A Study on the Factors Influencing Sunlight in Block Layout: A Case Study of Barcelona Sample

Abstract

Block layout is the main urban pattern in many city centers in the East and West, and this layout has a long history and will continue to develop in the future. However, there are relatively few studies on the quantitative analysis of this layout, especially its sunlight impact. This study examines the characteristics of the neighborhood-style layout. A sample of the small block dense street network block layout that evolved and developed based on Cerdà’s planned Barcelona was selected. The effects of urban latitude and the angle between the street and north–south are explored on the level of sunlight in the neighborhood space. By using the Ladybug plug-in to simulate the Cerda Barcelona neighborhood model, this study analyzes the quantitative impacts of different geographic latitudes and north–south angle changes on the daylight levels of streets, courtyards, building facades, and ground floor building elevations. The results show that changes in the latitude and north–south angle significantly affect the daylight level of each part of the space in the neighborhood, which provides a quantitative basis for the daylight adaptation analysis. Based on the simulation results, this paper proposes a regression model for the influencing factors of the neighborhood-style layout. The adaptive boundary conditions of this layout in a high-density urban environment are arranged by analyzing the regression model. To a certain extent, this study provides a theoretical basis and corresponding reference for tightening the daylight and environmental health requirements of urban layouts for high-density composite urban development.

1. Introduction

1.1. Background Introduction

Although it is not common in China, the layout of enclosed blocks is the basic and conventional layout of buildings in the central areas of many large Western cities. This approach ensures the humanized scale of ancient urban blocks and forms a moderately high-density and compact urban form. With the popularization of motor vehicles and public transportation in modern society, this pattern has not been eliminated but has adapted to various new technological challenges at the same time.

However, this compact layout can also be disrupted by many factors, such as winding rivers and mountains in the city center, as well as highways and railways in suburban areas. With the emergence of high-rise towers, people seem to believe that the buildings in the city center should be more point-style high-rise buildings. However, it seems that most point-style high-rise buildings in the West are only concentrated in a small area of the central district, while most residential and commercial areas in the city center still adopt block-type layouts. A block-type community can maintain a high plot ratio without increasing obstruction to surrounding land, and can freely combine multifunctional formats in urban architecture in both horizontal and vertical directions.

Due to the influence of the urban road network layout, it is not easy to find typical standard models of high-density block-style buildings that can be studied. Cities such as London and Paris adopt block-style layouts, and due to the influence of roads and rivers, the road network is not standardized, only simple height control can be achieved, and the community has not evolved to its extreme state.

This study focuses on the small block and dense road network layout that evolved from the Cerdà—planned Barcelona (as shown in Figure 1). Firstly, it is because it adopted a regular road network from the beginning of its planning, forming equally sized street blocks. Through more than 150 years of development, an expanded urban form has gradually taken shape, including streets, multi-level high-density blocks, and inner courtyard public spaces. This pattern is similar to the downtown or central urban areas of many mid to high-latitude cities such as New York, Vancouver, Seattle, Paris, etc. Unlike other high-density urban layouts, Barcelona’s block-style layout has evolved in the process of development. It is close to the coast and has more flat indoor areas. The basic urban layout remains uninterrupted by rivers or major linear public transportation routes. This results in a complete block layout. Such a layout is more suitable as a fundamental model for studying sunlight factors.

The Eisimple, as a milestone in 19th century urban planning, is the practical result of the “Plan Cerda” proposed by engineer Ildefons Cerd à in 1859.

The Zelda Plan adopts a grid-like urban layout, based on 20 m wide streets, with a main road set every 113 m, creating a clear and orderly urban structure. At the same time, 50 m wide regional or metropolitan tree-lined avenues were planned, such as Granvia Avenue, Diagonal Avenue, etc., which play an important connecting and guiding role in urban development [1]. At the same time, its grid−like street layout, octagonal block design (as shown in Figure 2), and balance between public and private spaces are still important models for urban research today [2].

This plan still has important guiding significance for the current urban layout in three aspects: urban living environment sanitation, transportation reform, and social equality [3]. In terms of hygiene, the 20 m wide street and courtyard design within the block ensure ventilation and lighting in residential areas and urban public spaces (as shown in Figure 3). In terms of transportation, the grid layout combined with diagonal roads such as Gracia Avenue foresaw the demand for mechanized transportation. In terms of social equality, a homogeneous block layout avoids class segregation and reflects the balance and equality of the living environment in the city.

In contrast, high-density residential areas in China often adopt point and slab layouts in order to obtain better indoor lighting and ventilation conditions. This layout sacrifices the hygiene and comfort of many public spaces in the city, and even makes it difficult to form a continuous east–west street interface. Through research, it has been found that the facade sunlight conditions of residential buildings in Barcelona’s block layout are significantly better than those of point and slab houses commonly used in China with a north–south layout. The sunshine conditions of urban public spaces such as streets, courtyards, squares, etc., in Barcelona’s small blocks and dense road network layout are also better than those in China’s existing high-density residential areas. In this case (as shown in Figure 4 and Figure 5), the building density in Barcelona can reach 4.6 or even higher, while China’s regulations stipulate that the upper limit of residential areas is around 3.1. Therefore, it is necessary to explore the factors affecting sunlight under high-density block layout, in order to provide suggestions for the renovation of old blocks and the planning and construction of new blocks under high-density layout.

In summary, the main contributions of this article are as follows:

• Establish a parameterized simulation model for high-density urban residential buildings. Focus on Barcelona, focusing on the small blocks and dense road network pattern of Barcelona’s Cerda grid layout. A high-density urban form with a plot ratio of 4.6 is used as the sample model, and the surrounding eight blocks are used as site occlusion objects. This study provides a new perspective for the comparative study of sunlight in high-density neighborhoods by simulating the experimental model with sunlight.
• Multi-dimensional simulation analysis. The influence of different latitudes from 31° N to 45° N and street angles from 0° to 45° on sunshine levels was simulated using the Ladybug tool. Through simulation, it was found that a 45° street angle has significant advantages in building facades (with a 14.4% increase in ground floor sunlight) and public spaces (with a street/square sunlight ratio of 24.8–33.2% for ≥2 h). This provides a basis for the selection of road network angles, façade, and courtyard design for residential areas in cities of different latitudes.
• Interdisciplinary data analysis methods. Combining parametric modeling with Grasshopper of rhino7.34 and IBM SPSS Statistics 26 regression analysis in Rhino, a trigonometric function fitting model is proposed based on the sun position formula. Introducing the formula of solar position relationship into the prediction of sunshine level can more accurately quantify the synergistic effect of latitude and street angle on sunshine.
• Comparison of international standards and adaptive strategies. Analyze and integrate sunshine regulations from multiple countries such as China, Japan, and Germany, and propose optimization strategies for dynamically adjusting street angles. Provide scientific planning basis for cities at different latitudes.
• Verified the sunshine adaptability of the high-density block model. This study provides design guidelines for microclimate regulation and solar energy utilization in high-density urban public spaces. Comparing multiple simulation results provides optimization directions for the width ratio of the courtyard and the layout of green plants on the streets, and promotes sustainable urban development.

