Conclusions: The pedelec emerges from this research as a viable active transport alternative for hilly cities. With adequate autonomy and power to overcome relief, one of the greatest deterrents for using the bicycle as main transport mode, it gives the ball back to politicians, who are responsible for providing cyclists with safe and comfortable pathways for exercising their choice for this mode. Investment on bike paths, bike lanes and adjustment of crossings is the natural next step to foster a more active and sustainable transport mode, from which all citizens would benefit.The pedelec is a basic type of electrically-assisted bicycle, designed to help cyclists overcome most slopes. This article presents a theoretical case study of a pedelec on the city of Coimbra, Portugal, which shows that even a low-end model provides enough power and autonomy for the daily transportation needs of a regular cyclist. It is only if battery wear is considered that a model of higher battery capacity is recommended, and even then only if the cyclist uses the pedelec very intensively. By overcoming what is arguably one of the greatest deterrents to cycling, the pedelec contributes towards materializing the concept of sustainable mobility. Overcoming the other major deterrent, safety concerns, is thus passed to the political decision makers, which will need to build and improve the urban infrastructures necessary for citizens to safely exercise their choice for this transport mode.info:eu-repo/semantics/publishedVersio

Gonçalves, Ana Esmeralda

Rodrigues, João Coutinho

Sousa, Nuno

The Repositório Aberto

Energy for Sustainability International Conference 2017 
Designing Cities & Communities for the Future 
Funchal, 8-10 February, 2017 
 
PEDELEC ON A HILLY CITY: A CASE STUDY IN COIMBRA 
N. Sousa12*, A.E. Gonçalves23 and J. Coutinho-Rodrigues24 
1: Departamento de Ciências e Tecnologia 
Universidade Aberta, Delegação de Coimbra 
R. Alexandre Herculano, 52 
3000-019 Coimbra, Portugal 
e-mail: nsousa@uab.pt,  web: http://www.uab.pt 
2: Instituto de Engenharia de Sistemas e Computadores de Coimbra 
Edifício do Departamento de Eng.ª Electrotécnica e de Computadores 
Universidade de Coimbra 
Rua Sílvio Lima, Polo II 
3030-290 Coimbra, Portugal 
web: http://www.uc.pt/en/org/inescc 
3: Energy for Sustainability, MSc Student 
Faculdade de Ciências e Tecnologia 
Universidade de Coimbra 
Rua Luís Reis Santos, Pólo II 
3030-788 Coimbra, Portugal 
e-mail: anaesmeralda6@hotmail.com 
4: Departamento de Eng.ª Civil 
Faculdade de Ciências e Tecnologia 
Universidade de Coimbra 
Rua Luís Reis Santos, Pólo II 
3030-788 Coimbra, Portugal 
e-mail: coutinho@dec.uc.pt,  web: http://www.uc.pt/fctuc/dec 
 
Keywords: Pedelec, Energy, Sustainability, Coimbra 
Abstract The pedelec is a basic type of electrically-assisted bicycle, designed to help 
cyclists overcome most slopes. This article presents a theoretical case study of a pedelec 
on the city of Coimbra, Portugal, which shows that even a low-end model provides enough 
power and autonomy for the daily transportation needs of a regular cyclist. It is only if 
battery wear is considered that a model of higher battery capacity is recommended, and 
even then only if the cyclist uses the pedelec very intensively. By overcoming what is 
arguably one of the greatest deterrents to cycling, the pedelec contributes towards 
materializing the concept of sustainable mobility. Overcoming the other major deterrent, 
safety concerns, is thus passed to the political decision makers, which will need to build 
and improve the urban infrastructures necessary for citizens to safely exercise their 
choice for this transport mode. 
Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 
2 
 
 
1. INTRODUCTION 
The 20th century has witnessed a sizeable increase in the flow of populations towards cities 
and their suburbs. Fueled by cheap automotive transport and favorable public policies, the 
subsequent urban sprawl ultimately led to inefficiencies related to traffic congestion and 
energy consumption, and environmental concerns. The recently signed Paris Agreement [1], 
perhaps the most symbolic and important of all measures concerning sustainability and 
climate change, shows that politicians are becoming ever more aware that the current state of 
affairs may not be sustainable in the long term. This awareness led transport policy makers to 
encourage a shift towards alternative, more sustainable travel modes. 
 
