HY8:Polynomial Coefficients: Difference between revisions

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Revision as of 23:15, 22 July 2011

For circular, box, elliptical, pipe arch, and concrete open-bottom arch (commonly called CON/SPAN) culverts, polynomial coefficients, found in Tables 1-5, are utilized in the inlet control headwater computations. Tables 6-10 show the HW/D points A(1) through A(10) for interpolation. Each row of coefficients represents different entrance conditions for different culvert shapes.


Table 1. Polynomial Coefficients - Circular

HY-8 Equation Inlet Edge Condition KE SR A BS C DIP EE F

1

Thin Edge Projecting

0.9

0.5

0.187321

0.56771

-0.156544

0.0447052

-0.00343602

8.96610E-05

2

Mitered to Conform to Slope

0.7

-0.7

0.107137

0.757789

-0.361462

0.1233932

-0.01606422

0.00076739

3

Square Edge with Headwall (Steel/Aluminum/Corrugated PE)

0.5

0.5

0.167433

0.538595

-0.149374

0.0391543

-0.00343974

0.000115882

4

Grooved End Projecting

0.2

0.5

0.108786

0.662381

-0.233801

0.0579585

-0.0055789

0.000205052

5

Grooved End in Headwall

0.2

0.5

0.114099

0.653562

-0.233615

0.0597723

-0.00616338

0.000242832

6

Beveled Edge (1:1)

0.2

0.5

0.063343

0.766512

-0.316097

0.0876701

-0.009836951

0.00041676

7

Beveled Edge (1.5:1)

0.2

0.5

0.08173

0.698353

-0.253683

0.065125

-0.0071975

0.000312451

8

sq. proj.

0.2

0.5

0.167287

0.558766

-0.159813

0.0420069

-0.00369252

0.000125169

9

Square Edge with Headwall (Concrete/PVC/HDPE)

0.5

0.5

0.087483

0.706578

-0.253295

0.0667001

-0.00661651

0.000250619

10

end sect.