Although Barcelona’s neighborhoods place greater emphasis on building density and continuity, they are also high-density neighborhoods with relatively high levels of sunlight. This layout to some extent promotes community interaction, while the 45-degree street also strives for good sunshine and sanitation conditions for the block. This study further revealed the factors that affect residential sunlight levels through simulation. Also, it provides layout recommendations for different high-density cities based on simulation results to improve sunlight levels and solar energy utilization efficiency. For the first time, the Barcelona grid layout is combined with multi-latitude sunshine simulation to propose a dynamic optimization theory for street angles and establish a universal design framework based on mathematical models, providing a new paradigm for high-density urban sunshine planning. Therefore, in future research, the adaptability of this model in non-grid cities and the relationship between other building form parameters and sunlight can be further explored.

The main framework of this article includes the following aspects: First, a review of relevant literature on sunshine and residential layout optimization, as well as cutting-edge practices of parametric tools in sunshine analysis. Next, we will provide a detailed introduction to the research methods used in this study, including model establishment, simulation experiments, and data analysis methods. The following chapters will present experimental results and summarize the patterns of sunlight levels at different latitudes and street angles. We have established a quantitative relationship model between latitude, street angle, and sunshine, providing a scientific planning tool for high-density cities. Finally, this article will propose optimization suggestions for a high-density residential layout from the perspective of sunlight and water, emphasizing the importance of improving solar energy utilization efficiency for urban sustainable development.

1.2. Related Research

Neighborhood layout is the main urban pattern in the central areas of cities in the East and West, with a long history. In the context of the increasing shortage of urban land, this layout pattern has become an effective exploration of compact and intensive urban development. Barcelona Cerdà planning, as a typical representative, adopts the layout of small neighborhoods and dense road networks, which provides an important reference for modern urban layout [4].

The small-scale neighborhood layout increases the density of the road network and also enhances the openness of public spaces. Smaller neighborhoods and denser road networks are one of the forms of pedestrian-friendly layouts. From a land use perspective, this type of neighborhood creates a pattern of high-density residential development. According to history, 150 years of evolution of Cerdà planning created the highest plot ratio of this layout, reaching 8.0 [5]. After 150 years of evolution, the layout has eventually developed a stable plot ratio of about 4.6, which is higher than the higher plot ratio of 3.0 for tower high-−rise residential development in China. From an urban public space perspective, courtyards and streets in neighborhoods become important public spaces with the potential to improve the microclimate.

In 2015, Barcelona embarked on a “Superblock” regeneration program. The plan combines the original nine small neighborhood units into one 400 m × 400 m superblock unit [6], which changes the spatial form of the neighborhood to a certain extent, altering the building spacing, height and even the form of public space. The influence of these factors may change the sunshine situation in the block space, so it is necessary to analyze and study the sunshine for 3 × 3 street layout.

For small neighborhoods, a dense road network planning layout involves street public spaces and traffic space on a scale that affects the level of daylight in the neighborhood. At present, research on the residential layout of small neighborhoods and dense road networks mainly focuses on building density and sunlight conditions. For example, Zhang et al. compared the differences between the slab and point residential layout in Tianjin and the small block layout in Barcelona under sunlight conditions, and the results of the study showed the importance of appropriate sunlight conditions for residential layouts in northern cities [7]. Han et al. revealed the problems of China’s current sunlight standards by using sunlight analysis software for case studies of specific residential areas, and put forward suggestions for improvement based on empirical studies, aiming to promote the efficient use of land resources and the continuous improvement of the living environment [8].

The relationship between neighborhood layout and daylighting is of great significance in sustainable urban development. With the acceleration of urbanization, the energy demand of the city is predicted to increase. As a kind of clean energy, the efficient utilization of solar energy is of great significance in reducing building energy consumption and promoting sustainable urban development. Existing studies show that urban buildings consume 70% of primary energy [9].

Liu’s study showed that the energy consumption of urban buildings is increasing year by year, and the proportion of this type of energy to the total energy consumption of the society has exceeded a quarter by 2021 [10], but winter insolation can effectively improve the energy consumption of buildings [11]. An et al. revealed the great potential of rooftops and façades in the utilization of solar energy, which provides valuable insights into the future of urban planning and sustainable development policies [12]. Therefore, improving the insolation of buildings is of great practical importance for reducing building energy consumption.

Current research on the relationship between building layout and insolation in cities mainly focuses on the optimization of solar energy potential and urban layout, the optimization of insolation quantification and building form, and the design optimization of courtyard microclimate.

Existing studies have shown that there is an inextricable relationship between urban layout and solar potential. For example, Košir et al. analyzed the effects of different building layouts on solar energy collection and pointed out that the optimization of building orientation and spacing is an important factor in improving the efficiency of solar energy use [13]. In order to further explore the issues related to solar energy potential in existing urban layouts, a study proposed that the two key factors for improving the efficiency of solar energy use are building orientation and spacing by analyzing the effects of different building layouts on the duration of sunlight [14]. By analyzing the effects of different urban layouts on building energy consumption and solar potential, one study proposed a framework for optimizing the urban form to improve energy efficiency [15,16].

In recent years, research in the field of residential building energy sustainability has shown that reasonable building layout and orientation design play a key role in improving energy efficiency and integrating renewable energy. Bekele and Atakara [17] and Khan et al. [18] explored passive and active solar energy utilization under different climatic backgrounds, providing important references for this study.

Bekele and Atakara [17] conducted research on energy efficiency optimization of residential buildings in the Mediterranean climate zone. The research aims to maximize solar energy utilization and reduce heat loss by optimizing building orientation and layout, as well as adopting high-performance glass and insulation measures. The results confirmed the significant effect of climate-responsive design, such as layout and sunshine adaptability optimization, on improving indoor thermal comfort and reducing energy consumption. This provides empirical evidence for optimizing the layout of urban residential buildings and utilizing sunlight. In contrast, Khan et al. [18] highlighted the relationship between building spatial layout and orientation and photovoltaic utilization efficiency by evaluating the potential of rooftop photovoltaic systems in Saudi Arabia. The results indicate the impact of building orientation on the available rooftop photovoltaic area. Khan et al. also pointed out that precise data on building orientation and urban planning should be collected to improve the accuracy of photovoltaic potential assessment, highlighting the impact of macro-level planning on the utilization of renewable energy in buildings.

The current study provides a comprehensive assessment of building solar potential based on daylight simulations, demonstrating the positive impact of daylight levels on urban form and climatic conditions [5]. However, how to improve the daylight level of courtyards, streets, squares, facades, and other parts of residential neighborhoods under the dense road network layout of small neighborhoods by adjusting the layout of residential neighborhoods needs to be further investigated.

