal expansion. But with greater clearance comes

increased rock and instability. By using a low clearance value,

it will allow the lubricant to make a thin film between the roller

bearing and housing. Also, less energy will be lost by vibration

and noise, removing these will allow the recumbent bike to

travel more efficiently [7]. However, disadvantages include

having the possibility of having a substantial amount of heat

build-up reducing fatigue life. The bearings will not be revolving

at incredible speed therefore not much heat will be generated and

the bearings only need to last an hour therefore, these

disadvantages do not pose a great problem and so the value of

0.3 mm seems ideal. [8].Now the factors affecting loaddistribution have been considered, the maximum roller bearings

load can be calculated.

The maximum rolling element load is calculated from equation (11).

rZJF

Q 0 (11)

mg Fn/2

A

B

Fn/2

m = mass of bike + rider

Fn = Normal contact force

= Angle of incline

A = P o s i t i o n o f f r o n t h u b

B = P o s i t i o n o f r e a r h u b

Figure 7: An analytical diagram of recumbent bike

Forks

Central

axle

S okes

Normalforce

Force fromtotal mass

Bearin s

Figure 8: Free body diagram of a bicycle hub


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Using the clearance value of 0.3 mm and the maximum

deflection approximated to be 1/30thof the bearing diameter in

small diameter bearings. We can calculate for a 3 mm bearing;

2.03.01.02

3.0

12

1

212

1

max

r

r

u

u

(12)

This value of 0.2 equates to a value of 0.1590 for rJ which can beseen from table A14. Inputting this value into equation (11), we can

calculate the maximum rolling element load, Q0. Where Z is the

number of rolling elements per row and can be approximated from

equation (13).

Z

D

DD

1

21 (13)

With Q0,we can calculate the maximum contact pressure from formulas (A1), (A2), (A3) and (A4) found in the

appendix, which are based on spheres, point contact. These calculations are then inputted into a spreadsheet to quickly

find the optimum values. The resulting tables can be seen in the appendix. The results for the front and rear hubs as

discussed can be found in tables A1, A2 and A3.

4.2.3 Bearing Conclusion

Table A2 shows the maximum contact pressure, for an ideally sized steel bearing being of acceptable value therefore,

the higher friction but lower contact pressure type roller bearings such as the roller bearing, tapered roller bearing and

spherical roller bearing can all be neglected as these will not provide advantageous properties to a high speed

recumbent bike.

It is possible to see from tables A1, A2 and A3, the effect of changing the radius of the roller bearings and

wheel axle aswell as the material of these two components. The columns highlighted in yellow are the columns are thecolumns being investigated whilst the rows highlighted in green highlights the value that is assumed to be the best

value for the task involved.

An ideal ball bearing would be as small as possible as smaller bearings deform less and therefore have smaller

energy losses. It would also be ideal to have a small as possible contact pressure. However, small contact pressures are

generally seen in large bearings so a compromise has to be made. Table A1 shows the radial value of 18 mm to be the

most appropriate value. This is when the contact pressures start to converge and it is also small enough to make an

efficient bearing. Similarly in table A2, the radius of the wheel axle of 50 mm, was decided upon by a similar method,

but with also considering the large increase in thrust loads that appears with larger axles due to a greater moment.

Table A3 provides a very narrow view of how the material affects the performance of a bearing. Table A3

shows the maximum contact force for such material and then further research has to be done of the material to see if

the material has the strength and properties to withstand such loads and provide smooth friction free motion. After

much research, Glide by Icicle came to the conclusion that hardened steel bearings with the axle layered with ultra

high molecular weight polyethylene (referred to as UHMWPE from here on in) would provide the best properties for

the bearings in the front and rear hubs. This was concluded because hardened steel with UHMWPE exhibits a very

low coefficient of friction of 0.2. Different materials are used because similar materials are prone to sticking due to

adhesion forces and bonding.

BallBearings F

D1

Centralaxle

Hub

housingD2

Q0

Q1 Q1

Q2Q2

Figure 9: A free body diagram showing the load

distribution in a wheel hub


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UHMWPE Hardened Steel

Extremely resistant to abrasion Extremely hard

Very tough Brittle and is difficult to deform

Extremely low coefficient of friction High melting temperature

Highest impact strength of any thermoplastic High impact strength

Self lubricating Can be machined to high tolerances

Highly resistant to corrosive materials Extremely resistant to abrasion Low moisture absorption

Under high contact pressure, UHMWPE possesses

a self-repairing ability[9]

Table 4: Table showing the properties of UHMWPE and Hardened Steel

For the remaining bearings on the recumbent bike, the exact same methodology was undertaken. The results to these

can be seen in tables A1-A9 found in the appendix whilst the final sizes and materials can be seen below in table 5.

4.3 Powertrain

4.3.1 Options for the powertrain

The main options available to the team are;

Chain and sprocketchain drives a sprocket attached to the front or rear wheel. The efficiency of a chain andsprocket system is usually over 99%. [10]

Gear cogsAchieved by mounting a cog to the front fork, which is then driven directly by the pedals. This thendrives another gear cog, which is attached to, and drives the front wheel. Limitations are that it is restricted to being a

single-speed, fixed gear system, which may not be able to produce the desired acceleration. Another problem is that in

order to pedal forwards, an idler gear would need to be inserted, decreasing the efficiency of the transmission.

Planetary gearssimilar mechanism to gear cogs on bicycles, providing a more compact system. Advantages ofthis design over traditional chain-driven bicycles are that there are less frictional losses without the chain; both front

and rear wheels can be made large, decreasing rolling resistance; and there is a good channelling of force, with no

torsion.[11]

Torque converter- The use of a torque converter would give a compromise between a fixed gear system and amulti-gear system. The application of force from the belt causes it to contract and slide into a v-shaped gulley

operating as a smaller cog. This small cog allows for a greater application of torque when accelerating. As top speed is

approached, the pulley begins to expand around a larger cog. This means the gear ratios vary continuously, so that it is

always producing the optimal gear ratio for the amount of torque applied to the crank, making the acceleration optimal

as the speed increases. There are also no jumps in the transmission caused by changing gear, as is the case with a

drailleur system.

