DE2417759A1 - REAR FUSELAGE WITH MINIMAL AIR RESISTANCE - Google Patents

Description

The invention relates to fuselage interior parts and in particular on the back of the fuselage with minimal air resistance.

An essential analytical and experimental development work has been used over the years to create streamlined shapes Bodies carried out, which have a low air resistance in a flow field. Body with low air resistance are particularly suitable for use in plug-in tools or in other, fast vehicles, the U.S. Describes U.S. Patent 2,596,139 e.g. a streamlined auxiliary fuel tank for Attachment to the wing tip of an aircraft, which fuel tank is designed in such a way that it supports the speed of the aircraft offers minimal resistance and that it does not affect the maneuverability of the aircraft. It Numerous manuals have already been published, which derive and explain formulas in order for rotational solids outlines with minimal Air resistance in subsonic, supersonic and hypersonic flow fields to determine. These investigations often end at flow velocities, which is based on the speed of sound approach Shern. In addition, these investigations are usually concerned with the total air resistance of a body, which air resistance among other things from the air resistance of the front part of the fuselage, of the fuselage behind parts and the base area. Since the shape of one part of the body can have an influence on the air resistance of another part of the body, the air resistance

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to coordinate the positions of the individual fuselage parts in relation to one another, in order to reduce the total air resistance to a minimum « As a result, the air resistance of each particular part of the fuselage is important not necessarily minimal. It is not yet known to design a rear fuselage part in such a way that this rear fuselage part has minimal air resistance.

Steel engine nacelles attached to the wing of a jet aircraft attached create an unavoidable drag. These gondolas usually have large rear hulls. So far, the outer outline of the rear part of the fuselage has been the nacelle determined on the basis of empirical values or through test and error procedures to achieve a low air resistance, since no particular textbook method is known for determining the fuselage rear part outline which has minimal air resistance guaranteed.

The object of the invention is to create a rear part of the fuselage with minimal air resistance.

According to the invention, the fuselage rear part of a body of revolution has a maximum cross-sectional area at its front end, which cross-sectional area decreases linearly in relation to the axial length of the fuselage rear part in the direction of a minimum cross-sectional area at the rear end of the fuselage rear part. A fuselage rear part designed according to the teaching of this invention has the smallest possible air resistance in a flow field for a large range of flow velocities in the vicinity of and including Mach 1.

Embodiments of the invention are shown in the drawings and are described in more detail below, it show:

Figure 1 is a side view of a slim body of revolution, which is attached by means of a tail in a wind tunnel.

Figure 2 is a graph of the cross-sectional area for a minimum air resistance depending on the length of the rear part of the fuselage.

Figure 3 is a graph of the radius fg _r a

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minimum air resistance depending on the length of the rear part of the fuselage.

FIG. 4 shows a sectional view of a nacelle for receiving a gas turbine engine.

FIG. 5 shows a graphical representation based on experimental tests to illustrate that the IMS value is in immediate There is a correlation to the air resistance of the rear part of the fuselage.

FIG. 6 shows a side view of a rofation body with a rear part of the fuselage, shaped in accordance with the present invention.

Figure. 7 shows a perspective illustration of an aircraft with a fuselage, which has two nacelles to accommodate gas turbine engines having.

FIG. 8 shows a sectional view along one through the longitudinal axis the vertical plane running through a nacelle of the aircraft according to FIG.

FIG. 1 shows one in a flow field by means of a Tail attached body of revolution, as is customary for experimental purposes in a wind tunnel. The fuselage has an anterior fuselage part and a fuselage behind part. The air flows from left to right in the direction of the axis of the fuselage, which in this example is denoted by X. For the purpose of the following derivation, X gMch 0 at the front end of the trunk is h in te r te i Ie s where the Rear part of the fuselage has a maximum radius R. The minimum

The radius of the trunk behind part is denoted by R and is located at X = JL . The radial direction is denoted by r. To determine the contour for the rear part of the fuselage, which ensures a minimum air resistance for a large range of flow velocities, e.g. the near-sound flow speeds, a parameter is required that is directly related to the air resistance of the rear part of the fuselage.