The form and layout of the building and its geographical location have a significant impact on the efficiency of solar energy utilization. GIS methods can now be utilized to assess the solar energy potential of urban residential environments. Additionally, optimization strategies based on GIS can be used to maximize solar energy utilization [14,19]. In order to improve the level of insolation and design a more rational building form, many researchers have quantified the insolation hours of buildings to explore the optimal design of building forms. For example, Shao established a quantitative relationship model between the daylight hours and the shape, size, height, and arrangement of buildings, which proved that choosing a shorter arrangement of slab-type buildings can effectively improve land use efficiency and satisfy certain daylight standards. The optimization strategy of the building form was proposed from the perspective of daylighting [20]. Another study by Liu et al. found that the height, spacing, and layout of buildings significantly affect the efficiency of solar energy acquisition through the simulation of energy consumption in different urban forms. A multi-objective optimization scheme was proposed for improving solar energy efficiency and reducing building energy consumption [15].

Currently, parametric modeling and simulation methods are widely used for building energy consumption simulation, especially in the field of solar energy utilization. This method can use quantitative analysis to analyze the solar energy potential of urban residential buildings under different block layout conditions. Tian and Ooka [21] used Grasshopper and Ladybug plugins to simulate solar radiation in a 3D model, exploring the effects of building height, block layout, and their interactions on the solar radiation utilization efficiency of residential building roofs and facades. The results indicate that the height of the target building and its spatial relationship with surrounding buildings play a decisive role in the utilization of solar energy on the building surface. Shakibamanesh used the Ladybug plugin in Grasshopper to simulate the solar radiation levels of different types of urban blocks [22].

The above research indicates that Grasshopper parametric modeling and Ladybug plugin for solar energy simulation have important guiding significance for block layout. This study will draw on the above methods to further explore the relationship between the impact of sunlight and urban block layout.

Existing studies have shown that the form of urban blocks in residential areas has a significant impact on the utilization of solar energy. Especially, parameters such as the floor area ratio have a significant influence [23], and in addition, the form of the block also has a significant impact on the utilization of solar energy [24]. These studies have highlighted that the architectural form and layout have a significant influence on sunlight. Although the research objects are different, enhancing the utilization of solar energy by optimizing the layout is an important measure to promote the utilization of clean energy at present.

In terms of smaller scales and outdoor spaces, most of the studies focused on the effects of courtyard spaces and building facades on the thermal environment and solar potential of buildings. For example, by simulating and analyzing the daylighting and ventilation performance of courtyards with different geometries, it was found that north–south oriented courtyards with high aspect ratios have significant cooling effects in hot climates and can improve thermal comfort. It provides a basis for the optimization of courtyard layout [16]. In terms of insolation potential, a study has proposed a method to quantify the solar energy utilization potential of building facades and roofs in urban areas by using the RADIANCE lighting simulation software. It was demonstrated that there is a significant difference in the façade solar energy collection potential of different building layouts at the same density [25].

Although existing studies have directed the study of urban insolation levels at the level of the building layout, little attention has been paid to the importance of natural energy sources such as insolation levels in spaces such as courtyards and streets [26,27]. Most studies have been conducted in terms of single elements such as urban density and building type [28,29].

It can be proved that the level of sunshine also affects the form of the building layout to a certain extent. Especially under the planning layout of small neighborhoods and dense road networks, courtyard space has gradually become an important component of urban public space, and the sunshine situation in the courtyard space affects the geometry and orientation of the courtyard to a certain extent. In addition, due to the aggravation of global climate change, more attention has been paid to the role of microclimate regulation in cities. Studies such as that reported by Liu et al. have explored sustainable strategies in architectural and urban design from three perspectives: courtyard design, urban form and solar potential, and the application of GIS in solar energy assessment of urban residential environments [16,19].

Existing studies have shown that Barcelona has a long history of neighborhood public space revitalization, and in recent years, neighborhood planning reforms aimed at revitalizing neighborhood road space have advocated giving roads back to pedestrians, providing useful references for promoting neighborhood-based residential patterns and neighborhood planning in China [5,30]. A study by Zhang et al. found that the road network layout in Barcelona helps to ensure good daylighting conditions for streets and buildings, and that daylighting requirements can be realized even at high latitudes [7,31].

In future research, it is necessary to deeply explore and practice the concept of Zelda planning under similar conditions in order to improve the balance of daylight and the efficiency of space utilization in urban design. At the same time, it is also necessary to conduct a comprehensive exploration of factors such as different latitudes and road network angles in order to find a more general and accurate optimization strategy.

2. Techniques Review

2.1. Parameter Modeling Based on Rhino and Grasshopper

This study used the Grasshopper plugin in Rhinoceros 3D to create a block model. Firstly, the courtyard scale was determined to be 65 m by 65 m. A building with a depth of 24 m was developed around the courtyard. Then, a 20 m-wide street was added around the building. Finally, a 15 m chamfer was made at the corner of the building to determine the basic dimensions of a model measuring 133.3 m by 133.3 m. To test for occlusion and self-occlusion, a block was formed every nine buildings, resulting in a 400 m by 400 m block model.

2.2. Sunshine Simulation Based on Ladybug

Ladybug is an open-source environment simulation tool based on the Rhino And Grasshopper parameterization platform. This study uses a sunshine analysis plugin in Ladybug Tools to accurately visualize sunshine paths and durations by reading and using open-source climate data files (such as EPW files) from various regions. Its software calculation accuracy does not exceed a typical daily error of 3 min and can be used as a tool for simulating sunlight in this study.

2.3. Standard for Calculation Parameters of Building Sunlight

The sunshine standard was established to ensure the hygiene standards of the indoor environment, as the minimum indicator to measure the sunshine effect. According to the relevant provisions of the Chinese national standards GB 50033 [32] and GB 50352-2005 [33], as well as GB 50180 [34] (as shown in

Table 1. Daylighting standards for residential buildings.