Bearinglocation

Appliedload, F Rbearing Raxle

Clearance(mm) Material

Hubs 480.1 0.0018 0.05 0.3 Hardened steel bearings w/ UHMWPE axle

Forks 30 0.001 0.015 0.3 Hardened steel bearings w/ UHMWPE axle

BottomBracket 230.1 0.001 0.03 0.3 Hardened steel bearings w/ UHMWPE axle

Pedal 180.1 0.0015 0.015 0.3 Hardened steel bearings w/ UHMWPE axle

Flywheel N/A N/A N/A 0.3 N/A

Table 5: Final bearing sizes and materials


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4.3.2 Gear ratio selectionThe procedure to determine an optimal gear ratio is given by:

Figure 10Procedure for determining the optimum gear ratio for a bicycle

For our design, the slope gradient can be assumed to be zero, as the competition will take place on flat ground. The

desired cruising velocity, in top gear, is determined by the currently existing record of 53.07 miles in one hour.Allowing for the time taken to accelerate up to this top speed, a cruising velocity of approximately 60mph should beappropriate. A driving wheel diameter of 700mm has been found to be optimal, so the rotational velocity for this sizeof wheel at this velocity is:

35.0

8.26

r

vrv (14)

rpmrads 5.7316.76 1

Davison, England, Vandy and De Leener found that for a race of an hour duration (albeit on an ordinary bike, on atrack), the optimum crank speed was 116 rpm. [10]Therefore, a top gear ratio of 1:6.3 (i.e. One turn of the pedalproduces 6.3 turns of the driving wheel) would be appropriate.

4.3.3 Powertrain Conclusion

Each of the power transmission systems reviewed here has a number of advantages and disadvantages, none of thembeing a perfect solution. Considering this, however, I would recommend that a front wheel drive mounted torqueconverter be used. Front wheel drive offers the advantage of increased efficiency over a rear wheel drive system, dueto the shorter pulley distance and associated increase in pulley tension, as well as decreasing the weight of thetransmission. Mounting the pedals and crank on the front fork has been successful in previous designs, and thereduction in cornering ability this causes would not affect the bicycle's performance on a wide oval track. The use of atorque converter also allows the optimal gear ratio to be used throughout the acceleration of the bicycle, and muchsmoother acceleration than a drailleur system. This compares well to the single-gear system that is defined by manyof these systems, where the acceleration of the bicycle will be poor, ultimately reducing the distance travelled in anhour. In a competition where races can be won, and records set, by a few seconds or less, this improvement inacceleration may mean the difference between winning and losing.

4.4 Bicycle brakes

There are many types of brake have been invented to improve the stopping power and safety of a bicycle. The maintypes are:

Rim brake - works by applying the force to the brake pads using the lever mounted on the handlebar and thiscauses the pads to contact and apply friction to the rim of the wheel.


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Drum brake - works by applying the force on the brake pads in the drum and the brake pads will press outwardagainst the inside of the drum. The drum brake has complicated components built in the hubs shell and it has lower

braking power compared to the rim brake.Disc brake - consists of a metal disc attached to the hub of the wheel and the callipers attached to the frame of thebicycle. The callipers actuate the brake pads to squeeze on the metal disc to apply the braking force.

4.4.1 Selection of brake for recumbent

bike

The need for braking in a recumbent bike built forcompetition is less compared to the other bikedisciplines such as mountain biking. However, thebrake is still essential to provide safety. For thisproject, the rim brake is recommended because it islightweight and provides adequate braking power.

4.4.2 Brake balance

The brake balance is a relationship between the vertical forces on the front and rear tyres of the recumbent bike withthe torques applied by the brakes at both sides. Normally for the bicycle, most of the braking power comes from thefront wheel. If the front wheel brake is too strong, the normal bicycle would have a tendency to flip over. Therecumbent bike has a long wheelbase and very low seating position so it has a very low centre of gravity. It is

impossible to flip over but the strong front brake can cause the front wheel to skid and lose the balance. On the otherhand, if the rear brake is too strong, the rear wheel will tend to deviate to the side.The normal force of a normal bicycle with a wheelbase L and a centre of mass halfway between the wheels at theheight h, with the both wheels locked can be analysed using the following equations:

L

hmgF

2

11

L

hmgF

2

12 , where is the coefficient of friction, m is the mass and g is the

acceleration of gravity [12]. When the h/L is greater than , the normal force on rear tyre will have a negative value

Figure 12: Free body diagram of the forces on a bike during braking

Figure 11:Example of the mechanism of rim brake


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17

and can cause the bicycle to flip over. For the recumbent bike, the height of centre of mass is usually less than half ofthe wheelbase. The front wheel will skid and can cause the instability.The optimum braking can be achieved when the brake torque distribution matches the dynamic weight distribution [13].The dynamic weight distribution can be calculated using the equation:

fs

CGt

df

WDWb

HtWW

[8] (15)

4.5 Breathing

A streamlined fairing on human powered vehicle provides greater impact on the performance because of less airturbulence when moving through air. But, such a compact fairing can make breathing harder. One suggestion toovercome this would be making ventilation into the inside of the fairing. Ventilation into the bicycle also helps cooldown the body. However, this will cause drag so any ventilation should be controlled carefully.

Another suggestion would be providing the rider with breathing apparatus, where the tubes would providebreathing and also a water supply. Through using an oxygen tank, the breathing apparatus could be designed toprovide the rider with a higher volume of oxygen in the air breathed in. This would to help optimise the ridersperformance, but should be weighed up with the negative consequences of the additional weight of the tank.

4.6 Riders Position

There are two main body position that can be considered for the design; prone and supine position. These twopositions have their own advantages and disadvantages.

Prone position is the position that involves the rider to lie flat on their chest.The prone position does not imply any problem with regards to breathing, as long as the body is supported at theshoulders and hips. Forehead support should also be used instead of chin support[14].

Supine position is the opposite of prone, where the rider is lying on his back. This position is the more natural andmore comfortable compared to the prone position.

The average power output is greatest in the 130and 140range of body configuration angle (BCA)[15], (see figure

14).

Figure 14:Illustration of body configuration angle

In order to decide which rider position is the best for this project, a weighted matrix analysis is performed. Theanalysis is based on several criteria, which can be seen in Appendix B1:


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The matrix is constructed with each criteria given the rank of 1-5. (1 being the worst, 5 being the best)

Criteria Supine Position Prone Position

Aerodynamics (x7) 5 5

Riders comfort (x6) 5 3

Efficiency (x5) 5 4Steering (x4) 5 4

Stability (x3) 5 4

Feasibility to design frame (x2) 3 5

Cost (x1) 3 4

total 134 115Table 16: Weighted matrix analysis to choose the rider position

From table 16, the supine position scored more marks compared to the prone position. Therefore, supine position willbe used to design the frame of the bike. However, having the rider to lie completely flat on his back will not allow for

maximum power output. Therefore the rider should be in supine position with 130-140body configuration angle.

4.7 Seating

Being decided on the type of riders position, we now come to the part to designing the seat. Several options can beconsidered, however only two most feasible options will be presented here: -

Hanging bodyo This can be done by chaining the rider to the frame of the bicycle. This will require an extra

horizontal pole in the frame

Traditional seatingo This is a meshed seat like most of other recumbent bicycle.

