HY8:Polynomial Coefficients: Difference between revisions

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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.
== Overview ==


   
For circular, box, elliptical, pipe arch, concrete open-bottom arch (commonly called CON/SPAN), and South Dakota Concrete Box culverts, polynomial coefficients, found in Tables 1-6, are utilized in the inlet control headwater computations. Other culvert shapes use Table 7, which shows the HW/D points A(1) through A(10) for interpolation.  Each row of coefficients represents different inlet configurations for different culvert shapes.
 
== Note About Coefficient Changes in HY-8 7.3 and Higher ==
 
In HY-8 7.3 and later versions of HY-8, several significant changes were made to the coefficients used in HY-8.  A summary of the changes to the HY-8 coefficients in this version follows:
 
=== Changes to Shapes Using Polynomial Coefficients ===
 
Changed the slope correction coefficient, SR, used for all the mitered inlet configurations to the recommended -0.7
 
=== Changes to Box Culverts ===
 
Changed the 1.5:1 Bevel Wingwall inlet configuration from HY-8 Equation 6 to equation 2.  For HY-8 Equations 2, 3, and 6, added 0.01 to the "A" Coefficient in the shape database to account for the fact that the equations were derived using a 2% slope (a 2% slope was used to derive the polynomial equations, meaning 0.5(0.02) was subtracted from each of the polynomial curves and needed to be added back into the equations before correcting for slopes).
 
=== Changes to Shapes using A(1) to A(10) Interpolation Coefficients ===
 
Added the slope correction term SR*Slope to the interpolation equations in the code and added 0.01 to the interpolation coefficients for thin, square, and bevel inlets.  Subtracted 0.01 for the mitered inlet.  Added the SR coefficients (All = 0.5 except for mitered which = -0.7) to the coefficient database and the documentation on this page.


== Table 1. Polynomial Coefficients - Circular ==
== Table 1. Polynomial Coefficients - Circular ==


[[Image:HY8Poly_Table_1.JPG]]
{| class="wikitable"
! HY-8 Equation !! Inlet Configuration !! 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
EQ #'s: REFERENCE


1-9 : Calculator Design Series (CDS) 3 for TI-59, FHWA, 198O, page 60
1-9 : Calculator Design Series (CDS) 3 for TI-59, FHWA, 1980, page 60


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




== Table 2. Polynomial Coefficients - Embedded Circular ==
{| class="wikitable"
! HY-8 Equation !! Inlet Configuration !! KE !! SR !! A !! BS !! C !! DIP !! EE !! F
|-
|
1
|
20% Embedded, Projecting End, Pond
|
1.0
|
0.5
|
0.0608834861787302
|
0.485734308768152
|
-0.138194248908661
|
0.027539172439404
|
-0.00214546773150856
|
0.0000642768838741702
|-
|
2
|
40% Embedded, Projecting End, Pond
|
1.0
|
0.5
|
0.0888877561313819
|
0.431529135749154
|
-0.073866511532321
|
0.0159200223783949
|
-0.00103390288198853
|
0.0000262133369282047
|-
|
3
|
50% Embedded, Projecting End, Pond
|
1.0
|
0.5
|
0.0472950768985916
|
0.59879374328307
|
-0.191731763062064
|
0.0480749069653899
|
-0.00424418228907681
|
0.00014115316932528
|-
|
4
|
20% Embedded, Square Headwall
|
0.55
|
0.5
|
0.0899367985347424
|
0.363046722229086
|
-0.0683746513605387
|
0.0109593856642167
|
-0.000706535544154146
|
0.0000189546410047092
|-
|
5
|
40% Embedded, Square Headwall
|
0.55
|
0.5
|
0.074298531535586
|
0.4273662972292
|
-0.0849120530113796
|
0.0157965200237501
|
-0.00102651687866388
|
0.0000260155937601425
|-
|
6
|
50% Embedded, Square Headwall
|
0.55
|
0.5
|
0.212469378699735
|
0.511461899639209
|
-0.174199884499934
|
0.0410961018431149
|
-0.00366309685788592
|
0.000123085395227651
|-
|
7
|
20% Embedded, 45 degree Beveled End
|
0.35
|
0.5
|
0.0795781442396077
|
0.373319755852658
|
-0.0821508852481996
|
0.0148670702428601
|
-0.00121876746632593
|
0.0000406896111847521
|-
|
8
|
40% Embedded, 45 degree Beveled End
|
0.35
|
0.5
|
0.0845740029462746
|
0.389113662011417
|
-0.0685090654986062
|
0.0117190357464366
|
-0.000790440416133214
|
0.0000226453591207209
|-
|
9
|
50% Embedded, 45 degree Beveled End
|
0.35
|
0.5
|
0.0732498224366533
|
0.426296207882289
|
-0.0825309806843494
|
0.0158108288973248
|
-0.00103586921012557
|
0.0000265873062363919
|-
|
10
|
20% Embedded, Mitered End 1.5H:1V
|
0.9
|
0.5
|
0.075018832861494
|
0.404532870578638
|
-0.0959305677963978
|
0.0172402567402576
|
-0.00121896053512953
|
0.0000338251697138414
|-
|
11
|
40% Embedded, Mitered End 1.5H:1V
|
0.9
|
0.5
|
0.086819906748455
|
0.362177446931189
|
-0.048309284166457
|
0.00870598247307798
|
-0.000359506993503941
|
2.89144278309283E-06
|-
|
12
|
50% Embedded, Mitered End 1.5H:1V
|
0.9
|
0.5
|
0.0344461003984492
|
0.574817400258578
|
-0.204079127155295
|
0.0492721656480291
|
-0.00436372397619383
|
0.000144794982321005
|}
EQ #'s: REFERENCE
1-12: NCHRP 15-24 report
== Table 3. Polynomial Coefficients - Box ==