Building Sunshine Standards
China (Residential Building)	Building Climate Zone Plan	I, II, III, VII Climate Zones		IV Climate Zone		V, VI Climate Zones
		Large City	Medium and Small Cities	Large City	Medium and Small Cities
	Sunlight Standard Day	Major Cold Day			Winter Solstice Day
	Sunlight Hours (h)	≥2	≥3		≥1
	Effective Sunlight Hours	8~16			9~15
	Calculation Start Point	Bottom Window Sill Surface (9 m)
Japanese	Relevant Regulations	Article 25 of the Constitution, Article 56 of the Building Standards Law
	Sunlight Duration Standard	2–5 h of daylight on the winter solstice (depending on the region and building conditions)
	Other Relevant Requirements	Restrict the impact of newly–built houses on the daylight of adjacent land through the “sun–shadow regulation”
South Korea (Republic of Korea)	Relevant Regulations	South Korean Building Regulations
	Sunlight Duration Standard	Meet the required daylight duration between 9 a.m. and 3 p.m.
	Other Relevant Requirements	The distance between the opposite exterior walls within the same plot should be no less than 1.25 times the building height
Germany	Relevant Regulations	Berlin Building Code
	Sunlight Duration Standard	At least 2 h of daylight per day for 250 days in a year
	Other Relevant Requirements	The minimum distance between buildings is usually twice the building height
England	Relevant Regulations	The “45-Degree Rule” in urban planning approval
	Sunlight Duration Standard	At least 25% of the annual daylight duration, with at least 5% in winter (from 21 September to 21 March of the following year)
	Other Relevant Requirements	If a new building causes the daylight duration of adjacent buildings to be lower than this standard and less than 80% of that before development, it is regarded as an obstruction to daylight

), each residential area should have at least one living space that receives sunlight. Bedrooms and living rooms in elderly and disabled housing, more than half of the wards and sanatoriums in hospitals and nursing homes, and more than half of the classrooms in primary and secondary schools should have a minimum of 2 h of sunlight on the winter solstice.

Sunlight in residential buildings is important for human life, health, building energy consumption, and urban sustainability. Sunlight standards developed in various countries are based on human needs, building lighting and ventilation, and other requirements, aiming to meet the sunlight needs of residents’ lives and livelihoods.

Since Spain has not yet developed a code related to sunlight, this study refers to sunlight standards in several countries, covering a wide range of situations and residential needs. Geography, climate, and urban development vary from country to country (Table 1). Therefore, the reference to multiple standards can provide a more comprehensive analysis perspective for the study of sunlight in Barcelona, avoiding the limitations of a single standard.

Considering the frontiers of standardization, developed countries such as Germany, Britain, South Korea, and Japan have all formulated sunlight standards in residential building design. To a certain extent, these standards can reflect the latest research results, which can be used as a reference for the sunlight standards in Barcelona. Considering that Barcelona has a Mediterranean climate, in order to avoid the limitation of the climate data of a single city, this study adds the sunlight requirements of China and Japan. China is a vast country covering a wide range of climatic conditions from tropical to temperate, and spanning several latitudes. Referring to the Chinese standard can provide a similar climate and insolation environment for this study. Japan has an oceanic climate that is similar to the Mediterranean climate of Barcelona. A comprehensive analysis of these insolation standards can provide a more adaptive reference for the Barcelona model.

Through the collation of each country’s sunshine standards, we found that other countries building regulations for sunshine hours are slightly different. In the United States, the sunshine duration standard is 1–2 h on winter solstice day without limiting the effective time period; in Germany, it is 2 h on a rainy day without limiting the effective time period; in Japan, it is winter solstice day with an effective time period of 9am–15pm in Hokkaido and 8am–16pm elsewhere, and the standard of sunshine duration is 2–4 h in an old urban area, 3–4 h in suburban areas, and 4–5 h in the suburbs of the city [35]. Therefore, the comprehensive consideration of the selection of sunshine duration standard for the effective period of the big cold day is 8am–16pm when the sunshine standard is used no less than 2 h.

According to the relevant provisions of the standard for daylighting parameters of buildings in China, the daylight simulation used in this study establishes a simplified geometric model, and the model contains the sheltered building, sheltered building (site), topography, and their interrelationships within the range of daylight calculation [36].

3. Problem Definition and Analysis

3.1. Selection of Simulation Model

The current layout of small neighborhoods and dense road networks in the city has evolved and developed based on Cerdà’s planned super block in Barcelona (as shown in Figure 6). This study selected the Eisimple area of Barcelona as the basic model, which has a complete and continuous grid layout and is located in the mid to high-latitude region. During the 150 year evolution process, the basic prototype of Cerdà’s planning layout was preserved, and the entire block was not affected by large-scale public infrastructure such as railways or natural terrain such as rivers and mountains during this development process. Therefore, the Eixample area of Barcelona is a suitable object for conducting sunshine simulation, and this paper chose the Eiample area of Barcelona as the research subject.

The initial planning of Cerdà determined the basic layout of the Eiample district blocks, and in the continuous evolution process, it always maintained the original block scale and street angle relationship (as shown in Figure 7). Therefore, fully understanding and analyzing the block layout of Eiample district in Barcelona is a key step in simulation modeling. Through research and satellite image recognition, representative block layout models were extracted, as shown in Figure 8.

3.2. Exploration of Factors Affecting Sunlight Exposure

At present, the basic principle of sunshine calculation is based on the formula for calculating the position of the sun, the principle of solar shadow, and the trajectory of solar shadow. China’s sunshine calculation adopts the sunshine-related calculation formula in Chapter 1 of the third edition of the Architectural Design Data Collection, as shown in

Table 2. Calculation formula for the solar position.

Formula Number	Calculation Formula	Notes
1	sinh = sinϕsinδ + cosϕcosδcost	−90° ≤ h ≤ 90°
2	sinA = cosδsint/cosh	−180° ≤ A ≤ 180°or 0° ≤ A ≤ 360°
3	cosA = (sinhsinϕ − sinδ)/coshcosϕ	−180° ≤ A ≤ 180° or 0° ≤ A ≤ 360°
4	sinh0 = cosϕcos(φ − δ)	When A = 0, t = 0 (solar altitude angle at noon)
5	h0 = 90° − (φ − δ)	φ > δ
6	h0=90° − (δ − φ)	δ > φ
7	h0=90° − φ	φ > δ Spring and Autumn Equinox Noon
8	h0 = 90° + φ	δ > φ Spring and Autumn Equinox Noon
9	sinA0 = cosδ	h = 0 (azimuth angle at sunrise and sunset)
10	cosA0 = −sinδ/cosφ	h = 0
11	cost0 = −tanϕtanδ	Negative values represent the sunrise angle, while positive values represent the sunset angle
12	t = 15°(n − 12)	n is time (24 h clock)

,

Table 3. Symbols Nomenclature.

Symbol	Description	Unit
θ	latitude	Degrees (°)
δ	solar declination angle	Degrees (°)
h0	Noon solar altitude angle	Degrees (°)
h	Solar altitude angle	Degrees (°)
A0	Noon sun azimuth angle	Degrees (°)
A	Solar azimuth angle	Degrees (°)
t	Hour angle of the sun	Degrees (°)
FAR	Floor Area Ratio	Dimensionless
PPF	Percentage of Potential Full-sunlight hours (threshold: ≥2 h)	%

[37]. According to the principle of sunlight, it is found that the solar altitude angle affects the trajectory of the solar shadow by affecting the length of the shadow, while the solar altitude is determined by the solar declination angle and latitude. Due to the periodic variation in the solar declination angle with seasons, the solar declination angle remains basically unchanged throughout the day. However, the sunshine simulation experiment is based on the solar trajectory on the winter solstice or Great Cold Day, so the trajectory of the solar shadow throughout the day is affected by latitude.

