61055638 Caterpillar Marine Analyst Hand Book

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Introduction . . . . . . . . . . . . . . . . . . . . . 1

Table of Contents . . . . . . . . . . . . . . . . . 3

Horsepower Formulas . . . . . . . . . . . . 11

Hull Speed vs Wave Pattern. . . . . . . . 25

Basic Propulsion Theory . . . . . . . . . . 27

Rules of Thumb for

Propeller selection . . . . . . . . . . . . . . . 59

Related Propeller Tables . . . . . . . . . . 61

Shallow Water Effect . . . . . . . . . . . . . 71

Ventilation Air Formulas . . . . . . . . . . . 75

Ventilation Duct Sizing . . . . . . . . . . . . 77


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Combustion Air Formulas. . . . . . . . . . 79

Combustion Air Duct Sizing . . . . . . . . 81

Exhaust System Sizing . . . . . . . . . . . 83

API°Gravity Formula . . . . . . . . . . . . . 89

Fuel System . . . . . . . . . . . . . . . . . . . . 93

Lubrication System. . . . . . . . . . . . . . 107

Cooling System . . . . . . . . . . . . . . . . 125

Corrosion . . . . . . . . . . . . . . . . . . . . . 149

Mounting and Alignment . . . . . . . . . 161

Vibration . . . . . . . . . . . . . . . . . . . . . . 169


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Sea Trial . . . . . . . . . . . . . . . . . . . . . . 175

Conversion Factors . . . . . . . . . . . . . 205

Physics Formulas . . . . . . . . . . . . . . . 223

Math Formulas . . . . . . . . . . . . . . . . . 225

Distance Tables . . . . . . . . . . . . . . . . 227

Geographic Range Tables . . . . . . . . 231

Glossary of Terms . . . . . . . . . . . . . . 233

Diagnostic Codes . . . . . . . . . . . . . . . 351


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CaterpillarEngine Division

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February 2001 - 4th Edition


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February 2001LEBV4830-03

This book contains a list of formulas and terms for useby qualified Caterpillar Marine Analyst. Many of the for-mulas are “Rules of Thumb” but they do provide guid-

ance in their respective areas. These formulas aregenerally accepted in the marine field. This book isintended as an aid to the Marine Analyst and NOT areplacement for professional ship design personnel.

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Table of Contents

Formula for Calculating Horsepower. . . . . . . . . . . . 11

Displacement Hull Calculation . . . . . . . . . . . . . . . . 12Horsepower Requirement forDisplacement Hulls . . . . . . . . . . . . . . . . . . . . . . . . . 13

Horsepower Requirement forSemi-Displacement Hulls . . . . . . . . . . . . . . . . . . . . 16

Horsepower Requirement for

Planing Hulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Hull Speed vs Wave Pattern . . . . . . . . . . . . . . . . . . 25

Basic Propulsion Theory . . . . . . . . . . . . . . . . . . . . . 27

Pitch Ratio by Vessel Application . . . . . . . . . . . . 29

Number of Propeller Blades . . . . . . . . . . . . . . . . 32

Propeller Tip Speed . . . . . . . . . . . . . . . . . . . . . . 33

Cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Reduction Gears. . . . . . . . . . . . . . . . . . . . . . . . . 35

Propeller Overhang. . . . . . . . . . . . . . . . . . . . . . . 36

Propeller Rotation . . . . . . . . . . . . . . . . . . . . . . . . 36

Multiple Propellers . . . . . . . . . . . . . . . . . . . . . . . 37

Propeller Pitch Correction . . . . . . . . . . . . . . . . . . . . 38Ducted Propellers . . . . . . . . . . . . . . . . . . . . . . . . 39

Propeller Formulas and Related Tables. . . . . . . . . . 40

Propeller Horsepower Curve Formula. . . . . . . . . 40

Displacement Speed Formula . . . . . . . . . . . . . . 40

Displacement-Length Ratio Formula . . . . . . . . . 41Maximum Speed – Length Ratio vs

DL Ratio Formula . . . . . . . . . . . . . . . . . . . . . . 41

Crouch’s Planing Speed Formula . . . . . . . . . . . . 41

Analysis Pitch Formula . . . . . . . . . . . . . . . . . . . . 42

Pitch Ratio Formula. . . . . . . . . . . . . . . . . . . . . . . 42

Theoretical Thrust Formula . . . . . . . . . . . . . . . . . 42Developed Area to Projected Area Formula . . . . 43

Mean Width Ratio Formula . . . . . . . . . . . . . . . . . 43

Disc Area Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Disc Area Ratio vs Mean Width Ratio . . . . . . . . . 44

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Developed Area vs Disc Area Ratio Formula . . . 44

Developed Area vs MeanWidth Ratio Formula. . . . . . . . . . . . . . . . . . . . 44

Developed Area for Any HubDiameter and MWR Formula . . . . . . . . . . . . . 45

Blade Thickness Fraction Formula . . . . . . . . . . . 45

Rake Ratio Formula. . . . . . . . . . . . . . . . . . . . . . . 46

Apparent Slip Formula . . . . . . . . . . . . . . . . . . . . 46

Slip vs Boat Speed Formula . . . . . . . . . . . . . . . . 47

DIA-HP-RPM Formula . . . . . . . . . . . . . . . . . . . . . 47

Optimum Pitch Ratio Formulas . . . . . . . . . . . . . . 47

Minimum Diameter Formula . . . . . . . . . . . . . . . . 48

Allowable Blade Loading Formula . . . . . . . . . . . 48

Actual Blade Loading Formula . . . . . . . . . . . . . . 49

Thrust Formula . . . . . . . . . . . . . . . . . . . . . . . . . . 49Approximate Bollard Pull Formula . . . . . . . . . . . 50

Taylor Wake Fraction Formula. . . . . . . . . . . . . . . 50

Wake Factor Formula . . . . . . . . . . . . . . . . . . . . . 50

Speed of Advance Formula . . . . . . . . . . . . . . . . 51

Wake Factor vs Block Coefficient Formulasfor vessels with a SL Ratio of under 2.5. . . . . 51

Block Coefficient Formula. . . . . . . . . . . . . . . . . . 51

Wake Factor vs Speed Formula . . . . . . . . . . . . . 52

Power Factor Formula. . . . . . . . . . . . . . . . . . . . . 52

Advance Coefficient Formula . . . . . . . . . . . . . . . 52

Displacement Speed withEfficiency Formula . . . . . . . . . . . . . . . . . . . . . 53

Planing Speed with Efficiency Formula . . . . . . . 54

Shaft Diameter Formula Solid TobinBronze Propeller Shafts . . . . . . . . . . . . . . . . . 54

Shaft Diameter Formula for

Monel 400 Propeller Shafts . . . . . . . . . . . . . . 55Shaft Bearing Spacing Formula. . . . . . . . . . . . . . . . 55

Propeller Weight Formulas (with 0.33Mean Width ratio and a hub diameterof 20%) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

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Three Bladed Propeller Weight . . . . . . . . . . . . . . . . 56

Four Bladed Propeller Weight . . . . . . . . . . . . . . . . . 56

Brake Horsepower vs LOA Formula – Tugs. . . . . . . 56

Towing Speed vs Brake Horsepower Formula . . . . 56D.W.T. of Barges Towed vs BHP Formulas . . . . . . . 57

Rules of Thumb for Propeller Selection . . . . . . . . . . 59

Related Propeller Tables . . . . . . . . . . . . . . . . . . . . . 61

Suggested Shaft Speeds . . . . . . . . . . . . . . . . . . 61

Minimum Tip Clearance . . . . . . . . . . . . . . . . . . . 61Shaft Material Characteristics. . . . . . . . . . . . . . . 62

Buttock Angle vs SL Ratio . . . . . . . . . . . . . . . . . 62

Crouch’s Formula Constants. . . . . . . . . . . . . . . . 62

Typical Slip Values . . . . . . . . . . . . . . . . . . . . . . . 63

Typical Slip Values – Twin Screw . . . . . . . . . . . . 63

Typical Properties of Various EngineeringMaterials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Onset of Shallow Water Effect . . . . . . . . . . . . . . . . . 71

Ventilation System Formulas . . . . . . . . . . . . . . . . . . 75

Ventilation Air Duct Sizing . . . . . . . . . . . . . . . . . . . . 77

Combustion Air Formulas . . . . . . . . . . . . . . . . . . . . 79Sizing Combustion Air Ducts. . . . . . . . . . . . . . . . . . 81

