**1. Introduction**

16 Mechanical Engineering

xd mm x coordinate of involutes cog profile generated on the base of parameter t yd mm y coordinate of involutes cog profile generated on the base of parameter t

Amirouche, F. (2004). *Principles of Computer-Aided Design and Manufacturing* (2nd edition),

Certified hardware configurations for CATIA V5 systems. (May 2011). Available from:

Cozzens, R. (2006). *Advanced CATIA V5 Workbook: Knowledgeware and Workbenches Release 16*.

Dassault Systemes – PLM solutions, 3D CAD and simulation software. (May 2011).

Karam, F. & Kleismit, C. (2004). *Using Catia V5*, Computer library, ISBN 86-7310-307-X,

Repcic, N. et al. (1998). *Mechanical Elements II Part*, Svjetlost, ISBN 9958-10-157-7 (ISBN 9958-

Repcic, N. & Muminovic, A. (2007). *Mechanical Elements II*, Faculty of Mechanical

Saric, I., Repcic, N. & Muminovic, A. (2006). 3D Geometric parameter modelling of belt

Saric, I., Repcic, N. & Muminovic, A. (1996). Parameter Modelling of Gears, *Proceedings of the*

Shigley, J.E., Mischke, C.R. & Budynas, R.G. (2004). *Mechanical Engineering Design* (7th

Spotts, M.F., Shoup, T.E. & Hornberger, L.E. (2004). *Design of Machine Elements* (8th edition),

Zamani, N.G. & Weaver, J.M. (2007). *Catia V5: Tutorials Mechanism Design & Animation*,

Prentice Hall, ISBN 0-13-126955-0, Upper Saddle River, New Jersey

transmissions and transmissions gear. *Technics Technologies Education Management –*

*14th International Research/Expert Conference "Trends in the Development of Machinery and Associated Technology – TMT 2010"*, pp. 557-560, ISSN 1840-4944, Mediterranean

Schroff Development Corporation (SDC Publications), ISBN 978-1-58503-321-8,

tc ° cutting angle used for contact point putting in zx plane

z1 - cog number of driver gear; number of turn of a worm

Prentice Hall, ISBN 0-13-064631-8, Upper Saddle River, New Jersey

<http://www.3ds.com/support/certified-hardware/overview/>

Dassault Systemes. (2007a). *CATIA Solutions Version V5 Release 18 English Documentation*  Dassault Systemes. (2007b). *CATIA Web-based Learning Solutions Version V5 Release 18*

t - involutes function parameter

(x,y) mm coordinates of involute points z - cog number

z2 - cog number of following gear

Available from: <http://www.3ds.com/home/> International Business Machines Corp. (IBM). (May 2011). Available from:

*TTEM,* Vol. 4, No. 2, (2009), pp. 181-188, ISSN 1840-1503

edition), McGraw-Hill, ISBN 007-252036-1, New York

Computer library, ISBN 978-86-7310-381-5, Cacak

tk mm keyway depth

V - pulley rim

**6. References**

Southern Utah University

<http://www.ibm.com/us/en/>

11-075-X), Sarajevo

Engineering, Sarajevo

Cruise, September 11-18, 2010

*Windows*

Cacak

Simulation is an effective tool for understanding the complex interaction of transmission components in dynamic environment. Vibro-dynamics simulation of faulty gears and rolling element bearings allows the analyst to study the effect of damaged components in controlled manners and gather the data without bearing the cost of actual failures or the expenses associated with an experiment that requires a large number of seeded fault specimens. The fault simulation can be used to provide the data required in training Neural network based diagnostic/prognostic processes.


The hardness of sigma phase in Fe-Cr alloys is approximately 68 HRC [1]. Fig. 10 shows the microstructure of austenitic matrix and network of sigma phase precipitation on grain boundary and also indenter effects on the surface at several locations. It can be seen that because of brittleness and higher hardness of sigma phase with respect to the austenite

**Figure 9.** Microstructure of austenitic matrix and network of sigma phase precipitation on grain boundary. It can be seen that because of sigma is brittle phase, often fractures during indentation

boundary, can lead to very early failure of high-temperature parts [12].

Therefore, a relatively small quantity of the σ phase, when it is nearly continuous at a grain

To eliminate segregation in the cast structure, it is frequently necessary to homogenize the part before usage to promote uniformity of chemical composition and microstructure. This treatment can also be used for complete dissolution of carbides and brittle and deleterious phases like sigma which are formed at operating conditions. In this method, steel is heated for a long enough period of time in order to complete the dissolution of carbides, and then the cooling starts at an appropriate rate to avoid formation of

matrix, this phase often fractures during indentation.

(indicated by the arrows) [12].

deleterious phases [12].

**5. Homogenization heat treatment**

**Figure 7.** Effect of time and temperature of aging treatment on the impact energy of austenitic steel Fe-25Cr-20Ni [23].

**Figure 8.** Time-temperature relationships to produce 25 and 100°C DBTTs for a 29Cr-4Mo ferritic stainless steel as a function of aging times that cover both the 475°C embrittlement range and the σ phase embrittlement range [24].

The hardness of sigma phase in Fe-Cr alloys is approximately 68 HRC [1]. Fig. 10 shows the microstructure of austenitic matrix and network of sigma phase precipitation on grain boundary and also indenter effects on the surface at several locations. It can be seen that because of brittleness and higher hardness of sigma phase with respect to the austenite matrix, this phase often fractures during indentation.

**Figure 9.** Microstructure of austenitic matrix and network of sigma phase precipitation on grain boundary. It can be seen that because of sigma is brittle phase, often fractures during indentation (indicated by the arrows) [12].

Therefore, a relatively small quantity of the σ phase, when it is nearly continuous at a grain boundary, can lead to very early failure of high-temperature parts [12].

### **5. Homogenization heat treatment**

104 Metallurgy – Advances in Materials and Processes

25Cr-20Ni [23].

phase embrittlement range [24].

**Figure 7.** Effect of time and temperature of aging treatment on the impact energy of austenitic steel Fe-

**Figure 8.** Time-temperature relationships to produce 25 and 100°C DBTTs for a 29Cr-4Mo ferritic stainless steel as a function of aging times that cover both the 475°C embrittlement range and the σ To eliminate segregation in the cast structure, it is frequently necessary to homogenize the part before usage to promote uniformity of chemical composition and microstructure. This treatment can also be used for complete dissolution of carbides and brittle and deleterious phases like sigma which are formed at operating conditions. In this method, steel is heated for a long enough period of time in order to complete the dissolution of carbides, and then the cooling starts at an appropriate rate to avoid formation of deleterious phases [12].

**Table 1.** Microstructures of selected failed roller steel, before and after the homogenization heat

Microstructures of selected failed roller steel, before and after the homogenization heat treatment at various temperatures for 2 h are shown in Table 1. Formation of the brittle sigma phase and precipitation of carbides is clear in the microstructure of specimen HH14 when compared to the microstructure of specimen HH11. As a result of slow cooling in the furnace, all the desirable changes in the homogenized structure are reversed. In other words, the formation of carbide precipitates in grains, inhomogeneity of austenite as the matrix phase, and the formation of intermetallic brittle phases like sigma phase, which are all results of slow cooling at temperatures between 650 and 950°C, cause the toughness of the steel to decrease greatly. Since the formation of the sigma phase is a time consuming process, formation of this phase has been minimized by cooling in the air. The lowest amounts of sigma phase and carbides are in specimen HH11, which shows homogeneity of microstructure and a decrease in microscopic segregation. Therefore, for roller straightening and a good toughness to be obtained, homogenization heat treatment should be performed

Fig. 11 shows the precipitation sites of sigma-phase in the failed roller before and after the homogenization heat treatment at 1100 °C for 2 h followed by air cooling. Fig. 12 and Table 2 illustrate the chemical composition at three scanning points indicated in Fig. 11 (a), (b) and (c). As can be seen in Fig. 11, the points 1, 2, and 3 were austenite matrix, delta-ferrite, and sigma-phase, respectively. Table 2 shows that the chromium, molybdenum, and silicon content in the sigma-phase were higher than that of the austenite-phase. Generally, deltaferrite and sigma-phase are Cr-rich. But, the weight percent of silicon and molybdenum in the delta-ferrite is higher than that of other phases (austenite and sigma). Silicon and molybdenum plays an important role in 2 δ σγ phase transformation and acts as strong

As can be seen in Fig. 11, the heat treatment at 1100°C followed by cooling in air led to changing the morphology of sigma phase from dendritic structure (Figs. 11(a) and (b)) to globular structure (Fig. 11(c)). The dendritic sigma phase indicates an unstable shape, and globular sigma phase exhibits a stable shape. Also, the dendritic structure is brittle, while, the globular structure is ductile. Therefore, it can be concluded that for completing the transformation of delta-ferrite to sigma phase, the temperature of homogenization heat treatment should be increased to 1100°C and the morphology of sigma phase be

HH14

1100

treatment for 2 h.

