Analysis of the geometric and natural properties of courtyards in historical houses of Isfahan (Iran)

Figures & data

Table 1. Review of research on central courtyards in Iran

References	City	Climate	Result
Soltanzadeh (2011)	-	-	Geographic factors have affected the quality and form of the courtyards in Iran.
Ahmadi (2012)	Yazd	Hot-arid	Pattern of central courtyard has critical role in creating sustainable, vernacular architecture in Yazd city.
Ghasemi Sichani and Memarian (2010)	Isfahan	Hot-arid	Based on the characteristics of architectural space, structure and decoration, houses of Qajar era can be divided into three different types (Safavi, second and third of Qajar).
Soltanzadeh and Ghaseminia (2012)	Golestan Province	Temperate	Vernacular residential architecture in Golestan provice can be categorized in three types: Vernacular architecture of the plain and flatlands, Residential units of hillside and Units in steep mountainous slopes.
Hedayat and Tabaian. (2016)	Bushehr	Hot-humid	Bushehr traditional housing is compatible with environmental, cultural, social and economic conditions.
Farahbakhsh, Hanachi, and Ghanaei (2018)	Mashhad	Hot-arid	Typology of historical houses in Mashhad city were categorized in three residential types in terms introversion and extroversion.
Khakpour, Ansari, and Tahernian (2010)	Rasht	Temperate	Four patterns of historical houses in Rasht city were recognized in terms of sequence and placement of open and enclosed spaces.
Moradi, Matin, and Dehbashi Sharif (2018)	Tabriz	Cold	In traditional courtyard houses of Tabriz city, physical structure, patterns and types have been studied.
(Soflaei, Shokouhian, and Shemirani 2015, Soflaei, Shokouhian, and Shemirani 2016)	Isfahan, Kerman, Mashhad, Shiraz, Tehran, Dezful, and Shushtar	Hot-arid and Hot-humid	Iranian traditional central courtyards act as microclimate modifiers.
(Zeinalian and Okhovat 2018)	Yazd and Dezful	Hot-dry and Hot-humid	There are structural differences in the courtyards of hot-dry and hot-humid climates.

Figure 1. Geographic location of Isfahan city in Iran

Table 2. Geometric and natural parameters and symbols in studying the courtyards

Parameter	Symbol	Parameter	Symbol
Deviation angle from North	DaN	Area of openings in courtyard’s East wall	AOEw
Courtyard length	LCy	Area of openings in courtyard’s West wall	AOWw
Courtyard width	WCy	Total area of openings in courtyard walls	ATOw
Average of courtyard height	HCy	Area of courtyard’s North wall	ANw
Height of North wall	HNw	Area of courtyard’s South wall	ASw
Height of South wall	HSw	Area of courtyard’s East wall	AEw
Height of East wall	HEw	Area of courtyard’s West wall	AWw
Height of West wall	HWw	Total area of courtyard walls	ATW
Length of North wall	LNw	Total area of house	ATH
Length of South wall	LSw	Area of courtyard	ACy
Length of East wall	LEw	Area of built spaces	ABS
Length of West wall	LWw	Area of water surface in courtyard	AWS
Area of openings in courtyard’s North wall	AONw	Area of plant coverage in courtyard	APC
Area of openings in courtyard’s South wall	AOSw

Table 3. Geometric characteristics of the studied courtyards (Source: Authors)

