HY8:Polynomial Coefficients

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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 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

HY8Poly Table 2.JPG

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

HY8Poly Table 3.JPG

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. Arch HW/D Values.

HY8Arch Table.JPG


Table 7. High Profile Arch HW/D Values.

HY8Arch High Profile.JPG


Table 8. Low Profile Arch HW/D Values.

HY8Arch Low Profile Table.JPG


Table 9. Metal Box HW/D Values.

File:HY8Metal Box.JPG


Table 10. User Defined HW/D Values.

HY8User Defined Table.JPG