Furnace

at 1100°C for at least 2 h followed by cooling in air [12].

stabilizers for delta-ferrite [5,20].

**Table 1.** Microstructures of selected failed roller steel, before and after the homogenization heat treatment for 2 h.

Microstructures (etched electrolytically by 10 M KOH solution)

Microstructures (etched by Marble's reagent)

Specimen Homogenization temperature (°C) Cooling environment

950

1050

1100

Air

Air

Air

HH1

HH2

HH8

HH11

Microstructures of selected failed roller steel, before and after the homogenization heat treatment at various temperatures for 2 h are shown in Table 1. Formation of the brittle sigma phase and precipitation of carbides is clear in the microstructure of specimen HH14 when compared to the microstructure of specimen HH11. As a result of slow cooling in the furnace, all the desirable changes in the homogenized structure are reversed. In other words, the formation of carbide precipitates in grains, inhomogeneity of austenite as the matrix phase, and the formation of intermetallic brittle phases like sigma phase, which are all results of slow cooling at temperatures between 650 and 950°C, cause the toughness of the steel to decrease greatly. Since the formation of the sigma phase is a time consuming process, formation of this phase has been minimized by cooling in the air. The lowest amounts of sigma phase and carbides are in specimen HH11, which shows homogeneity of microstructure and a decrease in microscopic segregation. Therefore, for roller straightening and a good toughness to be obtained, homogenization heat treatment should be performed at 1100°C for at least 2 h followed by cooling in air [12].

Fig. 11 shows the precipitation sites of sigma-phase in the failed roller before and after the homogenization heat treatment at 1100 °C for 2 h followed by air cooling. Fig. 12 and Table 2 illustrate the chemical composition at three scanning points indicated in Fig. 11 (a), (b) and (c). As can be seen in Fig. 11, the points 1, 2, and 3 were austenite matrix, delta-ferrite, and sigma-phase, respectively. Table 2 shows that the chromium, molybdenum, and silicon content in the sigma-phase were higher than that of the austenite-phase. Generally, deltaferrite and sigma-phase are Cr-rich. But, the weight percent of silicon and molybdenum in the delta-ferrite is higher than that of other phases (austenite and sigma). Silicon and molybdenum plays an important role in 2 δ σγ phase transformation and acts as strong stabilizers for delta-ferrite [5,20].

As can be seen in Fig. 11, the heat treatment at 1100°C followed by cooling in air led to changing the morphology of sigma phase from dendritic structure (Figs. 11(a) and (b)) to globular structure (Fig. 11(c)). The dendritic sigma phase indicates an unstable shape, and globular sigma phase exhibits a stable shape. Also, the dendritic structure is brittle, while, the globular structure is ductile. Therefore, it can be concluded that for completing the transformation of delta-ferrite to sigma phase, the temperature of homogenization heat treatment should be increased to 1100°C and the morphology of sigma phase be

transformed to stable globular structure. This structure leads to remarkable increase in the impact energy and ductility of continuous annealing furnace roller. In contrast, the formation of sigma-phase with dendritic morphology results in decrease in ductility and failure of the roller.

Homogenization Heat Treatment to Reduce the Failure of Heat Resistant Steel Castings 109

failure of the roller.

transformed to stable globular structure. This structure leads to remarkable increase in the impact energy and ductility of continuous annealing furnace roller. In contrast, the formation of sigma-phase with dendritic morphology results in decrease in ductility and

**Figure 10.** Morphology of sigma-phase. (a) and (b) after failure and before homogenization treatment, respectively and (c) after the homogenization heat treatment at 1100 °C for 2 h followed by air cooling.

110 Metallurgy – Advances in Materials and Processes

**Figure 10.** Morphology of sigma-phase. (a) and (b) after failure and before homogenization treatment, respectively and (c) after the homogenization heat treatment at 1100 °C for 2 h followed by air cooling.

**Figure 11.** The EDS analysis of: (a) austenite-phase (point 1 in Fig. 11(a)), (b) ferrite-phase (point 2 in Fig. 11(b)), and (c) sigma-phase (point 3 in Fig. 11(c)).

**Table 2.** Elemental composition of Fig. 12.

Fig. 13 shows the fracture surfaces of the failed sample before homogenization (Fig. 13(a)), the sample after the homogenization heat treatment at 1100 °C for 2 h followed by cooling in furnace (Fig. 13(b)), and the sample after the homogenization heat treatment at 1100 °C for 2 h followed by cooling in air (Fig. 13(c)). The EDS analysis of points 1 and 2 in Figs. 13(a) and 13(b), respectively indicated the presence of sigma-phase in definite crystallographic planes. In fact, the fracture surface of failed sample (Fig. 13(a)) contained a random arrangement of flat surfaces and surfaces with steps which is characteristic of brittle fracture. The fracture surface of the sample after the homogenization heat treatment at 1100 °C for 2 h followed by cooling in furnace (Fig. 13(b)) was a mixture of small dimples and layered surfaces that indicated brittle and ductile fractures in this sample. The EDS analysis of point 3 in Fig. 13(b) showed the presence of chromium in the form of carbide particles. The carbide

Fig. 11(b)), and (c) sigma-phase (point 3 in Fig. 11(c)).

**Table 2.** Elemental composition of Fig. 12.

**Figure 11.** The EDS analysis of: (a) austenite-phase (point 1 in Fig. 11(a)), (b) ferrite-phase (point 2 in

Cr Si Mo

Point Element (wt.%)

1 (gamma) 22.125 1.353 0.227 2 (delta) 27.639 2.896 1.341 3 (sigma) 34.641 2.544 1.021

Fig. 13 shows the fracture surfaces of the failed sample before homogenization (Fig. 13(a)), the sample after the homogenization heat treatment at 1100 °C for 2 h followed by cooling in furnace (Fig. 13(b)), and the sample after the homogenization heat treatment at 1100 °C for 2 h followed by cooling in air (Fig. 13(c)). The EDS analysis of points 1 and 2 in Figs. 13(a) and 13(b), respectively indicated the presence of sigma-phase in definite crystallographic planes. In fact, the fracture surface of failed sample (Fig. 13(a)) contained a random arrangement of flat surfaces and surfaces with steps which is characteristic of brittle fracture. The fracture surface of the sample after the homogenization heat treatment at 1100 °C for 2 h followed by cooling in furnace (Fig. 13(b)) was a mixture of small dimples and layered surfaces that indicated brittle and ductile fractures in this sample. The EDS analysis of point 3 in Fig. 13(b) showed the presence of chromium in the form of carbide particles. The carbide Homogenization Heat Treatment to Reduce the Failure of Heat Resistant Steel Castings 113

continuous at a grain boundary, can lead to very early failure of high-temperature parts. It is important to understand that the sigma-phase cannot undergo any significant plastic deformation; instead, it fractures even at relatively low strain levels. This is true at elevated temperatures, but even more so at ambient temperature. Where toughness and ductility are an important part of the system design, the sigma-phase cannot be tolerated. The formation of sigma-phase with dendritic morphology results in decrease in ductility and failure of heat resistant steels. The microstructural inhomogeneity (sigma-phase and carbides) can be eliminated by holding the sample at high temperatures for a sufficient time and cooling at an appropriate rate. The homogenization heat treatment under appropriate condition can led to change in the morphology of sigma phase from dendritic structure to globular structure. This structure leads to remarkable increase in the impact energy and ductility of

*Department of Advanced Materials and New Energy, Iranian Research Organization for Science and*

[1] ASM Handbook, Volume 1, Properties and Selection: Irons, Steels, and High-

[2] Lamb, S., Practical Handbook of Stainless Steels and Nickel Alloys, ASM International,

[5] Prager, M. and Svoboda, J., Cast High Alloy Mettalurgy, Steel Casting Metallurgy, Steel

[6] W. Trietschke and G. Tammnann, The Alloys of Iron and Chromium. Zh. Anorg.

[7] E.C. Bain and W.E. Griffiths, An Introduction to the Iron-Chromium-Nickel Alloys,

[8] P. Chevenard, Experimental Investigations of Iron, Nickel, and Chromium Alloys, Trav.

[9] F. Wever and W. Jellinghaus, The Two-Component System: Iron-Chromium, Mitt.

[11] ASM Handbook, Volume 11, Failure Analysis and Prevention, ASM International,

[10] E.O. Hall and S.H. Algie, The Sigma Phase, Metall. Rev., Vol 11, 1966, p 61−88.

[3] ASM Handbook, Volume 15, Casting, ASM International, Materials Park, Ohio, 2005. [4] Shi, S. and Lippold, J.C., "Microstructure Evolution During Service Exposure of Two Cast, Heat-Resisting Stainless Steels - Hp-Nb Modified and 20-32nb", Materials

Performance Alloys, ASM International, Materials Park, Ohio, 2005.