Exhaust System Formulas . . . . . . . . . . . . . . . . . . . . 83

Water Cooled Exhaust . . . . . . . . . . . . . . . . . . . . 83

Dry Exhaust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

API° Gravity Correction for Temperature . . . . . . . . . 89

Fuel System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Fuel Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Density and Specific Gravity . . . . . . . . . . . . . . . 98

Fuel API Correction Chart . . . . . . . . . . . . . . . . . . 99

Performance Analysis Rules of Thumb . . . . . . . . . 101

Fuel Temperature Correction Factors . . . . . . . . 101Fuel Density (API) Correction Factors. . . . . . . . 102

Intake Air Temperature CorrectionFactors for JWAC Engines . . . . . . . . . . . . . . 103

Inlet Air Pressure Correction Factors . . . . . . . . 104

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Power Calculations . . . . . . . . . . . . . . . . . . . . . . 105

Tolerances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Additional Formulas Used to DevelopMarine PAR Curves . . . . . . . . . . . . . . . . . . . 106

Lubrication System . . . . . . . . . . . . . . . . . . . . . . . . 107

Oil TBN vs Fuel Sulfur Content . . . . . . . . . . . . . 107

Additives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Anti-Wear Additive . . . . . . . . . . . . . . . . . . . . . . 109

API (American Petroleum Institute). . . . . . . . . . 109

API Engine Service Categories. . . . . . . . . . . . . 109

Ash Content . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

ASTM (American Society for Testingand Materials) . . . . . . . . . . . . . . . . . . . . . . . 112

Base Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Bid Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Blow-By. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

BMEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Borderline Pumping Temperature °C(ASTMD3829). . . . . . . . . . . . . . . . . . . . . . . . 113

Bulk Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Colloid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Color Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Crude Oil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Demerit Rating . . . . . . . . . . . . . . . . . . . . . . . . . 114

Detergent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Dispersant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Engine Deposits . . . . . . . . . . . . . . . . . . . . . . . . 115

EPA (Environmental Protection Agency). . . . . . 116

Fighting Grade Oil . . . . . . . . . . . . . . . . . . . . . . 116

Flashpoint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Merit Rating. . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Mineral Oil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

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OSHA (Occupational Safety and HealthAdministration) . . . . . . . . . . . . . . . . . . . . . . . 117

Oxidation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Oxidation Inhibitor. . . . . . . . . . . . . . . . . . . . . . . 117Oxidation Stability . . . . . . . . . . . . . . . . . . . . . . . 118

Pass – Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Pour Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Ring Land . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Ring Sticking. . . . . . . . . . . . . . . . . . . . . . . . . . . 119

SAE (Society of Automotive Engineers) . . . . . . 119

SAE Oil Viscosity Classification . . . . . . . . . . . . 119

Viscosity Grades for Engine Oils . . . . . . . . . . . 120

Single Grade Oil . . . . . . . . . . . . . . . . . . . . . . . . 120

Scote. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Shear Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 120Sludge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Soot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Synthetic Lubrication . . . . . . . . . . . . . . . . . . . . 121

Total Base Number (TBN) . . . . . . . . . . . . . . . . . 122

Toxicology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Viscosity Index (VI) . . . . . . . . . . . . . . . . . . . . . . 123

Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Cooling System . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

∆ T Flow Relationship . . . . . . . . . . . . . . . . . . . . 125

Piping Design – Flow Relationships . . . . . . . . . 125

Pipe Dimensions . . . . . . . . . . . . . . . . . . . . . . . . 126

Resistance of Valves and Fittings toFlow of Fluids . . . . . . . . . . . . . . . . . . . . . . . . 127

Flow Restriction of Fittings Expressedas Equivalent Feet of Straight Pipe . . . . . . . 128

Strainers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Typical Losses of Water in Pipe . . . . . . . . . . . . 129

Velocity vs Flow (Pipe) . . . . . . . . . . . . . . . . . . . 131

Velocity vs Flow (Tube) . . . . . . . . . . . . . . . . . . . 132

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Helpful Formulas for the Marine Analyst. . . . . . 133

Coolant Chemical and Physical Properties . . . 135

Boiling Point of Coolant at Varying

Antifreeze Concentrations . . . . . . . . . . . . . . 136Protection Temperatures for

Antifreeze Concentrations . . . . . . . . . . . . . . 136

Barometric Pressures and BoilingPoints of Water at Various Altitudes . . . . . . . 137

Caterpillar Diesel Engine Antifreeze

Protection Chart °F. . . . . . . . . . . . . . . . . . . . 138Caterpillar Diesel Engine Antifreeze

Protection Chart °C . . . . . . . . . . . . . . . . . . . 139

pH Scale for Coolant Mixture . . . . . . . . . . . . . . 140

Temperature Regulators . . . . . . . . . . . . . . . . . . 141

New Temperature Regulators . . . . . . . . . . . . . . 141

Diagnostic Tooling (Self-SealingProbe Adapters). . . . . . . . . . . . . . . . . . . . . . 143

Coolant Expansion Rates . . . . . . . . . . . . . . . . . 143

Densities of Liquids [at 60° F (16° C)] . . . . . . . 144

Supplemental Coolant Additive . . . . . . . . . . . . 145

Zinc Anode Summary . . . . . . . . . . . . . . . . . . . . 145Brass Plug Summary . . . . . . . . . . . . . . . . . . . . 147

Marine Growth. . . . . . . . . . . . . . . . . . . . . . . . . . 148

Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Galvanic Corrosion in Sea Water . . . . . . . . . . . 149

Dissimilar Metal Combinations to Avoid . . . . . . 149

The Protective Role of Zinc. . . . . . . . . . . . . . . . 150

Electro-chemical Series . . . . . . . . . . . . . . . . . . 151

Corrosion Rate of Various Metals inSea Water. . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Electrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Keel Cooler Performance CorrectionFactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

Keel Cooler Sizing Worksheet. . . . . . . . . . . . . . 158

Piping Symbol. . . . . . . . . . . . . . . . . . . . . . . . . . 159

Schedule of Piping . . . . . . . . . . . . . . . . . . . . . . 160

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Mounting and Alignment . . . . . . . . . . . . . . . . . . . . 161

Marine Engine Final AlignmentConditions . . . . . . . . . . . . . . . . . . . . . . . . . . 162

Marine Gear Output Flange Runout . . . . . . . . . 162Allowance for Expansion due to

Thermal Growth . . . . . . . . . . . . . . . . . . . . . . 163

Collision Blocks for Marine Engines . . . . . . . . . 163

Types of Misalignment . . . . . . . . . . . . . . . . . . . 164

Dial Indicator Quick Check. . . . . . . . . . . . . . . . 165

Required Foundation Depth forStationary Installations . . . . . . . . . . . . . . . . . 165

Pressure on Supporting Material . . . . . . . . . . . 166

General Torque Specifications. . . . . . . . . . . . . . . . 166

Torques for Bolts and Nuts withStandard Threads . . . . . . . . . . . . . . . . . . . . 166

Torques for Taperlock Studs . . . . . . . . . . . . . . . 167

Metric ISO Thread. . . . . . . . . . . . . . . . . . . . . . . 167

Vibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Vibration Summary . . . . . . . . . . . . . . . . . . . . . . 169

Order of Vibration . . . . . . . . . . . . . . . . . . . . . . . 171

Order of Firing Frequency. . . . . . . . . . . . . . . . . 171Data Interpretation . . . . . . . . . . . . . . . . . . . . . . 171

First Order Vibration Frequenciesfor Standard Rated Speeds . . . . . . . . . . . . . 172

Relationships of Sinusoidal Velocity,Acceleration, Displacement. . . . . . . . . . . . . 173

Sea Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Location Points . . . . . . . . . . . . . . . . . . . . . . . . . 175

Caterpillar Sea Trial Rules of Thumb. . . . . . . . . 178

3600 Performance Analysis Rulesof Thumb . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

Analysis of PAR Fuel Rate Curves . . . . . . . . . . . . . 184Sea Trial Formulas . . . . . . . . . . . . . . . . . . . . . . . . . 188

Aftercooler Water Inlet to InletManifold Temperature . . . . . . . . . . . . . . . . . 188

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Aftercooler Water Inlet to AftercoolerWater Outlet Temperature . . . . . . . . . . . . . . 189

Aftercooler Water Inlet Temperature to

Sea Water Temperature . . . . . . . . . . . . . . . . 189Jacket Water Circuit Analysis . . . . . . . . . . . . . . 190

Sea Water to Heat Exchanger/ Keel Cooler DT. . . . . . . . . . . . . . . . . . . . . . . 191

