# Application of Infrared Thermography in E-Bike Battery Pack Detail Analysis--Case Study
## 2 Electric Bicycles
### Technical and Regulatory Aspects of Electric Cycling  
The technical solution of the electric bicycle in the form of PEDELEC (pedal electric cycle) [28] is the closest to the initial idea of cycling. A greater demand for PEDELECs began in 2005 primarily thanks to the wider use of Li-ion batteries. PEDELEC is \"bicycles with pedals equipped with one auxiliary electric motor with a maximum continuous rated power of 0.25 kW, whose output value is constantly reduced and finally switched off when the vehicle reaches a speed of 25 km/h, or sooner if the cyclist stops stepping on the pedals\" and is given in the description of PEDELEC legislature, in EU Directive 2002/24/EC [24]. Despite its higher weight (approximately 27 kg and more) than a conventional bike (approximately 14 kg), PEDELEC allows an easier movement regardless of terrain configuration and helps to lower the physical exertion of the driver. European PEDELEC manufacturers for the USA and Canada market, owing to the difference in legislation, produce 350 W motors exclusively. Furthermore, the USA legislature even allows the use of electric motors up to 750 W and Canada up to 500 W. In Europe, Switzerland allows electric motors up to 500 W, but the speed limit is in accordance with the EU--limited to 25 km/h. Switzerland legislature supported their 500 W limitation due to the needs and specifics of their predominant terrain configuration. In the end, PEDELEC is subject to the requirements of the international standard related to bicycles EN 14764 \"City and trekking bicycles--Safety requirements and test methods\", but in addition, it must meet the requirements of EN 15194 \"Cycles--Electrically power assisted cycles--EPAC bicycles\", which refers to the electrical part only. When riding, the biggest problems for the rider are hills and strong winds. The average rider develops 100 W recreationally and up to 200 W when in a good physical condition. A professional rider can normally produce 200 W to 300 W during a non-competitive session and in races of up to 400 W continuously over a distance of 14 km. The power requirements for riding are best described in Figure 1[29]. The green interval indicates the average operational cycling speed that prevails during a cycling session, the orange-colored intervals present a maximum value of the power required, and a light-orange one is a power requirement in the event of the mean wind occurrence at the cycling site. In order to define, more precisely, the need for cycling power, it is necessary to deterministically describe such a process in the form of a deterministic mathematical relation. The mathematically defined and sufficiently accurately described need for cycling power is given with expression (1). The dependence and influential behavior of individual variables are in detail described in [14]. \[W=\left[K_{\text{a}}\cdot\left(V+V_{\text{w}}\right)^{2}+g\cdot\left(m_{\text{ r}}+m_{\text{b}}\right)\cdot\left(s+C_{\text{r}}\right)\right]\cdot V \tag{1}\]  
Figure 1: Power intervals required for cycling. where  
\(W\): mechanical power at the wheel, [W] (_which is slightly less than what the rider produces due to losses and coupling efficiency);_  
\(K_{\rm a}\): drag factor, [kg/m] (_usually in interval of_ 0.1 _to_ 0.3; _for a small recumbent rider_ 0.1; _large upright rider_ 0.3; _typical values_ 0.2-0.25);  
\(V\): bike velocity, [m/s];  
\(s\): road slope, [%], (e.g., 5% = 0.05);  
\(C_{\rm r}\): rolling resistance coefficient [1] (0.02 _for racing tires_; 0.08 for heavily grooved MTB; and 0.03 _typically for road bikes_);  
\(V_{\rm w}\): heading wind velocity, [m/s];  
\(m_{\rm r}\): driver mass, [kg];  
\(m_{\rm b}\): bike mass, [kg];  
\(g\): gravitational constant, [m/s2] (_taken an average value of_ 9.81 m/s2). The battery as a power source is a more critical element of an electric bicycle because it intrinsically poses a hazard in the event of overcharging, short circuit, or physical damage [10].