These two options are compared in a table below, where the advantages and disadvantages are discussed.

Seating Options Advantages Disadvantages

Hanging body Less weight UncomfortableLess power output

Traditional seat ComfortableHigher power output

Heavier

Table 17:table showing the advantages and disadvantages of both seating options

From table 17, hanging body has the advantage of less weight compared to the traditional seat. However, this mightnot be the case since a horizontal pole has to be added to the frame to do this. This addition might be even heavier thanthe meshed seat, since it has to be able to support the forces without failing. To validate this, a finite element analysisis done. The result of the test is shown in Appendix B2.

It is also stated in the disadvantages column that the hanging body option might produce less output power. This isbecause the hanging body option does not have a back support for the rider, which will not be able to stabilize himwhile riding.

After careful consideration and discussion, the group agreed to choose traditional style seat to be build into ourrecumbent bicycle. This is based on the feasibility of the design, the comfort of the rider and also the total weight ofthe bike.


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Design specifications:

Supine position with 130 body configuration angle

Traditional seating

Under seat steering

Torque converter

Front wheel drive

Safety Factor of 2 Maximum deflection of 3mm

Total mass of the frame 5 kg

Geometry of the frame

Based on the design specifications above, the sketch of the frame is as followed:

Figure 17: sketch of the frame

The frame is based on the triangulated frame system with front wheel driven.

Forces

We are considering 2 main forces acting on the frame. They are riders weight and pedalling force. Riders weight:

The riders weight is approximated to be around 80kg maximum.

The weight is distributed on the bar where the seat is located and acting vertically downward.

The weight will be multiplied by a factor of 3 in order to approximate the dynamic loading on the frame [18].

Pedalling force:

The power required is approximated to be 400W with the maximum speed of 60mph on the wheel as whathas been analysed in the Section 3.1.

The pedalling force is calculated and approximated to be around 626.4N

Modelling in finite element analysis

The frame is modelled using lines and the element used is beam3 type. Using this type of element, the structure isassumed to be constructed from the tubes with different cross sectional areas at different parts.The area moment of inertia is calculated using the following equation:


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444

rRIo

, where R is the outer radius and r is the inner radius of the tube. This is the equation for hollow

cylinder.

Result of finite element analysis is shown below:

Aluminium 2090-T83 AISI Steel 4130

Maximum deflection, mm 2.436 0.900

Total mass of the frame, kg 3.25 9.87

Safety Factor 113.6 100.5

Table 19: comparison of finite element results for both materials

In the table, the results show that aluminium alloy still meets the design specification while steel has exceeded themass limit of the frame. So, we decided to use aluminium 2090-T83.

Aluminium 2090-T83

Number of elements = 89

Figure 18: stresses and deflection on the frame


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22

AISI Steel 4130

Figure 19: stresses and deflection on the frame

4.10 Aerodynamics

Our goal is to break the one hour distance record for a human powered vehicle and therefore aerodynamics is of the upmost importance. The design should primarily focus around a recumbent speed bike where compromises will be madeto reduce the weight and increase the streamlining. This is because the cross sectional area of a recumbent bike is farless then that of an upright bike. Reducing the cross sectional area will directly reduce the effects of drag and thereforegreater speeds can be obtained by the same application of power.

It has also been proved that the position of the rider on a recumbent cycle can generate more power then an uprightdue to the rider being able to push back into the seat. [10]

Our bike design will include a fairing also. This is anouter shell that will enclose the bike and the rider in

order to dramatically reduce the effect of drag. Recentstudies have found that the use of a highly streamlinedfairing can in fact reduce the drag by an average of41.3% over a rider on an upright bike in the tuck position[19].

It can also be said that a rider would not be able to

sustain a tucked position for the one hour durationcomfortably, therefore there is a massive 73.4% dragreduction from a rider on an upright bike in an uprightposition over that of a highly streamlined recumbent.(41.3% over a tuck position and 32.1 over an uprightposition) [20]

Figure 20- Showing approximately a 40% reduction incross sectional area for a recumbent bike.


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4.10.1 Drag

As a body moves through a fluid it experiences a drag force due to the viscosity of that fluid, in our case air. There aretwo components to this, viscous drag and pressure drag.

Viscous drag comes from the interaction between the fluid and the surfaces over which it is flowing causing friction.

This is because of the no slip condition where the air at the surface has a velocity component parallel to the surface ofzero. The velocity of the air flow does increase rapidly with distance away from the surface. See fig 21

In our fairing design it can be said that the flow passing over the body is laminar. This means the air behaves like astack of flat sheets sliding over each other from zero velocity at the wall (or fairing) to the maximum velocity somedistance away. This occurs because the adjacent air molecules between each pair of sheets collide so that the sheetabove is slowed down by the sheet below; this causes friction and thus creates viscous drag. For our recumbent bikethe viscous drag will dominate the reduction in speed as the body will be streamlined and thuspressure drag influences of eddy currents shall be minimised.

The fairing that encloses the rider and bike will be smoothwith the fluid spending more time passing over the shell thenseparating at its rear. This streamlined design will reduce the

viscous drag coefficient for the bike and thus increase itsvelocity for the same application of power.

Pressure drag comes from turbulence or eddy currents thatare created within the fluid by the passing of the bike. Asour fairing design will be smooth and tear shaped there willbe no pressure drag effects over the fairing, only at its rearwhere the flow separates from the surface.

This is because for one to minimise the pressure drag it isimportant to keep the air flow attached to the fairing for aslong as possible. As the flow accelerates over the front of thefairing due to the increasing cross sectional area thus

distance travelled, this produces a reduction in pressure dueto Bernoullis relationship.

So air flowing from high to low pressure produces a favourable pressure gradient and separation is unlikely unlessthere is a bump or discontinuity over the fairings coating, therefore only viscous drag is present here. As discussedearlier the main contribution to pressure drag comes from the separation of air from the fairing at the rear of the bike.It occurs at the rear because the air slows down as it flows and thus the pressure over the rear section increases due toBernoullis relationship once more, causing an undesirable pressure relationship thus a separation point were theboundary layer becomes turbulent.

A turbulent boundary layer is characterised by being considerably thicker then the laminar one. There is a meanvelocity profile and eddy currents are created causing a wake and thus pressure drag is created. See fig 22 below.

X

Max Velocity

V=0m/s at the wall

Figure 21- showing how the parabolic flow velocityvaries with distance from the wall


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24

Figure 22- Showing the development of the boundary layer on the fairing surface [21]

The way to avoid this is to reduce the air speed, thus increasing the pressure as gradually as possible, this will send theenergy from the air flow into the boundary layer at a high enough rate to reduce or even prevent separation occurring.However this causes the boundary layer to thicken and again increases the viscous drag. So the idea is to reduce thecross sectional thickness as gradually as possible in order to increase pressure as gradually also.

