. STREAMLINED BODIES8.1 Nominal Dra

. STREAMLINED BODIES
8.1 Nominal Drag Force
A symmetric streamlined body at zero angle of attack experiences only a drag force, which has the form:

The drag coefficient CA has both pressure and skin friction components, and hence area Ao is usually that of the wetted surface. Note that the A-subscript will be used to denote zero angle of attack conditions; also, th
e sign of FA is negative, because it opposes the vehicle’s x-axis.
8.2 Munk Moment.

Any shape other than a sphere generates a moment when inclined in an inviscid flow. d’Alembert’s paradox predicts zero net force, but not necessarily a zero moment. This Munk moment arises for a simple reason, the asymmetric location of the stagnation points,where pressure is highest on the front of the body (decelerating flow) and lowest on the back (accelerating flow). The Munk moment is always destabilizing, in the sense that it acts to turn the vehicle perpendicular to the flow.



Azz>Axx for a slender body, and the negative sign indicates a negative pitch with respect to the vehicle’s pitch axis. The added mass terms Azz and Axx can be estimated from analytical expressions (available only for regular shapes such as ellipsoids), from numerical calculation, or from slender body approximation (to follow).

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. Streamlined Bodies
8.1 Nominal Drag Force
A streamlined symmetric at zero angle of attack of body experiences only a drag force, mà has the form: The drag coefficient CA has both Show pressure and skin friction components, and Hence area Ao is the wetted surface của Thường. Note là A-subscript used to denote Will Be zero angle of attack conditionsEND_SPAN; Also, th e sign of FA is negative, it opposes the vehicle's vì x-axis. 8.2 Moment Munk. Any other shape than a sphere generates a torque in an inviscid flow khi inclined. d'Alembert's paradox predicts net zero force, but not necessarily a zero torque. Munk This arises for a simple reason moment, the asymmetric location of the stagnation points, where pressure is on the front of the Highest body (decelerating flow) and lowest on the back (accelerating flow). The Munk destabilizing moment is always, in the sense có Acts to turn the vehicle it perpendicular to the flow. Azz> AXX for a slender body, and the negative sign with respect ngụ a negative pitch to the vehicle's pitch axis. The added mass terms AXX azz and analytical expressions can be Estimated from (available only for regular shapes như ellipsoids), from numerical calculation, or from slender body approximation (to follow).