Determine the Maximum Sea WaterTemperature Vessel can Operate. . . . . . . . . 191

Ventilation System. . . . . . . . . . . . . . . . . . . . . . . 192Maximum Ambient Air Temperature that

the Vessel can Operate as Tested . . . . . . . . 193

Engine Lubrication System . . . . . . . . . . . . . . . . 193

900 Number Test Locations for 3600 In-lineSeparate Circuit Systems (Drawings) . . . . . . . . 194

900 Number Test Locations for 3600 In-lineCombined Circuit Systems (Drawings). . . . . . . 199

Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . 205

Volume Conversions . . . . . . . . . . . . . . . . . . . . . . . 219

Temperature Conversions . . . . . . . . . . . . . . . . . . . 221

Physics Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . 223

Math Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

Atlantic Distance Table . . . . . . . . . . . . . . . . . . . . . 227

Pacific Distance Table . . . . . . . . . . . . . . . . . . . . . . 229

Geographic Range Table . . . . . . . . . . . . . . . . . . . 231

Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . 233

Cat Marine/Industrial EngineDiagnostic Codes . . . . . . . . . . . . . . . . . . . . . . . 351

Caterpillar Policy Conversions. . . . . . . . . . . . . . . . 357

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

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Formula for Calculating Horsepower

2 πr TORQUE RPMHorsepower = ______________________

33000

This formula was established by James Watt in the1800’s and requires some known values:

Average horse walks at 2 1–2 MPH

Average horse pulls with a force of 150 pounds

1 mile = 5,280 feet

r = distance from center line of shaft, usually 1 foot

With this background, we will be able to establish theHorsepower formulas used today.

5,280 feet 2 1–2 MPH = 13,200 FEET per HOUR

13200 FT/HR____________ = 220 FEET per MINUTE60 Minutes

220 FT/MIN 150 POUNDS = 33,000 FT. LBS

per MINUTE

2πr = 6.2831853

33000__________ = 52526.2831853

Thus we get the familiar formula used today in calcu-lating Hp.

Torque RPMHp = _____________ or expressed another way as

5252

Hp

5252Torque = __________RPM

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Displacement Hull Calculation

If a vessel’s displacement is not known, it can be deter-

mined from the dimensions of the vessel, using the fol-lowing formula.

L B D CbW = ________________

M

Where:

W = The vessel’s displacement expressed in long tons

L = The length of the vessel, in feet, measured at theactual or designed load waterline (LWL)

B = The extreme width or beam of the vessel, in feet,at the designed load waterline.

D = The vessel’s molded draft, in feet, measured atits midship section, exclusive of appendages orprojections such as the keel.

Cb = The block coefficient for the vessel.

Light Cargo, Fishing Vessels

and Sailing yachts .40 – .55Heavy Cargo, Fishing and Tugs .50 – .65

River Tow Boats .55 – .70

Self-propelled Barges .70 – .90

Barges .85 – .90

M = The volume of water (cubic feet) per long ton

35 for sea water

36 for fresh water

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13

Horsepower Requirements forDisplacement Hulls

A displacement hull is define by having a taper at thebow, a taper at the stern, and a 1–4 beam buttock angleof 8 degrees or greater.

The speed which corresponds to SL = 1.34 is referredto as the displacement hull limiting speed. Attemptingto power a displacement hull above this speed will

cause the stern of the vessel to “drop” into its own bowwave trough, exposing the oncoming water to theunderside of the vessel and entraining air in the pro-peller. This will effectively cause the vessel to “climbuphill” and reduce the amount of power the propeller iscapable of absorbing. This occurs at an SL = 1.34 fora pure displacement vessel, and any attempt to powera displacement vessel in excess of this speed wouldbe considered a waste of fuel and money.

Now that the limiting speed of a displacement hull isdefined, we can predict the power requirements to pro-pel displacement hulls at different speeds.

The amount of power required to drive a displacementor a semi-displacement hull of a given weight at a givenspeed can be approximated by the relationship of theweight to the horsepower (Lbs/Hp). This is expressedas the formula:

10.665SL = ______3

Lbs____Hp

SL = Speed – Length Ratio

Hp = Horsepower Delivered to the Propeller

Lbs = Vessel Displacement in Pounds


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This formula can be rewritten as :

10.665______ 3 = Lbs/Hp

( SL )Due to the bow wave limitation discussed earlier, onlythe portion of the SL versus Lbs/Hp relationship below1.34 applies to displacement hulls. This implies that itwould not be appropriate to power a displacement hullwith more than 1 horsepower delivered to the propeller

for each 504 pounds of vessel displacement.

An example of how to apply this relationship will helpclear this up. Consider a pure displacement hull withthe following characteristics:

Waterline length = 200 feet

Vessel displacement = 440,000 pounds loaded

Desired speed = 18 knots

1–4 beam buttock angle = 9 degrees

With a 1–4 beam buttock angle of 9 degrees (greater than8°), it can be assumed that this vessel will be subjectto the speed limit of 1.34.

The next step is to see if the designed SL is within thelimits established for a displacement hull, using theformula

Speed 18SL = ______ SL = _____ SL = 1.27WL 200

Since the 1.27 calculated SL is below the limit of 1.34the speed of 18 knots for this vessel is attainable.

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The next step is to determine the Lbs/Hp relationship forthis boat using the design SL of 1.27. This is done usingthe following formula:

10.665 10.665______ 3 = Lbs/Hp ______ 3 = 592 Lbs/Hp( SL ) ( 1.27 )The power required to drive this vessel at 18 knotswould then be:

440000 LbsHp = ___________592 Lbs/Hp

Hp = 743

This horsepower requirement seems low, but it must beconsidered that this is the required horsepower deliv-ered to the propeller, and it does not account for lossesin the shafting, marine gear, and engine. It also doesnot allow for reserve horsepower to allow for addedresistance due to wind and waves, towing, draggingnets, power takeoffs, or other load increases, whichmay occur. In actuality, the installed horsepower of this

vessel may be higher than the 743 Hp requirement justcalculated.

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Horsepower Requirements forSemi-Displacement Hulls

Because of the way these hulls ride in the water, thecalculations of required horsepower uses a differentformula. A semi-displacement hull is defined as havinga point at the bow and tapers to a full beam at the mid-section and then partially tapers to a narrow section atits stern. A semi-displacement hull can be describedas a displacement hull with a portion of its after body

cut off, or a planing hull with a portion of a tapered afterbody added on. Semi-displacement hulls can beexpected to have a 1–4 beam buttock angle of between2° and 8°.

Semi-displacement vessels have displacement hullcharacteristics in that they are somewhat limited inattainable speed by the bow wave phenomenon.However, semi-displacement hulls also have someplaning hull characteristics, which allow them to par-tially “climb” or plane out of the water at higher speeds.This partial planing characteristic causes the bow wavelimitation to occur at higher speed length ratios. In gen-

eral, speed-length ratios fall between roughly 1.4 and2.9 for semi-displacement vessels. Effectively, semi-displacement hulls operate at higher speeds than dis-placement hulls because of their partial planingcharacteristics, yet are not as sensitive to weight addi-tion as a planing hull, due to their partial displacementhull characteristics. These combined characteristics

allow for relatively large cargo or passenger carryingcapacity at speeds higher than displacement vesselsof similar size.

To determine the power requirements for a semi-dis-placement hull, the SL versus Lbs/Hp relationship is uti-lized in the same manner as with displacement hulls.

The problem in applying this relationship to semi-dis-placement hulls, however, lies in the fact that the limit-ing speed-length ratios can vary between 1.4 and 2.9for different hulls. Before attempting a power require-ment calculation for a semi-displacement hull at a givenspeed, it is first necessary to determine the SL ratio limit

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17

for the vessel to ensure that no attempt is made topower the vessel to speeds higher than this limit.

The limiting SL ratio for a semi-displacement hull isdetermined by evaluating a factor referred to as theDisplacement Length Ratio (DL). The DL ratio can bedefined by using the following formula:

disp TDL = _________

(.01XWL)3

Where:

DL = Displacement-length ratio

disp T = displacement in long tons(1 long ton = 2240 pounds)

WL = Waterline length in feet

Once the DL ratio has been calculated for a semi-dis-placement hull, the SL to DL relationship can be appliedto determine the limiting SL ratio. This SL ratio will thendefine the maximum attainable speed of the semi-dis-placement hull. No attempt should be made to power

a vessel over this maximum attainable speed, as this isthe point where the bow wave limitation occurs an asemi-displacement hull.