{| class="wikitable"
! HY-8 Equation !! Inlet Configuration !! KE !! SR !! A !! BS !! C !! DIP !! EE !! F
|-
|
1
|
Square Edge (90 degree) Headwall,


== Table 2. Polynomial Coefficients - Box ==
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,


[[Image:HY8Poly_Table_2.JPG]]
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
EQ #'s: REFERENCE
Line 29: Line 647:
1,3,4,6: Calculator Design Series (CDS) 3 for TI-59, FHWA, 1980, page 16
1,3,4,6: Calculator Design Series (CDS) 3 for TI-59, FHWA, 1980, page 16


== Table 3. Polynomial Coefficients - Ellipse ==
== Table 4. Polynomial Coefficients - Ellipse ==


[[Image:HY8Poly_Table_3.JPG]]
{| class="wikitable"
! HY-8 Equation !! PIPE !! Inlet Configuration !! 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
|
-0.7
|
-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
EQ #'s: REFERENCE
Line 39: Line 820:
31-33: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 22
31-33: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 22


== Table 5. Polynomial Coefficients - Pipe Arch ==


{| class="wikitable"
 
! HY-8 Equation !! PIPE !! Inlet Configuration !! KE !! SR !! A !! BS !! C !! DIP !! EE !! F
== Table 4. Polynomial Coefficients - Pipe Arch ==
|-
 