Characterization, Vol. 59, No. 8, pp. 1029−1040, 2008.

Founder's Society of America, Rocky River, OH, 1984.

Mem., Bur. Int. Poids et Mesures, Vol 17, 1927, p 90.

Kaiser-Wilhelm Inst., Vol 13, 1931, p 143−147.

heat resistant steels.

**Author details**

**7. References**

Mohammad Hosein Bina

*Technology, Tehran, Iran*

Materials Park, Ohio, 1999.

Chem., Vol 55, 1907, p 402−411.

Materials Park, Ohio, 2002.

Trans. AIME, Vol 75, 1927, p 166−213.

**Figure 12.** Fracture surfaces of: (a) the failed sample before homogenization, (b) the sample after the homogenization heat treatment at 1100 °C for 2 h followed by cooling in furnace, and (c) followed by cooling in air.

particles existed in the center of small dimples. According to EDS analysis of points 2 and 3, it can be said that due to slow cooling rate in the furnace, all the desirable changes that occur in homogenized structures are reversed and a new formation of the sigma-phase and precipitates in the sample results in a transition from ductile to almost brittle fracture. As can be seen in Fig. 13(c), formation of deep dimples is a main characteristic of ductile fracture. The EDS analysis of the point 4 was similar to the base metal. This figure indicated a considerable decrease in sigma phase and precipitates amounts after homogenization.

Therefore, before roller straightening, the homogenization heat treatment should be performed for dissolution of deleterious phases in austenite as the matrix phase and obtaining good toughness. In many cases, microstructural inhomogeneity can be eliminated by holding the sample at high temperatures for a sufficient time and cooling at an appropriate rate. Otherwise, the possibility of the formation of fine cracks during roller straightening is very high. These cracks can result in roller fracture during the straightening process and/or in the continuous-annealing furnace.

### **6. Conclusions**

The sigma phase tends to precipitate in the regions of high chromium content, such as the chromium carbides in the grain. A relatively small quantity of the σ phase, when it is nearly continuous at a grain boundary, can lead to very early failure of high-temperature parts. It is important to understand that the sigma-phase cannot undergo any significant plastic deformation; instead, it fractures even at relatively low strain levels. This is true at elevated temperatures, but even more so at ambient temperature. Where toughness and ductility are an important part of the system design, the sigma-phase cannot be tolerated. The formation of sigma-phase with dendritic morphology results in decrease in ductility and failure of heat resistant steels. The microstructural inhomogeneity (sigma-phase and carbides) can be eliminated by holding the sample at high temperatures for a sufficient time and cooling at an appropriate rate. The homogenization heat treatment under appropriate condition can led to change in the morphology of sigma phase from dendritic structure to globular structure. This structure leads to remarkable increase in the impact energy and ductility of heat resistant steels.

### **Author details**

114 Metallurgy – Advances in Materials and Processes

cooling in air.

**6. Conclusions**

**Figure 12.** Fracture surfaces of: (a) the failed sample before homogenization, (b) the sample after the homogenization heat treatment at 1100 °C for 2 h followed by cooling in furnace, and (c) followed by

particles existed in the center of small dimples. According to EDS analysis of points 2 and 3, it can be said that due to slow cooling rate in the furnace, all the desirable changes that occur in homogenized structures are reversed and a new formation of the sigma-phase and precipitates in the sample results in a transition from ductile to almost brittle fracture. As can be seen in Fig. 13(c), formation of deep dimples is a main characteristic of ductile fracture. The EDS analysis of the point 4 was similar to the base metal. This figure indicated a considerable decrease in sigma phase and precipitates amounts after homogenization.

Therefore, before roller straightening, the homogenization heat treatment should be performed for dissolution of deleterious phases in austenite as the matrix phase and obtaining good toughness. In many cases, microstructural inhomogeneity can be eliminated by holding the sample at high temperatures for a sufficient time and cooling at an appropriate rate. Otherwise, the possibility of the formation of fine cracks during roller straightening is very high. These cracks can result in roller fracture during the straightening

The sigma phase tends to precipitate in the regions of high chromium content, such as the chromium carbides in the grain. A relatively small quantity of the σ phase, when it is nearly

process and/or in the continuous-annealing furnace.

#### Mohammad Hosein Bina

*Department of Advanced Materials and New Energy, Iranian Research Organization for Science and Technology, Tehran, Iran*

### **7. References**

[12] Bina, M.H., Dini, G., Vaghefi, S.M.M., Saatchi, A., Raeissi, K. and Navabi, M., "Application of Homogenization Heat Treatments to Improve Continuous-Annealing Furnace Roller Fractures", Engineering Failure Analysis, Vol. 16, No. 5, pp. 1720−1726, 2009.

**Chapter 6**

© 2012 Pencea, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

95%[1, 2, 3]. The EN ISO 17025 [1] stipulates that the quality of a

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Pencea, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Multiconvolutional Approach**

Additional information is available at the end of the chapter

Ion Pencea

http://dx.doi.org/10.5772/50511

**1. Introduction**

exigency requires *p*

**to Treat the Main Probability Distribution**

**Uncertainties of Metallurgical Tests**

**Functions Used to Estimate the Measurement**

The quality of a metallic product is validated by tests results. Thus, the product quality is depicted by the quality of the testing results that furthermore depends on several factors such as: the incomplete knowledge about measurand, the adequacy of the testing method in relation to measurand, the equipment adequacy for method, the human factor; the statistical inference, etc. The influence factors of a measurement process, whether known or unknown, may alter the result of a measurement in an unpredictable way. Thus, a test result bears an intrinsic doubt about its closeness to the conventional true value of the measurand, fact which is commonly perceived as uncertainty about the test result. One of the most important tasks for the experimentalist is to specify an interval about the estimated value of the measurand (�̅�� [�̅ - *U*; �̅ + *U*] in which the true (conventional) value (μ) could be found with specified confidence level, i.e. the probability (*p*) that μ ∈ [�̅ - U; �̅ + U]. The practice

numeric test result is quantified by the expanded uncertainty *U(p%),* where *p* is the level of confidence (*p* � 95%). An alternative specification of *U* is its level of significance expressed as *1-p*. In order to obtain a higher quality of the test result, the experimentalist should perform a set of at least 30 repeated measurements [2, 4]. In the field of metallurgy this is quite impossible for technical and economical reasons. Therefore, the quality of the test result should be guaranteed by advanced knowledge about the testing method and by other means such as: equipment etalonation, Certified Reference Materials (CRMs) usage and, last but not least, correct uncertainty estimation based on proper knowledge about the probabilistic behavior of the compound random variable derived from a set of repeated


**Author details**

Noor Hafizah Amer1,2\*, Khisbullah Hudha1 , Hairi Zamzuri2 , Vimal Rau Aparow3 , Amar Faiz Zainal Abidin4 , Zulkiffli Abd Kadir1 and Muhamad Murrad1

1 Faculty of Engineering, Universiti Pertahanan Nasional Malaysia, Kuala Lumpur, Malaysia

2 Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia, Kuala Lumpur, Malaysia

3 Faculty of Engineering, The University of Nottingham Malaysia, Selangor, Malaysia

4 Faculty of Engineering Technology, Universiti Teknikal Malaysia Melaka, Melaka, Malaysia

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


**22.  Cationic liposomes are prepared using lipid molecules having a quaternary ammonium head group. Because cellular membranes carry negative charges, cationic liposomes interact with these cellular membranes [117]. The stability of liposomes in biological environment is improved with steric stability that can extend its blood circulation time after being administered [118]. Biodegradable polymers are usually used to enhance the steric stability of the liposomes. Natural biodegradable polymers that are suitable for drug delivery systems include proteins (collagen, gelatin, albumin, etc.) and polysaccharides (starch, dextran, chitosan, etc.) [119].