The limiting SL can be defined using the followingformula:

8.26SL ratio = _____DL.311

Where:

SL ratio = Speed-length ratio

DL ratio = Displacement-length ratio8.26 = constant used by Caterpillar

for this calculation


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The following example will help explain how to applythe formulas for calculating the horsepower requiredfor a semi-displacement hull.

Let’s use the following for boat characteristics:

WL = 62 feet

1–4 beam buttock angle = 3°

Displacement tons = 44 Long tons(98,560 pounds)

Designed speed = 11.5 knots

Beam width = 18 feet at mid-section,tapering to 15 feet at thestern.

Based on this information (3° and slight taper) we canrecognize a semi-displacement hull. Since this is asemi-displacement vessel and the DL ratio applies, theDL ratio must first be calculated in order to determinethe limiting SL ratio for this vessel. The DL ratio is cal-culated in the following formula:

44DL = __________(.01 62)3

DL = 184.6 ≈ 185

8.26SL = _______

(185).311

SL = 1.628 ≈ 1.63

Any speed used in predicting a power requirement forthis vessel must correspond to an SL less than 1.63.1.63 SL ratio corresponds to the maximum possible

speed of this vessel due to bow wave limitation.

Since the maximum SL ratio is 1.63 has been calcu-lated the next step is to determine the power requiredto drive the vessel 11.5 knots. As a check before pro-ceeding, the SL ratio corresponding to the design

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19

speed of the boat should be calculated to ensure thatit is less than the maximum attainable SL of 1.63.

11.5SL = _____62

SL = 1.46

Since 1.46 is less than 1.63, it is appropriate to try topower this vessel for 11.5 knots. If the SL had been

greater than the 1.63 maximum attainable SL then thedesign speed of the vessel would have to be reducedbefore attempting a power prediction.

Know that we have the design SL (1.46) we can go tothe formula used in the displacement hull problem. Thatformula was:

10.665 3LB/Hp = ______( SL )

10.665 3LB/Hp = ______( 1.46 )LB/Hp = 389.8 ≈ 390

98560 Lbs for vesselHP = ___________________

390 LB/Hp

Hp = 252.7≈

253 Hp

So to power this vessel to the 11.5 knots design speedit would need 253 Hp to the propeller. This is only for themovement of the vessel through the water and doesnot take into account auxiliary driven equipment, roughseas, or strong currents. There for the actual Hp of the

engine in the boat maybe larger than this calculation,due to the reserve Hp requirements.


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Horsepower Requirementsfor Planing Hulls

A planing hull is a hull of a form which allows it to climbup on a full plane at high speeds. When up on a fullplane, the reduced draft of the vessel causes the bowwave to become very small, and they do not limit thespeed of the boat as with displacement and semi-dis-placement hulls. Because of the reduced draft and lackof a bow wave limitation while up on plane, planing hulls

can achieve very high speeds. However, their perfor-mance is very sensitive to the addition of weight to theboat.

A planing hull begins with a point at its bow, and tapersto full beam at its midsection, then continues aft withno taper or at most a slight taper. The planing hull alsohas a 1–4 beam buttock angle 2° or less.

Very few accurate methods exist for determining powerrequirements and speed predictions on full planinghulls. Often times, planing hulls are equipped withengines based on past experience and tested during

sea trials to determine their level of performance. Onesimple method in existence for estimating planing hullspeed potential is referred to as Crouch’s Planing Speed Formula . The formula is:

CSpeed = _______

Lbs/Hp

Speed = Boat speed in knots

C = Coefficient Defining Hull Speed

Lbs = Vessel Weight in Pounds

Hp = Horsepower Delivered to the Propeller

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This formula develops a power to speed relationshipfor planing hulls, and experimentation has determinedwhich coefficients should be utilized to obtain accept-able results. The typical coefficients used at Caterpillarare:

150 = average runabouts, cruisers, passenger vessels

190 = high speed runabouts, light high-speed cruisers

210 = race boats

The following example will help explain how all of thisworks.

Let’s use a boat with a displacement of 14,000 pounds.The boat has a narrow beam, deep vee planing hullpowered by two (2) 435 Hp diesels. The boat is equippedwith performance propellers and low drag stern drives,so we can consider the boat a race type. It will there-fore have a “C” coefficient of 210.

First let’s take the Hp of the engines 435 2 = 870.Then we must take into account the reduction gear effi-ciency, typically 3%. 870 Hp .97 = 844 Hp available

Lbsto the propellers. Then we determine the ____ byHp

dividing the boat displacement by the horsepower14000 Lbs

available. In our case Lbs/Hp = _________ or844 Hp

Lbs/Hp = 16.59. Now that we have our Lbs/Hp we cancalculate the speed of the boat using Crouch’s PlaningSpeed Formula.

210Speed = _______ Speed = 51.56 Knots

16.59

Let’s say this customer wants 60 knots. We can calculate

the needed Hp by using the information from the pre-vious formula and working out the answer. The formula

Cfor this would be ______ = X. Then Lbs/ Hp = X2

Speed


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Putting the data in from the previous formula we get thefollowing:

210____ = 3.50

2

60

Lbs/Hp = 12.25

Since the weight of the boat is 14,000 pounds, we candivide the weight of the boat by the Lbs/Hp ratio of

12.25 to get the Hp needed to operate the vessel at the60 knot speed.

14000 Pounds_____________ = 1,143 Hp required.12.25 Lbs/Hp

Demand Horsepower, for a hull of the propulsion sys-tem on a engine is in a cubic relationship with the speedof the boat.

Example: A vessel is cruising at 20 knots. The demandhorsepower on the engine is 500 Hp. The captain nowwants to go 25 knots. How much horsepower will it take?

25 kts______ = 1.25 1.253 = 1.95312520 kts

500 Hp 1.953125 = 976.5625 Hp

Boat Speed(1) = 20 Knts

Act. Hp = 500 Hp New Hp = 977 Hp

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23

What is the new boat speed?

Speed2 = 3

New Hp_______ Boat Speed(1)

( Act Hp )Speed2 = 3

977 Hp_______

20 Knts = 3( 500 Hp )

1.250 20 = 25 Knts

1.954 20


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Hull Speed vs Wave Pattern

Miles per Hour 1.15 = Knots

Knots 101.3 = Feet per Minute

Miles per Hour 88 = Feet per Minute

VSPEED LENGTH RATIO (SLR) = ______

LWL

Where:

V = Vessel Speed

LWL = Loaded waterline length

The generally accepted SLR limits are as follows:

Displacement type hulls = SLR 1.34

Semi-displacement type hulls = SLR 2.3 – 2.5

Planing hulls = No specific highlimit, but not goodbelow a SLR of 2.0

The maximum vessel speed can be calculated usingthe following formula:

V = SLR LWL

The maximum vessel speed can also be estimated bywatching the wave action along a displacement hulltype of the vessel. When the crest to crest distance ofthe bow wave is equal to the LWL of the vessel, the hullis at its optimum speed. If the bow wave crest to crestdistance is equal to 1–2 the LWL then the vessel is atapproximately 1–2 the optimum hull speed.

Economical speed for displacement type vessels is inthe SLR range of 1.0 to 1.2. The crest to crest distancefor an SLR of 1.0 is (.56)(LWL). The crest to crest dis-tance for an SLR of 1.2 is (.8)(LWL)

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Basic Propulsion Theory

The essence of marine propulsion is the conversion of

engine power into thrust through some type of propul-sion device. Because of its simplicity and efficiency,the screw propeller – basically an axial flow pump – hasbecome the most widely used propulsive device.

Propellers

The ability of a propeller to move a vessel forward,through the water, depends upon several factors:

1. The rotational speed of the propeller, which corre-sponds to the propeller shaft RPM;

2. The angle or pitch of the propeller blades;

3. The diameter and blade area.

These factors, in combination impose a thrust force onthe propeller shaft. This thrust is transmitted through theshaft to the thrust bearing, the principle point wherethe forces generated by the rotating propeller act uponthe hull, and cause forward motion.

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FIGURE 1

Figure 1 shows a typical 3-bladed propeller. To more

intelligently understand the operation of a screw pro-peller, it is necessary to define the parts of a propeller:

• The blade does the work; it pulls water. Naturally, thewider the blade face, the more water it can pull. Themore water that can be pulled, the stronger the thruston the vessel and therefore, a greater amount of work

can be done.• Propeller diameter is the diameter of the circle described

by the tips of the rotating propeller blades.