This can also be seen by referring to fig #4 showing the flow patterns over a smooth cylinder. It can be seen that athigher Reynolds numbers (i.e. high velocity) the flow will separate from the rear of the sphere and thus increasepressure drag due to the separation of the boundary layer at this point. Note how in A there is no separation because

the Reynolds number is so small.

Also when studying bodies not of a cylindrical shape it can be seen that the higher the angle of attack open to theoncoming flow the higher the pressure drag and thus higher the drag coefficient. This is due to a higher undesirablepressure gradient and thus sooner separation of the flow.

Figure 23 - Flow patterns for flow over a cylinder: (A) Reynolds number =0.2; (B) 12; (C) 120; (D) 30,000; (E) 500,000.[21]

11-Negative static pressure2-Positice static pressure3-Stagnation point4-Velocity vector

5-Laminar boundary layer

6-Transition point7-Turbulent boundary layer8- Streamline9-Seperation point10-Seperated flow

11-Wake


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It is therefore of the up most importance that our design focuses on having a minimal cross sectional area, angle ofattack and separation point at the rear keeping the flow attached for as long as possible, thus reducing pressure drag byreducing the size of the fluid wake behind the bike as it moves. The best shape in order to fulfil all the desiredattributes above is the teardrop shape. It is able to exploit the benefits of a laminar boundary layer, has a smoothcontinues surface and also a gradually reducing cross sectional area. Fig 24 shows the typical values for the dragcoefficient obtained from this tear shaped geometry.

Figure 24- showing the variation of drag coefficient with fitness ratio l/d for the tear drop shape

The fineness ratio is a ratio specifically applicable to this shape and describes the maximum length divided by themaximum diameter and is said to yield the minimum drag when the length is approx 3 times that of the diameter[21],increasing the length decreases the pressure drag caused by eddys or wake at the rear. Now our total fairing length is

2.75m so in theory a cross sectional area of 1.1m would yield the best results for this shape. However as our fairingencloses a recumbent cycle that is much longer then it is wide therefore this shape can be modified in order to furtherreduce the drag co efficient. Our group decided that 60cm in width would be the thinnest possible option as this wouldbe the width of the driver. If the fineness ration was adapted for this width the resulting length giving a fineness ratioof 2.5 and thus the lowest drag coefficient possible would be 1.5m. Although this is not a feasible length as not onlyare the wheels so large that the fairing wouldnt be able to encase them but the driver wouldnt fit either. Therefore a

compromise was struck. The rear of the fairing shall be made 1.5m long, reducing the effects of pressure drag thusallowing all the energy from the air flow into the boundary layer at a high enough rate to reduce the separation. Theremaining 1.25m will be used for the front of the fairing allowing for a slender mid section at a width of 60cm. Ashaper tear drop shaped nose protruding to a point will be used, further reducing the drag coefficient by decreasing

the area normal to the on coming flow and therefore reducing the size of the stagnation point at the front of the fairing.This way the combined fineness ratio is 2.29, resulting in a drag coefficient of 0.32.

In order to test this fairing shape accurately a scaled model should be made and placed within a wind tunnel althoughthis would take time. Another way is to model the fairing using CFD (computational fluid dynamics) and viewing thepressure variations over the fairing. Ideally the fairing should be modelled in 3D flow however this could not be done.Instead an aeronautical website[23]was consulted which allowed the user to input the dimensions of an aerofoil,including the angle of attack and Reynolds number of 980700 (i.e. 90Km/h over the 60cm diameter at a pressure 1atm, temperature of 20 degrees). It was then simply a case of inputting the fairing dimensions, making the aerofoilsymmetrical and running the java script to view the pressure variations over the fairing. It can be seen in figure 25 thatthe pressure is fairly evenly distributed along the mid section. The pressure increases slowly at the tail allowing for theflow to remain attached to the fairing and not become turbulent.


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.

Figure 25- Showing the pressure distribution of the fairing design.

It should however be noted that the above simulation could not provide us with an accurate indication of the dragcoefficient. This is because the program was written for aerofoils and therefore would only give a drag coefficient

when an angle of attack was induced.

There is however a problem with this adapted tear drop shape shown in figure #6. As an object is placed nearer andnearer to the ground the air no longer flows around the object in a symmetrical way due top the ground and thisincrease the drag coefficients. For our design the bike will be very close to the ground in order to reduce any frictionaround the exposed tyres thus the design shall be adapted to account for this. If the tear drop shape is cambered tofurther look for like an aerofoil and shaped to induce more flow around and over the fairing it will allow for a lowercoefficient of drag to be achieved. Morelli[22]experimented with this and came up with the following graph. It showshow the ideal tear drop shape can be adjusted in order to account for the ground clearance. It can be noted that thegreatest result achievable is when the radius from the centre line to the upper outer shell divided by the length is 0.09.

Now for our design the distance from the centre line to the upper most outer shell is calculated as:

0.6/2=0.3m radius,

0.6/2.75=0.1091

This indicates that the camber on our fairing is similar to the greatest result found and therefore the drag coefficientcan be found via figure 26 by following the dotted cambered line and calculating the relative height of groundclearance divided by total length. The result is given to be 0.022 with a 6cm clearance and 2.75m overall fairinglength. This corresponds to a drag coefficient of 0.17. Even lower then that calculated previously, although it shouldbe noted that with 6cm of wheel protruding from the bottom on the fairing this value will increase.

Pressure spike

Favourable pressuregradient

Negative pressure gradientdecreasing at a low rateallowing for the reduction ofturbulence

Fairing Shape


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Figure 26- showing the effect of camber upon ground clearance.

The final fairing design was a combination of both the dimensions given and the ground clearance acceptable. Thewheels were encased as fully as possible by the fairing, allowing for at least 20 degrees lean of the bike to allow it to

respond to side winds without crashing.

Figure 27- showing the final fairing design for our recumbent bike.

2.75m

1.25m

0.6m

Sharpe nodereducing stagnationpoint.

Enclosed wheels furtherreducing drag

0.6m

0.06m


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5.0 Conclusion

The task of producing a human powered vehicle to break the Dempsey-MacCready hour record of 85.991Km wasproposed to our team. After deliberating over the best way to propel a vehicle to achieve a distance of over 86Km inan hour, a recumbent cycle design was selected as the best option.