The bicycle is a very efficient active travel mode that can be adopted in most cities, 
contributing to urban sustainability, given the associated environmental, economic and social 
advantages. Cycling, however, also has its deterrents. Among these, it is recognized that 
slopes play an important role in influencing the choice for this mode of travel [2] [3]. To 
overcome this limitation, and sipping from the winds of change, industry began offering 
consumers Electrically-Powered Assisted Cycles (EPAC), which aim to provide cyclists a 
normal, non-fatiguing ride on hilly cities. Regulatory authorities divided these vehicles into 
two standards: the pedelec and the e-bike. The pedelec is the basic electrically-assisted 
cycle, with maximum 250 W nominal electric power, as requested by EU regulation. The 
e-bike can have higher power, but requires some sort of driver’s license. Both are active 
transport modes because they combine human power with electrical assistance for 
locomotion, although the e-bike can rely solely on battery power. 
 
The aim of this study is to ascertain to what degree the most basic, and cheapest of these 
standards, the pedelec, can live up to expectations, i.e. comply with the demands posed by 
both high slopes and energy needs for assistance. For this purpose, the study determines 
whether the city is permeable to the pedelec, and whether its battery capacity is enough to 
allow for commuting trips and daily trips with multiple stops. This was done in the 
context of a real-life situation, the hilly, mid-sized city of Coimbra, Portugal (143 000 
inhabitants in 2011), resorting to Geographic Information Systems (GIS) technology and 
following the methodology that is now described. 
2. METHODOLOGY AND CASE STUDY 
For purposes of this study, the lowest-end pedelec available on the Portuguese market was 
considered. This was the B’Twin Bebike 500 model, with 250 W nominal power and a 
battery capacity of 219 Wh (788 kJ). The combined efficiency of ‘electric engine + 
mechanical parts’ was taken to be 80%, translating to 200 W maximum assistance power 
passed to the wheels. 
 
Performance and autonomy of this pedelec on Coimbra was assessed in a two-stage 
process, using the ESRI ArcGIS environment and its network analyst extension as the 
Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 
3 
 
 
main calculation tools. In the first stage, the streets network of Coimbra was programmed. 
More precisely, network arcs which require electric assistance for crossing were endowed 
with that energy, in both directions. Network turns were also parameterized, with a cost 
based on assistance energy for acceleration from rest to cruise speed added. In a second 
stage, city permeability to the pedelec and calculations for energy assistance needs were 
carried out and results analysed (an area is said to be ‘permeable to transport mode X’ if it 
allows trips between any two of its points using mode X). Service areas based on 
assistance energy for commuting trips to the city’s main employers were derived. These 
service areas also allowed permeability to be checked. Results for assistance energy needs 
for 72 longer circuits with 5 to 8 stop-points were subsequently derived and analysed. No 
recharge points were considered: the cyclist can only recharge the bicycle at his residence. 
2.1. Network programming 
A GIS shapefile of the streets network of Coimbra was available from previous projects. 
This contained altimetric information in the form of average uphill/downhill slopes and 
distances of each network arc, in the From-To direction. Network programming started 
with rounding off slopes to integers (see below) and restricting network arcs with uphill 
slope higher than 10% and downhill slope higher than 12%, in the From-To (FT) 
direction. The uphill restriction follows manufacturer guidelines, whereas the downhill 
restriction is due to difficulties controlling downhill speed, which may force the cyclist to 
dismount its bicycle. In the To-From (TF) direction the restrictions applied the other way 
around: restrict if the FT uphill slope (which is downhill in the TF direction) is higher 
than 12% or if the FT downhill slope is higher than 10%. These restrictions may cause an 
arc to be non-traversable in the FT or TF direction, or both. 
 
To calculate electric assistance energy needs, it was assumed that cyclists would try, as 
much as possible, to cycle the uphill slopes as if they were cycling in the flat. In other 
words, the human pedalling power was assumed to be the same as the pedalling power in 
the flat. Human average speeds for integer uphill slopes (this is the reason slopes were 
rounded off) were derived in the experimental study of [4] and are shown in table 1 below. 
Table 1. Average unassisted cycling speed as a function of slope, according to [4]. 
Slope (%) 0% 1% 2% 3% 4% 5% 6% 7% 
Speed (m/s) 6,01 5,61 5,21 4,81 4,41 4,01 3,61 3,21 
 
The corresponding power balance (P) can be derived from the physics formula below: 
 𝑃 = #$%&'( ∑𝑚𝑔 𝐶- + /011% + 03 𝐶4𝐴𝜌𝑣3     (1) 
 
with v bicycle speed, hmech the mechanical efficiency, m total mass (cyclist + bike), g 
gravitational acceleration, Cr the rolling resistance coefficient, s the slope (in %), Cd the 
Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 
4 
 
 
aerodynamic coefficient, A the frontal area (cyclist + bike), and r the air density. 
Assuming the values of [4] for formula parameters and an excess of 11 kg for the 
assistance devices (engine/battery, total man + machine: 106 kg), the human pedalling 
power for cycling at the statistical average of 6,01 m/s is, by (1), 156 W. It was thus 
assumed that the cyclist would always exert this pedalling power, regardless of uphill 
slope.  
 