For high UnSound Mach numbers and for axially symmetrical, slim ones Body reads the linear, frictionless flow equation:

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therein are: M ₀₀ the Mach number of the free flow and Q the streaming potential, a simpler, subscript after the letter Q means the first partial derivative of Q in relation to this subscript and a double, subscript after the letter Q means the second partial derivative of Q in relation to this subscript.

A common solution to this equation (according to slender body theory) is:

where: U ^ the free flow velocity, A the cross-sectional area of the body perpendicular to its axis as a function of x, A ¹ equals r, ^ an integration changer,

A. equal to (1 - M ₀₀ ) and ^ the length of the body. Equation (2) can be differentiated to obtain the following velocities at the body surface:

* t ^ o tf-ir J i

AJL

where ^ - is a dimensionless speed. With high subsonic Mach numbers (for example Mach numbers close to 1.0) and if the length of the body is at least equal to the maximum radius of the body (ie for a slim body), the result is that (χ -Jf) is greater than —-τ- da ^ « 4.0 . Accordingly, the denominator of the integrand in equation (3) can be expanded as follows:

(4) Equation (3) is now given the following form

- - - λ * fl'w * £ y

i / o ⁼ ^ fT ₀ J ^ Yy \ ^ j. 3aW (5)

TT

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since (χ - Y ) is greater than -, the greatest contribution to the integral is in the area where Y approaches χ. For this point we therefore develop A (Y) in a Taylor series expansion and bring the integral close to a high degree of accuracy. If one only keeps expressions of the first order in this expansion one obtains the following approximation for equation (5):

Α '' ^Λ

ο LiX η + T / fJ (6)

I / o «""^ ⁷⁷ "

^r "V ^ sSY

2.7Γ 3 / LA

For values of -1, which are much larger than "

the value of the integraJ.es in equation (7) is directly fixed and is - ^. Accordingly, equation (7) decreases as follows i

^c * Al

V? -

where C- is a constant and since A = ^ R, A can be set equal to R. where R is the radius of the trunk behind te iles and depends on χ is. For slim body can for the. Pressure coefficient along a body can be derived the following equation;

where Cp is the pressure coefficient. By combining the equations (8) and (9) one obtains:

where R ^{1 is} equal to dR / dx. The air resistance of a body can be obtained from the following equation, which represents an integration of the pressure force along the torso interior:

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where: D is the air resistance, θ is the dynamic pressure

A is the minimum cross-sectional area of the body and A is the maximum e m

Cross-sectional area of the body. Combining equations (10) and (11) one obtains:

MmT " Ct _ß / p »j I / ß

β-1

For slim fuselage interiors where the difference between the minimum and the maximum cross-sectional area is not great, as illustrated by the fuselage rear part in FIG. 1, the prerequisites made in this derivation are correct for high subshell numbers. The following expressions also apply:

R « Rm (13)

/ Rm'Re \

\ ~ Ä J

where y is a variable and equal to (R ._ R) and y 'is the first derivative of y with respect to χ. Applying this approximation in equation (12), ζ

^θ ~ -ii-n ~ 4>.

(16)

or

where C is the drag coefficient and the right-hand side of the equation represents the integration of the mean slope of the cross-sectional area for the course of the cross-sectional area. By making suitable expressions dimensionless, equation (17) has the following form:

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where D is the equivalent diameter or ^! is.

The above expression is an approximation and a reciprocal one Parameter that can be used for Mach numbers close to noise and that can be justified using the determining flow equations is. A similar expression can be obtained very quickly by using a concurrent approximation for small supersonic Mach numbers. In this case the determining friction-free flow equation is:

(15)

and the resulting mutual air resistance parameter reads s

(2o)

where IMS is an abbreviated expression for the mutual parameter and stands for the integral of the mean slope.

Experimental tests have shown that IMS has a direct correlation with the air resistance of the rear of the trunk stands in a flow field with a Mach number of 0.5 - 2.0. FIG. 5 is a graph made by experimental tests for Mach numbers of 1.2 was determined and where IMS is on the haazontal axis and the drag coefficient (C) are plotted on the vertical axis. These Attempts were made for rear parts of the fuselage with cross-sectional ratios

-e. of 0.1 and 0.2 performed. You can see that IMS is

is essentially one-to-one with respect to resistance. The IMS value can thus be used to predict the pressure and the frictional resistance at Mach numbers close to sound. It is believed that the correlation is even with Mach numbers greater than 2, ο exists.