**153**

*Biomaterials for Drug Delivery: Sources, Classification, Synthesis, Processing, and Applications*

Polysaccharides are many monosaccharide repeating units with high molecular weight. It is biodegradable, biocompatible, and water soluble which make suitable for drug delivery. There are several different types of polysaccharides having differ-

Alginic acid is a linear hetero polysaccharide, nonbranched, high-molecularweight binary copolymer of (1–4) glycosidic linkage with β-D-mannuronic acid and α-L guluronic acid monomers [120, 121]. Natural alginic acid can be obtained from the cell walls of brown algae. Its acidic nature helps in its spontaneous formation of salts and later gels in the presence of divalent cations like calcium ions. This occurs by the interaction of divalent cations with guluronic acid blocks present on other polysaccharide chains. The gel property paves way for the encapsulation of molecules that can act as drugs within alginate gels with negligible side effects. The drug delivery mechanism of alginates is hinged on the drug polymer interaction and chemical immobilization of the drug on the polymer backbone via reactive carbox-

Starch, which is a carbohydrate source can be isolated from corn, wheat, potato,

tapioca, rice, etc., and consists of two glucosidic macromolecules: 20–30% of linear molecule—amylase and 70–80% of branched molecule—amylopectin. The products of starch processing include thin films, fibers, and porous matrices. It is an important polymer for thermoplastic biodegradable materials due to its low cost, availability, biocompatibility, biodegradability, and having renewable resources [125]. The products of starch degradation include fructose and maltose that are low molecular weight sugar [126]. Microspheres from starch have bioadhesive drug

Dextran is a natural polysaccharide of large glucose molecules with long and branched chains of varying lengths from 3 to 2000 Kd at 1,6- and partly at 1,3-glucosidic linkages. It is synthesized from sucrose via lactic-acid bacteria like *Leuconostoc mesenteroides*, *Streptococcus mutans*, and lactic acid bacterium *Lactobacillus brevis*. It is colloidal and hydrophilic in nature; it is inert to the in vivo environment with no effect on cell viability [128]. Dextran is used as an antithrombotic (antiplatelet), to reduce blood viscosity, and as a volume expander in anemia [129]. Dextran can be degraded by enzyme dextranase in the colon and thus can

Pullulan occurs naturally as linear homopolysaccharide polymer with maltotriose units of 3-glucose or D-glucopyranose units which are linked by α-(1 → 4) glycosidic linkages. It is edible, bland, and tasteless and thus is added to food and beverages. It serves as a coating agent in pharmaceutics, breath fresheners, or oral hygiene products [130]. Consecutive maltotriose units are linked to one another via

delivery system potential for nasal delivery of proteins [127].

serve as a colonic drug delivery system.

*DOI: http://dx.doi.org/10.5772/intechopen.93368*

ent functional groups, which are as follows:

**22.2 Alginic acid or alginates**

ylate groups [122–124].

**22.3 Starch**

**22.4 Dextran**

**22.5 Pullulan**

**22.1 Polysaccharides**

*Biomaterials for Drug Delivery: Sources, Classification, Synthesis, Processing, and Applications DOI: http://dx.doi.org/10.5772/intechopen.93368*


6. Conclusions

meticulous reflection. According to Paul, strong critical thinking is what teachers need to give form and encouragement to their classes, if they want students to overcome their prejudices or other equally harmful manifestations of intellectual

Stone Wiske [1], unlike Perkins [2], identifies four prototypical levels of comprehension, among which are: (a) naive understanding-acuptation of information directly in the world, there is no awareness of the links that exist between activity and its application in our life-, (b) comprehension of newbies-mechanisms and rituals-, (c) apprentice comprehension-obey disciplinary modes of thinkingand (d) understanding of mastery-critical, holistic, creative and flexible-. Each of these dimensions describe the multidimensional nature of understanding. However, "deep understanding involves the ability to use knowledge in all dimensions" ([1], p. 239). Its dimensions vary according to the specificity and interiority of each of its dimensions. To understand in depth the meaning and meaning of levels of understanding, it is necessary to refer to comprehension performances, that is, various ways in which subjects demonstrate what they have learned. Table 2 presented below summarizes

Returning to the contributions of Stone Wiske [1], in relation to the four

(b) methods, (c) summary of the dimension of purposes and d) forms of communication of what was learned. It also adds criteria associated with each of the

Main manifestations

schooling systems

steps to achieve something

experts in the domain" (p. 240)

understandings indicated above

interactions, confrontations

solve a particular problem

transform it

• Lack of reflective ways about which knowledge is

• They are linked to mediation systems of tests and

• Comprehension performance is based on an application mechanism, contemplating the development of a set of

• Flexible use of these ideas within a specific discipline. According to Stone Wiske [1] "the construction of knowledge is seen as a complex task, which follows procedures and criteria that are prototypically used by

• The student moves with flexibility between each of the

• Complex knowledge construction, resulting from complex

• They use knowledge to act in reality, to intervene in it and

• Foster a disciplinary (meta-disciplinary) understanding, the subject of learning combines several disciplines to

dimensions of understanding, identifies unlike Perkins [2]: (a) content,

Naive understanding • Characterized by a disconnection from real life

Apprentice comprehension • Reproduce disciplinary ways of thinking

Master's comprehension • Operate through integration: flexible, holistic

expressed Understanding of newbies • Describe the purposes of the nature of knowledge

narrowness ([2], p. 118).

Metacognition in Learning

the main characteristics described by Stone Wiske [1].

dimensions indicated above (Table 3).

Dimension of understanding according to Stone Wiske [1]

Source: Stone Wiske [1].

Understanding styles.

Table 2.

146


**A Model of Urban Infrastructural Planning in a Traditional African City: A Case Study of Ilorin, Nigeria**

Olutoyin Moses Adedokun1 and Dickson Dare Ajayi2 *1Department Of Geography, Federal College Of Education, Zaria, 2Department Of Geography, University Of Ibadan, Ibadan Nigeria*

#### **1. Introduction**

60 Advances in Spatial Planning

Bagwell, P. S. (1974). The Transportation Revolution from 1770. New York, Barnes & Noble. Bokor, Z., Török, Á. (2011). Introduction of a capacity sensitive OD matrix estimation

Burgess, R. (2000). The compact city debate: A global perspective. In: M. Jenks and R.

Chicago Area Transportation Study, (April 1962). Chicago, Illinois, Harrison Lithographing,

Dixit, A. K., Stiglitz, J. E. (1977). Monopolistic Competition and Optimum Product Diversity.

Hagerstrand, T. (1970). What about people in regional science? Regional Science Association

Krugman, P. (1991). Increasing returns and economic geography. Journal of Political

Russo, F., Musolino, G. (2009). Multiple equilibria in spatial economic transport interaction

Samuelson, P. (1941). The Stability of Equilibrium: Comparative statics and dynamics. Vol.

Samuelson, P. (1948). Consumption theory in terms of revealed preference. Econometrica

Samuelson, P. (1954). The Pure of Theory of Public Expenditure: The Review of Economy

Smith, A. (1776.). An Inquiry into the Nature and Causes of the Wealth of Nations. London,

Wegner, M., Fürst, F. (1999). Land-Use Transport Ineraction: State of the Art. TRANSLAND

WCED: World Commission on Environment and Development. (1987). The Brundtland

Maslow, A. (1943). A Theory of Human Motivation. Psychological Review 50(4), 370-96. Pareto, V. (1897). The New Theories of Economics. Journal of Political Economy 5, 485-502. Plátōn. The Republic (Politeia) http://etext.lib.virginia.edu/ebooks, Virginia: Copyright 2000, by the Rector and Visitors of the University of Virginia, 144. p. Ruiter, E. R., Ben-Akiva, M. E. (1978). Disaggregate Travel Demand Models for the San

Francisco Bay Area. Transportation Research Record 673, 121-128.

models. Association for European Transport and contributors.

project. Universitat Dortmund – Fakultat Raumplanung.

Report, Our Common Future. Oxford: Oxford University Press.

Carey, H. C. (1877). Priciples of Social Sciences. Philadelphia, J.B. Lippincott & Co.

Gubbins, E. J. (2002). Managing Transport Operation. London, Kogan Page Ltd.

Hunyady, Gy., Székely, M. (2003). Economic psychology. Osiris, Budapest. Jávor, B. (2005). The living urban machine. Ökotrend, Budapest, 2, 20-21.

Conference on Transport Research, Lisbon.

II) July 1960., Transportation Plan (Volume III).

The American Economic Rewiew. Pp. 297-308.

Juhász, J. (2003). Hungarian Dictionary. Budapest, Academy.

E & FN Spon, pp. 9–24.

Papers 24, 7–21.

Kornai, J. (1971). Anti-Equilibrium. Budapest.

and Statistics. Vol. 36., Nr.4.

Walras, L. (1876). Éléments d'économie politique pure.

Methuen & Co., Ltd.

Economy 99, 483–499.

9., Nr.2.

15.: 243-253.

process applying genetic algorithm based calibration of SCGE model. World

Burgess, Editors, Compact cities: Sustainable urban forms for developing countries,

1959-1962. (Study Findings (Volume I) December 1959., Data Projections (Volume

A model is defined as a simplified structure of reality, an organized principle, a synthesis of idea or a mental construct in which an actual life situation may fit in (Timmermans, 2000). Analysis of urban areas, structure of cities, urban activities and their linkages at the level of individual city has witnessed, over the years a number of improved models (Carter, 1975, Ayeni, 1979; Wegner 2001). These are the ecological/economic competition model, spatial interaction models, urban activity pattern and activity system models, spatial behavioural and microbehavioural models. The paper is viewed within the urban activity pattern and activity system models, spatial behavioural model, and microbehavioural model. These models were reviewed as a precursor to the proposed model - the model of Urban Neighbourhood Activity Centers.