Due to the periodic variation in the solar declination angle with seasons (reference + declination angle diagram), the solar declination angle remains basically unchanged throughout the day, while the sunshine simulation experiment is based on the solar trajectory on the winter solstice or Great Cold Day. Therefore, the trajectory of the sun’s shadow throughout the day is influenced by latitude, and the influence of the sun’s declination angle can be ignored. In summary, this article explores latitude as a factor affecting sunshine levels.

The road network in Barcelona is arranged at a 45-degree angle, while the road network in China is generally arranged in a north–south or slightly angled manner. This difference in street angles may cause variations in sunlight levels. Preliminary calculations were made for the building facades, ground floor (below 6 m) facades, courtyards, streets, squares, and different street levels of the Barcelona model at four street angles of 45$°$, 30°, 15°, and 0° north latitude (as shown in Figure 9) (as shown in

Table 4. Barcelona model (41° N) sunshine percentage.

Ratio	Street Angle	<0.5 h	[0.5 h, 1 h)	[1 h, 2 h)	≥2 h
Facade	45°	21.3	30.3	5.5	42.9
	30°	34.8	3.2	21.2	40.8
	15°	39.1	2.3	12	46.6
	0°	39.5	3.2	9.7	47.6
Low facade	45°	46.2	25.7	13.7	14.4
	30°	58.9	7.3	24.1	9.7
	15°	66.7	3.4	24.1	5.8
	0°	67.8	2.6	22.1	7.5
Yard	45°	70.9	5.6	10.4	13.1
	30°	71.6	4.9	9.6	13.9
	15°	74.4	2.4	7.1	16.1
	0°	78.5	0.1	2.8	18.6
Street	45°	4.7	28.6	41.9	24.8
	30°	36.4	9.3	45.7	8.6
	15°	38.9	6.5	46.2	8.4
	0°	38.6	5.9	45.8	9.7
Square	45°	12.3	12.9	41.6	33.2
	30°	24.7	15	57.3	3
	15°	23.1	13.9	63	0
	0°	21.7	14.6	63.7	0
Left street	45°	0	35.1	47.6	17.3
	30°	0	2.5	73.8	23.7
	15°	0	0	72.5	27.5
	0°	0	0	68.1	31.9
Right street	45°	0	34.8	48	17.2
	30°	85.5	9	5.5	0
	15°	97	3	0	0
	0°	99.9	0.1	0	0

Note: The green part in the table represents the maximum percentage of different sunshine durations at four different angles.

). By separately calculating the percentage of areas with sunshine duration below 0.5 h, greater than or equal to 0.5 h but less than 1 h, greater than or equal to 1 h but less than 2 h, and greater than or equal to 2 h, this study explores the impact of latitude and road network torsion angle on sunshine.

3.3. Daily Average Quality of External Space

From Table 3, it can be seen that the sunshine level data are comparable at different street angles at the same latitude. From the perspective of the proportion of sunshine in the streets and small squares exceeding 2 h, a 45-degree road network has significant advantages. Although the proportion of courtyards with more than 2 h of sunshine at a 45- degree angle is not significantly higher than at other angles, it remains relatively high. The insolation level of 13.1% at 45 degrees Celsius is second only to 18.6% at 0 degrees.

3.4. Analysis of Sunshine Level on the Ground Floor and Full Facade of the Building

Although the proportion of sunlight exceeding 2 h at a 45-degree angle on the entire facade (42.9%) is slightly lower than that at 0 degrees (47.6%) and 15 degrees (46.6%), the overall performances are quite similar. The proportion of facades below 6 m with more than 2 h of sunlight exposure also shows an advantage at a 45-degree angle, at 14.4%, which is higher than other angles.

Overall, a 45-degree street angle has a significant advantage in terms of sunlight level, especially in terms of the proportion of sunlight greater than 2 h in external spaces such as streets and small squares. In addition, the sunlight level of the lower facade also shows an advantage at a 45-degree angle.

In order to further explore the relationship between the sunshine level and factors of the street angle and latitude, this paper uses Ladybug to conduct sunshine simulation and uses IBM SPSS Statistics 26 for fitting. Latitude and street angle are used as two factors to predict the sunshine level at different latitudes and street angles. Suggestions are made for the residential layout of small block dense road network from the perspective of sunshine.

4. Method

4.1. Research Design

This study takes Barcelona as an example and conducts sunshine simulation tests under different dimensions and road network torsion angles. Further statistics and analysis are conducted on the proportion of simulated sunshine hours and sunshine shadows under different conditions.

Using the Rhino And Grasshopper method to establish a Barcelona test model, the test model takes the central small block of the dense road network as the main experimental object and self-occlusion model. Eight block models in the surrounding directions of east, west, north, south, southeast, southwest, northeast, and northwest are used as occlusion models for sunlight simulation experiments (as shown in Figure 10).

In this study, a 3 × 3 regional block was selected as the test area after the occlusion analysis. The grid plan layout of Barcelona has blocks of similar heights and wider roads, The result is that areas outside the 3 × 3 area have almost negligible effect on the experimental subjects. The 3 × 3 area was chosen for the following reasons:

First, from the point of view of planning layout. The land where the model is selected for this study is the Barcelona expansion area that adopts a grid-based urban planning. The height and spacing of each block is basically the same, and the road width between blocks is usually 20 m. Secondly, in terms of topographic conditions. The topography of the expansion area is flat with no significant height differences. The flat terrain leads to the effect of the outside of the 3 × 3 area on the level of daylighting of the experimental subjects. In addition, the principle of distance attenuation exists in the daylight simulation. The shading effect of the shading object decreases with the increase in the distance, and the buildings outside the 3 × 3 area are farther away from the experimental subjects and the setup angle is also smaller.

In the end, the scope of the shading analysis is reasonable, and the 3 × 3 area contains all the buildings that directly affect the sunlight of the experimental subjects. Due to the standardized planning and design of the expansion area and the limitation of the road width, its external influence will also be insignificant in the experiment.

4.2. Variable Types and Scope

4.2.1. Independent Variable 1—Latitude

Latitude represents the angle of incidence of the sun, which affects the altitude angle of the sun and thus affects the variation in the solar shadow, ultimately leading to different levels of sunshine. This experiment takes a value every 2 degrees from latitude 31 degrees north to latitude 45 degrees north as the latitude variable.

4.2.2. Independent Variable 2—Street Angle

According to preliminary experiments, it can be observed that the sunshine level varies from different street angles, and overall, the sunshine level under a 45° road network is better than that under a 0° road network. This study aims to further investigate the effect of the street angle on sunshine level by taking a value every 5 degrees from 45° to 0° as the angle variable (as shown in Figure 11).