Case No.	House	DaN	LCy	WCy	HCy	LCy/WCy	HCy/LCy	HCy/WCy	Plan	3D view	Image
01	Mosavar olmolki	18° SE-NW	15.85	10.75	6.09	1.47	0.38	0.57
02	Moghni	30° SW-NE	11.45	8.75	4.93	1.31	0.43	0.56
03	Yadollahi	3° SE-NW	15.6	8.9	4.97	1.75	0.32	0.56
04	Martha Peters	8° SE-NW	22.45	14.36	4.86	1.56	0.22	0.34
05	Sheikh Harandi	8° SW-NE	14.63	11.55	4.67	1.27	0.32	0.40
06	Vasigh	86° SE-NW	17.25	13.55	5.78	1.27	0.34	0.43
07	Samaeian	2° SE-NW	14.9	11.3	5.11	1.32	0.34	0.45
08	Haritash	7° SW-NE	25.96	15.5	6.13	1.67	0.24	0.40
09	Sheikh ol Islam	2° SW-NE	31.55	20.85	6.77	1.51	0.21	0.32
10	Kadkhodaei	78° SE-NW	20	16.2	6.73	1.23	0.34	0.42
11	Kahkeshani	22° SW-NE	18.65	15.4	5.28	1.21	0.28	0.34
12	Javaheri	30° SW-NE	11.5	10.5	4.31	1.10	0.37	0.41
13.1	Ghazviniha	1° SW-NE	25.53	17.53	6.67	1.46	0.26	0.38
13.2	Ghazviniha	11° SE-NW	15.6	11.06	5.74	1.41	0.37	0.52
14	Dehdashti	10° SW-NE	10.65	8.25	3.03	1.29	0.28	0.37
15	Khoshnevisan	15° SW-NE	20.35	15.25	5.28	1.33	0.26	0.35
16	Beheshtian	82° SE-NW	10.5	8.6	4.61	1.22	0.44	0.54
17	Labaf	35° SE-NW	28.3	22.6	6.45	1.25	0.23	0.29
18	Shiran	11° SE-NW	11.5	9.55	4.39	1.20	0.38	0.46
19	Jamal Ghodsie	1° SW-NE	25.85	17.5	6.45	1.48	0.25	0.37
20	Alam	3° SW-NE	18.3	13.88	6.73	1.32	0.37	0.48
21	Charmi	19° SW-NE	24.95	18.65	6.50	1.34	0.26	0.35
22	Allame Fani	7° SE-NW	21.3	15.4	5.00	1.38	0.23	0.32
23	Arastooyi	38° SE-NW	6.25	4.4	2.81	1.42	0.45	0.64
24	Bajoghli	46° SW-NE	16.2	15.55	10.34	1.04	0.64	0.66
25.1	Najafi	13° SW-NE	22.48	16.75	5.10	1.34	0.23	0.30
25.2	Najafi	14° SW-NE	21.21	19.52	5.28	1.09	0.25	0.27
26.1	Seifoor Ghasemi	1° SE-NW	14	13.2	4.42	1.06	0.32	0.33
26.2	Seifoor Ghasemi	2° SE-NW	8.8	7	2.94	1.26	0.33	0.42
27	Jangjooyan	10° SW-NE	10	9.5	4.83	1.05	0.48	0.51
28	Toosi zadeh	7° SE-NW	19.36	16.75	6.72	1.16	0.35	0.40
29	Bekhradi	32° SW-ilNE	18.9	13.1	6.23	1.44	0.33	0.48
30	Kazeruni	19°SE-NW	21.15	15.2	4.68	1.39	0.22	0.31

Figure 2. Deviation angle from North in studied courtyards (Source: Authors)

Figure 3. The ratios of length/width, height/length and height/width in studied courtyards (Source: Authors)

Figure 4. Visual guide of: the courtyard’s dimension and deviation angle(Left), the walls’ dimension and opening area(Right)

(Source: Authors)

Table 4. Dimensions and proportions of the courtyards’ walls (Source: Authors)

Case No.	HNw	HSw	HEw	HWw	HNw/LNw	HSw/LSw	HEw/LEw	HWw/LWw
01	7.73	6.38	6.07	4.18	0.72	0.59	0.38	0.26
02	4.30	5.37	4.50	5.56	0.37	0.46	0.51	0.63
03	6.37	4.50	4.50	4.50	0.71	0.50	0.28	0.28
04	6.19	6.25	4.10	2.90	0.43	0.43	0.18	0.12
05	6.40	3.88	4.50	3.90	0.55	0.33	0.30	0.26
06	4.11	4.11	7.25	7.65	0.23	0.23	0.53	0.57
07	3.95	5.75	5.35	5.40	0.34	0.51	0.35	0.36
08	7.15	6.15	5.60	5.60	0.46	0.39	0.21	0.21
09	6.04	8.80	6.71	5.54	0.19	0.27	0.32	0.26
10	6.45	6.45	6.45	7.55	0.39	0.40	0.32	0.37
11	7.40	4.50	4.20	5.00	0.48	0.29	0.22	0.26
12	5.45	4.10	3.72	3.96	0.52	0.39	0.32	0.34
13.1	8.41	5.72	6.30	6.23	0.48	0.32	0.24	0.24
13.2	6.28	5.48	5.80	5.41	0.56	0.50	0.37	0.34
14	3.80	2.70	2.85	2.75	0.46	0.33	0.26	0.25
15	7.75	4.46	4.46	4.46	0.51	0.29	0.21	0.21
16	3.80	3.80	5.26	5.58	0.36	0.36	0.61	0.64
17	8.45	5.55	6.26	5.55	0.37	0.24	0.22	0.19
18	4.50	4.35	4.35	4.35	0.47	0.45	0.37	0.37
19	6.75	7.76	5.65	5.65	0.38	0.44	0.21	0.21
20	11.25	5.25	5.20	5.20	0.81	0.37	0.28	0.28
21	10.25	5.25	5.25	5.25	0.55	0.28	0.21	0.21
22	5.68	5.68	2.95	5.68	0.36	0.36	0.13	0.26
23	2.45	2.95	2.40	3.45	0.39	0.47	0.54	0.78
24	10.80	11.35	9.55	9.65	0.66	0.69	0.61	0.62
25.1	5.75	7.30	3.83	3.50	0.34	0.44	0.17	0.15
25.2	7.30	4.10	4.05	5.65	0.37	0.21	0.19	0.26
26.1	5.20	4.60	4.36	3.50	0.39	0.34	0.31	0.25
26.2	2.20	5.16	2.20	2.20	0.31	0.74	0.25	0.25
27	5.80	4.50	4.50	4.50	0.58	0.45	0.47	0.47
28	7.12	7.80	5.97	5.97	0.42	0.46	0.30	0.30
29	7.50	5.80	5.80	5.80	0.57	0.44	0.30	0.30
30	5.20	4.50	4.50	4.50	0.34	0.29	0.21	0.21
Average	6.296	5.464	4.983	5.048	0.457	0.402	0.315	0.325

