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FHWA-HRT-06-138 (Corrected) Inlet Configuration Catalog

Reference:

  • Title: Effects of Inlet Geometry on Hydraulic Performance of Box Culverts
  • Report: FHWA-HRT-06-138 (Corrected Errata Version)
  • Publisher: Federal Highway Administration
  • Year: 2006 / Corrected 2007

1. Overview

This document extracts the corrected Table 11 and Table 12 coefficients for new inlet geometries introduced in this report. They supplement HDS-5 for the listed physical configurations; they do not replace generic box coefficients.

2. Table 11 Extracted Coefficients (Form 1 / Form 2)

Description $K_e$ $K_1$ $M_1$ $K_2$ $M_2$ $c$ $Y$
30° flared wingwalls, top edge beveled at 45° - - - - - - -
Single barrel 0.26 0.005 1.05 0.44 0.74 0.04 0.48
2, 3, and 4 multiple barrels 0.32 - - 0.47 0.68 0.04 0.62
2:1 to 4:1 span-to-rise ratio 0.20 - - 0.48 0.65 0.041 0.57
15° skewed headwall, multiple barrels 0.36 - - 0.69 0.49 0.029 0.95
30° to 45° skewed headwall, multiple barrels 0.45 - - 0.69 0.49 0.027 1.02
0° flared wingwalls, extended sides - - - - - - -
Square-edged at crown 0.79 0.055 0.68 0.55 0.64 0.047 0.55
45° straight bevel at crown, 0/6-in corner fillets 0.48 - - 0.56 0.62 0.045 0.55
45° straight bevel at crown, multiple barrels 0.52 - - 0.55 0.59 0.038 0.69
45° straight bevel at crown, 2:1 to 4:1 S/R ratio 0.37 - - 0.61 0.57 0.041 0.67
Crown rounded at 8-in rad, 0/6-in corner fillets 0.24 - - 0.56 0.62 0.038 0.67
Crown rounded at 8-in rad, 12-in corner fillets 0.3 - - 0.56 0.62 0.038 0.67
Crown rounded at 8-in rad, 12-in fillets, multiple b. 0.54 - - 0.55 0.60 0.023 0.96
Crown rounded at 8-in rad, no fillets, 2:1 to 4:1 S/R 0.30 - - 0.61 0.57 0.033 0.79

Note: Dashes indicate missing, uncomputed, or group-heading cells.

3. Table 12 Extracted Polynomial Coefficients

The polynomial regression approach (Eq. 24) is given as:

$ \frac{HW}{D} = a + b X + c X^2 + d X^3 + e X^4 + f X^5 $

where $X = \frac{Q}{A \sqrt{gD}}$. This is the dimensionless discharge used by the report; omitting $g$ changes the independent variable and invalidates the fit.

Description a b c d e f
30° flared wingwalls, top edge beveled at 45° - - - - - -
Single barrel 0.163450 0.127103 0.256193 -0.131630 0.025211 -0.001600
2, 3, and 4 multiple barrels 0.112542 0.375074 0.002657 -0.026380 0.006867 -0.000470
2:1 to 4:1 span-to-rise ratio 0.182681 0.209471 0.158774 -0.092970 0.019381 -0.001310
15° skewed headwall, multiple barrels 0.182031 0.686256 -0.277040 0.0821130 -0.011670 0.000654
30° to 45° skewed headwall, multiple barrels 0.363958 0.283523 0.069040 -0.044221 0.008965 -0.000595
0° flared wingwalls, extended sides - - - - - -
Square-edged at crown 0.278122 -0.002930 0.448521 -0.228310 0.044973 -0.00299
45° straight bevel at crown, 0/6-in corner fillets 0.244295 0.129322 0.339620 -0.189660 0.038635 -0.0026
45° straight bevel at crown, multiple barrels 0.164261 0.43842 -0.03128 -0.01919 0.006288 -0.00046

| 45-degree straight bevel at crown, 2:1 to 4:1 S/R ratio | 0.254968 | 0.273934 | 0.154712 | -0.09911 | 0.020506 | -0.00135 | | Crown rounded at 8-in radius, 0/6-in corner fillets | 0.203424 | 0.31092 | 0.10783 | -0.07609 | 0.015779 | -0.00102 | | Crown rounded at 8-in radius, 12-in corner fillets | 0.203424 | 0.31092 | 0.10783 | -0.07609 | 0.015779 | -0.00102 | | Crown rounded at 8-in radius, 12-in fillets, multiple barrels | 0.10315 | 0.619895 | -0.23147 | 0.071093 | -0.01075 | 0.000628 | | Crown rounded at 8-in radius, no fillets, 2:1 to 4:1 S/R | 0.199715 | 0.446748 | -0.02414 | -0.02334 | 0.006761 | -0.00048 |

Source locator: corrected Table 12, printed page 86 (local PDF page 99). Table 11 is on printed page 85 (local PDF page 98). The values are implemented by the typed, fail-closed ModernBoxInlet catalogue; the local corrected PDF remains the authoritative transcription check.

The report states on printed pages 72–73 (local PDF pages 85–86) that these polynomials cover the measured range and have a useful operating range of approximately 0.4 < HW/D < 2.3. At low head they approach the nonzero intercept and above about HW/D = 2.3 they reach a maximum. HY-8 manual page 45 explicitly says its South Dakota-box polynomials were recomputed for 0.5 <= HW/D <= 3.0; HY-8's values must not be attributed to corrected Table 12.

4. Analysis and Impact

  • Multi-barrel configurations have a pronounced effect on both the entrance loss coefficient $K_e$ and the polynomial regression fits.
  • resolve_modern_box_inlet_coefficients uses span-to-rise ratio, multi-barrel quantity, flare, crown treatment, skew, and fillet size; unsupported combinations do not fall back.
  • Geometry identity must also include wingwall flare, top-edge treatment, corner-fillet size, skew, and net area. A barrel count alone is insufficient.
  • Appendix D's FC-D-30 Q25 and Q100 cases are recorded in fixture_candidates.md. The Q25 FC-D-30 case is now exercised with FilletedRectangularGeometry, Sketch 2, and the published approach area.