4.2.3. Dependent Variable—Percentage of Sunshine Area at Different Times for Streets, Courtyards, and Building Facades

The proportion of sunlight in different parts of the building was obtained through sunlight simulation, including the proportion of sunlight at different times in the building facade, the bottom floor facade (below 6 m), courtyards, streets, and squares (as shown in Figure 12). We calculated the proportion of sunshine area with sunshine duration less than 0.5 h, greater than or equal to 0.5 h but less than 1 h, greater than or equal to 1 h but less than 2 h, and greater than or equal to 2 h (as shown in

Table 5. Barcelona model (41° N) sunshine percentage.

Variable Name		Variable Value
Argument	Latitude	45° N, 43° N, 41° N, 39° N, 37° N, 35° N, 33° N, 31° N
	Street angle	45°, 40°, 35°, 30°, 25°, 20°, 15°, 10°, 5°, 0°
Dependent variable	Facade	PPF ≤ 0.5 h, PPF ∈ [0.5 h, 1 h), PPF ∈ [1 h, 2 h), PPF ≥ 2 h
	Low facade	PPF ≤ 0.5 h, PPF ∈ [0.5 h, 1 h), PPF ∈ [1 h, 2 h), PPF ≥ 2 h
	Yard	PPF ≤ 0.5 h, PPF ∈ [0.5 h, 1 h), PPF ∈ [1 h, 2 h), PPF ≥ 2 h
	Street	PPF ≤ 0.5 h, PPF ∈ [0.5 h, 1 h), PPF ∈ [1 h, 2 h), PPF ≥ 2 h
	Square	PPF ≤ 0.5 h, PPF ∈ [0.5 h, 1 h), PPF ∈ [1 h, 2 h), PPF ≥ 2 h
	Left street	PPF ≤ 0.5 h, PPF ∈ [0.5 h, 1 h), PPF ∈ [1 h, 2 h), PPF ≥ 2 h
	Right street	PPF ≤ 0.5 h, PPF ∈ [0.5 h, 1 h), PPF ∈ [1 h, 2 h), PPF ≥ 2 h

Note: Square brackets indicate a closed interval, including the two endpoints of the interval; The parentheses indicate the open interval, excluding the two endpoints of the interval.

). The simulation results with PPF ≥ 2 h were selected as the regression fitting data for meeting the sunshine standard, while other ratios were used as reference data for evaluating the sunshine level.

4.3. Experimental Steps

4.3.1. Data Acquisition and Preprocessing

According to Google Maps, a basic block model of Barcelona with a continuous layout and relatively standard geometric shapes was selected. By comparing the block layouts of different districts in Barcelona, the final decision was made to select the block layout of Eisimple district as the basis for the sunshine simulation model. Further measuring of the basic dimensions of the block model in the Eiample district of Barcelona, and based on the existing block dimensions and the evolution of the Barcelona block over 150 years, ultimately form the specific dimensions of this research simulation model: the size of a block is 133.3 m by 133.3 m, with a courtyard of 65 m by 65 m square, a building depth of 24 m, a floor height of 3 m, a total of nine floors of 27 m, a street width of 20 m, and a building corner size of 15 m at the intersection of the block. (As shown in Figure 8).

4.3.2. Modeling, Sunshine Simulation, and Parameter Setting

We use Grasshopper to establish a basic model, use Ladybug for sunlight simulation, and set the sunlight simulation parameters according to the Chinese standard “Architectural Lighting Design Standard” GB 50033 [25]. The eight hours period from 8 am to 4 pm on January 20th, the coldest day, was selected as the sunshine statistics time period, with a calculated time step of 1 min, and the minimum continuous time (cumulative sunshine) of 5 min (as shown in

Table 6. Parameter settings for sunshine simulation.

Parameter Category	Variable Value
Meteorological parameters	EPW (Energy Plus Weather) file obtained based on Ladybug EPWMap
Test date	20 January (Great Cold Day)
Test period	8:00–16:00
Calculate step size	1 min
Minimum continuous time	5 min

).

4.4. Data Analysis Methods

SPSS was used to analyze the response relationship between the percentage of PPF ≥ 2 h in different building parts and the two factors of latitude and street angle.

The correlation matrix column in Figure 13 indicates that latitude is generally negatively correlated with the proportion of insolation hours in each part of the building. This negative correlation is most significant for the courtyard. In contrast, the correlation with the square is less pronounced. The significance between street angle and insolation ratio is low. The relationship between the two factors and the sunshine level was further analyzed, and four models were used for regression fitting, including multiple linear regression, trigonometric regression, independent variable logarithmic regression, and full variable logarithmic regression.

5. Research Results

5.1. Model Validation

Based on the simulation results of sunlight, we established a multiple linear regression model to predict the percentage of sunlight duration in various parts of the building with respect to the angle and latitude of the road network. In order to explore the more precise relationship between independent and dependent variables, four types of regression models were established: basic model, trigonometric function model, logarithmic model of independent variables, and logarithmic model of all variables (as shown in

Table 7. Interpretation of the independent and dependent variables for the percentage of sunshine regression from the fit model.

Model	Dependent Variable	Interpretation of Dependent Variable	Independent Variables		Interpretation of Independent Variables
Basic linear model	$\mathrm{f}\left(\mathrm{x}\right)$ ≥ 2	Percentage of cumulative sunlight hours in the tested area	d	Constant	-
			X1	Street angle	Street angle radianization values
			X2	Latitude	Radianization values for latitude
			X3	Lag_RES_X1	Lagged residual
Trigonometric function model	$\mathrm{f}\left(\mathrm{x}\right)$ ≥ 2		d	Constant	-
			X1	COS_angle	Trigonometric function (COS) values after radianization of the street angles
			X2	COS_Latitude	Trigonometric (COS) values after radianization of latitude
			X3	Lag_RES_X1	Lagged residual
Independent logarithmic model	$\mathrm{f}\left(\mathrm{x}\right)$ ≥ 2		d	Constant	-
			X1	Lg10_angle	Logarithmic value of the street angle after radianization
			X2	Lg10_Latitude	Logarithmic values after radianization of latitude
			X3	Lag_RES_X1	lagged residual
All variable logarithmic model	$\mathrm{f}\left(\mathrm{x}\right)$ ≥ 2	The logarithmic transformation of the percentage of cumulative sunshine hours at the tested site was used as the dependent variable	d	Constant	-
			X1	Lg10_angle	Logarithmic value of the street angle after radianization
			X2	Lg10_Latitude	Logarithmic values after radianization of latitude
			X3	Lag_RES_X1	Lagged residual