Electric assistance was considered to be zero for all downhill slopes and uphill slopes up 
to (but not including) 3%, as cyclists are known to be insensitive to slope up to this value. 
For 3-10% slopes, assistance begins to be necessary and it was assumed cyclists would 
maintain the speed they had when the incline reached 3%, which was taken to be the one 
indicated in table 1 above (4,81 m/s). At 3%, maintaining that speed requires, by (1) and 
along with the 156 W provided by the cyclist, an extra 97 W of electric assistance power. 
Since pedelecs allow for variable assistance levels, it was also assumed the cyclist would 
adjust assistance level to the power required to maintain speed at 4,81 m/s. 
 
As slope rises, the assistance power required to sustain a 4,81 m/s speed increases as well. 
It is possible to keep a 4,81 m/s speed up to 5% slope. At this point the electric engine 
operates at full power (200 W at the wheel, 250 W nominal), so it is not possible to climb 
6-10% slopes at 4,81 m/s while keeping human power stable at 156 W. Consequently, 
uphill speed for 6-10% decreases to what is possible to achieve for a combined 156 W + 
200 W = 356 W. At 6% slope, for instance, speed decreases to 4,28 m/s and at 10% it goes 
down to 2,92 m/s. 
 
The calculated speed and assistance power for 3-10% slopes was added to the streets 
network associated table using ArcGIS tool field calculator. The nominal assistance 
energy necessary to cross each arc was then added via the field calculator formula: 
 
    𝐸 = 𝑃 9:;$#       (2) 
 
where E is the assistance energy required to cross the arc, P the assistance power, lup the 
uphill length, h the efficiency (80%), and v the speed. This calculation was performed for 
both directions, leading to EFT and ETF fields in the associated table.  
 
Finally, at intersections it was assumed that the cyclist would always stop when taking the 
left turn or going straight ahead, and stop about 50% of the time when turning right. It 
would then use full assistance, together with 120 W of human power [4], to accelerate 
back to the cruise speed on the flat of 6,01 m/s. This would require the battery to put 1490 
J at the wheel, translating into network turn costs of 1860 J (recall h = 80%) for left turns 
and straight ahead, and 900 J was considered for right turns. Programming was completed 
with creation of a network dataset, with EFT and ETF as impedances, and turn costs. 
Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 
5 
 
 
2.2. Service areas for commuting and city permeability to the pedelec 
With the network programmed, it was then possible to answer the first main question of 
this study: Does a pedelec have enough autonomy to provide full assistance for a 
commuting trip in Coimbra, regardless of house and job locations? 
 
This is arguably the most important trip of a cyclist’s day, so it is fundamental to know 
whether the pedelec can support it. For this purpose, service areas with respect to 
assistance energy were derived (towards facility and away from facility), with job location 
as the facility, energy breaks of 50 kJ, and polygon trimming of 25 m. Results for the most 
energy-demanding job location, the “Fórum Coimbra” shopping centre, located at a 
faraway hill-top, are shown in figure 1 below. 
 
    
Figure 1. Assistance energy service areas to Fórum Coimbra, towards (left) and away (right). 
The figure and its legend allow for two conclusions. First, it can be seen that most of the study 
area is fully cyclable with a pedelec. The city of Coimbra is thus permeable to this means of 
transport, except for some southwest and southeast areas with very high inclines. This is a 
vast improvement over the non-assisted bicycle, for which a permeability analysis [5] 
revealed a considerably smaller permeable area, furthermore divided into four disconnected 
zones. Second, the maximum assistance energy costs of 196 kJ (towards) and 223 kJ (away) 
sum up to a theoretical maximum of 419 kJ for commuting needs, which is far from the 
battery capacity of 788 kJ. The real round-trip maximum needs should be smaller than 419 kJ, 
as the geographical locations of the towards and away maxima do not coincide. 
Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 
6 
 
 
2.3. Daily circuits using the pedelec 
Having ascertained that pedelec autonomy is sufficient for commuting trips, it was left to 
determine whether it could allow for more a demanding daily use, i.e.: Does a pedelec 
have enough autonomy to provide full assistance for circuit trips that include stops at 
multiple locations and are representative of a busy day of a cyclist? 
 