The team Glide by Icycles allocated each member of the group an important component from a recumbentbike and studied its strengths, its weaknesses and its requirements to maximise the chances of breaking the record.Eventually the best components which fulfilled our requirements were chosen in order to produce the most efficient,lightweight design, giving us the best chance of achieving our aims and objectives. Below is an overview of eachcomponent set up along with the final pro desktop and finite element designs;

Firstly the bearings were studied. Bearings were required in several places on the design. Hardened steel was

chosen to provide the best properties for the ball bearings in the front and rear hubs, with an UHMWPE coated axle.

This was mainly due to the extremely low coefficient of friction of these combined materials.Once the bearings had been selected the tyres were investigated. It was decided that tubular tyres should be

used because they give a greater weight reduction compared to the traditional clincher type. The tyres are to beinflated to high pressure, to ensure that there is minimal deformation and energy losses in the tyres. Very smooth treadon the tyres is also desirable to reduce rolling resistance coefficients.

The power transmission was selected to be via a front wheel drive mounted torque converter because the front

wheel drive offered the advantage of increased efficiency over a rear wheel drive system. The use of a torqueconverter also allowed the optimal gear ratio to be used throughout the acceleration of the bicycle and obtain itsmaximum speed. Also the brakes were selected to be rim brakes because they provide low weight and adequatebraking power.

The supine position was decided upon as the most effective and comfortable means of positioning the driver.

However the group further researched the idea and found that the rider should be in a supine position with 130 -140body configuration angle to obtain the greatest trade off between power applications, comfort and ease of use at suchspeeds. The driver would also benefit from under seat steering and a traditional seat set up rather then a hangingdesign.The aerodynamic fairing was designed to enclose the whole bike and allow for greater speeds with a reducedapplication of power. The final fairing design took the following shape and dimensions.

Figure 28: Final fairing design


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Figure 29: Translucent view of final fairing design

The frame was also designed to give as low a weight, coupled with as high a strength, as possible.

Figure 30: Design of the bicycle frame

The only thing left to do now is to build and test it


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6.0 References

[1] Data from Cycle Design lecture notes, Richard Lukes. Reference (Broker, 2003)[2] en.wikipedia.org/wiki/Racing_bicycle[3] en.wikipedia.org/wiki/Bicycle_wheel[4]www.canecreek.com/wheel_tech.html

[5] http://science.howstuffworks.com/bicycle2.htm[6] http://en.wikipedia.org/wiki/Ball_bearing

[7] www.ahrinternational.com/bearing_radial_clearance_explained.htm

[8]www.engineparts.com/techbulletins/CL77-1-205R.pdf[9] Large-scale friction and wear tests on a hybrid UHMWPE-pad/primer coating combination used as bearingelement in an extremely high-loaded ball-joint - Tribology International, - P. Samyn, L. Van Schepdael, J.S.Leendertz, A. Gerber, W. Van Paepegem, P. De Baets and J. Degrieck (Vol 39, No. 8, August 2006, pp.796-811)[10] Bicycling Science 3rdEditionD.G. WilsonThe MIT Press (2004)[11] Direct Drive (Chainless) Recumbent BicyclesThomas KretschmerbHuman Power (No. 49, Winter 1999-2000).[12] www.sae.orgstudentspresentationsbrakes.ppt[13] www.sae.orgstudentspresentationsbrakes.ppt[14,15] Project Cadence: Human Powered Vehicle- Adam Christensen, Mordechai Cohen, Amoz Eckerson, John

Vesely IIthesis 2003[16,17] http://en.wikipedia.org/wiki/Recumbent_bike[18] http://www.sheldonbrown.com/rinard/fea.htm[19] Bicycle dynamics and controlIEEE Control system magazineAstrom, Klein, Lennartssomn (Aug. 2005)[20] http://www.mueller-hp.com/windtunnel.htm[21] Year one notes, Introduction to aerospace engineering, University of Liverpool, Dr D Nicolaou, 93/02/1999[22] Aerodynamics of Road VehiclesFrom Fluid Dynamics to Fluid EngineeringEdited by Wolf-Heinrich Hucho(4thEdition 1998)

[23] http://www.desktopaero.com/appliedaero/airfoils1/interactiveaf.html

Bibliography

Richard's Mountain Bike BookCharles Kelly, Nick CraneRichard's Bicycle Books Ltd. (1988)

Bicycle Dynamics and ControlAnstrom, Klein, LennartssonIEEE Control Systems Magazine (Aug. 2005) The Speed of a CyclistWim HannekamPhysics Education (Issue 25, 1990)

An Ergonomic Study on the Optimal Gear Ratio for a Multi-Speed BicycleChang K Cho, Myung Hwan Yun,Chang S Yoon, Myun W Lee International Journal of Industrial Ergonomics (Issue 23, 1999).

Experimental Examination of Bicycle Chain ForcesMD Kidd, NE Loch, RL ReubenExperimental Mechanics(Vol. 39 No. 4, Dec. 1999)

Backward Versus Forward Pedalling: Comparison TestsRamondo SpinnettiHuman Power (Vol. 6 No. 3, Fall1987)

Front-Wheel-Drive Recumbent BicyclesMichael EliasohnHuman Power (Vol.9 No.2, Summer 1991)

Front Wheel Drive BicyclesMarek Utkin - Human Power (Vol.9 No.2, Summer 1991)

Cha-Cha BikeBernd Zwikker, Bram Moens - Human Power (Vol.9 No.2, Summer 1991)

Front Wheel Drive RecumbentsTom Traylor - Human Power (Vol.9 No.2, Summer 1991)

Analysis of Rolling Element BearingsWan Changsenpp.82-89, 1991 (in English).

Large-scale friction and wear tests on a hybrid UHMWPE-pad/primer coating combination used as bearingelement in an extremely high-loaded ball-joint - Tribology International, - P. Samyn, L. Van Schepdael, J.S.Leendertz, A. Gerber, W. Van Paepegem, P. De Baets and J. Degrieck (Vol 39, No. 8, August 2006, pp.796-811)

Images from

Figure 3www.ultimatepursuits.co.uk/products/list.aspx
http://www.canecreek.com/wheel_tech.htmlhttp://www.canecreek.com/wheel_tech.htmlhttp://www.canecreek.com/wheel_tech.htmlhttp://www.engineparts.com/techbulletins/CL77-1-205R.pdfhttp://www.engineparts.com/techbulletins/CL77-1-205R.pdfhttp://www.engineparts.com/techbulletins/CL77-1-205R.pdfhttp://www.ultimatepursuits.co.uk/products/list.aspxhttp://www.ultimatepursuits.co.uk/products/list.aspxhttp://www.ultimatepursuits.co.uk/products/list.aspxhttp://www.ultimatepursuits.co.uk/products/list.aspxhttp://www.engineparts.com/techbulletins/CL77-1-205R.pdfhttp://www.canecreek.com/wheel_tech.html


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Figure 4Bicycle Design and AnalysisRichard LukesFigure 10 - An Ergonomic Study on the Optimal Gear Ratio for a Multi-Speed Bicycle Chang K Cho, Myung Hwan Yun, ChangS Yoon, Myun W LeeInternational Journal of Industrial Ergonomics (Issue 23, 1999).)