Figure 5. Highest ratios of height to length among courtyards’ walls (Right), Highest ratios of opening area to wall area among courtyards’ walls (Left)

(Source: Authors)

Table 5. Proportions of the opening area to the wall area in the studied courtyards (Source: Authors)

Case No.	AONw/ANw	AOSw/ASw	AOEw/AEw	AOWw/AWw	Case No.	AONw/ANw	AOSw/ASw	AOEw/AEw	AOWw/AWw
01	0.48	0.17	0.32	0.43	17	0.32	0.00	0.26	0.21
02	0.21	0.25	0.75	0.43	18	0.54	0.13	0.27	0.35
03	0.43	0.14	0.00	0.13	19	0.58	0.48	0.65	0.45
04	0.28	0.26	0.26	0.00	20	0.49	0.27	0.47	0.47
05	0.46	0.31	0.35	0.00	21	0.55	0.23	0.32	0.32
06	0.44	0.40	0.28	0.36	22	0.58	0.00	0.45	0.00
07	0.42	0.55	0.32	0.28	23	0.41	0.44	0.14	0.22
08	0.55	0.00	0.47	0.45	24	0.46	0.52	0.00	0.57
09	0.29	0.21	0.00	0.27	25.1	0.58	0.38	0.38	0.32
10	0.36	0.00	0.58	0.48	25.2	0.48	0.34	0.40	0.00
11	0.48	0.00	0.40	0.25	26.1	0.67	0.00	0.12	0.43
12	0.51	0.33	0.47	0.42	26.2	0.58	0.45	0.55	0.55
13.1	0.35	0.62	0.61	0.47	27	0.44	0.35	0.32	0.00
13.2	0.54	0.48	0.36	0.38	28	0.37	0.34	0.12	0.00
14	0.28	0.36	0.33	0.37	29	0.56	0.48	0.58	0.58
15	0.51	0.00	0.40	0.40	30	0.48	0.00	0.56	0.45
16	0.31	0.26	0.35	0.33
Average						0.454	0.265	0.359	0.314

Table 6. Ratios of courtyard area to built space area in studied courtyards (Source: Authors)

Case No.	ACy/ATH	ABs/ATH	ABs/ACy	Case No.	ACy/ATH	ABs/ATH	ABs/ACy
01	0.239	0.761	3.18	17	0.337	0.663	1.97
02	0.235	0.765	3.26	18	0.185	0.815	4.41
03	0.367	0.633	1.72	19	0.368	0.632	1.72
04	0.288	0.712	2.47	20	0.311	0.689	2.22
05	0.294	0.706	2.40	21	0.237	0.763	3.22
06	0.21	0.79	3.76	22	0.492	0.508	1.03
07	0.281	0.719	2.56	23	0.202	0.798	3.95
08	0.34	0.66	1.94	24	0.365	0.635	1.74
09	0.367	0.633	1.72	25.1	0.436	0.564	1.29
10	0.313	0.687	2.19	25.2	0.436	0.564	1.29
11	0.387	0.613	1.58	26.1	0.412	0.588	1.43
12	0.26	0.74	2.85	26.2	0.412	0.588	1.43
13.1	0.235	0.765	3.26	27	0.313	0.687	2.19
13.2	0.235	0.765	3.26	28	0.361	0.639	1.77
14	0.276	0.724	2.62	29	0.329	0.671	2.04
15	0.309	0.691	2.24	30	0.206	0.794	3.85
16	0.21	0.79	3.76
Average					0.31	0.69	2.43