To answer this question, 72 circuit trips were randomly generated and analysed, starting 
and ending at a residential area and going through in-between stops, for a total of 5-8 
stop-points. Locations of urban facilities of Coimbra (available from previous projects) 
were added to the GIS and 12 types of circuits were considered (table 2 below), for which 
6 samples were derived. 
Table 2. Daily circuit types considered. 
1. Home–School–Workplace–Grocery store–Home 
2. Home–Primary healthcare–Grocery store–Bakery–Home 
3. Home–Post Office–Workplace–Bakery–Home 
4. Home–Workplace–Restaurant–Shopping center–Home 
5. Home–Pharmacy–Workplace–School–Grocery store–Bakery–Home 
6. Home–School–Post Office–Grocery store–Local government–School–Bakery–Home 
7. Home–School–Workplace–Sports place–School–Grocery store–Home 
8. Home–Church–Cultural association–Elderly care residence–Bakery–Home 
9. Home–School–Local government–Entertainment place–Park–Home 
10. Home–School–Workplace–School–Primary healthcare–Home 
11. Home–School–Workplace–Cultural association–Sports place–School–Shopping center–Home 
12. Home–Primary healthcare–Pharmacy–Police squad–Post Office–Grocery store–Home 
 
The circuit trips were calculated in the network analyst using 3D length as impedance and 
energy as accumulation variable. Length was used instead of energy because cyclists tend 
to minimize travel distance, not energy assistance (doing the same for the service areas of 
section 3.2 would require a different approach). Results are shown in figure 2 histogram. 
  
Figure 2. Pedelec assistance energy needs for 72 circuit trips in the city of Coimbra. 
Only 5 out of 72 circuits required more than 600 kJ of assistance energy, and the most 
demanding circuit needed 758 kJ, still below battery capacity of 788 kJ. The pedelec can 
thus complete all the trips of a cyclist’s busy day without draining out its battery 
Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 
7 
 
 
completely. One caveat that might emerge in the mid-long term is battery degradation. 
Batteries are known to lose storage capacity with time and use, a loss which can come to 
20-30% after a few years. For the city of Coimbra and the pedelec model considered, this 
would jeopardize assistance for the subset of circuit trips over 600 kJ. It would thus be 
advisable for cyclists who use the pedelec very intensively to purchase a model of higher 
battery capacity. 
 
In general, however, battery degradation is not expected to be a problem. Industrial 
production is continuously improving and 219 Wh batteries will soon be replaced by 
higher capacity ones. Currently it is already possible to acquire 300+ Wh batteries for just 
about the same price. It is also likely that in the future cities will have recharge points for 
assisted-cycles. 
3. CONCLUSIONS AND FUTURE WORK 
The pedelec emerges from this research as a viable active transport alternative for hilly 
cities. With adequate autonomy and power to overcome relief, one of the greatest 
deterrents for using the bicycle as main transport mode, it gives the ball back to 
politicians, who are responsible for providing cyclists with safe and comfortable pathways 
for exercising their choice for this mode. Investment on bike paths, bike lanes and 
adjustment of crossings is the natural next step to foster a more active and sustainable 
transport mode, from which all citizens would benefit. 
ACKNOWLEDGEMENTS 
This work was partially supported by the Portuguese Foundation for Science and 
Technology under grant PEst-OE/EEI/UI308/2014. 
REFERENCES 
[1] United Nations Framework Convention on Climate Change, Paris Agreement, 
(2015). http://unfccc.int/paris_agreement/items/9485.php  
[2] J. Parkin, M. Wardman and M. Page, “Estimation of the determinants of bicycle 
mode share for the journey to work using census data”, Transportation Vol. 31, No. 
1, pp. 93-109, (2008). DOI: 10.1007/s11116-007-9137-5 
[3] P. Rietveld and V. Daniel, “Determinants of bicycle use: do municipal policies 
matter?”, Transp. Res. Part A, Vol. 38, No. 7, pp. 531-550, (2004). DOI: 
10.1016/j.tra.2004.05.003 
[4] J. Parkin and J. Rotheram, “Design speeds and acceleration characteristics of bicycle 
traffic for use in planning, design and appraisal”, Transport Policy Vol. 17, pp. 335-
341, (2010). DOI: 10.1016/j.tranpol.2010.03.001 
[5] L. Tralhao, N. Sousa, N. Ribeiro and J. Coutinho-Rodrigues, “Design of bicycling 
suitability maps for hilly cities”, Municipal Engineer Vol. 168, No. 2, pp. 96-105, 
(2015). DOI: 10.1680/muen.14.00009 