Pitch Angle

Boss

Hub

Blade

Tip

Blade

KeywayBore

Diameter

Hub

HubDiameter

Right Hand

Left Hand

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• Blade Angle is the angle the blade makes in relationto the center line of the hub. It is normally expressedas the distance, in inches. Pitch is the distance theblade would advance in one revolution, if it were ascrew working in a solid substance.

An important concept in understanding propellers isthe pitch ratio. The pitch ratio expresses the relationbetween the pitch and the diameter of the propeller;often it is referred to as the pitch/diameter ratio. It isobtained by dividing the pitch by the diameter. For

example, if a propeller is 60 inches in diameter and has42 inches of pitch (written as 60" 42") then the pitchratio is 42/60 = 0.70.

A general guide for the selection of approximate pitchratio values is shown, by vessel application, in Figure 2.

PITCH RATIO BY VESSEL APPLICATION

Deep water tug boat .50 – .55

River towboat .55 – .60

Heavy round bottom work boat .60 – .70

Medium wt. round bottom work boat .80 – .90

Planing hull .90 – 1.2

FIGURE 2

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The propeller may be viewed as an axial pump that isdelivering a stream of water aft of the vessel. It is thisstream of water, equivalent in size to the diameter ofthe propeller, that is the power that provides thrust tomove the vessel through the water. However, to pro-duce thrust, the propeller must accelerate the mass ofwater it pulls against. In so doing, a portion of the pitchadvance is lost to the work of accelerating the watermass. This is known as propeller slip; Figure 3 illus-trates this concept.

FIGURE 3

A propeller with a fixed pitch theoretically has a pitchvelocity or linear speed it would travel in the absenceof slip. However, because of the work needed to accel-erate a mass of water, slip manifests itself as the dif-ference between the pitch velocity and the velocity ofthe propeller through the vessel’s wake or speed ofadvance.

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As a vessel moves through the water, hull resistance,wave formation and converging water at the stern havea tendency to follow the hull. This results in a movementof water under the stern in a forward direction knownas wake. The added factor of wake reduces slip to whatis known as apparent slip. It also adds to the speed ofadvance to produce the actual vessel speed. It is obvi-ous from this that propellers function in a very complexmanner. There are many factors to be considered whenselecting a propeller. The point to realize is that there is

no formula that will automatically provide the ideal pro-peller size for a given vessel and application. This canonly be approximated to various degrees of accuracy.The only true test is trial and error under actual operatingconditions. Remember, all propellers are a compromise.The general practice is to use the largest diameter pro-peller turning at the best speed for the vessel’s appli-

cation within practical limits. These limitations are:1. The size of the aperture in which the propeller is to

be installed.

2. The application or type of work the vessel will bedoing – towboat, crew boat, pleasure craft, and soforth.

3. Excessive shaft installation angles that may be re-quired when using large diameter propellers.

4. The size of shafting that can be accommodated bythe structural members of the hull where the shaftpasses through.

5. Comparative weight of propellers, shafts and marinegears with respect to the size of the vessel.

6. The size of marine gears which the hull can accom-modate without causing an inordinate degree ofshaft angularity.

7. The vessel’s inherent ability to absorb the high torque

that results from the use of large slow turning propellers.

8. Comparing the cost of using large diameter propellersagainst any increases in efficiency or performance.

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Number Of Propeller Blades

In theory, the propeller with the smallest number ofblades (i.e. two) is the most efficient. However, in mostcases, diameter and technical limitations necessitatethe use of a greater number of blades.

Three-bladed propellers are more efficient over a widerrange of applications than any other propeller. Four andsometimes five-bladed propellers are used in cases

where objectionable vibrations develop when using athree-bladed propeller.

Four-bladed propellers are often used to increase bladearea on tow boats operating with limited draft. They arealso used on wooden vessels where deadwood aheadof the propeller restricts water flow. However, two blades

passing deadwood at the same time can cause objec-tionable hull vibration.

All other conditions being equal, the efficiency of a four-blade propeller is approximately 96% that of a three-blade propeller having the same pitch ratio and bladesof the same proportion and shape. A “rule of thumb”

method for estimating four-blade propeller requirementsis to select a proper three-blade propeller from pro-peller selection charts, then multiply pitch for the three-blade propeller by .914. Maximum diameter of afour-blade propeller should not exceed 94% of the rec-ommended three-blade propeller’s diameter. Therefore,we multiply diameter by .94 to obtain the diameter of afour-blade propeller.

For example, if a three-blade recommendation is:48 34

Multiply pitch (34") by .914 = 31"

Multiply diameter (48") by .94 = 45"

Four-blade recommendation 45" 31"

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As a word of caution, remember that this is a generalrule...for estimating only. Due to the wide variation inblade area and contours from different propeller man-ufacturers, consult your particular manufacturer beforefinal specifications are decided upon.

A “Rule of the Thumb” for all propeller selection is:

“Towboats – big wheel, small pitch”

“Speedboats – little wheel, big pitch”

All other applications can be shaded between thesetwo statements of extremes.

Propeller Tip Speed

Tip speed, as the name implies, is the speed at whichthe tips of a rotating propeller travel in miles per hour(MPH). The greater the tip speed, the more power con-sumed in pure turning. As an example, a 30 inch propellerwith a tip speed of 60 MPH absorbs approximately 12horsepower in pure turning effort. This is a net horse-power loss because it contributes nothing to the for-

ward thrust generated by the propeller.

The following formula can be used to calculate tipspeed:

D SHAFT RPM 60 πT = _________________________

12 5280

Where:

T = Tip speed in MPH

D = Propeller diameter in inches

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Cavitation

When propeller RPM is increased to a point where suc-tion ahead of the propeller reduces the water pressurebelow its vapor pressure, vapor pockets form, inter-rupting the solid flow of water to the propeller. This con-dition is known as cavitation.

One of the more common causes of cavitation is exces-sive tip speed, a propeller turning too fast for water to

follow the blade contour. Cavitation can usually beexpected to occur at propeller tip speeds exceeding130 MPH. Cavitation results in a loss of thrust and dam-aging erosion of the propeller blades.

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Reduction Gears

The reduction gear enables the propulsion engine andpropeller to be matched so they both operate at theirmost efficient speeds.

The proper selection of the reduction gear ratio is animportant decision in preparing a marine propulsionsystem. There is a range of commercially availablereduction ratios that can help assure optimum vessel

performance under a given set of operating conditions.

It is difficult to discuss the selection of reduction gearratios without mentioning some of the other factors thatcan influence the selection. The major influencing fac-tors are:

• Expected vessel speed • Type of vessel

• Vessel duty cycle • Pitch Ratio

• Propeller tip speed • Engine horsepower

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Propeller Overhang

The maximum distance from the stern bearing to thepropeller should be limited to no more than one shaftdiameter. Propeller shafts are apt to vibrate and pro-duce a whip action if these limits are exceeded. Thiscondition is greatly accelerated when a propeller is outof balance due to faulty machining or damage.

Propeller Rotation

Propeller rotation is determined from behind the ves-sel, facing forward. The starboard side is on the rightand the port side on the left. Rotation of the propeller isdetermined by the direction of the wheel when the ves-sel is in forward motion. Thus, a clockwise rotation

would describe a right-hand propeller and a counter-clockwise rotation would be a left-hand propeller.

Right-hand propellers are most frequently used in sin-gle screw installations. Twin screw vessels in the U.S.are normally equipped with outboard turning wheels.However, there are some installations where inboard

turning wheels will be found. A rotating propeller tendsto drift sideways in the direction of the rotation. In a sin-gle screw vessel this can be partially offset by thedesign of the sternpost and the rudder. In a twin screwvessel this can be completely eliminated by usingcounter-rotating propellers. Although the question ofinboard and outboard rotating propellers has been

debated many times, authorities on the subject agreethat there are no adverse effects on maneuverabilitywith either rotation. In fact, there are those who feel thata gain in maneuverability is obtained with outboardrotating propellers. One point in favor of inboard rota-tion is a decreased tendency for the propellers to pick-up debris off the bottom in shallow water.

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Multiple Propellers

The most efficient method of propelling a vessel is bythe use of a single screw. However, there are other fac-tors which, when taken into consideration, make theuse of a single propeller impossible. If a vessel has tooperate in shallow water, the diameter of the propelleris limited. Therefore, it may be necessary to install twoand sometimes three propellers to permit a proper pitchratio for efficient propulsion.

Another condition requiring multiple propellers is encoun-tered when higher speed yachts need more horse-power than a single engine can develop and still beaccommodated in the engine space. As a general ruleto follow for calculations in this text, the total SHP of allengines is used when making estimated speed calcu-

lations. For calculating propeller size, SHP of each indi-vidual engine is used.