#### **2. Models of urban analysis**

#### **2.1 Models of urban activity pattern and activity system**

Most theoretical work in the area of activity analysis stems from geography and urban planning. This is largely based on two important publications in the 1970s first by Haggerstrand (1969) and Chapin (1974). The formulation of the Activity Approach in the 1970's was a reaction against certain weaknesses of the four stage modelling approach such as: appropriateness of the model structure, poor data quality, poor quality of the model calibration and on poor quality of forecasts made with it. (Atkins, 1987, Axhausen, 1990). Until the end of the 1980s, these questions were not thought to be serious enough to challenge the practical use of the models. The propositions of Activity Approach have been explained by Clarke (1985), Eurotopp (1989) , Axhausen (1990) and Kwan (2005) as follows: (i) activities are primary, travel is secondary (ii) activities and travel take place in time-space (iii) behaviour is influenced by space-time and other constraints (iv) household activity patterns are related to household structure (v) interactions within households change over time (vi) activity and travel behaviour is constrained by the experience of the traveler.

The 'Activity Approach' stands apart from the other traditions of modeling identified by Pas (1988). The concern of the 'Activity Approach' has not been the derivation of mathematical

A Model of Urban Infrastructural Planning

repetitive urban spatial behaviour (Pipkin, 1981).

elements of the urban space.

**2.3 The micro-behavioral approach**

in a Traditional African City: A Case Study of Ilorin, Nigeria 63

that emerged from the travel diary of the urban residents, it is evident that the set of locations actually contacted is but a small sub-set of the cognitive opportunity. Cadwallader (1978) used information and preference surfaces in explaining individual's cognitive space. Preference surface reflects the varying attractiveness as a place to live in, which people attach to different locations. It was, however, discovered that the underlying structures of information and preference surfaces are more difficult to disentangle, especially in the case of information

Information about the objective environment as stored subjectively in the individual's brain is called the cognitive constructs of the urban environment. Cognitive image is, however, different from locational schematic or mental map. The term "cognitive" is used to indicate the non-locational character of most images, and to suggest that thinking and verbal behaviour form a stronger component of cognitive images than concrete visual imagery (Wong, 1979). Cognitive affective maps are mental orderings of the environment that involve preference ratings that guide residential choice, but personal and financial considerations often preclude selection of the preferred location (Preston, 1982). Behavioural models provide psychological oriented accounts of the destination choice process in

Behavioural approach is increasingly finding a place in urban and transportation planning in an attempt to improve the policy contents of plan proposals (Chorkor, 1986a; 1987, 1988). The earlier approach of urban/transportation planners has leaned heavily towards the environmentalists' viewpoint which, according to Herz (1982) maintains that spatial behaviour, including personal and social constraints is essentially a function of the material environment. Thus, what appears to be close to environmental deterministic view of behaviour has been jettisoned and planners are currently adopting behavioural approach, which sees the spatial structure, material environment and man as mutually interacting

Man is considered as having the ability to evaluate, interprete and react to his environment as observed and perceived. However, Lundqvist (1978) observes that existing planning models are not capable of integrating structure and behaviour in a theoretically sound way and at a level of detail that is useful for planning purposes. He suggests that it may be necessary to work with less ambitious approaches built on iteractive use of structural and behavioural models. This problems is still evident despite the fact that sophisticated techniques are being developed and employed in planning to analyse spatial behaviour (Burnett, 1977: Arad and Berechman, 1978; Smith, *et al*, 1982). Timmermans and Veldhuisen (1982) observe that behavioural models offer a potentially more valuable approach to predict the likely effects of physical planning schemes as compared with the gravity-type approaches. They, however, noted that behavioural models share with the gravity type models the problem of whether equations could be developed solely on the basis of policy

The micro-behavioral approach, otherwise known as systems approach to urban activity network, seeks to explain urban spatial structure, not in a mechanistic term as done by the neo-classical economists. Rather it explains urban spatial structure, especially the interactions

sensitive factors or whether other influential factors should be included.

surface, and there is no evidence that these structures are strongly related.

descriptions of human behaviour as was the concern of social physics, econometric and psychometric but to derive a modeling system to explain human spatial behaviour. One important concept that emerged from the models of urban activity pattern and activity system is the concept of "Action Space" which is the collection of all urban locations about which the individual has information and the subjective utility or preference associated with these locations (Horton and Reynolds, 1971).

The core of an individual's action space is termed the "activity space" which is the subset of action space, that is, all locations or areas that an individual has ever visited or had direct contact with as a result of day-to-day activities. In terms of activity system, persons and firms are regarded as behavioural units, which perform some activities in some locales. The activity space is the most structured by individuals because it comprises locations, which have actually been visited. A location will change from being part of the action space to being part of the activity space once a trip has been made. The difference between activity space and action space is that although both are part of time-space environment, action space is a part of time space environment for which an individual has positive information through media, relatives or friends while activity space is a part of time- space environment frequently used.

The pattern displayed by individuals as they carry out their activities is the "activity pattern" of individuals. An Activity Pattern (AP) is an ordered sequence of activities of an individual that takes place within a space-time continuum, the activities being linked by travel. An activity pattern is, therefore, an activity programme with its schedule. An activity programme, on the other hand, is the collection of all the activity undertaken during a certain period of time irrespective of the order of their occurrence. The activity pattern is determined by individual's propensity and opportunity to engage in particular activities (Chapin. 1974), based on "predisposition" factors (such as role obligations, traits, etc.) Associated with activity pattern are certain features, which characterized its inherent utility to the individual. These features include (i) the total number and types of activities and activity types included in activity pattern, (ii) time of the day each activity was performed, (iii) duration of each activity, (iv) activity sequence, (v) location of each activity, (vi) total distance travel, and (vii) amount of flexibility or space-time autonomy.

The advantages of the activity system approach is that it is broad: its values - behavioural patterns framework permits the introduction of the widest range of operating factors without limiting assumptions and deductive arguments which characterized the neoclassical economic/ecology models that ignore all the competing forces and identifying only one link - that with the centre of the city.

#### **2.2 Spatial behavioral models**

The weakness of economic and ecological models gave rise to spatial behavioural models. Lloyd (1976) attempted an examination of the linkages among *cognition*, *preferences* and *migration behaviour* in different states in the United States of America and found a strong structural linkage among them. He concluded that, based on the three components, it is possible to predict the direction of movement in that preferred locations of cognitive space would receive larger percentages of migrants and vice-versa. Hanson (1977) revealed that when the spatial form and extent of information levels are compared with the travel patterns

descriptions of human behaviour as was the concern of social physics, econometric and psychometric but to derive a modeling system to explain human spatial behaviour. One important concept that emerged from the models of urban activity pattern and activity system is the concept of "Action Space" which is the collection of all urban locations about which the individual has information and the subjective utility or preference associated with

The core of an individual's action space is termed the "activity space" which is the subset of action space, that is, all locations or areas that an individual has ever visited or had direct contact with as a result of day-to-day activities. In terms of activity system, persons and firms are regarded as behavioural units, which perform some activities in some locales. The activity space is the most structured by individuals because it comprises locations, which have actually been visited. A location will change from being part of the action space to being part of the activity space once a trip has been made. The difference between activity space and action space is that although both are part of time-space environment, action space is a part of time space environment for which an individual has positive information through media, relatives or friends while activity space is a part of time- space environment

The pattern displayed by individuals as they carry out their activities is the "activity pattern" of individuals. An Activity Pattern (AP) is an ordered sequence of activities of an individual that takes place within a space-time continuum, the activities being linked by travel. An activity pattern is, therefore, an activity programme with its schedule. An activity programme, on the other hand, is the collection of all the activity undertaken during a certain period of time irrespective of the order of their occurrence. The activity pattern is determined by individual's propensity and opportunity to engage in particular activities (Chapin. 1974), based on "predisposition" factors (such as role obligations, traits, etc.) Associated with activity pattern are certain features, which characterized its inherent utility to the individual. These features include (i) the total number and types of activities and activity types included in activity pattern, (ii) time of the day each activity was performed, (iii) duration of each activity, (iv) activity sequence, (v) location of each activity, (vi) total

The advantages of the activity system approach is that it is broad: its values - behavioural patterns framework permits the introduction of the widest range of operating factors without limiting assumptions and deductive arguments which characterized the neoclassical economic/ecology models that ignore all the competing forces and identifying only

The weakness of economic and ecological models gave rise to spatial behavioural models. Lloyd (1976) attempted an examination of the linkages among *cognition*, *preferences* and *migration behaviour* in different states in the United States of America and found a strong structural linkage among them. He concluded that, based on the three components, it is possible to predict the direction of movement in that preferred locations of cognitive space would receive larger percentages of migrants and vice-versa. Hanson (1977) revealed that when the spatial form and extent of information levels are compared with the travel patterns

distance travel, and (vii) amount of flexibility or space-time autonomy.

one link - that with the centre of the city.