English

Pedelec on a hilly city: a case study in Coimbra

Conclusions: The pedelec emerges from this research as a viable active transport alternative for hilly cities. With adequate autonomy and power to overcome relief, one of the greatest deterrents for using the bicycle as main transport mode, it gives the ball back to politicians, who are responsible for providing cyclists with safe and comfortable pathways for exercising their choice for this mode. Investment on bike paths, bike lanes and adjustment of crossings is the natural next step to foster a more active and sustainable transport mode, from which all citizens would benefit.The pedelec is a basic type of electrically-assisted bicycle, designed to help cyclists overcome most slopes. This article presents a theoretical case study of a pedelec on the city of Coimbra, Portugal, which shows that even a low-end model provides enough power and autonomy for the daily transportation needs of a regular cyclist. It is only if battery wear is considered that a model of higher battery capacity is recommended, and even then only if the cyclist uses the pedelec very intensively. By overcoming what is arguably one of the greatest deterrents to cycling, the pedelec contributes towards materializing the concept of sustainable mobility. Overcoming the other major deterrent, safety concerns, is thus passed to the political decision makers, which will need to build and improve the urban infrastructures necessary for citizens to safely exercise their choice for this transport mode.PEst-OE/EEI/UI308/2014info:eu-repo/semantics/publishedVersio