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Now that an expression has been derived that is both analytically and experimentally directly correlated to air resistance it is relatively easy to use this expression reduced to a minimum in order to get a formula which the outline of a minimum air resistance for a rear part of the fuselage expresses. Equation (18) or (2o) can be converted into a more manageable form as follows:

R _m (R _m -f> e) J UxJ

(21) O

since A equals 7t R, equation (21) can be written as follows:

(22)

It should be emphasized at this point that if the expression for IMS in equation (22) is reduced to a minimum, man receives an expression which represents the outline of a minimum air resistance for a rear fuselage part. The problem of Reducing the IMS integral term to a minimum therefore includes the simplified integral term

(RRJ

O' (23)

reduced to a minimum. In order for I to be minimal, there is one from the standpoint of the infinitesimal calculus of variables necessary and in this case a sufficient requirement, namely:

* cL / oF \ ■ ό * "/) '

(25)

by combining the equations (24) and (25) one obtains the following, determining differential equation, which is the optimal

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Outline for minimal drag expresses:

O ₍₂₆₎

By ordering, equation (26) is given the following form:

(27)

The solution to equation (27) is:

^ ^Ä "V ^ 5 ^{X +} £ * (28)

As can be seen from Figure 1, the appropriate boundary conditions are. gen as follows:

XO at R * Rnt \

Χ «Λ for« _S «e J < ²⁹ >

Inserting these boundary conditions into equation (28), solves for C- and C. and transfers these values back to the Equation (28) we get:

This can be expressed in terms of the cross-sectional area as follows will:

Rrr> J Oil)

R = CfX + c $ ( _31a )

where C _n = - ^e ~ ^m and C ₁ . = A.
5 λ 6 m

Substituting equation (31) into equation (21) and by Integrating you get the following expression for a minimum IMS value:

(32)

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Since the air resistance of the rear part of the fuselage with the IMS value such as one to one correlates expressing the equations (31) and (31a) rear parts of the trunk with minimal air resistance the end. Equation (31a) says that for a trunk rear part whose outer surface is a surface of revolution and that of a maximum cross-sectional area perpendicular to its axis at its front end to a minimum cross-sectional area perpendicular to its axis at its rear end changes, the cross-sectional area of the rear part of the fuselage linearly in relation to the axial length of the rear part of the fuselage from the maximum. Cross-sectional area should decrease to the minimum cross-sectional area, so that the fuselage behind part have minimal air resistance. Equation (31a) is in the graphic Representation of Figure 2 represented by a straight line, the axial length (x) of the rear part of the fuselage on the The horizontal axis is plotted and the vertical axis represents the cross-sectional area (A) of the fuselage interior. The maximal The cross-sectional area of the rear part of the fuselage is located in the Zero point of the horizontal axis and is plotted in this way in Figure (2). The minimum cross-sectional area is located at the rear end of the fuselage rear part at an axial distance ^. the Change in cross-sectional area along the axial length, which causes minimal air resistance in the fuselage behind parts is represented by the straight line connecting these two points. The graph according to FIG. 2 can be modified in accordance with FIG. 3 to show the radii. The graphic representation of FIG. 3 thus shows the actual outer outline of a rear part of the fuselage with minimal air resistance. Along the length of the back of the trunk the product of the inclination and the radius of the rear part of the fuselage is a constant. This can be expressed by the following formula will:

= C, 33,

where: R is the radius, which is variable, and R ^{1 is} the first derivative of the radius with respect to the axial length (ie the slope) and C is a constant.

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As can be seen from FIG. 3, the curvature of the rear parts of the fuselage increases with minimal drag along the axial length if the diameter decreases · This is exactly the opposite of the design of the known rear fuselage parts. By examining the Equation (33) shows that the slope becomes infinitely great if the diameter approaches zero. It is known that the flow breaks away from the surface of the rear part of the fuselage if the curvature in relation to the speed of the Flow field is too large. Put the expressions derived above assume that there will be no stall. At one point along the axial length of the rear part of the fuselage where the stall occurs occurs the equations are not applicable and they are not used to determine an outline for minimum air resistance downstream of the stall point. It is accordingly desirably the outline downstream of the stall point of the fuselage behind parts in such a way that there is no stall occurs. The formulas derived above cannot be used to determine these sections of the trunk back te rte ile.