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Propeller Pitch Correction

An overpitched propeller will overload the engine. To

permit the engine to reach its Full power and speed theload must be removed. The load must be reduced byamount proportional to the engine RPM ratio. This canbe defined by the following formula:

RPM1LF = ______

RPM2

Where:

LF = % of Load

RPM1 = The engine RPM while overloaded “ What youhave.”

RPM2 = The anticipated engine RPM “What you wantto have.”

EXAMPLE FORMULA

The M/V Cat has an engine that produces Full powerat 1800 engine RPM. While being tested the engine

would only turn to 1750 RPM. Applying the above for-mula we get the following equation:

1750LF = _____

1800

LF = .97 100

LF = 97%

This means to get the engine to turn the correct RPM wewould have to reduce the load by 3%. If the overloadis due to an overpitched propeller then the amount ofpitch to be taken out of the current propeller can be

determined using the following formula:

RPM1Pr = Pp ______

RPM2

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39

Where:

Pr = Propeller pitch required

Pp = Present propeller pitch

RPM1 = The engine RPM while overloaded “ What youhave.”

RPM2 = The anticipated engine RPM “What you wantto have.”

Ducted Propellers

Ducted propellers are best used on vessels such astrawlers, tugs, and towboats with towing speeds of 3-10knots. Ducted propellers should not be used on vesselswith relative high speeds.

To help assist in the selection of a ducted propeller, youcan perform the following calculation. If the resultantBp is


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Propeller Formulasand Related Tables

(5252 Hp) Hp = HorsepowerTorque = ____________Rpm Rpm = Revolutions per minute

Propeller Horsepower Curve Formula

PHp = Csm Rpmn

Csm = sum matching constant

n = exponent from 2.2 to 3.0, with 2.7 being usedfor average boats

Rpm = Revolutions per minute

Displacement Speed Formula

10.665SL Ratio = ______

3

LB____SHP

Where:

SL Ratio = Speed-Length Ratio

and

Knts.SL Ratio = _____WL

Knts = Speed in knots = Boat speed or V

SHP = Shaft Horsepower at propeller

LB = Displacement in pounds


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41

Displacement – Length Ratio Formula

disp TDL Ratio = ___________

(00.01XWL)3

Where:

disp T = Displacement in long tons of 2,240 pounds,mt = 1.016 long tons


Maximum Speed-Length Ratiovs DL Ratio Formula

8.26SL Ratio = ______

3.215DL Ratio

Where:

SL = Speed-length ratio

DL = Displacement-length ratio

Crouch’s Planing Speed Formula

CKnts = ________

Lb/SHP

Where:Knts = Speed in knots = Boat Speed = V

C = Constant chosen for the type of vessel beingconsidered


SHP = Horsepower at the propeller shaft

The speed predicted by this formula assumes a pro-peller has been selected that gives between 50%and 60% efficiency, with 55% a good average.


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Analysis Pitch Formula

101.33VaP0 =________

N0

Where:

Va = Speed in knots through wake at zero thrust

N0 = Shaft Rpm at zero thrust

Pitch Ratio Formula

Pitch Ratio = P/D

Where:

P = PitchD = Diameter

Theoretical Thrust Formula

Thrust = Force = F

WF = MA or F = __ (V0 – V1)

g

Where:

W = Weight in pounds the column of water acceler-ated astern by the propeller

g = the acceleration of gravity, 32.2 ft/sec.

V0 = velocity of water before entering the propeller infeet per second

V1 = velocity of water after leaving propeller in feet per

second

M = Mass in slugs

A = Acceleration in feet per second squared

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Developed Area to Projected Area Formula

Ap___ = 1.0125 – (0.1 PR) – (0.0625 PR2)

Ad

Where:

Ap___ = Approximate ratio of projectedarea to developed areaAd

PR = Pitch ratio of propeller

Mean-Width Ratio Formula

Mean-Width Ratio = MWR

Average Blade Width,MWR = ____________________ orD

Expanded Area of One BladeMWR = ___________________________ ÷ D

Blade Height from Root to Tip

Where:

D = Diameter

Disc-Area Ratio

πD2Disc Area = ____ or 0.7854D2

4

Disc-Area Ratio = DAR

Expanded Area of all BladesDAR = __________________________

Disc Area

Where:

D = Diameter

π ≈ 3.1412


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Disc-Area Ratio vs Mean-Width Ratio

DAR = Number of Blades 0.51 MWR

or

DARMWR = ________________________

Number of Blades 0.51

Where:

DAR = Disc-area ratio

MWR = Mean-width Ratio

Note:These ratios assume a hub that is 20% of over-all diameter, which is very close to average. Smallpropellers for pleasure craft may have slightly

smaller hubs, while heavy, workboat propellers, par-ticularly controllable-pitch propellers, may haveslightly larger hubs.

Developed Area vs Disc-Area Ratio Formula

D 2Ad = π __ DAR(2 )Developed Area vs Mean-Width Ratio Formula

D 2

Ad = π __ MWR 0.51 Number of Blades(2 )where for both the above formulas:

Ad = Developed Area

D = Diameter

DAR = Disc-area ratio

MWR = Mean-width ratio

π ≈ 3.1412


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Developed Area for Any Hub Diameterand MWR Formula

DAd = MWR D (1 – Hub%) __ Number ofBlades2

or

D2Ad = MWR __ (1 – Hub%) Number of Blades

2

Where:

Ad = Developed Area

MWR = Mean-width ratio

D = Diameter

Hub % = Maximum hub diameter divided by overalldiameter, D

Blade-Thickness Fraction Formula

t0BTF = __D

Where:

BTF = Blade-Thickness Fraction

D = Diameter

t0 = Maximum Blade Thickness as Extended to ShaftCenterline

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Rake Ratio Formula___BO

Rake Ratio = ___

D

Where:___BO = Distance between tip of blade projected down to

the shaft centerline and face of blade extendeddown to shaft centerline

D = Diameter

Apparent Slip Formula

P__ RPM – (Knts 101.3)(12 )

Slip A =__________________________

P__ RPM(12 )

Which can be restated as:

Knts 1215.6

P =_________________RPM (1 – Slip A)

Where:

Slip A = Apparent Slip

P = Propeller face pitch in inches

Knts = Boat speed through the water or V in Knots

RPM = Revolutions per minute of the propeller

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Slip vs Boat Speed Formula

1.4Slip = _______

Knts0.057

Where:

Knts = Boat speed in knots

DIA-HP-RPM Formula

632.7 SHP0.2D = ______________

RPM0.6

Where:


SHP = Shaft Horsepower at the propeller

RPM = Shaft RPM at the propeller

Optimum Pitch Ratio Formulas

Average Pitch Ratio = 0.46 Knts0.26

Maximum Pitch Ratio = 0.52 Knts0.28

Minimum Pitch Ratio = 0.39 Knts0.23

These formulas have been found to check well witha wide variety of vessels.

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Minimum Diameter Formula

Dmin = 4.07 (BWL Hd)0.5

Dmin = Minimum acceptable propeller diameter in inches

BWL = Beam on the waterline in feet

Hd = Draft of hull from the waterline down (exclud-ing keel,skeg or deadwood) in feet

(Hull draft is the depth of the hull body to the fair-body line, rabbet, or the hull’s intersection with thetop of the keel. It thus excludes keel and/or skeg.)

Dmin for twin screws = 0.8 Dmin

Dmin for triple screws = 0.65 Dmin

Allowable Blade Loading Formula

PSI = 1.9 Va0.5 Ft0.08

Where:

PSI = Pressure, in pounds per square inch, at whichcavitation is likely to begin

Va = The speed of the water at the propeller in knots

Ft = The depth of immersion of the propeller shaftcenterline, during operation, in feet

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Actual Blade Loading Formula

326 SHP ePSI = _______________

Va

Ad

Where:

PSI = Blade loading in pounds per square inches


e = Propeller efficiency in open water

Va = Speed of water at the propeller, in knots

Ad = Developed area of propeller blades, in squareinches

Thrust Formula

326 SHP eTA = _______________

Va

Where:

T = Thrust


e = Propeller efficiency

Va = Speed of water at the propeller, in knots

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Approximate Bollard Pull Formula

DTs = 62.72 (SHP

__ )0.67

12

Ts = Static thrust or bollard pull, in pounds



This formula can also be expressed as:

Ts ton = 0.028 (SHP Dft)0.67

Ts ton = Thrust in long tons of 2240 pounds

SHP = Shaft Horsepower

Dft = Propeller diameter, in feet

Taylor Wake Fraction Formula

V – VaWt = ______V

or

Va = V (1 – Wt)

Where:

Wt = Taylor wake fractionV = Boat speed through the water

Va = Speed of the water at the propeller

Wake Factor Formula

Wf = 1 – Wt

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Speed of Advance Formula

Va = V Wf

Where:

V = Boat Speed

Wf = Wake Factor

Wt = Taylor Wake Fraction

Wake Factor vs Block Coefficient Formulasfor vessels with a SL Ratio of under 2.5

Single Screw Wf = 1.11 – (0.6 Cb)

Twin Screw Wf = 10.6 – (0.4 Cb)

Where:

Wf = Wake factor (percent of V “seen” by the propeller

Cb = Block coefficient of the hull.