7.0 Appendix

Front and Rear Hub BearingsTables A1-A3

Rbearing Raxle R E1 E2 E* a P0 Z Q0

0.0010 0.03 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000568 3654.40 97.34 24.661

0.0015 0.03 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000744 3138.82 65.94 36.404

0.0018 0.03 0.0019 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000841 2923.73 55.47 43.273

0.0020 0.03 0.0021 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000902 2803.60 50.24 47.781

0.0025 0.03 0.0027 2.10E+11 2.10E+11 0.3 1.05E+11 0.0001048 2558.30 40.82 58.807

0.0030 0.03 0.0033 2.10E+11 2.10E+11 0.3 1.05E+11 0.0001185 2366.11 34.54 69.499

0.0035 0.03 0.0040 2.10E+11 2.10E+11 0.3 1.05E+11 0.0001314 2208.67 30.05 79.872

0.0040 0.03 0.0046 2.10E+11 2.10E+11 0.3 1.05E+11 0.0001439 2075.58 26.69 89.94

0.0045 0.03 0.0053 2.10E+11 2.10E+11 0.3 1.05E+11 0.0001559 1960.44 24.07 99.716

0.0050 0.03 0.0060 2.10E+11 2.10E+11 0.3 1.05E+11 0.0001675 1859.02 21.98 109.21

0.0055 0.03 0.0067 2.10E+11 2.10E+11 0.3 1.05E+11 0.00017887 1768.42 20.27 118.44Table A1: Table showing how varying the ball bearing radius affects the resulting properties for the bearings present in the front and rear h

Rbearing Raxle R E1 E2 E* a p0 Z Q0

0.0018 0.01 0.0022 2.10E+11 2.10E+11 0.3 1.05E+11 0.0001225 3714.58 20.58 116.6

0.0018 0.02 0.0020 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000964 3244.91 38.03 63.12

0.0018 0.03 0.0019 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000841 2923.73 55.47 43.27

0.0018 0.04 0.0019 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000764 2697.35 72.92 32.92

0.0018 0.05 0.0019 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000709 2526.98 90.36 26.57

0.0018 0.06 0.0019 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000667 2392.47 107.81 22.27

0.0018 0.07 0.0018 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000633 2282.50 125.25 19.17

0.0018 0.08 0.0018 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000606 2190.22 142.70 16.82

0.0018 0.09 0.0018 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000582 2111.21 160.14 14.99

0.0018 0.10 0.0018 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000562 2042.46 177.58 13.52

Table A2: Table showing how varying the wheel axle radius affects the resulting properties for the bearings present in the front and rear hubs

Material Rbearin Raxle R E1 E2 E* a pm Z Q0

Rubber 0.0018 0.05 0.0019 5.00E+07 5.00E+07 0.3 2.49E+07 0.0011434 9.71 90.36 26.57

Low DensityPolyethylene 0.0018 0.05 0.0019 2.00E+08 2.00E+08 0.3 9.96E+07 0.0007203 24.46 90.36 26.57

Nylon 0.0018 0.05 0.0019 5.00E+09 5.00E+09 0.3 2.49E+09 0.0002463 209.14 90.36 26.57

Wood (Oak) 0.0018 0.05 0.0019 1.10E+10 1.10E+10 0.3 5.48E+09 0.0001894 353.77 90.36 26.57

AluminiumAlloy 0.0018 0.05 0.0019 6.90E+10 6.90E+10 0.3 3.43E+10 0.0001027 1203.25 90.36 26.57

Glass 0.0018 0.05 0.0019 7.20E+10 7.20E+10 0.2 3.60E+10 0.0001011 1240.53 90.36 26.57

UHMWPE 0.0018 0.05 0.0019 6.90E+08 6.90E+08 0.3 3.43E+08 0.0004767 55.85 90.36 26.57

Titanium 0.0018 0.05 0.0019 1.10E+11 1.10E+11 0.3 5.48E+10 8.791E-05 1642.04 90.36 26.57

HardenedSteel 0.0018 0.05 0.0019 2.10E+11 2.10E+11 0.3 1.05E+11 7.087E-05 2526.98 90.36 26.57

CarbonFibre 0.0018 0.05 0.0019 3.00E+11 3.00E+11 0.3 1.49E+11 6.292E-05 3205.31 90.36 26.57

TungstenCarbide 0.0018 0.05 0.0019 6.00E+11 6.00E+11 0.3 2.99E+11 4.994E-05 5088.12 90.36 26.57

Diamond 0.0018 0.05 0.0019 1.15E+12 1.15E+12 0.3 5.72E+11 4.02E-05 7850.94 90.36 26.57

Hardenedsteel

bearings w/UHMWPE 0.0018 0.05 0.0019 2.10E+11 6.90E+08 0.3 6.26E+08 0.0003902 83.35 90.36 26.57


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32

Table A3: Table showing how varying the wheel axle and ball bearing material radius affects the resulting properties for the

bearings present in the front and rear hubs

Bottom Bracket BearingsTables A4-A6

Rbearing Raxle R E1 E2 E* a p0 Z Q00.00050 0.04 0.0005 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000254 3343.21 254.34 4.5235

0.00075 0.04 0.0008 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000333 2902.27 170.61 6.7436

0.00100 0.04 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000404 2620.33 128.74 8.9366

0.00125 0.04 0.0013 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000468 2417.19 103.62 11.103

0.00150 0.04 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000529 2260.31 86.87 13.243

0.00175 0.04 0.0018 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000586 2133.52 74.91 15.358

0.00200 0.04 0.0021 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000641 2027.70 65.94 17.448

0.00225 0.04 0.0024 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000694 1937.23 58.96 19.512

0.00250 0.04 0.0027 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000744 1858.45 53.38 21.553

0.00275 0.04 0.0030 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000793 1788.83 48.81 23.57

0.00300 0.04 0.0032 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000841 1726.55 45.01 25.563

Table A4: Table showing how varying the ball bearing radius affects the resulting properties for the bearings present in the bottom brack


0.0010 0.01 0.0011 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000643 3851.63 34.54 33.309

0.0010 0.02 0.0011 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000509 3218.77 65.94 17.448

0.0010 0.03 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000444 2859.86 97.34 11.819

0.0010 0.04 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000404 2620.33 128.74 8.9366

0.0010 0.05 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000375 2444.79 160.14 7.1843

0.0010 0.06 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000353 2308.36 191.54 6.0066