**2.2 Spatial behavioral models**

these locations (Horton and Reynolds, 1971).

frequently used.

that emerged from the travel diary of the urban residents, it is evident that the set of locations actually contacted is but a small sub-set of the cognitive opportunity. Cadwallader (1978) used information and preference surfaces in explaining individual's cognitive space. Preference surface reflects the varying attractiveness as a place to live in, which people attach to different locations. It was, however, discovered that the underlying structures of information and preference surfaces are more difficult to disentangle, especially in the case of information surface, and there is no evidence that these structures are strongly related.

Information about the objective environment as stored subjectively in the individual's brain is called the cognitive constructs of the urban environment. Cognitive image is, however, different from locational schematic or mental map. The term "cognitive" is used to indicate the non-locational character of most images, and to suggest that thinking and verbal behaviour form a stronger component of cognitive images than concrete visual imagery (Wong, 1979). Cognitive affective maps are mental orderings of the environment that involve preference ratings that guide residential choice, but personal and financial considerations often preclude selection of the preferred location (Preston, 1982). Behavioural models provide psychological oriented accounts of the destination choice process in repetitive urban spatial behaviour (Pipkin, 1981).

Behavioural approach is increasingly finding a place in urban and transportation planning in an attempt to improve the policy contents of plan proposals (Chorkor, 1986a; 1987, 1988). The earlier approach of urban/transportation planners has leaned heavily towards the environmentalists' viewpoint which, according to Herz (1982) maintains that spatial behaviour, including personal and social constraints is essentially a function of the material environment. Thus, what appears to be close to environmental deterministic view of behaviour has been jettisoned and planners are currently adopting behavioural approach, which sees the spatial structure, material environment and man as mutually interacting elements of the urban space.

Man is considered as having the ability to evaluate, interprete and react to his environment as observed and perceived. However, Lundqvist (1978) observes that existing planning models are not capable of integrating structure and behaviour in a theoretically sound way and at a level of detail that is useful for planning purposes. He suggests that it may be necessary to work with less ambitious approaches built on iteractive use of structural and behavioural models. This problems is still evident despite the fact that sophisticated techniques are being developed and employed in planning to analyse spatial behaviour (Burnett, 1977: Arad and Berechman, 1978; Smith, *et al*, 1982). Timmermans and Veldhuisen (1982) observe that behavioural models offer a potentially more valuable approach to predict the likely effects of physical planning schemes as compared with the gravity-type approaches. They, however, noted that behavioural models share with the gravity type models the problem of whether equations could be developed solely on the basis of policy sensitive factors or whether other influential factors should be included.

#### **2.3 The micro-behavioral approach**

The micro-behavioral approach, otherwise known as systems approach to urban activity network, seeks to explain urban spatial structure, not in a mechanistic term as done by the neo-classical economists. Rather it explains urban spatial structure, especially the interactions

A Model of Urban Infrastructural Planning

**2.4 Spatial interaction function model**

Element Linkages as shown in Figure 2.

Population Social contact (1)

in a Traditional African City: A Case Study of Ilorin, Nigeria 65

Figure 1 represents a very simple working day. Solid lines represent the path of all obligatory activities and dotted lines the prism or feasible regions of movement in periods for which there are no fixed activities. The worker is assumed to be effectively fixed at home until 7:30am to 8:00am where he can conveniently sleep and take breakfast. He must then take a direct route to work, where he is obliged to stay until lunchtime. During the lunch hour he has a certain amount of freedom; he must be back in the office exactly an hour. From 2pm until about 5pm he is again expected to stay at work. But after 5pm he has no need to be home until 7pm for supper. In this period, 5-7pm, he can stay on at work or he can go somewhere near or stop off on the way back for a drink or visit. The main feature implicit in this model of daily behaviour is the idea that certain activities are fixed in both space and time. This model (of the individual's activity -time -space decision) is based on a set of assumptions Six of these assumptions were identified by Cullen and Godson (1975). They are: organised behaviour, the

The Spatial Interaction Function has made it possible to recognize the interaction between people (Population), activities, locations (of the activities) and times (of the day) when the activities took place. This is not in the conventional mechanistic method, but rather in terms of attractiveness of places. Also through this modeling, it is possible to predict at any point the location and quantity of new population through what can be described as Inter-

Action Space, Priorities, Constraint, Flexibility of Activities and Scheduling.

Activities Activity pattern (2) Activity Transition (3)

Fig. 2. Inter-element Linkages. Source: *Procos and Harvey*, 1977

technique (Abler *et al*, 1992, Ayeni, 1979; 1992).

**2.5 The functioning model**

Locations Individual spatial behaviour (4) Activity Location (5) Time (6) Time Individual Temporal behaviour (7) Activity Timing (8) Use Density (9) Population Activities Locations

Figure 2 shows the linkages among the time and the space in which the activities of a given population take place. Linkages between population sub-groups would produce social contacts (cell 1). On the other hand, the linkages between locations and population, locations and activities and locations and locations produce individual spatial behaviour, activity location and time of day when activities take place (cells 4, 5 and 6). Finally the linkages between time and population, time and activities and time and locations produce individual temporal behaviour, activity timing and use density of land respectively (cells 7, 8 and 9).This modeling technique is thus unique and different from the conventional method which only explains linkages through origin destination using the gravity modeling

The Function Model unlike the conventional modeling technique did not consider the attractivity of a space in a mechanistic or unidirectional way rather it recognizes attractivity in terms of interaction between population (people), location activities and times. The most important aspect of this modeling technique is its multidirectionality as shown in the **Figure 4.**

in an urban setting, as an interaction between population (people), activities, locations and time. This approach is different from activity system model, in the sense that it incorporates the time element and individual instance of behaviour and activity, obtained in the form of disaggregated data. The important features of this approach are (i) incorporating time as a commodity, (ii) giving new meaning to land (multiplicity of land use), (iii) perceiving people's behaviour as linked to the ways in which they perceive space, and (iv) providing a holistic approach to urban structure. This approach of integrating individual spatial behaviour overtime was pioneered by Hãggerstrand (1969). He used a simple diagram to illustrate his concept of space-time dimensions. Hãggertrand postulated the geographers' two-dimensional space on the surface of the earth or on the surface of a map. A line on this surface indicated movement in space but not in time. He suggested a third dimension to signify time.

Fig. 1. Man's Daily Space-time Dimensions. Source: *Adapted from Haggerstrand* (1969).

in an urban setting, as an interaction between population (people), activities, locations and time. This approach is different from activity system model, in the sense that it incorporates the time element and individual instance of behaviour and activity, obtained in the form of disaggregated data. The important features of this approach are (i) incorporating time as a commodity, (ii) giving new meaning to land (multiplicity of land use), (iii) perceiving people's behaviour as linked to the ways in which they perceive space, and (iv) providing a holistic approach to urban structure. This approach of integrating individual spatial behaviour overtime was pioneered by Hãggerstrand (1969). He used a simple diagram to illustrate his concept of space-time dimensions. Hãggertrand postulated the geographers' two-dimensional space on the surface of the earth or on the surface of a map. A line on this surface indicated

movement in space but not in time. He suggested a third dimension to signify time.

Fig. 1. Man's Daily Space-time Dimensions. Source: *Adapted from Haggerstrand* (1969).

Figure 1 represents a very simple working day. Solid lines represent the path of all obligatory activities and dotted lines the prism or feasible regions of movement in periods for which there are no fixed activities. The worker is assumed to be effectively fixed at home until 7:30am to 8:00am where he can conveniently sleep and take breakfast. He must then take a direct route to work, where he is obliged to stay until lunchtime. During the lunch hour he has a certain amount of freedom; he must be back in the office exactly an hour. From 2pm until about 5pm he is again expected to stay at work. But after 5pm he has no need to be home until 7pm for supper. In this period, 5-7pm, he can stay on at work or he can go somewhere near or stop off on the way back for a drink or visit. The main feature implicit in this model of daily behaviour is the idea that certain activities are fixed in both space and time. This model (of the individual's activity -time -space decision) is based on a set of assumptions Six of these assumptions were identified by Cullen and Godson (1975). They are: organised behaviour, the Action Space, Priorities, Constraint, Flexibility of Activities and Scheduling.

#### **2.4 Spatial interaction function model**

The Spatial Interaction Function has made it possible to recognize the interaction between people (Population), activities, locations (of the activities) and times (of the day) when the activities took place. This is not in the conventional mechanistic method, but rather in terms of attractiveness of places. Also through this modeling, it is possible to predict at any point the location and quantity of new population through what can be described as Inter-Element Linkages as shown in Figure 2.

Fig. 2. Inter-element Linkages. Source: *Procos and Harvey*, 1977

Figure 2 shows the linkages among the time and the space in which the activities of a given population take place. Linkages between population sub-groups would produce social contacts (cell 1). On the other hand, the linkages between locations and population, locations and activities and locations and locations produce individual spatial behaviour, activity location and time of day when activities take place (cells 4, 5 and 6). Finally the linkages between time and population, time and activities and time and locations produce individual temporal behaviour, activity timing and use density of land respectively (cells 7, 8 and 9).This modeling technique is thus unique and different from the conventional method which only explains linkages through origin destination using the gravity modeling technique (Abler *et al*, 1992, Ayeni, 1979; 1992).