Block Coefficient Formula

DisplacementCb = _____________________________

WL BWL Hd 64 Lb/cu.ft.

Where:

Displacement = Vessel displacement, in pounds

WL = Waterline length, in feet

BWL = Waterline beam, in feet

Hd = Hull draft, excluding keel, skeg ordeadwood, in feet

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Wake Factor vs Speed Formula

Wf = 0.83 Knts0.047

Where:

Wf = Wake Factor

Knts = Speed in knots

Power Factor Formula

(SHP)0.5 NBp = ____________

Va2.5

Where:

Bp = Power Factor


N = Number of shaft revolutions

Va = Speed of advance of the propeller through thewake

Advance Coefficient Formula

N Dft = _______Va

or

N D = _______

12 Va

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This may also be restated as:

= Va 12D = ___________ ,

N

Where:

= Advance coefficient

N = Shaft RPM

Dft = Propeller diameter in feet


Va = Speed of advance of the propeller through thewake

Displacement Speed with Efficiency Formula

10.665SL Ratio = ______

3

LB____SHP

Where:

SL Ratio = Speed-length ratio


SHP = Shaft horsepower at the propeller

= Propeller efficiency

If the speed in knots is already known, we can multiplythe speed directly by

3

____0.55

3

____0.55

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Planing Speed With Efficiency Formula

CKnts = ______

LB____SHP

Where:

Knts = Boat speed in knots


SHP = Shaft horsepower at the propeller

= Propeller efficiency

If the speed in knots is already known, we can multiplythe speed directly by

3

____0.55

Shaft Diameter Formula Solid TobinBronze Propeller Shafts

3 321000 SHP SF

Ds = ___________________St RPM

Ds = Shaft Diameter, in inches

SHP = Shaft Horsepower

SF = Safety factor (3 for yachts and light commercialcraft, 5 to 8 for heavy commercial craft and rac-ing boats)

St = Yield strength in torsional shear, in PSI

RPM = Revolutions per minute of propeller shaft

3

____

0.55

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67/370

Propeller Weight Formulas (with 0.33 meanwidth ratio and a hub diameter of 20%)

Three-Bladed Propeller Weight

Wgt = 0.00241 D3.05

Four-Bladed Propeller Weight

Wgt = 0.00323 D3.05

Where:

Wgt = Weight of propeller in pounds

D = Diameter of propeller in inches

Brake Horsepower vs LOA Formula – Tugs

LOA4.15BHP = 100 + _______(111000)

Where:BHP = Maximum brake horsepower of engine

LOA = Length overall of the tug at waterline, in feet

Towing Speed vs Brake Horsepower Formula

Knts = 1.43 BHP0.21

Where:

Knts = Average speed in knots during average tow

BHP = Maximum brake horsepower of engine

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D.W.T. of Barges Towed vs BHP Formulas

Low D.W.T. = (1.32 BHP) – 255.25

Avg D.W.T. = (3.43 BHP) – 599.18

High D.W.T. = (5.57 BHP) – 943.10

Where:

DWT = Deadweight tons of barges towed

BHP = Maximum brake horsepower of engine

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Rules of Thumb forPropeller Selection

1. One inch in diameter absorbs the torque of two to three inches of pitch. This is a good rough guide.Both pitch and diameter absorb the torque gener-ated by the engine. Diameter is, by far, the mostimportant factor. Thus, the ratio of 2 to 3 inches ofpitch equals 1 inch of diameter is a fair guide. It isno more than that, however. You could not select a

suitable propeller based only on this rule.

2. The higher the pitch your engine can turn near top horsepower and RPM, the faster your boat can go. This is accurate as far as it goes. The greaterthe pitch, the greater the distance your boat willadvance each revolution. Since top engine RPM is

constant, increasing the pitch means more speed.Then, why aren’t all propellers as small in diameteras possible, with gigantic pitches?

The answer is simply that when the pitch gets toolarge, the angle of attack of the propeller blades tothe onrushing water becomes too steep and they

stall. This is exactly the same as an airplane wing’sstalling in too steep a climb. If the pitches and pitchratios selected are optimum, then within these limitsit is worthwhile, on high-speed craft, to use the small-est diameter and greatest pitch possible.

3. Too little pitch can ruin an engine. This is quitetrue if the pitch and diameter combined are so lowthat it allows the engine to run at speeds far over itstop rated RPM. Never should the engine be allowedto operate at more than 103% to 105% of rated RPM,while underway and in a “normal” operation. If yourengine exceeds that figure, a propeller with increasedpitch or diameter is indicated.

4. Every two-inch increase in pitch will decrease engine speed by 450 RPM, and vice versa. This isa good rough guide for moderate- to high-speedpleasure craft, passenger vessels, and crew boats.Like all rule of thumbs, though, it is no more than arough guide.

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5. A “square” wheel (a propeller with exactly the same diameter and pitch) is the most efficient.This is not true! There is nothing wrong with a squarewheel; on the other hand, there is nothing specialabout it, either.

6. The same propeller can’t deliver both high speed and maximum power. This is true! A propeller sizedfor high speed has a small diameter and maximumpitch. A propeller sized for power or thrust has alarge diameter. For some boats you can compro-

mise on an in-between propeller, but for either realspeed or real thrust there is little common ground.

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Related Propeller Tables

Suggested Shaft Speeds

Range ofType of Vessel SL Ratio Shaft RPM

Heavy Displacement hulls(Tugs, Push boats,Heavy Fishing Vessels) Under 1.2 250 – 500

Medium-to-LightDisplacement hulls(Fishing vessels, trawlers,workboats, trawler yachts) Under 1.45 300 – 1,000

Semi-displacement Hulls(Crew boats, Patrol boats,motor yachts) 1.45 – 3.0 800 – 1,800

Planing hulls (Yachts, fastcommuters and ferries,high-speed patrol boats) over 3.0 1,200 – 3,000 +

Minimum Tip Clearance

MinimumTip

RPM SL Ratio Clearance

200 – 500 Under 1.2 8%

300 – 1,800 1.2 – 2.5 10%

1,000 and above over 2.5 15%

High-speed Planing Craft over 3.0 20%

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Shaft Material Characteristics

YieldStrength in

Torsional Modulus of DensityShear Elasticity Lb/Shaft Material PSI PSI Cu. In.

Aquamet 22 70,000 28,000,000 0.285

Aquamet 18 60,000 28,800,000 0.281

Aquamet 17 70,000 28,500,000 0.284

Monel 400 40,000 26,000,000 0.319

Monel K500 67,000 26,000,000 0.306

Tobin Bronze 20,000 16,000,000 0.304

Stainless Steel 304 20,000 28,000,000 0.286

Buttock Angle vs SL RatioButtock Angle Type Hull SL Ratio

Less than 2° Planing 2.5 or Higher

2°– 8° Semi-displacement 1.4 – 2.9

Greater than 8° Displacement 1.34 Maximum

Crouch’s Formula Constants

C Type of Boat

150 Average runabouts, cruisers, passenger vessels

190 High-speed runabouts, very light high-speed cruisers

210 Race boat types

220 Three-point hydroplanes, stepped hydroplanes

230 Racing power catamarans and sea sleds

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Typical Slip Values

Speed PercentType of Boat in Knots of Slip

Auxiliary sailboat, barges Under 9 45%

Heavy powerboats, workboats 9 -15 26%

Lightweight powerboats, cruisers 15 -30 24%

High-speed planing boats 30 -45 20%

Planing race boats, vee-bottoms 45 -90 10%

Stepped hydroplanes, catamarans over 90 7%

Typical Slip Values – Twin Screw

Speed PercentType of Boat in Knots of Slip

Auxiliary sailboat, barges Under 9 42%

Heavy powerboats, workboats 9 -15 24%

Lightweight powerboats, cruisers 15 -30 22%

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T y p i c a l P r o p e r t i e s o f V a r i o u s E n g i n e e r i n g M a t e r i a l s