Repositório Aberto da Universidade Aberta

Energy for Sustainability International Conference 2017 Designing Cities & Communities for the Future Funchal, 8-10 February, 2017  PEDELEC ON A HILLY CITY: A CASE STUDY IN COIMBRA N. Sousa12*, A.E. Gonçalves23 and J. Coutinho-Rodrigues24 1: Departamento de Ciências e Tecnologia Universidade Aberta, Delegação de Coimbra R. Alexandre Herculano, 52 3000-019 Coimbra, Portugal e-mail: nsousa@uab.pt,  web: http://www.uab.pt 2: Instituto de Engenharia de Sistemas e Computadores de Coimbra Edifício do Departamento de Eng.ª Electrotécnica e de Computadores Universidade de Coimbra Rua Sílvio Lima, Polo II 3030-290 Coimbra, Portugal web: http://www.uc.pt/en/org/inescc 3: Energy for Sustainability, MSc Student Faculdade de Ciências e Tecnologia Universidade de Coimbra Rua Luís Reis Santos, Pólo II 3030-788 Coimbra, Portugal e-mail: anaesmeralda6@hotmail.com 4: Departamento de Eng.ª Civil Faculdade de Ciências e Tecnologia Universidade de Coimbra Rua Luís Reis Santos, Pólo II 3030-788 Coimbra, Portugal e-mail: coutinho@dec.uc.pt,  web: http://www.uc.pt/fctuc/dec  Keywords: Pedelec, Energy, Sustainability, Coimbra Abstract The pedelec is a basic type of electrically-assisted bicycle, designed to help cyclists overcome most slopes. This article presents a theoretical case study of a pedelec on the city of Coimbra, Portugal, which shows that even a low-end model provides enough power and autonomy for the daily transportation needs of a regular cyclist. It is only if battery wear is considered that a model of higher battery capacity is recommended, and even then only if the cyclist uses the pedelec very intensively. By overcoming what is arguably one of the greatest deterrents to cycling, the pedelec contributes towards materializing the concept of sustainable mobility. Overcoming the other major deterrent, safety concerns, is thus passed to the political decision makers, which will need to build and improve the urban infrastructures necessary for citizens to safely exercise their choice for this transport mode. Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 2   1. INTRODUCTION The 20th century has witnessed a sizeable increase in the flow of populations towards cities and their suburbs. Fueled by cheap automotive transport and favorable public policies, the subsequent urban sprawl ultimately led to inefficiencies related to traffic congestion and energy consumption, and environmental concerns. The recently signed Paris Agreement [1], perhaps the most symbolic and important of all measures concerning sustainability and climate change, shows that politicians are becoming ever more aware that the current state of affairs may not be sustainable in the long term. This awareness led transport policy makers to encourage a shift towards alternative, more sustainable travel modes.  The bicycle is a very efficient active travel mode that can be adopted in most cities, contributing to urban sustainability, given the associated environmental, economic and social advantages. Cycling, however, also has its deterrents. Among these, it is recognized that slopes play an important role in influencing the choice for this mode of travel [2] [3]. To overcome this limitation, and sipping from the winds of change, industry began offering consumers Electrically-Powered Assisted Cycles (EPAC), which aim to provide cyclists a normal, non-fatiguing ride on hilly cities. Regulatory authorities divided these vehicles into two standards: the pedelec and the e-bike. The pedelec is the basic electrically-assisted cycle, with maximum 250 W nominal electric power, as requested by EU regulation. The e-bike can have higher power, but requires some sort of driver’s license. Both are active transport modes because they combine human power with electrical assistance for locomotion, although the e-bike can rely solely on battery power.  The aim of this study is to ascertain to what degree the most basic, and cheapest of these standards, the pedelec, can live up to expectations, i.e. comply with the demands posed by both high slopes and energy needs for assistance. For this purpose, the study determines whether the city is permeable to the pedelec, and whether its battery capacity is enough to allow for commuting trips and daily trips with multiple stops. This was done in the context of a real-life situation, the hilly, mid-sized city of Coimbra, Portugal (143 000 inhabitants in 2011), resorting to Geographic Information Systems (GIS) technology and following the methodology that is now described. 2. METHODOLOGY AND CASE STUDY For purposes of this study, the lowest-end pedelec available on the Portuguese market was considered. This was the B’Twin Bebike 500 model, with 250 W nominal power and a battery capacity of 219 Wh (788 kJ). The combined efficiency of ‘electric engine + mechanical parts’ was taken to be 80%, translating to 200 W maximum assistance power passed to the wheels.  Performance and autonomy of this pedelec on Coimbra was assessed in a two-stage process, using the ESRI ArcGIS environment and its network analyst extension as the Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 3   main calculation tools. In the first stage, the streets network of Coimbra was programmed. More precisely, network arcs which require electric assistance for crossing were endowed with that energy, in both directions. Network turns were also parameterized, with a cost based on assistance energy for acceleration from rest to cruise speed added. In a second stage, city permeability to the pedelec and calculations for energy assistance needs were carried out and results analysed (an area is said to be ‘permeable to transport mode X’ if it allows trips between any two of its points using mode X). Service areas based on assistance energy for commuting trips to the city’s main employers were derived. These service areas also allowed permeability to be checked. Results for assistance energy needs for 72 longer circuits with 5 to 8 stop-points were subsequently derived and analysed. No recharge points were considered: the cyclist can only recharge the bicycle at his residence. 