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

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

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	0.5	0.5	0.2212801152	0.6022032341	-0.1672369732	0.0313391792	-0.0024440549	0.0000743575
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
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
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
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
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
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

References for South Dakota Concrete Box polynomial coefficients:

• Thiele, Elizabeth A. Culvert Hydraulics: Comparison of Current Computer Models. (pp. 121-126), Brigham Young University Master's Thesis (2007).
• Effects of Inlet Geometry on Hydraulic Performance of Box Culverts (FHWA Publication No. FHWA-HRT-06-138, October 2006)

Table 6. Arch 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

Table 7. High Profile Arch HW/D Values.

Table 8. Low Profile Arch HW/D Values.

Table 10. User Defined HW/D Values.