An application for a fuselage section with minimal air resistance For example, the rear of the fuselage is part of a gondola, which is a encased gas turbine engine attached to an aircraft, usual Gas turbine engines have a relatively constant Diameter from its front end to near its rear end and then the diameter decreases to form an outlet nozzle. In the case of Ma η te 1st rom drives η the diameter is essentially maximum at the front end and decreases from a point close to the front end to the rear end to a minimum diameter to form the outlet nozzle. In any case, the rear part of the nacelle surrounds the engine and this rear part of the nacelle increases from a maximum diameter at a point in front of the rear end of the engine to a minimum diameter at rear end of the engine. FIG. 4 shows a typical gondola (designated as a whole by 10) for a by means of dashed lines Gas turbine engine 11 shown in lines.

In this embodiment, the front part 12 has the nacelle

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a constant diameter. This part of the nacelle 10 is referred to below as the fuselage front part 12. A coordinate system 14 is entered in FIG. 4, the horizontal axis 14 coinciding with the engine axis, which is also on the Axis of the gondola 10 is located. The vertical axis 18 lies at the rear end of the fuselage front part 12, which is also the front part Forms the end of the rear part of the fuselage 2o of the nacelle 10. In the previous one In the description, the formulas were derived for determining the outline of the outer surface 22 of the rear part of the fuselage 20 so that this rear part of the fuselage 20 have minimal air resistance target. These formulas state that if the axial distribution of the cross-sectional area is perpendicular to the axis of the rear part of the fuselage decreases linearly from the front end to the rear end of the rear part of the fuselage (i.e. from the maximum radius to the minimum Radius) then the air resistance of the area 22 of the rear part of the fuselage is minimal. One way to find the outline for minimum drag is to use a curve similar to the Record curve according to Figure 2. Since the engine dimensions determine the maximum radius and the minimum radius of the nacelle 10, the maximum cross-sectional area and the minimum cross-sectional area f The surface of the back of the trunk 20 is also known. By This cross-sectional area η is entered in a graphic representation corresponding to the representation according to FIG. 2 and by means of a connection of these points by means of a straight line one obtains the cross-section f surface η perpendicular to axis 16 for all other points between the front end and the rear end of the fuselage interior » 20. This cross-sectional area η can of course be converted into radii.

As already described above, for the outline of a rear part of the fuselage with minimal air resistance theoretically for the diameter 0 the curvature can be infinite and thus one obtains the inevitable state that the flow at a point in front of the tear off the rear end. The application of the derived formulas to engine nacelles is particularly advantageous because the nacelles are separate do not reduce to the zero diameter at its rear end. As long as the length of the fuselage interior of the gondola is so long

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is that the diameter of the nacelle does not decrease too quickly (the above formulas were derived using slim body theory) stalling will not be a problem be.

It was found that for some cross-section of the fuselage front part 12, one formed in accordance with the present invention Rear fuselage part 2o generates the smallest possible air resistance. However, this only applies to the extent that the above formulas presuppose an infinite flow field or a flow field which approaches an infinite flow field. If the fuselage front part 12 is designed such that it runs along the flow field the trunk behind part 2o interrupts so that it is not as infinite Flow field can be treated, so can the derived Formulas of course are not applied.

The nacelle 10 is used for fastening under an aircraft wing, but for certain steel engines, especially in combat aircraft used engines, these engines are installed in the rear section of the aircraft fuselage. This back section is to be compared in its function with the gondola 10 according to Figure 4, and the application of the present invention to a such nacelle, as well as on other fuselage rear parts, is in the frame the invention.

In this context, FIG. 7 can be viewed, which shows an aircraft in perspective. The aircraft includes one Fuselage, which is marked overall with SO. The hull has one left nacelle 52 and a right nacelle 54 which are interconnected and each nacelle contains a gas turbine engine (not shown). FIG. 8 shows one of the gondolas in a vertical longitudinal section. The rear of the nacelle 52 includes a Fuselage behind part 58. The fuselage behind part 58 consists of a Rotary body 60, which is arranged from the longitudinal axis 56 at a distance is and at its front end in the plane 62 a maximum cross-sectional area and a minimum cross-sectional area its rear end 64, which is the outlet end of the nacelle 52 forms. The axial distribution of the cross-sectional area perpendicular to the longitudinal axis 56, which passes through the surface 60

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is true, is linear from the maximum cross-sectional area in the plane 62 to the minimum cross-sectional area at the rear end 64. Experimental tests have shown that an airplane, such as airplane 50, with nacelles, interparts accordingly with the Rurapfh the fuselage part 58 formed 360 kg less Air resistance has as an aircraft with the second best known nacelle shape. In other words, the drag of each nacelle was reduced by 180 kg compared to other tested gondolas.

