Contraction Reach Lengths

Ranges of contraction ratios (CR) for different conditions are presented in Table B-3.

These values should be used as starting values and for studies which do not justify a sophisticated evaluation of the contraction reach length. Note that this table does not differentiate the ranges on the basis of the degree of constriction. For each range the higher values are typically associated with higher discharges and the lower values with lower discharges.

Table B-3 Ranges of Contraction Ratios (CR)

	nob / nc = 1	nob / nc = 2	nob / nc = 4
S = 1 ft/mile	1.0 - 2.3	0.8 - 1.7	0.7 - 1.3
5 ft/mile	1.0 - 1.9	0.8 - 1.5	0.7 - 1.2
10 ft/mile	1.0 - 1.9	0.8 - 1.4	0.7 - 1.2

When the conditions are within or near those of the data, the contraction reach length regression equation (1) may be used with confidence:

1)	$\begin{array}{l}\displaystyle \displaystyle L_c = 263+38.8 \left( \frac{F_{c_2}}{F_{c_1}} \right) +257 \left( \frac{Q_{ob}}{Q} \right) ^2 -58.7 \left( \frac{n_{ob}}{n_c} \right) ^{0.5} + 0.161 \overline{L} _{obs}\end{array}$

Symbol	Description	Units
$\begin{array}{l}\overline{L} _{obs}\end{array}$	average length of obstruction as described earlier in this chapter	ft
$\begin{array}{l}Q_{ob}\end{array}$	the discharge conveyed by the two overbanks, at the approach section (Section 4)	cfs
$\begin{array}{l}n_{ob}\end{array}$	the average Manning n value for the overbanks at Section 4
$\begin{array}{l}n_c\end{array}$	the average Manning n value for the main channel at Section 4

In cases where the floodplain scale and discharge are significantly larger or smaller than those that were used in developing the regression formulae, (1) should not be used. The recommended approach for estimating the contraction ratio at this time is to compute a value from (2) and check it against the values in Table B-3:

2)	$\begin{array}{l}\displaystyle \displaystyle CR=1.4-0.333 \left( \frac{F_{c_2}}{F_{c_1}} \right) +1.86 \left( \frac{Q_{ob}}{Q} \right) ^2 -0.19 \left( \frac{n_{ob}}{n_c} \right) ^{0.5}\end{array}$

As with the expansion reach lengths, the modeler must use (1) and (2) and the values from Table B-2 with extreme caution when the prototype is outside of the range of data used in this study. The contraction ratio should not exceed 2.5:1 nor should it be less than 0.3:1.