0.0010 0.07 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000335 2198.00 222.94 5.1606

0.0010 0.08 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000320 2106.09 254.34 4.5235

0.0010 0.09 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000308 2027.83 285.74 4.0264

0.0010 0.10 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000297 1960.03 317.14 3.6277Table A5: Table showing how varying the wheel axle radius affects the resulting properties for the bearings present in the bottom

bracket

Material Rbearing Raxle R E1 E2 E* a pm Z Q0

Rubber 0.0010 0.03 0.0010 5.00E+07 5.00E+07 0.3 2.49E+07 0.0007169 10.99 97.34 11.8194


Nylon 0.0010 0.03 0.0010 5.00E+09 5.00E+09 0.3 2.49E+09 0.0001545 236.69 97.34 11.8194

Wood (Oak) 0.0010 0.03 0.0010 1.10E+10 1.10E+10 0.3 5.48E+09 0.0001188 400.37 97.34 11.8194

AluminiumAlloy 0.0010 0.03 0.0010 6.90E+10 6.90E+10 0.3 3.43E+10 6.439E-05 1361.75 97.34 11.8194

Glass 0.0010 0.03 0.0010 7.20E+10 7.20E+10 0.2 3.60E+10 6.342E-05 1403.94 97.34 11.8194

UHMWPE 0.0010 0.03 0.0010 6.90E+08 6.90E+08 0.3 3.43E+08 0.0002989 63.21 97.34 11.8194

Titanium 0.0010 0.03 0.0010 1.10E+11 1.10E+11 0.3 5.48E+10 5.512E-05 1858.35 97.34 11.8194

Steel 0.0010 0.03 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 4.443E-05 2859.86 97.34 11.8194CarbonFibre 0.0010 0.03 0.0010 3.00E+11 3.00E+11 0.3 1.49E+11 3.945E-05 3627.54 97.34 11.8194


Diamond 0.0010 0.03 0.0010 1.15E+12 1.15E+12 0.3 5.72E+11 2.521E-05 8885.12 97.34 11.8194

Hardenedsteel

bearings w/UHMWPE 0.0010 0.03 0.0010 2.10E+11 6.90E+08 0.3 6.26E+08 0.0002447 94.33 97.34 11.8194

axle


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33

axle

Table A6: Table showing how varying the wheel axle and ball bearing material radius affects the resulting properties for the bearings

present in the bottom bracket

Pedal BearingsTables A7-A9

Rbearin Raxle R E1 E2 E* a p0 Z Q0

0.00050 0.04 0.0005 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000234 3081.03 254.34 3.5405

0.00075 0.04 0.0008 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000307 2674.67 170.61 5.2782

0.00100 0.04 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000372 2414.84 128.74 6.9947

0.00125 0.04 0.0013 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000432 2227.63 103.62 8.6904

0.00150 0.04 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000488 2083.05 86.87 10.366

0.00175 0.04 0.0018 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000540 1966.20 74.91 12.021

0.00200 0.04 0.0021 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000591 1868.68 65.94 13.656

0.00225 0.04 0.0024 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000639 1785.31 58.96 15.272

0.00250 0.04 0.0027 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000686 1712.71 53.38 16.87

0.00275 0.04 0.0030 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000731 1648.54 48.81 18.448

0.00300 0.04 0.0032 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000775 1591.15 45.01 20.008

Table A7: Table showing how varying the ball bearing radius affects the resulting properties for the bearings present in the pedals


0.0015 0.005 0.0021 2.10E+11 2.10E+11 0.3 1.05E+11 0.0001006 3125.19 13.61 66.181

0.0015 0.010 0.0018 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000779 2941.00 24.07 37.407

0.0015 0.015 0.0017 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000678 2708.84 34.54 26.071

0.0015 0.020 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000615 2525.79 45.01 20.008

0.0015 0.025 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000571 2381.14 55.47 16.233

0.0015 0.030 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000537 2263.75 65.94 13.656

0.0015 0.035 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000510 2166.05 76.41 11.786

0.0015 0.040 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000488 2083.05 86.87 10.3660.0015 0.045 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000469 2011.33 97.34 9.2511

0.0015 0.050 0.0015 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000453 1948.47 107.81 8.3529

Table A8: Table showing how varying the wheel axle radius affects the resulting properties for the bearings present in the pedal

Material Rbearing Raxle R E1 E2 E* a pm Z Q0

Rubber 0.0015 0.015 0.0017 5.00E+07 5.00E+07 0.3 2.49E+07 0.001094 10.41 34.54 26.071


Nylon 0.0015 0.015 0.0017 5.00E+09 5.00E+09 0.3 2.49E+09 0.0002357 224.19 34.54 26.071

Wood (Oak) 0.0015 0.015 0.0017 1.10E+10 1.10E+10 0.3 5.48E+09 0.0001812 379.23 34.54 26.071

AluminiumAlloy 0.0015 0.015 0.0017 6.90E+10 6.90E+10 0.3 3.43E+10 9.826E-05 1289.84 34.54 26.071

Glass 0.0015 0.015 0.0017 7.20E+10 7.20E+10 0.2 3.60E+10 9.678E-05 1329.80 34.54 26.071UHMWPE 0.0015 0.015 0.0017 6.90E+08 6.90E+08 0.3 3.43E+08 0.0004561 59.87 34.54 26.071

Titanium 0.0015 0.015 0.0017 1.10E+11 1.10E+11 0.3 5.48E+10 8.412E-05 1760.21 34.54 26.071

Steel 0.0015 0.015 0.0017 2.10E+11 2.10E+11 0.3 1.05E+11 6.781E-05 2708.84 34.54 26.071

CarbonFibre 0.0015 0.015 0.0017 3.00E+11 3.00E+11 0.3 1.49E+11 6.021E-05 3435.98 34.54 26.071


Diamond 0.0015 0.015 0.0017 1.15E+12 1.15E+12 0.3 5.72E+11 3.847E-05 8415.92 34.54 26.071

Hardenedsteel 0.0015 0.015 0.0017 2.10E+11 6.90E+08 0.3 6.26E+08 0.0003734 89.35 34.54 26.071


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34

bearings w/UHMWPEaxle


bearings present in the pedals

Fork Bearings

Tables A10-A12


0.00050 0.04 0.0005 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000129 1695.24 254.34 0.589762

0.00075 0.04 0.0008 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000169 1471.65 170.61 0.879215

0.00100 0.04 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000205 1328.69 128.74 1.165139

0.00125 0.04 0.0013 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000238 1225.68 103.62 1.447597

0.00150 0.04 0.0016 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000268 1146.14 86.87 1.726652

0.00175 0.04 0.0018 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000297 1081.84 74.91 2.002365