). Due to the fact that the street angles and latitudes used in the architectural design are expressed in degrees, which can affect the accuracy of the regression model. Therefore, these two types of independent variables are converted to radians for regression. At the same time, in order to eliminate the errors caused by the autocorrelation of independent variables in the regression model, lagged residuals (X3-Llag RES_X1) were introduced into the regression equation. The expression of the regression equation is described in Equation (1).

$$\mathrm{y}={\mathrm{k}}_1{\mathrm{X}}_1+{\mathrm{k}}_2{\mathrm{X}}_2+{\mathrm{k}}_3{\mathrm{X}}_3+\mathrm{b}$$

(1)

The independent variables used in the basic model are the street angle and latitude after radianization, and the dependent variable is the percentage value of sunshine duration. The independent variables used in the trigonometric model are the trigonometric function (COS) values after street angle radianization and latitude radianization, and the dependent variable is the percentage value of sunshine duration. The independent variables used in the logarithmic model are the logarithm of the street angle after radianization and the logarithm of latitude after radianization, and the dependent variable is the percentage of sunshine duration. The independent variables used in the full variable logarithmic model are the logarithm of the street angle after radianization and the logarithm of the latitude after radianization, and the dependent variable is the logarithm of the cumulative sunshine duration (h) of the tested area converted as the dependent variable.

The goodness of the fit of all the models was assessed through the R² value, which was aimed at determining which model was able to best explain the variability in the data. By comparing the four models, it was found that the trigonometric regression model had the highest R² value, indicating that the model was able to best fit the data (e.g.,

Table 8. Comparison of the fit of the four types of regression models for percent sunshine for each component.

	Façade ≥ 2 h	Low Façade ≥ 2 h	Yard ≥ 2 h	Street ≥ 2 h	Square ≥ 2 h	left Street ≥ 2 h	Right Street ≥ 2 h
Basic linear model	0.911	0.938	0.99	0.79	0.887	0.873	0.712
Trigonometric function model	0.933	0.96	0.992	0.832	0.91	0.878	0.768
Independent logarithmic model	0.87	0.888	0.983	0.737	0.84	0.872	0.641
All variable logarithmic model	0.864	0.847	0.839	0.762	0.676	0.772	0.871

Note: Blue indicates negative correlation, red indicates positive correlation, and the darker the color, the higher the correlation.

).

Blue and red colors in Table 8 indicate high and low fitting values, respectively, where the darker the blue color the higher the fit and the darker the red color the lower the fit. It can be seen that the fit of each model is different under different conditions. Among them, the trigonometric model has a relatively high fit in several conditions, such as 0.992 in the yard ≥ 2 h condition.

Therefore, in order to simplify the results and highlight the best fit, this study decided to show the regression results for this model only. Although the other three regression models also showed some fitting ability. For example, the basic regression model had an R² of 0.911 for facade ≥ 2 h and 0.990 for yard ≥ 2 h. However, the delta function regression model significantly outperformed the other models.

Therefore, for space considerations, only the detailed results of the delta function regression model are shown in this paper. The regression coefficients and their significance levels based on the best-fitting delta function regression model are shown in

Table 9. Parameters of the fitted model for the regression of percent sunshine for each component.

Trigonometric Function Model	R2	Durbin-−Watson	Independent Variables	Variable Coefficients	p-Value	VIF
Façade ≥ 2 h	0.933	2.078	d	−64.779	0	-
			X1	24.054	0	1.002
			X2	117.206	0	1.041
			X3	0.401	0	1.040
Low façade ≥ 2 h	0.960	1.763	d	−44.563	0	-
			X1	−45.714	0	1.002
			X2	127.128	0	1.025
			X3	0.591	0	1.024
yard ≥ 2 h	0.992	1.727	d	−205.656	0	-
			X1	19.423	0	1.003
			X2	270.591	0	1.337
			X3	0.404	0	1.338
street ≥ 2 h	0.832	1.990	d	−54.165	0	-
			X1	−82.057	0	1.014
			X2	186.119	0	1.005
			X3	0.257	0	1.015
square ≥ 2 h	0.910	1.640	d	−65.000	0	-
			X1	−129.059	0	1.022
			X2	252.274	0	1.012
			X3	0.384	0	1.030
left street ≥ 2 h	0.878	1.606	d	−158.604	0	-
			X1	19.907	0	1.014
			X2	217.785	0	1.020
			X3	0.449	0	1.030
right street ≥ 2 h	0.768	1.822	d	12.966	0.304	-
			X1	6.843	0	1.015
			X2	13.441	0	1.014
			X3	0.087	0	1.025

Note: Street angle and home orientation are different names for the same indicator.

.

This regression model shows that the latitude and cosine angle have a significant effect on the level of sunlight of a building. The optimal insolation situation can be calculated based on the latitude of the city in which the building is located when designing a neighborhood. Thus, the street angle and building orientation can be adjusted to provide a good sunlight environment for the residence.

Taking the latitude of Beijing 39°N as an example, when the street angle is 0°, the sunlight level of each part is optimal, so we can consider arranging the buildings in north–south orientation to improve the sunlight level of residential buildings. According to the experimental simulation results in the street is 45°when the full facade, courtyard sunshine level and 0° is not much difference, and in the ground floor facade and the street 45° street is more advantageous. For residential buildings, the sunlight of the ground floor facade is important for young children, while for high-rise buildings it may be more important to pay attention to the overall uniformity of sunlight. Consequently, for middle and high latitudes the street angle can be moderately adjusted to improve the daylight level of the building and its environment.

At the same time, daylight levels are a key environmental factor in building design, especially in terms of energy use, sustainability, and comfort.

In terms of improving energy efficiency and promoting building sustainability, taking into account the latitude and orientation of the building can select a more suitable sunlight environment for the building, thus realizing the optimal adaptation of the building to the natural environment. For example, a rational design of the building’s orientation can maximize daylight hours and light intensity, thereby reducing the need for artificial lighting and energy consumption. In addition, the level of sunlight reflects the local solar potential. In cold regions, by adjusting residential orientation and street layout, the amount of daylight in winter can be maximized and solar heat can be increased, thus effectively reducing heating demand. At the same time, by calculating the sunshine level of a residence, the installation angle and location of solar energy equipment can be rationally planned, further improving the efficiency of solar energy utilization.

In terms of improving indoor comfort, the level of sunshine directly affects the indoor temperature. Thus, it is possible to calculate the required sunshine situation based on the latitude where the residence is located. This helps designers to rationally configure windows and shading facilities to maximize the use of sunlight to provide warmth in winter and avoid overheating in summer. At the same time, reasonable sunlight design also helps to improve indoor air quality and the mental health of the occupants. The right amount of natural light can help boost mood, promote vitamin D synthesis, and improve rest and relaxation patterns, avoiding health problems caused by prolonged exposure to darkness.

