HY8:Polynomial Coefficients
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
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
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, 198O, page 16
Table 3. Polynomial Coefficients - Ellipse
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
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 |
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 |
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 |
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 |
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 |
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 |
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 | |
| 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 | |
| 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 | |
| Sketch 4: 30 degree-flared wingwalls; top edge beveled at 45 degrees; 15 degrees skewed headwall with multiple barrels |
References for South Dakota Concrete Box polynomial coefficients:
Table 6. Arch HW/D Values.
Table 7. High Profile Arch HW/D Values.
Table 8. Low Profile Arch HW/D Values.
Table 9. Metal Box HW/D Values.
Table 10. User Defined HW/D Values.
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