12.2. Aerodynamic moment of a body of revolution. Coordinate of aerodynamic center.

According to the theory of a thin (elongated) body the longitudinal moment is determined under the formula

(12.14)

As the lifting (normal) force was determined for separate parts of a body of revolution (for nose, cylindrical and rear parts), and moment characteristics are expedient for calculating also for parts of body of revolution.

12.2.1. Aerodynamic moment of a nose and coordinate of an aerodynamic center.

Let's use the results of the theory of an elongated body, according to which the factor of pressure on surface of the body of revolution at streamlining under the angle of attack is determined by the formula (12.1) .

We have

,

. (12.15)

Let's consider an integral function :

²

Having accounted it an aerodynamic moment of the nose part

, (12.16)

where - relative volume of the nose part.

Coordinate of the nose aerodynamic center relatively to nose of the body of revolution in shares of length of the nose part :

- at absence of the air intake in the nose part .

- at presence of the air intake in the nose part .

Obtained formulae can be used at any Mach numbers (despite of the fact that the theory of an elongated body was applied which is fair for calculation of the derivative only at subsonic speeds ).

	For conical nose part .
	For chambered nose part .

It is necessary to mark, that for bodies with the parabolic nose part coordinate of the aerodynamic center practically does not vary with increase of Mach numbers .

12.2.2. Coordinate of the aerodynamic center of the cylindrical part.

In the subsonic flow ( ) lift of the cylindrical part , therefore the moment characteristics of the cylindrical part are not calculated.

In the supersonic flow ( ) coordinate of the aerodynamic center , as well as the derivative , depends on Mach number, aspect ratio of the nose and type of coupling of nose and cylindrical parts (Fig. 12.7):

.

Let's express a coordinate of the aerodynamic center of the cylindrical part in shares of fuselage nose length

, , (12.17)

where the factor value can be accepted as the following ones:

- for conical nose part ;

- for a nose with chambered generative line and tangent coupling .

Fig. 12.7. Coordinate of the aero-dynamic center of the cylindrical part

Let's mark, that at a coordinate of the aerodynamic center depends only on the attitude of aspect ratios of cylindrical and nose parts of the body of revolution .

At presence of smooth coupling of the nose and cylindrical parts the aerodynamic center locates a little bit distant, than in case of conical nose and intersecting coupling.

12.2.3. Coordinate of the aerodynamic center of the rear part.

Irrespectively of the shape of the rear part, for any Mach numbers coordinate of the aerodynamic center of rear part can be calculated by the formula

(12.18)

i.e. we accept, that rear part aerodynamic center locates in its middle.

12.2.4. Coordinate of the aerodynamic center of body of revolution in a whole.

Let's consider the configuration of a body of revolution (Fig. 12.8). In this case coordinate of the aerodynamic center relatively to nose is determined as :

Fig. 12.8.

, (12.19)

where .

It is necessary to mark, that at subsonic speeds ( ) and small angles of attack, at which the aerodynamic center of the body of revolution can place ahead of a nose, i.e. .

1 _{Is used.}

2 Is used

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