# Examining the Efficiency of Electric-Assisted Mountain Biking across Different Types of Terrain
## 2 Materials and Methods  
### Study Design  
An off-road riding on a 4.5 km long lap with four sections was monitored. The first \"uphill\" section was 1.6 km long with 128 m of elevation and consisted of a compact gravel terrain. The second \"downhill\" section was 1.4 km long, consisting of packed gravel and grass terrain, and was followed by an 800 m \"flat\" section with mixed open forestry roadsand a paved surface. The fourth and last section of the lap was 700 m in length and included a technically demanding single track with frequent obstacles, such as rocks, roots, and many curves. A repeated measures design was employed. The participants cycled on a mountain bike course with different off-road terrains (i.e., uphill, downhill, flat section, technically demanding terrain) at their self-pace (as fast as possible) on electric-assisted and conventional mountain bike. The two testing conditions were separated by two days and were randomly performed. Before each measurement, a 10-min warm-up was performed. Two types of mountain bikes were used for the study: a conventional model (Scott Genius 700 PLUS), which is shown in Figure 1, and an electric-assisted version (Scott e-Genius PLUS 700), which is shown in Figure 2. The electric-assisted bike, which was equipped with a battery, engine, and the necessary controls of the Bosch Performance CX drive system, weighed 7.5 kg more than the conventional bike. The Bosch Performance CX motor (Abstatt, Germany), which remained untuned, retained its original 250 W output and was powered by a 500 Wh battery. The electric motor was configured to provide assistance only up to a speed of 25 km/h.\"  
During all measures, the altitude, distance, velocity, cadence, and power output (PO) values were recorded at a 1 Hz sampling rate. All the values were sensed with the Garmin Vector pedals and Garmin Edge 820 receivers (Garmin, Olathe, KS, USA). The results are shown as mean power output (MPO), peak power output (PPO), and normalized power output (NPO)= a 30 s rolling average of the power data. Heart rate was recorded with a Polar v800 device (Polar, Kempele, Finland). Each participant wore a portable breath-by-breath gas analyzer (Cosmed K4b2, Rome, Italy) during the measurements. Oxygen uptake (VO2), ventilation (Ve), respiration frequency (Rf), and energy expenditure were recorded. Gross efficiency (GE) was calculated following [PERSON] et al. [17]. For these parameters, averages for all four sections (uphill, downhill, flat, technical demanding terrain) and the total course were calculated. At each point of observation along the off-road course, the pedaling power (Pp) needed to overcome air drag (Pd), rolling resistance (Pr), and gravity (Pg) as well as the power to produce acceleration (Pa) were calculated, where Pd was defined as Pd = Pd \(\times\) v, where v is the velocity and Pd is the air drag force based on a previous study Pd = 0.1929 \(\times\) v\({}^{2.0531}\)[18]. Similarly, Pr was calculated as: Pr = CrFg \(\times\) v, where Fg is the total weight of the cyclist and the bicycle, and Cr was linearly estimated based on the rolling resistance test results for mounted Schwalbe Racing Ralph TLR tires [19] for a tire pressure of 2 bars. The Pg was calculated as: Pg = Fg \(\times\) v, and Pa as: Pa = FMa \(\times\) v, where 'a' is acceleration and M is the total mass of the cyclist and the bicycle. Velocity was filtered with the Rauch-Tung-Striebel algorithm [20], which uses two unscented Kalman filters running forward and  
Figure 1: The specifications of the electric-assisted mountain bike (E-MTB) used in the study. Figure 2: The specifications of the mountain bike (MTB) used in the study. backward in time and performs fixed-interval offline smoothing of the estimated signals. The Kalman filter has also been used to estimate non-measurable acceleration optimally and was implemented using the Kalman filter toolbox [21] in Matlab 7.9 (Mathworks Inc., Natick, MA, USA).