2.1. Network programming A GIS shapefile of the streets network of Coimbra was available from previous projects. This contained altimetric information in the form of average uphill/downhill slopes and distances of each network arc, in the From-To direction. Network programming started with rounding off slopes to integers (see below) and restricting network arcs with uphill slope higher than 10% and downhill slope higher than 12%, in the From-To (FT) direction. The uphill restriction follows manufacturer guidelines, whereas the downhill restriction is due to difficulties controlling downhill speed, which may force the cyclist to dismount its bicycle. In the To-From (TF) direction the restrictions applied the other way around: restrict if the FT uphill slope (which is downhill in the TF direction) is higher than 12% or if the FT downhill slope is higher than 10%. These restrictions may cause an arc to be non-traversable in the FT or TF direction, or both.  To calculate electric assistance energy needs, it was assumed that cyclists would try, as much as possible, to cycle the uphill slopes as if they were cycling in the flat. In other words, the human pedalling power was assumed to be the same as the pedalling power in the flat. Human average speeds for integer uphill slopes (this is the reason slopes were rounded off) were derived in the experimental study of [4] and are shown in table 1 below. Table 1. Average unassisted cycling speed as a function of slope, according to [4]. Slope (%) 0% 1% 2% 3% 4% 5% 6% 7% Speed (m/s) 6,01 5,61 5,21 4,81 4,41 4,01 3,61 3,21  The corresponding power balance (P) can be derived from the physics formula below:  𝑃 = #$%&'( ∑𝑚𝑔 𝐶- + /011% + 03 𝐶4𝐴𝜌𝑣3     (1)  with v bicycle speed, hmech the mechanical efficiency, m total mass (cyclist + bike), g gravitational acceleration, Cr the rolling resistance coefficient, s the slope (in %), Cd the Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 4   aerodynamic coefficient, A the frontal area (cyclist + bike), and r the air density. Assuming the values of [4] for formula parameters and an excess of 11 kg for the assistance devices (engine/battery, total man + machine: 106 kg), the human pedalling power for cycling at the statistical average of 6,01 m/s is, by (1), 156 W. It was thus assumed that the cyclist would always exert this pedalling power, regardless of uphill slope.   Electric assistance was considered to be zero for all downhill slopes and uphill slopes up to (but not including) 3%, as cyclists are known to be insensitive to slope up to this value. For 3-10% slopes, assistance begins to be necessary and it was assumed cyclists would maintain the speed they had when the incline reached 3%, which was taken to be the one indicated in table 1 above (4,81 m/s). At 3%, maintaining that speed requires, by (1) and along with the 156 W provided by the cyclist, an extra 97 W of electric assistance power. Since pedelecs allow for variable assistance levels, it was also assumed the cyclist would adjust assistance level to the power required to maintain speed at 4,81 m/s.  As slope rises, the assistance power required to sustain a 4,81 m/s speed increases as well. It is possible to keep a 4,81 m/s speed up to 5% slope. At this point the electric engine operates at full power (200 W at the wheel, 250 W nominal), so it is not possible to climb 6-10% slopes at 4,81 m/s while keeping human power stable at 156 W. Consequently, uphill speed for 6-10% decreases to what is possible to achieve for a combined 156 W + 200 W = 356 W. At 6% slope, for instance, speed decreases to 4,28 m/s and at 10% it goes down to 2,92 m/s.  The calculated speed and assistance power for 3-10% slopes was added to the streets network associated table using ArcGIS tool field calculator. The nominal assistance energy necessary to cross each arc was then added via the field calculator formula:      𝐸 = 𝑃 9:;$#       (2)  where E is the assistance energy required to cross the arc, P the assistance power, lup the uphill length, h the efficiency (80%), and v the speed. This calculation was performed for both directions, leading to EFT and ETF fields in the associated table.   Finally, at intersections it was assumed that the cyclist would always stop when taking the left turn or going straight ahead, and stop about 50% of the time when turning right. It would then use full assistance, together with 120 W of human power [4], to accelerate back to the cruise speed on the flat of 6,01 m/s. This would require the battery to put 1490 J at the wheel, translating into network turn costs of 1860 J (recall h = 80%) for left turns and straight ahead, and 900 J was considered for right turns. Programming was completed with creation of a network dataset, with EFT and ETF as impedances, and turn costs. Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 5   2.2. Service areas for commuting and city permeability to the pedelec With the network programmed, it was then possible to answer the first main question of this study: Does a pedelec have enough autonomy to provide full assistance for a commuting trip in Coimbra, regardless of house and job locations?  This is arguably the most important trip of a cyclist’s day, so it is fundamental to know whether the pedelec can support it. For this purpose, service areas with respect to assistance energy were derived (towards facility and away from facility), with job location as the facility, energy breaks of 50 kJ, and polygon trimming of 25 m. Results for the most energy-demanding job location, the “Fórum Coimbra” shopping centre, located at a faraway hill-top, are shown in figure 1 below.      