0.4

0.5

0.120659

0.630768

-0.218423

0.0591815

-0.00599169

0.000229287

EQ #'s: REFERENCE

1-9 : Calculator Design Series (CDS) 3 for TI-59, FHWA, 198O, page 60

1-10: Hydraulic Computer Program (HY) 1, FHWA, 1969, page 18

Table 2. Polynomial Coefficients - Box

HY-8 Equation Inlet Edge Condition KE SR A BS C DIP EE F

1

Square Edge (90 degree) Headwall,

Square Edge (90 & 15 degree flare) Wingwall

0.5

0.5

0.122117

0.505435

-0.10856

0.0207809

-0.00136757

0.00003456

2

1.5:1 Bevel (90 degree) Headwall,

1.5:1 Bevel (19-34 degree flare) Wingwall

0.2

0.5

0.1067588

0.4551575

-0.08128951

0.01215577

-0.00067794

0.0000148

3

1:1 Bevel Headwall

0.2

0.5

0.1666086

0.3989353

-0.06403921

0.01120135

-0.0006449

0.000014566

4

Square Edge (30-75 degree flare) Wingwall

0.4

0.5

0.0724927

0.507087

-0.117474

0.0221702

-0.00148958

0.000038

5

Square Edge (0 degree flare) Wingwall

0.7

0.5

0.144133

0.461363

-0.0921507

0.0200028

-0.00136449

0.0000358

6

1:1 Bevel (45 degree flare) Wingwall

0.2

0.5

0.0995633

0.4412465

-0.07434981

0.01273183

-0.0007588

0.00001774

EQ #'s: REFERENCE

1-6: Hydraulic Computer Program (HY) 6, FHWA, 1969, subroutine BEQUA

1,4,5: Hydraulic Computer Program (HY) 3, FHWA, 1969, page 16

1,3,4,6: Calculator Design Series (CDS) 3 for TI-59, FHWA, 1980, page 16

Table 3. Polynomial Coefficients - Ellipse

HY-8 Equation PIPE Inlet Edge Condition KE SR A BS C DIP EE F

27

CSPE

headwall

0.5

0.5

0.01267

0.79435

-0.2944

0.07114

-0.00612

0.00015

28

CSPE

mitered

0.7

0.5

-0.14029

1.437

-0.92636

0.32502

-0.04865

0.0027

29

CSPE

bevel

0.3

0.5

-0.00321

0.92178

-0.43903

0.12551

-0.01553

0.00073

30

CSPE

thin

0.9

0.5

0.0851

0.70623

-0.18025

0.01963

0.00402

-0.00052

31

RCPE

square

0.5

0.5

0.13432

0.55951

-0.1578

0.03967

-0.0034

0.00011

32

RCPE

grv. hdwl

0.2

0.5

0.15067

0.50311

-0.12068

0.02566

-0.00189

0.00005

33

RCPE

grv. proj

0.2

0.5

-0.03817

0.84684

-0.32139

0.0755

-0.00729

0.00027

EQ #'s: REFERENCE

27-30: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 20

31-33: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 22

Table 4. Polynomial Coefficients - Pipe Arch

HY8Polynomial PipeArch.JPG

EQ #'s: REFERENCE

12-23: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 17

24-26: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 24

12,16,20: Hydraulic Computer Program (HY) 2, FHWA, 1969, page 17


Table 5. Polynomial Coefficients - Concrete Open-Bottom Arch

Span:Rise Ratio Wingwall Angle (Inlet Edge Condition) KE SR A BS C DIP EE F Diagram/Notes
2:1

0 Degrees (Mitered to Conform to Slope)

0.7

0.0

0.0356

0.5701

-0.162

0.0322

-0.0023

0.00006

0DegreeWingwallConspanCulvertDiagram.png

2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.

2:1

45 Degrees (45-degree Wingwall)

0.5

0.0

0.0393

0.5828

-0.1518

0.0284

-0.002

0.00005

45DegreeWingwallConspanCulvertDiagram.png

2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.

2:1

90 Degrees (Square Edge with Headwall)

0.5

0.0

0.0459

0.5762

-0.1436

0.0269

-0.0019

0.00005

90DegreeWingwallConspanCulvertDiagram.png

2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.

4:1

0 Degrees (Mitered to Conform to Slope)

0.7

0.0

0.0309

0.5211

-0.1258

0.0207

-0.0013

0.00003

0DegreeWingwallConspanCulvertDiagram.png

4:1 coefficients are used if the span:rise ratio is greater than 3:1

4:1

45 Degrees (45-degree Wingwall)

0.5

0.0

0.0318

0.5446

-0.1467

0.0273

-0.0019

0.00005

45DegreeWingwallConspanCulvertDiagram.png

4:1 coefficients are used if the span:rise ratio is greater than 3:1

4:1

90 Degrees (Square Edge with Headwall)

0.5

0.0

0.0283

0.5739

-0.1584

0.0292

-0.002

0.00005

90DegreeWingwallConspanCulvertDiagram.png

4:1 coefficients are used if the span:rise ratio is greater than 3:1

References for Concrete Open-bottom Arch polynomial coefficients:

  • Thiele, Elizabeth A. Culvert Hydraulics: Comparison of Current Computer Models. (pp. 121-126), Brigham Young University Master's Thesis (2007).
  • Chase, Don. Hydraulic Characteristics of CON/SPAN Bridge Systems. Submitted Study and Report (1999)


Table 6. Polynomial Coefficients - South Dakota Concrete Box

Description KE SR A BS C DIP EE F Diagram/Notes
Sketch 1: 30 degree-flared wingwalls; top edge beveled at 45 degrees

0.5

0.5

0.0176998563

0.5354484847

-0.1197176702

0.0175902318

-0.0005722076

-0.0000080574

HY8SouthDakotaSketch1.png

Sketch 2: 30 degree-flared wingwalls; top edge beveled at 45 degrees; 2, 3, and 4 multiple barrels

0.5

0.5

0.0506647261

0.5535393634

-0.1599374238

0.0339859269

-0.0027470036

0.0000851484

HY8SouthDakotaSketch2.png

Sketch 3: 30 degree-flared wingwalls; top edge beveled at 45 degrees; 2:1 to 4:1 span-to-rise ratio