Meanwhile, by comparing the corresponding values of four sunshine percentage models with low facade ≥ 2 h, yard ≥ 2 h, street ≥ 2 h, square ≥ 2 h, left street ≥ 2 h, and right street ≥ 2 h (

Table 10. The regression fitting model equation for the sunshine percentage of each component.

Trigonometric Function Model	Calculation Formula
facade ≥ 2 h	$\mathrm{y}=24.054{\mathrm{X}}_1+117.206{\mathrm{X}}_2+0.401{\mathrm{X}}_3+(-64.779$)
low facade ≥ 2 h	$\mathrm{y}=-45.714{\mathrm{X}}_1+127.128{\mathrm{X}}_2+0.591{\mathrm{X}}_3+(-44.563$)
yard ≥ 2 h	$\mathrm{y}=19.423{\mathrm{X}}_1+270.591{\mathrm{X}}_2+0.404{\mathrm{X}}_3+(-205.656$)
street ≥ 2 h	$\mathrm{y}=-82.057{\mathrm{X}}_1+186.119{\mathrm{X}}_2+0.257{\mathrm{X}}_3+(-54.165)$
square ≥ 2 h	$\mathrm{y}=-129.059{\mathrm{X}}_1+252.274{\mathrm{X}}_2+0.384{\mathrm{X}}_3+(-65.000)$
left street ≥ 2 h	$\mathrm{y}=19.907{\mathrm{X}}_1+217.785{\mathrm{X}}_2+0.449{\mathrm{X}}_3+(-158.604)$
right street ≥ 2 h	$\mathrm{y}=6.843{\mathrm{X}}_1+13.441{\mathrm{X}}_2+0.087{\mathrm{X}}_3+12.966$

), the results indicate that the trigonometric function model (Model 2) is the best model for different building parts. Compared with other models, it has the highest explanatory power, lower residual autocorrelation, and less obvious multicollinearity problem (lower VIF value).

Comparing the R² values of the trigonometric models for sunshine percentage in different locations vertically, the high explanatory power (R² > 0.90) is found in the four locations of facade, low facade, yard, and square. The sunshine level of these parts is mainly affected by latitude and street angle, and the model can explain this relationship well, indicating that in design and planning, adjusting these two factors can significantly affect the sunshine conditions of these parts. The moderate explanatory power (0.80 < R² ≤ 0.90) is for streets and left streets, where the level of sunlight is largely influenced by latitude and street angle, but there may also be other factors at play. This suggests that in addition to considering latitude and street angles, other possible influencing factors also need to be taken into account in design and planning. The lower explanatory power (R² ≤ 0.80) is right street, where the sunlight level is relatively less affected by latitude and street angle. The model has weak explanatory power and may be influenced more by other factors. This suggests that further research and identification of these influencing factors are needed to improve sunlight conditions.

5.2. Interpretation of Results

Among the four models, the trigonometric function model has the highest fitting degree for different building parts, which may be related to the formula for the solar position. There is a threefold relationship between the position of the sun and latitude, and the shadow of the sun also shows this relationship with latitude. Sunshine is a transformation manifestation of the shadow, so the fitting level of the trigonometric function model is higher.

In the four parts with high explanatory power, the R² value of the courtyard is the most significant, followed by the lower level building facade and the entire building facade, while the significance of the square is the lowest. This may be due to the fact that the courtyard is completely enclosed and has the simplest geometric form, with minimal influence from other factors, thus exhibiting the best fitting level. Due to its height, the facade of low-rise buildings is more susceptible to the influence of latitude and torsion angle, resulting in a higher level of fitting. Although the geometric shape of the square is relatively simple, it is subject to street interference and has a relatively poor fit.

Due to the interruption of the continuity of the street at around 100 m, the street is affected by the angle of the road network, which may affect the sunshine fitting degree of the street section. May be influenced by more other factors. Further exploration of these influencing factors is needed in future research to improve sunlight conditions.

6. Conclusions

This study explores the impact of different latitudes and street angles on the sunlight level of buildings under the layout of dense road networks in small blocks through sunshine simulation and data analysis. Research has found that a 45-degree street angle has significant advantages in optimizing the sunlight conditions of buildings and public spaces, especially in areas such as building facades, ground floor facades, and courtyards. The research results provide optimization strategies for the residential layout of small blocks and dense road networks in cities, emphasizing the importance of rational use of street angles and latitudes in high-density layouts, and providing a basis for optimizing building heights, and street and courtyard proportions at different latitudes and angles.

Through the above analysis, we can have a clear understanding of the factors affecting sunlight in different parts of the building. Different optimization strategies can be adopted for different parts of the process of urban renewal or renovation. For example, for building facades, ground floor facades, and courtyards, it is possible to focus on adjusting latitude and street angles to optimize sunlight conditions. For streets and right streets, more factors need to be comprehensively considered. In addition, when planning new residential areas, a fitting formula can be used to obtain the road network angle at the optimal sunshine level based on the latitude of the city where the residential area is located, thereby improving the sunshine level of the residential area.

Although this study reveals the impact of different latitudes and street angles on building sunlight levels, there are still some limitations and challenges. As for the universality of the model, although Barcelona’s block layout is representative, the geographical, climatic, and architectural characteristics of different cities may affect the applicability of the results. In addition, the simulation parameters of this study’s model were selected within the latitude range of 31–45° N, focusing on mid to high-latitude regions. Further research is needed to predict the sunshine level of higher latitude cities. Secondly, the accuracy of the data, simulation accuracy, and parameter settings may have an impact on the results, and future research needs to verify and improve these parameters. Other influencing factors, such as building height, street width, and building density, may also affect the sunshine level of streets and right streets, and further exploration is needed in the future.

While the 3 × 3 area-based analysis in this study was able to model the shading effects of buildings within the Barcelona expansion area well, we recognize that the 3 × 3 analysis range may not be sufficient to fully capture the effects of sunlight in areas with significant differences in building heights or the presence of taller buildings over a larger area. This deserves further optimization and validation in future studies.

The analysis in this study is limited to the Barcelona Extension area, which has relatively simple and flat topographic features. However, in urban environments with complex topography, topographic height differences may be a key factor influencing the distribution of sunlight. The methodology of this study can be used as a reference for flat terrain areas, but further exploration of areas with different topological conditions is recommended for future studies.

According to existing research results, urban layout can be optimized from the following perspectives to improve sunshine conditions: Optimization of the street angle. In high-density urban areas, a 45-degree street angle should be prioritized to improve the sunlight level of buildings and public spaces; Adjusting urban planning, in the process of urban planning and design, it is necessary to conduct sunshine simulation based on actual conditions, optimize building layout and street design, and ensure good sunshine conditions for public spaces and residential buildings; To establish and improve standards, the government should develop and improve sunshine standards and planning guidance, encourage and support the adoption of scientific and reasonable sunshine optimization strategies in urban planning, in order to enhance the livability and sustainable development level of cities.