0.00200 0.04 0.0021 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000325 1028.18 65.94 2.274795

0.00225 0.04 0.0024 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000352 982.31 58.96 2.544002

0.00250 0.04 0.0027 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000377 942.37 53.38 2.810041

0.00275 0.04 0.0030 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000402 907.06 48.81 3.072969

0.00300 0.04 0.0032 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000426 875.48 45.01 3.33284

Table A10: Table showing how varying the ball bearing radius affects the resulting properties for the bearings present in the forks

Table A11: Table showing how varying the wheel axle radius affects the resulting properties for the bearings present in the forks


0.0010 0.005 0.0013 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000415 2209.83 18.84 7.961783

0.0010 0.010 0.0011 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000326 1953.05 34.54 4.342791

0.0010 0.015 0.0011 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000284 1766.04 50.24 2.985669

0.0010 0.020 0.0011 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000258 1632.14 65.94 2.274795

0.0010 0.025 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000239 1530.63 81.64 1.837335

0.0010 0.030 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000225 1450.15 97.34 1.54099

0.0010 0.035 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000214 1384.17 113.04 1.3269640.0010 0.040 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000205 1328.69 128.74 1.165139

0.0010 0.045 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000197 1281.12 144.44 1.038493

0.0010 0.050 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 0.0000190 1239.68 160.14 0.93668

Rbearing Raxle R E1 E2 E* a pm Z Q0

Rubber 0.0010 0.03 0.0010 5.00E+07 5.00E+07 0.3 2.49E+07 0.000364 5.57 97.34 1.54099Low DensityPolyethylene 0.0010 0.03 0.0010 2.00E+08 2.00E+08 0.3 9.96E+07 0.000229 14.04 97.34 1.54099

Nylon 0.0010 0.03 0.0010 5.00E+09 5.00E+09 0.3 2.49E+09 7.83E-05 120.02 97.34 1.54099

Wood (Oak) 0.0010 0.03 0.0010 1.10E+10 1.10E+10 0.3 5.48E+09 6.02E-05 203.01 97.34 1.54099AluminiumAlloy 0.0010 0.03 0.0010 6.90E+10 6.90E+10 0.3 3.43E+10 3.27E-05 690.50 97.34 1.54099

Glass 0.0010 0.03 0.0010 7.20E+10 7.20E+10 0.2 3.60E+10 3.22E-05 711.90 97.34 1.54099

UHMWPE 0.0010 0.03 0.0010 6.90E+08 6.90E+08 0.3 3.43E+08 0.000152 32.05 97.34 1.54099Titanium 0.0010 0.03 0.0010 1.10E+11 1.10E+11 0.3 5.48E+10 2.8E-05 942.31 97.34 1.54099Steel 0.0010 0.03 0.0010 2.10E+11 2.10E+11 0.3 1.05E+11 2.25E-05 1450.15 97.34 1.54099CarbonFibre 0.0010 0.03 0.0010 3.00E+11 3.00E+11 0.3 1.49E+11 2E-05 1839.42 97.34 1.54099TungstenCarbide 0.0010 0.03 0.0010 6.00E+11 6.00E+11 0.3 2.99E+11 1.59E-05 2919.89 97.34 1.54099Diamond 0.0010 0.03 0.0010 1.15E+12 1.15E+12 0.3 5.72E+11 1.28E-05 4505.38 97.34 1.54099Hardenedsteel 0.0010 0.03 0.0010 2.10E+11 6.90E+08 0.3 6.26E+08 0.000124 47.83 97.34 1.54099


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35


bearings present in the forks

Tables relating to bearing propertiesTables A13 and A14

Material

Density

(kg/m3)

Bearing

radius

(m)

Wheel

Radius

(m)

Revolutions

(1/s)

Angular

Velocity

(rad/s)

Centrifugal

Force (N)

Steel 7860 0.03 0.20 19.89 125 0.42

Nylon 1150 0.03 0.20 19.89 125 0.06

Rubber 910 0.03 0.20 19.89 125 0.05

Steel 7860 0.03 0.40 9.95 63 0.10

Nylon 1150 0.03 0.20 19.89 125 0.06

Rubber 910 0.03 0.10 39.79 250 0.19

Steel 7860 0.08 0.20 19.89 125 1.11

Nylon 1150 0.03 0.20 19.89 125 0.06

Rubber 910 0.01 0.20 19.89 125 0.02

rJ (PointContact)

rJ (PointContact)

0 1/Z 0.8 0.2559

0.1 0.1156 0.9 0.2576

0.2 0.1590 1.0 0.2576

0.3 0.1892 1.25 0.2289

0.4 0.2117 1.67 0.1871

0.5 0.2288 2.5 0.1339

0.6 0.2416 5.0 0.0711

0.7 0.2505 0

Formulas for solving maximum contact pressure for spherical bearings with point contact

Relative radius of curvature, R,

21

111

RRR (A1)

Reduced Modulus, E*

2

2

2

1

2

111

*1

EEE

(A2)

Dimensions of contact

3

*4

3

E

PRa (A3)

Maximum contact pressure, pm

bearings w/UHMWPEaxle

Table A13: Table showing the centrifugal force on bearings with different materials

Table A14: A table showing the corresponding rJ values for varying load


36/37

36

22

3

a

Ppo

(A4)

B1 Aerodynamics: This criterion is based on how high the aerodynamics of the bike can be designed with the

position chosen. This criteria is given the weight of x7

Riders comfort: the comfort is considered for the whole one-hour period of the record. This criterion is basedon the ease of the rider to cycle and produce maximum power throughout the ride. This criteria will be giventhe weight of x6

Efficiency: this is based on the adaptability of the rider to the position, i.e. in prone position the unflexedposition of the hip and torso will require extensive training. This criteria is given the weight of x5

Steering: the ease of steering the bike. This criteria is given the weight of x4

Stability: the ease of keeping the bike upright and stable. This criteria is given the weight of x3

Feasibility to design frame: this criterion is based on the ease to design the frame upon selecting the type ofriders position. This criteria is given the weight of x2

Cost: the position will determine the frame design, hence affecting the cost of production. This criteria is given

the weight of x1

B2

Design for mesh seat with material specified to be aluminium

produced a total mass of 3.25 kg. The frame has maximum

deflection of 2.4 mm.


37/37

37

Design for hanging body option with material specified to be

steel produced a total mass of 5.9 kg. Steel was chosen because

it can produce maximum deflection under 3 mm. The deflection

for this design was found to be 2.09 mm.

design of human powered vehicle

Documents

recumbent bike design

final design

effects of design changes

finalised design wasthen

recumbent bike4

recumbent bike components4

ourrecumbent bike

project statement2