|
[[Image:HY8Polynomial_PipeArch.JPG]]
12
|
CSPA
|
proj.
|
0.9
|
0.5
|
0.08905
|
0.71255
|
-0.27092
|
0.07925
|
-0.00798
|
0.00029
|-
|
13
|
CSPA
|
proj.
|
0.9
|
0.5
|
0.12263
|
0.4825
|
-0.00002
|
-0.04287
|
0.01454
|
-0.00117
|-
|
14
|
CSPA
|
proj.
|
0.9
|
0.5
|
0.14168
|
0.49323
|
-0.03235
|
-0.02098
|
0.00989
|
-0.00086
|-
|
15
|
CSPA
|
proj.
|
0.9
|
0.5
|
0.09219
|
0.65732
|
-0.19423
|
0.04476
|
-0.00176
|
-0.00012
|-
|
16
|
CSPA
|
mitered
|
0.7
|
-0.7
|
0.0833
|
0.79514
|
-0.43408
|
0.16377
|
-0.02491
|
0.00141
|-
|
17
|
CSPA
|
mitered
|
0.7
|
-0.7
|
0.1062
|
0.7037
|
-0.3531
|
0.1374
|
-0.02076
|
0.00117
|-
|
18
|
CSPA
|
mitered
|
0.7
|
-0.7
|
0.23645
|
0.37198
|
-0.0401
|
0.03058
|
-0.00576
|
0.00045
|-
|
19
|
CSPA
|
mitered
|
0.7
|
-0.7
|
0.10212
|
0.72503
|
-0.34558
|
0.12454
|
-0.01676
|
0.00081
|-
|
20
|
CSPA
|
headwall
|
0.5
|
0.5
|
0.11128
|
0.61058
|
-0.19494
|
0.05129
|
-0.00481
|
0.00017
|-
|
21
|
CSPA
|
headwall
|
0.5
|
0.5
|
0.12346
|
0.50432
|
-0.13261
|
0.0402
|
-0.00448
|
0.00021
|-
|
22
|
CSPA
|
headwall
|
0.5
|
0.5
|
0.09728
|
0.57515
|
-0.15977
|
0.04223
|
-0.00374
|
0.00012
|-
|
23
|
CSPA
|
headwall
|
0.5
|
0.5
|
0.09455
|
0.61669
|
-0.22431
|
0.07407
|
-0.01002
|
0.00054
|-
|
24
|
RCPA
|
headwall
|
0.5
|
0.5
|
0.16884
|
0.38783
|
-0.03679
|
0.01173
|
-0.00066
|
0.00002
|-
|
25
|
RCPA
|
grv. hdwl
|
0.2
|
0.5
|
0.1301
|
0.43477
|
-0.07911
|
0.01764
|
-0.00114
|
0.00002
|-
|
26
|
RCPA
|
grv. proj
|
0.2
|
0.5
|
0.09618
|
0.52593
|
-0.13504
|
0.03394
|
-0.00325
|
0.00013
|}


EQ #'s: REFERENCE
EQ #'s: REFERENCE
Line 55: Line 1,179:
12,16,20: Hydraulic Computer Program (HY) 2, FHWA, 1969, page 17
12,16,20: Hydraulic Computer Program (HY) 2, FHWA, 1969, page 17


 
== Table 6. Polynomial Coefficients - [[HY8:Concrete Open Bottom Arch|Concrete Open-Bottom Arch]] ==
 
== Table 5. Polynomial Coefficients - [[WMS:HY-8_Concrete_Open_Bottom_Arch|Concrete Open-Bottom Arch]] ==
{| class="wikitable"
{| class="wikitable"
! Span:Rise Ratio !! Wingwall Angle (Inlet Edge Condition) !! KE !! SR !! A !! BS !! C !! DIP !! EE !! F !! Diagram/Notes
! width="150" | Span:Rise Ratio !! width="200" | Wingwall Angle (Inlet Configuration) !! width="100" | KE !! width="100" | SR !! width="200" | A !! width="200" | BS !! width="200" | C !! width="200" | DIP !! width="200" | EE !! width="200" | F !! width="200" | Diagram/Notes
|-
|-
| 2:1
| 2:1
Line 69: Line 1,191:
0.0
0.0
|
|
0.0356
0.0389106557
|
|
0.5701
0.6044131889
|
|
-0.162
-0.1966160961
|
|
0.0322
0.0425827445
|
|
-0.0023
-0.0035136880
|
|
0.00006
0.0001097816
|
|
[[File:0DegreeWingwallConspanCulvertDiagram.png]]
[[File:0DegreeWingwallConspanCulvertDiagram.png|250px]]


2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.
2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.
Line 93: Line 1,215:
0.0
0.0
|
|
0.0393
0.0580199163
|
|
0.5828
0.5826504262
|
|
-0.1518
-0.1654982156
|
|
0.0284
0.0337114383
|
|
-0.002
-0.0026437555
|
|
0.00005
0.0000796275
|
|
[[File:45DegreeWingwallConspanCulvertDiagram.png]]
[[File:45DegreeWingwallConspanCulvertDiagram.png|250px]]


2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.
2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.
Line 117: Line 1,239:
0.0
0.0
|
|
0.0459
0.0747688320
|
|
0.5762
0.5517030198
|
|
-0.1436
-0.1403253664
|
|
0.0269
0.0281511418
|
|
-0.0019
-0.0021405250
|
|
0.00005
0.0000632552
|
|
[[File:90DegreeWingwallConspanCulvertDiagram.png]]
[[File:90DegreeWingwallConspanCulvertDiagram.png|250px]]