Figure 6. Proportions of built space area to courtyard area in studied courtyards (Source: Authors)

Figure 7. Visual guide of the areas of natural elements and built space (Source: Authors)

Table 7. Ratios of water surface area and plant coverage area in studied courtyards (Source: Authors)

Case No.	AWs/ATH	APc/ATH	AWs/ABs	APc/ABs	AWs/ACy	APc/ACy	APc/AWs
01	0.022	0.049	0.029	0.065	0.093	0.207	2.226
02	0.012	0.012	0.016	0.016	0.052	0.053	1.019
03	0.054	0.075	0.085	0.119	0.146	0.205	1.404
04	0.005	0.108	0.006	0.151	0.016	0.374	23.375
05	0.010	0.036	0.015	0.052	0.035	0.124	3.543
06	0.018	0.022	0.023	0.027	0.085	0.103	1.212
07	0.019	0.038	0.026	0.052	0.067	0.134	2.000
08	0.030	0.089	0.045	0.134	0.087	0.261	3.000
09	0.013	0.104	0.021	0.164	0.036	0.283	7.861
10	0.031	0.080	0.045	0.117	0.099	0.256	2.586
11	0.034	0.046	0.056	0.074	0.089	0.118	1.326
12	0.010	0.028	0.013	0.037	0.038	0.106	2.789
13.1	0.023	0.055	0.030	0.072	0.099	0.233	2.354
13.2	0.015	0.096	0.020	0.126	0.065	0.409	6.292
14	0.019	0.060	0.026	0.082	0.068	0.216	3.176
15	0.032	0.081	0.047	0.117	0.104	0.262	2.519
16	0.013	0.037	0.016	0.047	0.062	0.175	2.823
17	0.018	0.063	0.027	0.095	0.053	0.187	3.528
18	0.004	0.030	0.005	0.037	0.023	0.164	7.130
19	0.022	0.171	0.036	0.271	0.061	0.466	7.639
20	0.039	0.066	0.057	0.096	0.127	0.213	1.677
21	0.030	0.069	0.040	0.090	0.128	0.290	2.266
22	0.008	0.220	0.016	0.433	0.017	0.447	26.294
23	0.016	0.023	0.019	0.029	0.077	0.116	1.506
24	0.010	0.112	0.016	0.176	0.028	0.307	10.964
25.1	0.015	0.055	0.027	0.097	0.035	0.126	3.600
25.2	0.044	0.055	0.079	0.097	0.102	0.125	1.225
26.1	0.036	0.087	0.061	0.147	0.087	0.210	2.414
26.2	0.000	0.044	0.000	0.075	0.000	0.107	0.000
27	0.023	0.042	0.034	0.061	0.074	0.134	1.811
28	0.014	0.109	0.023	0.171	0.040	0.303	7.575
29	0.052	0.093	0.077	0.139	0.158	0.284	1.797
30	0.015	0.062	0.019	0.078	0.073	0.302	4.137
Average	0.021	0.070	0.032	0.108	0.070	0.221	4.638

Figure 8. Ratios of water surface area to courtyard area in studied courtyards (Source: Authors)

Figure 9. Ratios of plant coverage area to courtyard area (Right). Ratios of plant coverage area to water surface area (Left) (Source: Authors)

Figure 10. Linear equations and R-squared value between geometric parameters of the courtyards, (a) length versus width, (b) height versus length, (c) height versus width, (d) courtyard area versus total area of house, (e) water surface area versus courtyard area, (f) plant coverage area versus courtyard area (Source: Authors)

Table 8. Estimated equations and relationships between parameters of the courtyards (Source: Authors)

Parameters	Correlation Coefficient	Equation
LCy, WCy	0.923	LCy = 1.3347WCy-0.1644
HCy, LCy	0.559	HCy = 0.129LCy+3.1367
HCy, WCy	0.629	HCy = 0.21WCy+2.6041
ACy, ATH	0.895	ACy = 0.2809ATH+23.165
AWs, ACy	0.675	AWS = 0.0637ACy+2.1523
APc, ACy	0.835	APc = 0.2843ACy-10.096

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