Figure 9.11. Typical drag polar with high-lift devices

Total aircraft drag:

CD = 0.019 + 0.205 + 0.31 = 0.534

Drag polar with a high-lift device extended is plotted as shown in Figure 9.11 (after Figure 9.1) at various deflections. It is cautioned that this graph is intended only for coursework; practicing industry-based engineers must use data generated by tests and CFD.

A typical value of CL/CD for high-subsonic commercial transport aircraft at takeoff with flaps deployed is on the order of 10 to 12; at landing, it is reduced to 6 to 8.

A more convenient method is shown in Figure 9.12, and it is used for the coursework example (civil aircraft) worked out in Section 9.19.

9.14.2 Dive Brakes and Spoilers Drag

To decrease aircraft speed, whether in combat action or at landing, flat plates – which are attached to the fuselage and shaped to its geometric contour when retracted – are used. They could be placed symmetrically on both sides of the wing or on the upper fuselage (i.e., for military aircraft). The flat plates are deployed during subsonic flight. Use CDл brake = 1.2 to 2.0 (average 1.6) based on the projected frontal area of the brake to air stream. The force level encountered is high and controlled by the level of deflection. The best position for the dive brake is where the aircraft moment change is the least (i.e., close to the aircraft CG line).

9.14.3 Undercarriage Drag

Undercarriages, fixed or extended (i.e., retractable type), cause considerable drag on smaller, low-speed aircraft. A fixed undercarriage (not streamlined) can cause

Figure 9.12. Drag polar with single-slotted Fowler flap extended (undercarriage retracted)

up to about a third of aircraft parasite drag. When the undercarriage is covered by a streamlined wheel fairing, the drag level can be halved. It is essential for high-speed aircraft to retract the undercarriage as soon as it is safe to do so (like birds). Below a 200-ft altitude from takeoff and landing, an aircraft undercarriage is kept extended. Again, it is cautioned that the data in this book are intended for coursework so readers have some sense of the order of magnitude involved.

The drag of an undercarriage wheel is computed based on its frontal area: Aπ wheel product of wheel diameter and width (see Figure 7.15). For twin side-by- side wheels, the gap between them is ignored and the wheel drag is increased by 50% from a single-wheel drag. For the bogey type, the drag also would increase – it is assumed by 10% for each bogey, gradually decreasing to a total maximum 50% increase for a large bogey. Finally, interference effects (e.g., due to doors and tubing) would double the total of wheel drag. The drag of struts is computed separately. The bare single-wheel CD wheel based on the frontal area is in Table 9.6 (wheel aspect ratio = D/Wb).

For the smooth side, reduce by half. In terms of an aircraft:

CDp wheel = (CDπ wheel × Aπ wheel)/SW

A circular strut has nearly twice the amount of drag compared to a streamlined strut in a fixed undercarriage. For example, the drag coefficient of a circular strut based on its cross-sectional area per unit length is CDπ strut = 1.0 because it

Table 9.6. Bare single-wheel drag with side ridge (Figure 7.15)