2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.
2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.
Line 141: Line 1,263:
0.0
0.0
|
|
0.0309
0.0557401882
|
|
0.5211
0.4998819105
|
|
-0.1258
-0.1249164198
|
|
0.0207
0.0219465031
|
|
-0.0013
-0.0015177347
|
|
0.00003
0.0000404218
|
|
[[File:0DegreeWingwallConspanCulvertDiagram.png]]
[[File:0DegreeWingwallConspanCulvertDiagram.png|250px]]


4:1 coefficients are used if the span:rise ratio is greater than 3:1
4:1 coefficients are used if the span:rise ratio is greater than 3:1
Line 165: Line 1,287:
0.0
0.0
|
|
0.0318
0.0465032346
|
|
0.5446
0.5446293346
|
|
-0.1467
-0.1571341119
|
|
0.0273
0.0312822438
|
|
-0.0019
-0.0024007467
|
|
0.00005
0.0000704011
|
|
[[File:45DegreeWingwallConspanCulvertDiagram.png]]
[[File:45DegreeWingwallConspanCulvertDiagram.png|250px]]


4:1 coefficients are used if the span:rise ratio is greater than 3:1
4:1 coefficients are used if the span:rise ratio is greater than 3:1
Line 189: Line 1,311:
0.0
0.0
|
|
0.0283
0.0401619369
|
|
0.5739
0.5774418238
|
|
-0.1584
-0.1693724912
|
|
0.0292
0.0328323405
|
|
-0.002
-0.0024131276
|
|
0.00005
0.0000668323
|
|
[[File:90DegreeWingwallConspanCulvertDiagram.png]]
[[File:90DegreeWingwallConspanCulvertDiagram.png|250px]]


4:1 coefficients are used if the span:rise ratio is greater than 3:1
4:1 coefficients are used if the span:rise ratio is greater than 3:1
Line 210: Line 1,332:
* Chase, Don.  Hydraulic Characteristics of CON/SPAN Bridge Systems.  Submitted Study and Report (1999)
* Chase, Don.  Hydraulic Characteristics of CON/SPAN Bridge Systems.  Submitted Study and Report (1999)


 
== Table 7. Polynomial Coefficients - [[HY8:South Dakota Concrete Box|South Dakota Concrete Box]] ==
== Table 6. Polynomial Coefficients - [[WMS:HY-8_South_Dakota_Concrete_Box|South Dakota Concrete Box]] ==
{| class="wikitable"
{| class="wikitable"
! width="225" | Description !! KE !! SR !! A !! BS !! C !! DIP !! EE !! F !! Diagram/Notes
! width="225" | Description !! KE !! SR !! A !! BS !! C !! DIP !! EE !! F !! Diagram/Notes
Line 426: Line 1,547:
* [http://fhwicsint01.fhwa.dot.gov/publications/research/infrastructure/hydraulics/06138/ '''Effects of Inlet Geometry on Hydraulic Performance of Box Culverts'''] (FHWA Publication No. FHWA-HRT-06-138, October 2006)
* [http://fhwicsint01.fhwa.dot.gov/publications/research/infrastructure/hydraulics/06138/ '''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. ==
== Table 8. User Defined, Open Bottom Arch, Low-Profile Arch, High-Profile Arch, and Metal Box HW/D Values. ==




[[Image:HY8Arch%20Table.JPG]]
{| class="wikitable"
! colspan="4" | Q/A*D^.5 = !! 0.5 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
 
|-
== Table 7. High Profile Arch HW/D Values. ==
! HY-8 Interpolation Coefficients !! Inlet Configuration !! KE !! SR !! A(1) !! A(2) !! A(3) !! A(4) !! A(5) !! A(6) !! A(7) !! A(8) !! A(9) !! A(10)
 
|-
 
|
[[Image:HY8Arch%20High%20Profile.JPG]]
1
|
 
Thin Edge Projecting
== Table 8. Low Profile Arch HW/D Values. ==
|
 
0.9
 
|
[[Image:HY8Arch%20Low%20Profile%20Table.JPG]]
0.5
|
 
0.31
== Table 9. Metal Box HW/D Values. ==
|
 
0.48
 
|
[[Image:HY8Metal%20Box.JPG]]
0.81
 
|
 
1.11
== Table 10. User Defined HW/D Values. ==
|
 
1.42
 
|
[[Image:HY8User%20Defined%20Table.JPG]]
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


{{HY8Main}}
{{HY8Main}}
[[Category:HY-8 Analysis|P]]
[[Category:External Links]]

Latest revision as of 21:34, 6 October 2016

Overview

For circular, box, elliptical, pipe arch, concrete open-bottom arch (commonly called CON/SPAN), and South Dakota Concrete Box culverts, polynomial coefficients, found in Tables 1-6, are utilized in the inlet control headwater computations. Other culvert shapes use Table 7, which shows the HW/D points A(1) through A(10) for interpolation. Each row of coefficients represents different inlet configurations for different culvert shapes.

