In part 2 of Wing Sizing, we used a value for 
Method for trailing-edge flaps
In section 6.1.1.3, maximum section lift with high-lift and control devices (think flaps and ailerons) is covered.
Slotted Flaps
The crucial factor in the design of a slotted flap is the slot. The slot sheds the boundary layer at the slot lip and allows a new boundary layer to develop over the flap. The slot also directs air in a direction tangential to the surface of the flap. Flow attachment can therefore be maintained to relatively large flap deflections. For instance, efficiently designed double-slotted flaps can prevent flow separation at deflections as high as 60°.
The design of slots for slotted flaps is very critical. Several rules of thumb have been developed for efficiently designing these flaps. First, the flap (and vane) and airfoil must overlap for all deflections when viewed in planform. Secondly, the jet issuing from the slot should also be directed in a direction tangential to the flap surface. Long shroud lengths often show advantages, since they have better control over the direction of the jet.
The flaps (and vanes) of a slotted flap carry considerably more lift than the corresponding plain flap with the same chord and deflection angle. These surfaces are, in reality, in tandem with the wing and derive beneficial induced-camber effects associated with tandem configurations.
DATCOM p. 6.1.1.3-3
The maximum lift increment provided is:
$$\small \Delta c_{lmax} = k_1 \cdot k_2 \cdot k_3 \left( \Delta c_{lmax} \right)_{base} $$
$$\small \Delta c_{lmax} = (1.0) (1.0) (1.0) (1.58) = 1.58^{*} $$
*see discussion at end of post for reduction
where:
$$\scriptsize k_1$$
is a factor accounting for flap-to-airfoil-chord ratios other than 0.25 from Figure 6.1.1.3-12b.
$$\scriptsize k_1 = 1.0$$
$$\scriptsize k_2$$
is a factor accounting for flap deflections other than the reference values from Figure 6.1.1.3-13a.
$$\scriptsize k_2 = 1.0$$
$$\scriptsize k_3$$
is a factor accounting for flap motion as a function of flap deflection from Figure 6.1.1.3-13b.
$$\tiny \frac{ \text{actual flap angle}}{ \text{reference flap angle}} = \scriptsize \frac{ 45^{\circ}}{45^{\circ}} = 1.0$$
$$\scriptsize k_3 = 1.0$$
$$\scriptsize ( \Delta c_{lmax} )_{base}$$
is the section maximum lift increment for 25% chord flaps at the reference flap deflection angle from Figure 6.1.1.3-12a. (Reference flap deflection angles are denoted in Figure 6.1.1.3-13a.)
$$\scriptsize ( \Delta c_{lmax} )_{base} = 1.58$$
Comparison to Experimental Data
Table 6.1.1.3-A provides a summary of experimental data, comparing wind-tunnel testing to calculated values. The results for single-slotted flaps are reproduced here:
| Airfoil | $$ R_e \\ \scriptsize \text{x } 10^{6} $$ | $$ \frac{c_f}{c}$$ | $$ \delta_f \\ \scriptsize ( \text{deg} ) $$ | $$c_{l_{max}} \\ \scriptsize (\delta_f = 0) $$ | $$ \Delta c_{l_{max}} \\ \scriptsize ( \text{calc}) $$ | $$ \Delta c_{l_{max}} \\ \scriptsize (\text{test}) $$ | percent error |
|---|---|---|---|---|---|---|---|
| 66,2-116 a=0.6 | 6.0 | 0.2505 | 45 | 1.45 | 1.67 | 1.29 | +29.5 |
| 65-210 | 2.4 | .25 | 30 | 1.22 | 0.79 | 0.90 | -12.2 |
| 65-210 | 2.4 | .25 | 30 | 1.22 | 0.79 | 0.84 | -6.0 |
| 23012 | 3.5 | .30 | 40 | 1.55 | 1.24 | 1.36 | -8.8 |
| 66,2-216 a=0.6 | 5.1 | .25 | 45 | 1.46 | 1.67 | 1.42 | +17.6 |
| 23012 | 3.5 | .2566 | 30 | 1.52 | 0.88 | 1.03 | -14.6 |
| 23012 | 3.5 | .40 | 40 | 1.53 | 1.27 | 1.30 | -2.3 |
Probably the two most relevant examples are the NACA 65-210 tests at Re = 2.4×106 (since our Riblett airfoil is of a similar family and that is the closest Re to our stall speed). Both underperformed relative to the DATCOM-calculated values.
Based on this data, it is apparent that the quality of flap design execution can vary quite a bit and we think it would be prudent to reduce our calculated 
$$\scriptsize ( \Delta c_{lmax} )_{base} = 0.85 \cdot 1.58 = 1.34$$
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