C a r b o n a n d

A l u m i n u m

C o p p e r

M a g n e

s i u m

M a t e r i a l P r o p e r t y

L o w A l l o y S t e e l

B a s e A l l o y s

B a s e A l l o

y s

B a s e A

l l o y s

U t l T e n s S t r , P S I

6 0 - 2 0 0 , 0 0 0 +

1 9 - 5 3 , 0 0 0

2 1 - 1 2 5 , 0 0 0

2 2 - 4 5

, 0 0 0

T e n s Y i e l d S t r , P S I

3 0 - 1 7 0 , 0 0 0 +

8 - 4 3 , 0 0 0

1 1 - 1 0 0 , 0 0 0

1 1 - 3 0

, 0 0 0

C o m p S t r , P S I

6 0 - 2 0 0 , 0 0 0

X X X X

X X X X

X X X X

C o m p Y i e l d S t r , P S I

X X X X

A b o u t 8 - 4 3 , 0 0 0

8 - 6 0 , 0 0 0

A b o u t 1 1

- 3 0 , 0 0 0

S h e a r S t r , P S I

X X X X

1 4 - 3 6 , 0 0 0

X X X X

1 4 - 2 1

, 0 0 0

D u c t i l i t y ( % E l o n

g i n 2 i n . )

3 5 - 5

2 2 - 0

5 2 - 0

1 2 - 1

R e d o f A r e a , %

6 5 - 5

X X X X

4 0 - 4

X X X X

B r i n e l l H a r d n e s s

( L o a d )

1 3 0 - 7 5 0 ( 3 0 0 0 k g )

4 0 - 1 4 0 ( 5 0 0 k g

)

4 7 - 4 2 5 ( 5 0 0

k g )

4 5 - 8 4 ( 5

0 0 k g )

S t i f f n e s s ( M o d o

f E l a s t i c i t y , P S I )

3 0 , 0 0 0 , 0 0 0

1 0 , 3 0 0 , 0 0 0

9 . 1 - 2 0 , 0 0 0 , 0 0 0

9 , 0 0 0 - 1

3 , 0 0 0

E n d u r a n c e L i m i t , P S I

0 . 4 - 0 . 5

U T S

6 , 5 0 0 - 2 3 , 0 0 0

4 , 0 0 0 - 1 5 , 0

0 0

9 , 0 0 0 - 1

3 , 0 0 0

I m p a c t R e s i s t a n c e ( C h a r p y , f t - l b )

3 t o 6 5

0 t o 8

0 . 5 t o 4 0 ( I Z

O D )

0 . 5 t o 1 0

( I Z O D )

D e n s i t y @ 6

8 ° F

( l b / c u i n . )

0 . 2 8 2 - 0 . 2 8 4

0 . 0 9 3 - 0 . 1 0 7

0 . 2 6 4 - 0 . 3 4 3

0 . 0 6 5 - 0 . 0 6 7

C o e f f o f T h e r m E

x p ( 1 0 - 6 i n / i n ° F )

6 . 1 - 7 . 1 ( 3 2 - 2 1 2 ° F )

1 1 . 6 - 1 5 . 0 ( 6 8 - 5 7 2

° F ) 9 . 0 - 1 2 . 0 ( 6 8 - 1 6 5 2 ° F )

1 4 . 5 ( 6 8 - 2 1 2 ° F )

M e l t i n g R a n g e , °

F

2 6 0 0 - 2 7 7 5

1 0 0 0 - 1 2 2 0

1 6 7 5 - 1 9 3

0

8 3 0 - 1

1 9 0

C a s t i n g R a n g e , ° F

2 8 5 0 - 3 1 5 0

1 1 7 5 - 1 4 7 5

1 7 5 0 - 2 3 5

0

1 2 0 0 - 1 5 5 0

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T y p i c a l P r o p e r t i e s o f V a r i o u

s E n g i n e e r i n g

M a t e r i a l s ( c o n

t i n u e d )

C a r b o n a n d

A l u m i n u m

C o p p e r

M a g n e

s i u m


L o w A l l o y S t e e l

B a s e A l l o y s

B a s e A l l o

y s

B a s e A

l l o y s

M a c h i n a b i l i t y

<

O t h e r F e r r o u s A l l o y s

G o o d t o E x c e l l e

n t

F a i r t o G o o d

E x c e l l e n t

D e p e n d s o n H a r d n e s s

D a m p i n g C a p a c i t y

X X X X

X X X X

X X X X

X X X X

W e a r R e s i s t a n c e

G o o d , I m p r o v e d b y

P o o r t o E x c e l l e n t

G o o d t o E x c e l l e n t

P o o r t o E

x c e l l e n t

( L u b . S l i d i n g F r i c t i o n )

H e a t T r e a t m e n t

S u i t a b i l i t y a s a B

e a r i n g M a t e r i a l

I n f e r i o r t o C a s t I r o n

P o o r E x c e p t f o r

G o o d t o E x c e l l e n t

P o o r

S p e c i a l B e a r i n g A

l l o y

A b r a s i v e W e a r

E x c e l l e n t

P o o r

P o o r t o G o

o d

P o o r

F l u i d i t y

I n f e r i o r t o C a s t I r o n

E x c e l l e n t

F a i r t o G o o d

G o o d t o E

x c e l l e n t

65


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T y p i c a l P r o p e r t i e s o f V a r i o u

s E n g i n e e r i n g

M a t e r i a l s ( c o n

t i n u e d )

F e r r i t i c

P e a r l i t i c


G r a y C a s t I r o n

M a l l e a b l e I r o n

M a l l e a b l e I r o n

D u c t i l e I r o n

U t l T e n s S t r , P S I

2 0 - 6 0 , 0 0 0

4 8 - 6 0 , 0 0 0

6 0 - 1 2 0 , 0 0 0

6 0 - 1 6 0

, 0 0 0 +

T e n s Y i e l d S t r , P S I

S a m e a s T e n S t r

3 0 - 4 0 , 0 0 0

4 3 - 9 5 , 0 0

0

4 0 - 1 3 5 , 0 0 0

C o m p S t r , P S I

7 0 - 2 0 0 , 0 0 0

= U T S

= U T S

1 - 1 . 2

U T S

C o m p Y i e l d S t r , P S I

X X X X

X X X X

X X X X

X X X X

S h e a r S t r , P S I

1 . 0 - 1 . 6

U T S

0 . 9

U T S

0 . 9

U T

S

0 . 9

U T S

D u c t i l i t y ( % E l o n

g i n 2 i n . )

< 1

2 6 - 1 0

1 2 - 1

2 6 - 1

R e d o f A r e a , %

0

2 3 - 1 8

1 5 - 0

3 0 - 0

B r i n e l l H a r d n e s s

( L o a d )

1 3 5 - 3 5 0 + ( 3 0 0 0 k g )

1 1 0 - 1 4 5 ( 3 0 0 0 k

g )

1 6 0 - 2 8 5 + ( 3 0 0 0 k g )

1 4 0 - 3 3 0 + ( 3 0 0 0 k g )

S t i f f n e s s ( M o d o

f E l a s t i c i t y , P S I )

1 2 - 1 8 , 0 0 0 , 0 0 0

2 5 , 0 0 0 , 0 0 0

2 8 , 0 0 0 , 0 0

0

2 3 - 2 6 , 0 0 0 , 0 0 0

E n d u r a n c e L i m i t , P S I

0 . 4 - 0 . 6

U T S

0 . 4 - 0 . 6

U T S

0 . 4 - 0 . 6 U

T S

0 . 4 - 0 . 5 5

U T S

I m p a c t R e s i s t a n c e ( C h a r p y , f t - l b )

U p t o 5

1 6 . 5

5 - 1 2

1 6 . 5

D e n s i t y @ 6

8 ° F

( l b / c u i n . )

0 . 2 5 - 0 . 2 6 6

0 . 2 5 8 - 0 . 2 7 4

0 . 2 5 8 - 0 . 2 7 4

0 . 2 5 - 0 . 2 8

C o e f f o f T h e r m E

x p ( 1 0 - 6 i n / i n ° F )

5 . 8 ( 3 2 - 2 1 2 ° F )

6 . 6 ( 6 8 - 7 5 0 ° F )

S o m e w h �

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