Note About Coefficient Changes in HY-8 7.3 and Higher

In HY-8 7.3 and later versions of HY-8, several significant changes were made to the coefficients used in HY-8. A summary of the changes to the HY-8 coefficients in this version follows:

Changes to Shapes Using Polynomial Coefficients

Changed the slope correction coefficient, SR, used for all the mitered inlet configurations to the recommended -0.7

Changes to Box Culverts

Changed the 1.5:1 Bevel Wingwall inlet configuration from HY-8 Equation 6 to equation 2. For HY-8 Equations 2, 3, and 6, added 0.01 to the "A" Coefficient in the shape database to account for the fact that the equations were derived using a 2% slope (a 2% slope was used to derive the polynomial equations, meaning 0.5(0.02) was subtracted from each of the polynomial curves and needed to be added back into the equations before correcting for slopes).

Changes to Shapes using A(1) to A(10) Interpolation Coefficients

Added the slope correction term SR*Slope to the interpolation equations in the code and added 0.01 to the interpolation coefficients for thin, square, and bevel inlets. Subtracted 0.01 for the mitered inlet. Added the SR coefficients (All = 0.5 except for mitered which = -0.7) to the coefficient database and the documentation on this page.

Table 1. Polynomial Coefficients - Circular

HY-8 Equation Inlet Configuration 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, 1980, page 60

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


Table 2. Polynomial Coefficients - Embedded Circular

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

1

20% Embedded, Projecting End, Pond

1.0

0.5

0.0608834861787302

0.485734308768152

-0.138194248908661

0.027539172439404

-0.00214546773150856

0.0000642768838741702

2

40% Embedded, Projecting End, Pond

1.0

0.5

0.0888877561313819

0.431529135749154

-0.073866511532321

0.0159200223783949

-0.00103390288198853

0.0000262133369282047

3

50% Embedded, Projecting End, Pond

1.0

0.5

0.0472950768985916

0.59879374328307

-0.191731763062064

0.0480749069653899

-0.00424418228907681

0.00014115316932528

4

20% Embedded, Square Headwall

0.55

0.5

0.0899367985347424

0.363046722229086

-0.0683746513605387

0.0109593856642167

-0.000706535544154146

0.0000189546410047092

5

40% Embedded, Square Headwall

0.55

0.5

0.074298531535586

0.4273662972292

-0.0849120530113796

0.0157965200237501

-0.00102651687866388

0.0000260155937601425

6

50% Embedded, Square Headwall

0.55

0.5

0.212469378699735

0.511461899639209

-0.174199884499934

0.0410961018431149

-0.00366309685788592

0.000123085395227651

7

20% Embedded, 45 degree Beveled End

0.35

0.5

0.0795781442396077

0.373319755852658

-0.0821508852481996

0.0148670702428601

-0.00121876746632593

0.0000406896111847521

8

40% Embedded, 45 degree Beveled End

0.35

0.5

0.0845740029462746

0.389113662011417

-0.0685090654986062

0.0117190357464366

-0.000790440416133214

0.0000226453591207209

9

50% Embedded, 45 degree Beveled End

0.35

0.5

0.0732498224366533

0.426296207882289

-0.0825309806843494

0.0158108288973248

-0.00103586921012557

0.0000265873062363919

10

20% Embedded, Mitered End 1.5H:1V

0.9

0.5

0.075018832861494

0.404532870578638

-0.0959305677963978

0.0172402567402576

-0.00121896053512953

0.0000338251697138414

11

40% Embedded, Mitered End 1.5H:1V

0.9

0.5

0.086819906748455

0.362177446931189

-0.048309284166457

0.00870598247307798

-0.000359506993503941

2.89144278309283E-06

12

50% Embedded, Mitered End 1.5H:1V

0.9

0.5

0.0344461003984492

0.574817400258578

-0.204079127155295

0.0492721656480291

-0.00436372397619383

0.000144794982321005

EQ #'s: REFERENCE

1-12: NCHRP 15-24 report

Table 3. Polynomial Coefficients - Box

HY-8 Equation Inlet Configuration 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 4. Polynomial Coefficients - Ellipse

HY-8 Equation PIPE Inlet Configuration 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

-0.7

-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 5. Polynomial Coefficients - Pipe Arch

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

12

CSPA

proj.