#### **2.5 The functioning model**

The Function Model unlike the conventional modeling technique did not consider the attractivity of a space in a mechanistic or unidirectional way rather it recognizes attractivity in terms of interaction between population (people), location activities and times. The most important aspect of this modeling technique is its multidirectionality as shown in the **Figure 4.**

A Model of Urban Infrastructural Planning

in a Traditional African City: A Case Study of Ilorin, Nigeria 67

The model groups the elemental decisions of the daily activity schedule into five tiers or hierarch: (a) daily activity pattern, (b) primary tour time of day, (c) primary destination and mode, (d) secondary tour time of day, and (e) secondary tour destination and mode (Fig.5).

Fig. 5. The daily activity schedule. Source: *Adapted from Timmermans (2000)*

The choice of daily activity pattern determines the number of secondary tours in the daily activity schedule. The choice of secondary tour time, destination and mode are conditioned upon the choice of a daily activity pattern. For daily activity patterns with 2 or more secondary tours, the conditional choice probabilities of the secondary tours are mutually independent, calculated from the same models. This approach, though represent a state-ofthe art in modeling, it is, however, deficient in the sense that it ignores time and space constraints across secondary tours, but simplifies the model structure. (Timmermans, 2000) Most of the works in developed countries especially in the United States have been in the field of transportation geography especially in the area of urban travel activity pattern and telecommuting in the city. A few of the most recent time-use studies have examined the impact of new Information Technology (IT) on people's everyday lives. For instance, Robinson *et al* (1997) compared the mass media use and social life of internet users, based on a 1998 survey of 3,993 adults in the U.S. They found no significant or consistent evidence of time displacement by mass media use of social activities as a result of internet or computer use. Another study by University of California, Los Angeles Center for Communication Policy (UCLA – CCP, 2000) involving 2096 households in the U.S found that internet use has considerable impact on a person's time use pattern and shopping behavior. The literature, although revealing about how people spend their time, have shown that studies do not explicitly incorporate the spatial dimension in their data collection procedure and analysis. The time displacement perspective therefore needs to be expanded to a space-time displacement perspective to be useful for understanding people's activity pattern in space time and the urban economy. The space- time displacement perspective suggests that there are distinctive geographical consequences associated with such time displacement Kwan

Fig. 3. Cycle of Inter-Element Interaction. Source: *Procos and Harvey, 1977*

Fig. 4. The daily activity schedule. Source: *Adapted from Timmermans* (2000).

Recent works on time-space activity unlike the earlier ones, have been largely concentrated on modeling time-space activity pattern (Zahavi, 1978; Lantrip, 1990; Axhausen and Garling 1991; Garling, Kwan and Golledge, 1993; Vander Knaap 1996; Golledge, Kwan and Garlin 1994; Bhat, 1997; Garling, Romanes and Vilhelmson, 1996; Timpf, 2002), computational process and the application of Geographical Information System (GIS) in modeling timespace activity (Hirsh Prashkea and Akiva, 1988; Kitamira, 1988; Axhausen, 1990; Kwan, 2000; Root and Recker 1990; Timmermams 2000; Golob and Mcklally, 1995; Ben-Akiva *et al* 1996; Kwan, 2003, 2004, 2005; LLoyd and Shuttle 2005). For instance Ben-Akiva *et al* (1996) applied the daily activity schedule model to data from the Boston metropolitan area, including a 24-hour household travel diary survey collected in 1991, as well as zonal and transportation system attributes from the same time period to produce the daily activity schedule model.

Fig. 3. Cycle of Inter-Element Interaction. Source: *Procos and Harvey, 1977*

Fig. 4. The daily activity schedule. Source: *Adapted from Timmermans* (2000).

schedule model.

Recent works on time-space activity unlike the earlier ones, have been largely concentrated on modeling time-space activity pattern (Zahavi, 1978; Lantrip, 1990; Axhausen and Garling 1991; Garling, Kwan and Golledge, 1993; Vander Knaap 1996; Golledge, Kwan and Garlin 1994; Bhat, 1997; Garling, Romanes and Vilhelmson, 1996; Timpf, 2002), computational process and the application of Geographical Information System (GIS) in modeling timespace activity (Hirsh Prashkea and Akiva, 1988; Kitamira, 1988; Axhausen, 1990; Kwan, 2000; Root and Recker 1990; Timmermams 2000; Golob and Mcklally, 1995; Ben-Akiva *et al* 1996; Kwan, 2003, 2004, 2005; LLoyd and Shuttle 2005). For instance Ben-Akiva *et al* (1996) applied the daily activity schedule model to data from the Boston metropolitan area, including a 24-hour household travel diary survey collected in 1991, as well as zonal and transportation system attributes from the same time period to produce the daily activity The model groups the elemental decisions of the daily activity schedule into five tiers or hierarch: (a) daily activity pattern, (b) primary tour time of day, (c) primary destination and mode, (d) secondary tour time of day, and (e) secondary tour destination and mode (Fig.5).

Fig. 5. The daily activity schedule. Source: *Adapted from Timmermans (2000)*

The choice of daily activity pattern determines the number of secondary tours in the daily activity schedule. The choice of secondary tour time, destination and mode are conditioned upon the choice of a daily activity pattern. For daily activity patterns with 2 or more secondary tours, the conditional choice probabilities of the secondary tours are mutually independent, calculated from the same models. This approach, though represent a state-ofthe art in modeling, it is, however, deficient in the sense that it ignores time and space constraints across secondary tours, but simplifies the model structure. (Timmermans, 2000)

Most of the works in developed countries especially in the United States have been in the field of transportation geography especially in the area of urban travel activity pattern and telecommuting in the city. A few of the most recent time-use studies have examined the impact of new Information Technology (IT) on people's everyday lives. For instance, Robinson *et al* (1997) compared the mass media use and social life of internet users, based on a 1998 survey of 3,993 adults in the U.S. They found no significant or consistent evidence of time displacement by mass media use of social activities as a result of internet or computer use. Another study by University of California, Los Angeles Center for Communication Policy (UCLA – CCP, 2000) involving 2096 households in the U.S found that internet use has considerable impact on a person's time use pattern and shopping behavior. The literature, although revealing about how people spend their time, have shown that studies do not explicitly incorporate the spatial dimension in their data collection procedure and analysis. The time displacement perspective therefore needs to be expanded to a space-time displacement perspective to be useful for understanding people's activity pattern in space time and the urban economy. The space- time displacement perspective suggests that there are distinctive geographical consequences associated with such time displacement Kwan

A Model of Urban Infrastructural Planning

energy consuming travel.

in a Traditional African City: A Case Study of Ilorin, Nigeria 69

Fig. 6. A Model of Urban Neighbourhood Activity Centers. Source: *O.M. Adedokun,* 2009.

Figure 6 shows the linkages among population, time and space and urban activities. Given a medium size urban centre with its population, there would emerge various types of urban activity located in different parts of the city. The location of these activities would in turn generate activity pattern with space and time (or spatio-temporal) dimensions. The activity pattern itself would generate human spatio-temporal behavior. In this paper, it is shown that human behaviour in space and time is fixed. The fixity in human spatial behaviour is shared between home and office/work place. The urban neighbourhood activity centre model is of the view, therefore, that in planning for a medium size urban centre in developing world, there is the need to adopt a strategy that would incorporate the behaviour of the people. Instead of strict land use zonation approach; facilities may be located closely to or around neighborhoods where people are fixed. In this case and as demonstrated, facilities and infrastructures should be located between homes and work places. Obviously, if there is a demonstrable linkage between two activities in time, it makes sense to locate the facilities housing them in the same space so as to eliminate time and

(2000) explored and implemented the extensibility diagram as an analytical tool within a three dimensional (3D) geographical information system (GIS). Using the navigational history of a person's web browser and data collected through personal interview, she developed a method that takes into account the multiple spatial scales and temporal complexities (simultaneity and disjuncture) involved in individual activities both in the physical and virtual worlds. Kwan (2002, 2003) also proposed a conceptual frame work of human cyberspatial behaviour based on time - geographic perspective, she argued that space-time constraint are still important even in the information age.

Although all these recent time geographical studies observed that the telecommuting did not induce a significant increase in non-work trips and activities, they also suggested that significant insights can be gained through examining the impact of new IT on people's space time constraint, and indicated the kind of data and methods useful for geographical studies of everyday life and the urban economy (Mokhtarian, 1990; Mokhtarian et al 1995, 1999; Kwan, 2001). But as noted by Kwan (2003, 2004 and 2005); Kwan, Murray, O'Kelly and Tiefelsdorf (2003), Weber and Kwan (2002, 2003) this kind of research (IT - Cyber spatial - Time geographic research) is still uncommon in geography to date in both advanced and developing countries. This is due to the fact that the required data are complex, costly and time consuming to collect, and there are a few established methods for analyzing these complex data.