Figure 1. Assistance energy service areas to Fórum Coimbra, towards (left) and away (right). The figure and its legend allow for two conclusions. First, it can be seen that most of the study area is fully cyclable with a pedelec. The city of Coimbra is thus permeable to this means of transport, except for some southwest and southeast areas with very high inclines. This is a vast improvement over the non-assisted bicycle, for which a permeability analysis [5] revealed a considerably smaller permeable area, furthermore divided into four disconnected zones. Second, the maximum assistance energy costs of 196 kJ (towards) and 223 kJ (away) sum up to a theoretical maximum of 419 kJ for commuting needs, which is far from the battery capacity of 788 kJ. The real round-trip maximum needs should be smaller than 419 kJ, as the geographical locations of the towards and away maxima do not coincide. Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 6   2.3. Daily circuits using the pedelec Having ascertained that pedelec autonomy is sufficient for commuting trips, it was left to determine whether it could allow for more a demanding daily use, i.e.: Does a pedelec have enough autonomy to provide full assistance for circuit trips that include stops at multiple locations and are representative of a busy day of a cyclist?  To answer this question, 72 circuit trips were randomly generated and analysed, starting and ending at a residential area and going through in-between stops, for a total of 5-8 stop-points. Locations of urban facilities of Coimbra (available from previous projects) were added to the GIS and 12 types of circuits were considered (table 2 below), for which 6 samples were derived. Table 2. Daily circuit types considered. 1. Home–School–Workplace–Grocery store–Home 2. Home–Primary healthcare–Grocery store–Bakery–Home 3. Home–Post Office–Workplace–Bakery–Home 4. Home–Workplace–Restaurant–Shopping center–Home 5. Home–Pharmacy–Workplace–School–Grocery store–Bakery–Home 6. Home–School–Post Office–Grocery store–Local government–School–Bakery–Home 7. Home–School–Workplace–Sports place–School–Grocery store–Home 8. Home–Church–Cultural association–Elderly care residence–Bakery–Home 9. Home–School–Local government–Entertainment place–Park–Home 10. Home–School–Workplace–School–Primary healthcare–Home 11. Home–School–Workplace–Cultural association–Sports place–School–Shopping center–Home 12. Home–Primary healthcare–Pharmacy–Police squad–Post Office–Grocery store–Home  The circuit trips were calculated in the network analyst using 3D length as impedance and energy as accumulation variable. Length was used instead of energy because cyclists tend to minimize travel distance, not energy assistance (doing the same for the service areas of section 3.2 would require a different approach). Results are shown in figure 2 histogram.   Figure 2. Pedelec assistance energy needs for 72 circuit trips in the city of Coimbra. Only 5 out of 72 circuits required more than 600 kJ of assistance energy, and the most demanding circuit needed 758 kJ, still below battery capacity of 788 kJ. The pedelec can thus complete all the trips of a cyclist’s busy day without draining out its battery Sousa, N., Gonçalves, A.E. and Coutinho-Rodrigues, J. 7   completely. One caveat that might emerge in the mid-long term is battery degradation. Batteries are known to lose storage capacity with time and use, a loss which can come to 20-30% after a few years. For the city of Coimbra and the pedelec model considered, this would jeopardize assistance for the subset of circuit trips over 600 kJ. It would thus be advisable for cyclists who use the pedelec very intensively to purchase a model of higher battery capacity.  In general, however, battery degradation is not expected to be a problem. Industrial production is continuously improving and 219 Wh batteries will soon be replaced by higher capacity ones. Currently it is already possible to acquire 300+ Wh batteries for just about the same price. It is also likely that in the future cities will have recharge points for assisted-cycles. 3. CONCLUSIONS AND FUTURE WORK The pedelec emerges from this research as a viable active transport alternative for hilly cities. With adequate autonomy and power to overcome relief, one of the greatest deterrents for using the bicycle as main transport mode, it gives the ball back to politicians, who are responsible for providing cyclists with safe and comfortable pathways for exercising their choice for this mode. Investment on bike paths, bike lanes and adjustment of crossings is the natural next step to foster a more active and sustainable transport mode, from which all citizens would benefit. ACKNOWLEDGEMENTS This work was partially supported by the Portuguese Foundation for Science and Technology under grant PEst-OE/EEI/UI308/2014. REFERENCES [1] United Nations Framework Convention on Climate Change, Paris Agreement, (2015). http://unfccc.int/paris_agreement/items/9485.php  [2] J. Parkin, M. Wardman and M. Page, “Estimation of the determinants of bicycle mode share for the journey to work using census data”, Transportation Vol. 31, No. 1, pp. 93-109, (2008). DOI: 10.1007/s11116-007-9137-5 [3] P. Rietveld and V. Daniel, “Determinants of bicycle use: do municipal policies matter?”, Transp. Res. Part A, Vol. 38, No. 7, pp. 531-550, (2004). DOI: 10.1016/j.tra.2004.05.003 [4] J. Parkin and J. Rotheram, “Design speeds and acceleration characteristics of bicycle traffic for use in planning, design and appraisal”, Transport Policy Vol. 17, pp. 335-341, (2010). DOI: 10.1016/j.tranpol.2010.03.001 [5] L. Tralhao, N. Sousa, N. Ribeiro and J. Coutinho-Rodrigues, “Design of bicycling suitability maps for hilly cities”, Municipal Engineer Vol. 168, No. 2, pp. 96-105, (2015). DOI: 10.1680/muen.14.00009 

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Pedelec on a hilly city: a case study in Coimbra

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