0.9

0.5

0.08905

0.71255

-0.27092

0.07925

-0.00798

0.00029

13

CSPA

proj.

0.9

0.5

0.12263

0.4825

-0.00002

-0.04287

0.01454

-0.00117

14

CSPA

proj.

0.9

0.5

0.14168

0.49323

-0.03235

-0.02098

0.00989

-0.00086

15

CSPA

proj.

0.9

0.5

0.09219

0.65732

-0.19423

0.04476

-0.00176

-0.00012

16

CSPA

mitered

0.7

-0.7

0.0833

0.79514

-0.43408

0.16377

-0.02491

0.00141

17

CSPA

mitered

0.7

-0.7

0.1062

0.7037

-0.3531

0.1374

-0.02076

0.00117

18

CSPA

mitered

0.7

-0.7

0.23645

0.37198

-0.0401

0.03058

-0.00576

0.00045

19

CSPA

mitered

0.7

-0.7

0.10212

0.72503

-0.34558

0.12454

-0.01676

0.00081

20

CSPA

headwall

0.5

0.5

0.11128

0.61058

-0.19494

0.05129

-0.00481

0.00017

21

CSPA

headwall

0.5

0.5

0.12346

0.50432

-0.13261

0.0402

-0.00448

0.00021

22

CSPA

headwall

0.5

0.5

0.09728

0.57515

-0.15977

0.04223

-0.00374

0.00012

23

CSPA

headwall

0.5

0.5

0.09455

0.61669

-0.22431

0.07407

-0.01002

0.00054

24

RCPA

headwall

0.5

0.5

0.16884

0.38783

-0.03679

0.01173

-0.00066

0.00002

25

RCPA

grv. hdwl

0.2

0.5

0.1301

0.43477

-0.07911

0.01764

-0.00114

0.00002

26

RCPA

grv. proj

0.2

0.5

0.09618

0.52593

-0.13504

0.03394

-0.00325

0.00013

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 6. Polynomial Coefficients - Concrete Open-Bottom Arch

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

0 Degrees (Mitered to Conform to Slope)

0.7

0.0

0.0389106557

0.6044131889

-0.1966160961

0.0425827445

-0.0035136880

0.0001097816

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

0.0580199163

0.5826504262

-0.1654982156

0.0337114383

-0.0026437555

0.0000796275

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

0.0747688320

0.5517030198

-0.1403253664

0.0281511418

-0.0021405250

0.0000632552

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

0.0557401882

0.4998819105

-0.1249164198

0.0219465031

-0.0015177347

0.0000404218

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

0.0465032346

0.5446293346

-0.1571341119

0.0312822438

-0.0024007467

0.0000704011

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

0.0401619369

0.5774418238

-0.1693724912

0.0328323405

-0.0024131276

0.0000668323

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 7. 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 8. 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 Configuration 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

v • e
HY-8
Introduction:Getting Started   •   Layout   •   Vena Contracta   •   Building a Project   •   Locate Project   •   Culvert Crossing Data   •   Run Analysis   •   Report Generation
Crossing and Culvert Data:Crossings   •   Discharge Data   •   Roadway Data   •   Tailwater Data   •   Irregular Channel   •   Culvert Data   •   Site Data   •   Culvert Invert Data   •   Embankment Toe Data
AnalysisProject Units   •   Roadway Overtopping   •   Inlet Control Computations   •   Outlet Control Computations   •   Tables and Plots
Energy DissipationScour Hole Geometry   •   Increased Resistance   •   Tumbling Flow   •   USBR Type IX Baffled Apron   •   Drop Structures   •   Stilling Basins   •   Streambed Level Structures
MethodsAquatic Organism Passage   •   Low Flow Hydraulics
TroubleshootingDifferences from DOS HY-8   •   Limitations   •   HY-8 User Manual
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