3. 2 Making capital and running costs commensurate 49 3. 3 Optimum speed of a tanker 50 3. 4 The optimisation of the sag:span ratio of a suspension bridge 52 3. 5 Optimisation with more than one degree of freedom: heat exchanger 55 3. 6 Putting a price on heat-exchanger performance 57 3. 7 Variation of costs with application 59 3. 8 Further aspects of heat-exchanger optimisation 59 3. 9 An elementary programming problem 60 3. 10 Classification of optimisation problems and methods of solution 62 3. 11 The design of rotating discs: an optimum structure 66 3. 12 Hubdesign 73 3. 13 Summary 73 Questions 73 Answers 74 4 Insight 4. 1 Introduction 76 4. 2 Rough calculations 76 4. 3 Optimisation of compressor shaft diameter 83 4. 4 The optimum virtual shaft: a digression 85 4. 5 Useful measures and concepts 87 4. 6 Bounds and limits 91 4. 7 Scale effects 94 4. 8 Dimensional analysis and scaling 98 4. 9 Proportion 99 100 4. 10 Change of viewpoint Questions 102 104 Answers 5 Matching 5. 1 Matching: the windlass 107 5. 2 An extended example of matching: ship propulsion 107 5. 3 Matching within a single machine III 5. 4 Further aspects of ship propulsion 112 5. 5 Specific speeds: degrees of freedom 113 5. 6 Matching of a spring to its task liS 5. 7 Matching in thermodynamic processes 117 5. 8 Two old cases of matching 121 5.