It is known that when designing gondolas for twin-engine Aircraft, such as aircraft 50, experience mutual interference between adjacent nacelles due to their proximity side by side and due to the connections between the two gondolas. It is often the In the event that a nacelle outline that has low drag when tested alone is unsatisfactory, if it in combination with an aveiten, arranged next to the first gondola Gondola being tested. Accordingly, substantial work is required to create the outlines of the gondola and the outlines for the to determine the aircraft parts connecting the nacelle in order to obtain an acceptable air resistance. By applying the nacelle outline according to the present invention, however, one obtains the smallest possible air resistance regardless of the distance between the nacelles or the various forms of aircraft components between the two nacelles. Regardless of the distance and the Airframe, is the outline of the rear part of the fuselage of the nacelle, which causes minimal air resistance, always the linear cross-sectional distribution, as described above.

Another embodiment of the invention is shown in FIG. The rotational body 30 according to FIG. 6 has a longitudinal axis 32 and is used in a flow field which moves in the direction of the axis 32 at a relative speed from left to right with respect to the rotating body 30.

The maximum diameter D of the rotating body 30 is located

m "

in plane 34. The part of the solid of revolution 3O on the left On the side or upstream of level 34 is the front part of the fuselage

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The reference number 38! »Denotes a plane which is perpendicular to the axis 32 by the dimension d downstream of the plane of the maximum diameter 34. In this exemplary embodiment, d is equal to or greater than zero. The reference number 40 indicates a plane which is perpendicular to the axis 32 and is offset inward by an amount ρ or lies behind the plane 38 in the direction of flow. In this embodiment, the part of the body 30 between the planes 38 and 40 forms the trunk rear part 42. The trunk rear part 42 has a maximum cross-sectional area in the plane 38 and a minimum cross-sectional area in the plane 40. The axial distribution of the cross-sectional areas perpendicular to The axis 32 from the plane 38 to the plane 40 (the front end or the rear end of the fuselage behind part 42) is linear. This means that the distribution of he ^fl QuerschnittsflSchen between the planes 38 and 40 corresponds to the equation (31).

A rotational body 30 was described in the above description, which has a minimal resistance of the rear part of the fuselage 32 of the body 30. In other words, for a body 30 of any shape upstream of plane 38 and downstream of the plane 40, no other rear fuselage part 42 can be constructed which has a lower air resistance. One may however, in no event believe that the fuselage 30 as a whole has minimal overall drag. It is highlighted that the only part of the body 30 which has minimal air resistance is the rear part of the trunk 42.

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Claims (4)

_ ie- 241775S PATENTANS PRUECHE. 1. Fuselage with a minimal air resistance Hull behind part where the fuselage behind part has a longitudinal axis has a front end, a rear end and a sweet surface, which is arranged at a radial distance from the axis and extends from the front end to the rear end, wherein the Fla'che is a surface of revolution about the longitudinal axis and the surface is a maximum cross-sectional area of the fuselage behind parts at the front End perpendicular to the longitudinal axis and a minimal cross-sectional area, which is greater than zero, at the rear end perpendicular to the longitudinal axis having, characterized in that the cross-sectional area linear in relation to the axial LSngedss fuselage behind part of the maximum Cross-sectional area at the front end for the minimum cross-section, area decreases at the far end of the trunk rear part. 2. Fuselage according to claim 1, characterized in that it has a Forms nacelle for receiving an aircraft gas turbine engine. 3. Fuselage according to claim 2, characterized in that the nacelle for receiving the gas turbine engine at the rear end of an aircraft fuselage it is trained. 4. Fuselage according to claim 3, characterized in that a second Gondola to accommodate a gas turbine engine next to the first nacelle is arranged at the rear end of the fuselage of the aircraft. 409884 / -Q856