0.5

0.5

0.0518005829

0.5892384653

-0.1901266252

0.0412149379

-0.0034312198

0.0001083949

HY8SouthDakotaSketch3.png

Sketch 4: 30 degree-flared wingwalls; top edge beveled at 45 degrees; 15 degrees skewed headwall with multiple barrels

0.5

0.5

0.2212801152

0.6022032341

-0.1672369732

0.0313391792

-0.0024440549

0.0000743575

HY8SouthDakotaSketch4.png

Sketch 5: 30 degree-flared wingwalls; top edge beveled at 45 degrees; 30 degrees to 45 degrees skewed headwall with multiple barrels

0.5

0.5

0.2431604850

0.5407556631

-0.1267568901

0.0223638322

-0.0016523399

0.0000490932

HY8SouthDakotaSketch5.png

Sketches 6 & 7: 0 degree-flared wingwalls (extended sides); square-edged at crown and 0 degree-flared wingwalls (extended sides); top edge beveled at 45 degrees; 0- and 6-inch corner fillets

0.5

0.5

0.0493946080

0.7138391179

-0.2354755894

0.0473247331

-0.0036154348

0.0001033337

HY8SouthDakotaSketch6.png

HY8SouthDakotaSketch7.png

Sketches 8 & 9: 0 degree-flared wingwalls (extended sides); top edge beveled at 45 degrees; 2, 3, and 4 multiple barrels and 0 degree-flared wingwalls (extended sides); top edge beveled at 45 degrees; 2:1 to 4:1 span-to-rise ratio

0.5

0.5

0.1013668008

0.6600937637

-0.2133066786

0.0437022641

-0.0035224589

0.0001078198

HY8SouthDakotaSketch8.png

HY8SouthDakotaSketch9.png

Sketches 10 & 11: 0 degree-flared wingwalls (extended sides); crown rounded at 8-inch radius; 0- and 6-inch corner fillets and 0 degree-flared wingwalls (extended sides); crown rounded at 8-inch radius; 12-inch corner fillets

0.5

0.5

0.0745605288

0.6533033536

-0.1899798824

0.0350021004

-0.0024571627

0.0000642284

HY8SouthDakotaSketch10.png

HY8SouthDakotaSketch11.png

Sketch 12: 0 degree-flared wingwalls (extended sides); crown rounded at 8-inch radius; 12-inch corner fillets; 2, 3, and 4 multiple barrels

0.5

0.5

0.1321993533

0.5024365440

-0.1073286526

0.0183092064

-0.0013702887

0.0000423592

HY8SouthDakotaSketch12.png

Sketch 13: 0 degree-flared wingwalls (extended sides); crown rounded at 8-inch radius; 12-inch corner fillets; 2:1 to 4:1 span-to-rise ratio.

0.5

0.5

0.1212726739

0.6497418331

-0.1859782730

0.0336300433

-0.0024121680

0.0000655665

HY8SouthDakotaSketch13.png

References for South Dakota Concrete Box polynomial coefficients:

Table 6. User Defined, Open Bottom Arch, Low-Profile Arch, High-Profile Arch, and Metal Box HW/D Values.

Q/A*D^.5 = 0.5 1 2 3 4 5 6 7 8 9
HY-8 Interpolation Coefficients Inlet Edge Condition KE SR A(1) A(2) A(3) A(4) A(5) A(6) A(7) A(8) A(9) A(10)

1

Thin Edge Projecting

0.9

0.5

0.31

0.48

0.81

1.11

1.42

1.84

2.39

3.03

3.71

4.26

2

Mitered to Conform to Slope

0.7

-0.7

0.34

0.49

0.77

1.04

1.45

1.91

2.46

3.06

3.69

4.34

3

Square Edge with Headwall

0.5

0.5

0.31

0.46

0.73

0.96

1.26

1.59

2.01

2.51

3.08

3.64

4

Beveled Edge

0.2

0.5

0.31

0.44

0.69

0.89

1.16

1.49

1.81

2.23

2.68

3.18

Reference for User-defined interpolation coefficients: FHWA HDS-5, Appendix D, Chart 52B