## 3 Results and Discussion
### Model Development

Table 3: Summary of analyzed model types to correlate the distance and \(V_{85}\) and \(V_{m}\) and obtained \(R^{2}\). Similarly, for predicting the average speed in an intermediate point, Equation (2) is proposed. \[V_{m}=30.67+0.055\cdot d \tag{2}\]  
where \(V_{m}\) is the average speed in an intermediate point between consecutive vertical traffic calming measures and \(d\) is described as in Equation (1). Figure 10 shows the plot of both models. Table 4 presents the Analysis of Variance (ANOVA) of the model of Equation (1) and Table 5 the ANOVA of the model of Equation (2). As observed, both models are significant (\(p\)-value of the F-test below 0.05), and each of the coefficients of the variables and the intercept are statistically significant too (\(p\)-values \(<\) 0.05). Furthermore, the hypotheses assumed in a linear regression model were verified: high value of the Pearson coefficient (\(R\)); the Durb  
The proposed models indicate that the \(V_{85}\) is increased by 0.75 km/h along with every additional 10 m distance between the TCMs. Furthermore, when reducing the distance towards zero, a minimum value for \(V_{85}\) would be achieved, 34.4 km/h. These values correspond to the average value of the observed 85 th percentile in the TCMs (34.7 km/h), shown in Table 2. Therefore, the model is consistent. The average \(V_{85}\) crossing a TCM is 34.7 km/h and depending on the distance from the previous TCM, the speed is increased by 0.75 km/h along with every additional 10 m distance. Similarly, the intercept of Equation (2) (30.67) would mean the minimum value of the average speed when two TCM are very close, and it corresponds with the average value of the observed average values within the investigated TCM types (28.8 km/h). Once again, the model is consistent and indicates that the average value 30.7 km/h is achieved at any vertical TCM. The speed in the middle point between two consecutive TCMs is increased as a function of the distance from the obstacle, 0.55 km/h every 10 m.  
It must be noted that these models are only dependent on the distance between TCMs and do not consider other variables like the geometry of the vertical measures. The design of a very specific TCM that could imply a great speed reduction is not considered. We only considered typical geometries, employed in two different countries of the EU. Other factors were not taken into account, such as, the percentage of vehicles turning in the crossings or making maneuvers for parking. Hence, when the values of these variables are important, obtained speed can be highly influenced by them. If obtained values are compared with previous studies in the literature, it must be said that [PERSON] (1959) indicated a speed increase between 0.26 and 0.53 km/h every additional 10 m distance and in this study speed increases between 0.55 and 0.75 km/h were obtained, implying that at present, drivers tend to accelerate more rapidly between TCMs. [PERSON] et al. [PERSON] _et al._ (2016) recommended a maximum distance of 200 m, 100 m, and 75 m, for speed limits of 50 km/h, 40 km/h and 30 km/h, respectively. Using developed models, for a \(V_{85}\) of 50 km/h a maximum distance of 200 m is also recommended. However, for a \(V_{85}\) of 40 km/h in the midpoints, a maximum spacing of 75 m is suggested. However, for a value of 30 km/h in the 85 th percentile of the speed distribution, proposed model is not recommended, because the minimum value that can be achieved (and even the measured values in the TCMs) are over this value (\(>\) 30 km/h). For a more restricted area of 30 km/h, the model of [PERSON] et al. [PERSON] _et al._ (2019) is suggested, which was mainly measured in school and pedestrian areas, with distances between TCMs in the range of 23 and 90 m.  
These models are verified for distances between 63 and 293, so it can be proposed for distances between 60 and 250 m.