In developing countries in general and Nigeria in particular, works on urban activity linkages through time and space are rare or non-existing. The few existing works in Nigeria like those of the American and European scholars focus mainly on interaction or movement within urban areas. For instance, Fadare (1986, 1989) and Ojo (1990) examined the factors affecting household trip generation in Ibadan while Aderamo (1990, 2000, 2004) examined the impact of road development on urban expansion in Ilorin, the spatial pattern of Intra-Urban trips and the role of transport factor in the structure and growth of Ilorin. Adeniji-Soji (1995) also analyzed the pattern of telecommuting and intra-city travel in Ibadan. Others such as Adagbasa (1995) and Bello (1995) studied intra-pattern urban movement in Benin City. One thing that is common to all these works is that they are all carried out within the framework of transportation geography without necessarily linking movement in space with the activity of the people. Thus a study was conducted to explore the missing link between people, their activities, locations of these activities and the times of the day when these activities take place with the aim of providing information that could be used to develop a model applicable to activity location and land use planning and management in a traditional African city in transition (Adedokun, 2008, 2009). From the data collected and analyzed in the study area, about 90 percent of the respondents had their activities fixed in space especially at home/place of work and about 89 percent also had their respondents are engaged in informal sector and are self-employed. These population characteristics and the activity pattern (fixed in space and time) generated mainly home and office/work place based activities which the people have adjusted and accustomed to. The implication of this is that certain spaces would be in greater (or lesser) demand at a particular time. This forms the basis for the proposed model for this study.

#### **3. A model of urban neighbourhood activity centres**

Based on the foregoing, we would like to construct a generalized model of land use planning and facility location in a traditional medium size urban center using Ilorin as a case study (see Figure6).

(2000) explored and implemented the extensibility diagram as an analytical tool within a three dimensional (3D) geographical information system (GIS). Using the navigational history of a person's web browser and data collected through personal interview, she developed a method that takes into account the multiple spatial scales and temporal complexities (simultaneity and disjuncture) involved in individual activities both in the physical and virtual worlds. Kwan (2002, 2003) also proposed a conceptual frame work of human cyberspatial behaviour based on time - geographic perspective, she argued that

Although all these recent time geographical studies observed that the telecommuting did not induce a significant increase in non-work trips and activities, they also suggested that significant insights can be gained through examining the impact of new IT on people's space time constraint, and indicated the kind of data and methods useful for geographical studies of everyday life and the urban economy (Mokhtarian, 1990; Mokhtarian et al 1995, 1999; Kwan, 2001). But as noted by Kwan (2003, 2004 and 2005); Kwan, Murray, O'Kelly and Tiefelsdorf (2003), Weber and Kwan (2002, 2003) this kind of research (IT - Cyber spatial - Time geographic research) is still uncommon in geography to date in both advanced and developing countries. This is due to the fact that the required data are complex, costly and time consuming

to collect, and there are a few established methods for analyzing these complex data.

In developing countries in general and Nigeria in particular, works on urban activity linkages through time and space are rare or non-existing. The few existing works in Nigeria like those of the American and European scholars focus mainly on interaction or movement within urban areas. For instance, Fadare (1986, 1989) and Ojo (1990) examined the factors affecting household trip generation in Ibadan while Aderamo (1990, 2000, 2004) examined the impact of road development on urban expansion in Ilorin, the spatial pattern of Intra-Urban trips and the role of transport factor in the structure and growth of Ilorin. Adeniji-Soji (1995) also analyzed the pattern of telecommuting and intra-city travel in Ibadan. Others such as Adagbasa (1995) and Bello (1995) studied intra-pattern urban movement in Benin City. One thing that is common to all these works is that they are all carried out within the framework of transportation geography without necessarily linking movement in space with the activity of the people. Thus a study was conducted to explore the missing link between people, their activities, locations of these activities and the times of the day when these activities take place with the aim of providing information that could be used to develop a model applicable to activity location and land use planning and management in a traditional African city in transition (Adedokun, 2008, 2009). From the data collected and analyzed in the study area, about 90 percent of the respondents had their activities fixed in space especially at home/place of work and about 89 percent also had their respondents are engaged in informal sector and are self-employed. These population characteristics and the activity pattern (fixed in space and time) generated mainly home and office/work place based activities which the people have adjusted and accustomed to. The implication of this is that certain spaces would be in greater (or lesser) demand at a particular time. This forms

Based on the foregoing, we would like to construct a generalized model of land use planning and facility location in a traditional medium size urban center using Ilorin as a

space-time constraint are still important even in the information age.

the basis for the proposed model for this study.

case study (see Figure6).

**3. A model of urban neighbourhood activity centres**

Fig. 6. A Model of Urban Neighbourhood Activity Centers. Source: *O.M. Adedokun,* 2009.

Figure 6 shows the linkages among population, time and space and urban activities. Given a medium size urban centre with its population, there would emerge various types of urban activity located in different parts of the city. The location of these activities would in turn generate activity pattern with space and time (or spatio-temporal) dimensions. The activity pattern itself would generate human spatio-temporal behavior. In this paper, it is shown that human behaviour in space and time is fixed. The fixity in human spatial behaviour is shared between home and office/work place. The urban neighbourhood activity centre model is of the view, therefore, that in planning for a medium size urban centre in developing world, there is the need to adopt a strategy that would incorporate the behaviour of the people. Instead of strict land use zonation approach; facilities may be located closely to or around neighborhoods where people are fixed. In this case and as demonstrated, facilities and infrastructures should be located between homes and work places. Obviously, if there is a demonstrable linkage between two activities in time, it makes sense to locate the facilities housing them in the same space so as to eliminate time and energy consuming travel.

A Model of Urban Infrastructural Planning

Volume 7, pp. 307 – 325.

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#### **4. Conclusion**

Over the years, studies on urban land use have been dominated by increasing mechanistic approach. These studies have not elucidated on a better understanding on dynamic model of urban infrastructural planning. We are not oblivious of the fact that oftentimes, models showcase the peculiarity of the context within which they are produced. Also, most of the earlier models were based on experiences of European and American cities that have little or direct bearing with orthogenetic or traditional African cities in transition. There is, therefore, the need for an active involvement of those who are directly impinged upon (the people) in issues relating to land use planning and activity location. Here lies the importance of Urban Neighbourhood Activity Centers Model. This model if implemented, especially in medium sized traditional or orthogenetic cities, where modern day town planning theory is alien and unenforceable, will help to achieve efficiency and optimality in land use planning and activity location. It will also help to achieve and ensure spatial and social justice, equity and equal opportunity for all environmental (urban land users) consumers.

Although this research used disaggregated data to determine house hold activities which were latter classified into three category of activities i.e. home based, office/work place and outdoor based activities respectively and the linkages between the populations these activities, their location in time and space. Future research frontiers could pick on any of the three groups (home, workplace and outdoor activities) and further disaggregate them to determine their locations, time spent on each and the level of linkages between the activities. Furthermore, future research could focus on larger cities that are not necessarily state capitals (even two adjacent or contiguous cities (Conurbations) and compare their spatiotemporal activity linkages for the purpose of achieving optimality in urban land use planning and management.

#### **5. References**

Over the years, studies on urban land use have been dominated by increasing mechanistic approach. These studies have not elucidated on a better understanding on dynamic model of urban infrastructural planning. We are not oblivious of the fact that oftentimes, models showcase the peculiarity of the context within which they are produced. Also, most of the earlier models were based on experiences of European and American cities that have little or direct bearing with orthogenetic or traditional African cities in transition. There is, therefore, the need for an active involvement of those who are directly impinged upon (the people) in issues relating to land use planning and activity location. Here lies the importance of Urban Neighbourhood Activity Centers Model. This model if implemented, especially in medium sized traditional or orthogenetic cities, where modern day town planning theory is alien and unenforceable, will help to achieve efficiency and optimality in land use planning and activity location. It will also help to achieve and ensure spatial and social justice, equity and

Although this research used disaggregated data to determine house hold activities which were latter classified into three category of activities i.e. home based, office/work place and outdoor based activities respectively and the linkages between the populations these activities, their location in time and space. Future research frontiers could pick on any of the three groups (home, workplace and outdoor activities) and further disaggregate them to determine their locations, time spent on each and the level of linkages between the activities. Furthermore, future research could focus on larger cities that are not necessarily state capitals (even two adjacent or contiguous cities (Conurbations) and compare their spatiotemporal activity linkages for the purpose of achieving optimality in urban land use

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**Part 2**

**Quantitative and Computer**

**Spatial Planning Methods**