LINDA HALL LIBRARY

LINDA HALL LIBRARY Science Engineering Technology

5109 Cherry Street Kansas City M O 64110 U S A

R E P O R T N O . 85!Q

DATED August 22, 1952

LOCKHEED AIRCRAFT CORPORATION B U R B A N K , C A L I F O R N I A

TITLE

A STUDY OF THE LOAD DISTRIBUTION

IN A CONICAL RIBBON TYPE PARACHUTE

SUBMITTED UNDER

M O D E L Oeneral R E F E R E N C E B.W.A. U658

PREPARED BY GROUP Qulded Missiles Division J. A. Jaeger I. H. Culver R. P. DeUa-Vedowr^^

C H E C K E D B Y A P P R O V E D BY I. H. Culver F

N O P A G E S N O P I C T U R E S F. P. Jems

NO D R A W I N G S -

R E V I S I O N S

REV 9V P A G E S A F F E C T E D R E M A R K S

L O C K H E E D A I R C R A F T C O R P O R A T I O N R E P O R T 3 & 1 .

A STUDY OF THE LOAD DISTRIBUTION IN A CONICAL RIBBON TYPE PARACHUTE

ABSTRACT

Analyses are presented for the determination of the shape the chute structure assumes under load, location of the maximum loaded horizontal ribbon and the loads carried by the horizontal ribbons and radial lines. Also included is a note on the chute opening process.

The results obtained are based on assumptions} but consistency of results, cross-plotting and spot checks gave confidence that the data presented are close approximations.

f o r „ c 7 £ 7

UNDA HALL LIBRARY ^ KAM6A8 CITY, MO

L O C K H E E D A I R C R A F T C O R P O R A T I O N 1 REPORT G72!I

INTRODUCTION

Any attest to make an exact load analysis of a parachute immediately becomes a problem of extreme conylexity. Furthermore, each parachute, only slightly different from the first, would require a separate analysis. From the start it was recognized that basic assunptions would have to be made, and although reasonable, they could not be exact. Further assumptions during analysis would also have to be made, which would undergo refinements as the analysis progressed to result in a usable set of formulae.

The analysis presented here applies to conical ribbon type parachutes having horizontal, rather than diagonal, ribbons, and is considered quite satisfactory for design use. Diagonal ribbon chutes, baseball chutes, square chutes, or parachutes constructed of highly elastic or diagonally woven fabrics in which changes in loads greatly affect the shape of the chute structure, all require separate tailored load analyses.

In any case, to attempt an exact load analysis of a particular parachute would require a tremendous amount of effort, and, since the result would be of only limited use, the value of such an academic project would be question-able. The use of a few well-chosen assumptions and short-cuts makes it possible to conduct a load analysis that will prove extremely valuable for design purposes and at the same time will not require the endless work necessary to make the analysis exact. With this attitude and thought in mind, and recognizing the limitations of application, this analysis is presented.

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L O C K H E E D A I R C R A F T C O R P O R A T I O N 1 REPORT G72!I

A STUDY OF THE LOAD DISTRIBUTION IN A CONICAL RIBBON TYPE PARACHUTE

Experience gained in experimental test drops using conical ribbon type parachutes has pointed up the necessity for a tangible theoretical approach to the design of recovery systems for decelerating heavy objects from high initial velocities.

When circumstances require a parachute of minimum weight and packed volume, a hit-or-miss development program (expensive and time consuming) cannot be relied upon. Test drops indicated that large load variations existed along the radials and in different rows of horizontal ribbons. The optimum design of a parachute intended for a particular purpose can be attained only by a successful stress analysis of the component parts of the drag producing areas.

The following analysis is a first attempt at a theoretical approach for the solution of a few of the quantities involved.

At the outset, the following basic and simplifying assumptions were made on the basis of theory, logic, and motion picture studies.

1. The parachute is stable in all respects and load distributions are axially symmetric.

2. The shape of the pressure field is a function only of the pressure distribution and the distribution of elastic supporting structural loads.

3. A uniform pressure differential exists across the canopy in the in-flated portion.

It. The chute structure has no bending stiffness and all loads are carried in elastic tension.

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L O C K H E E D A I R C R A F T C O R P O R A T I O N 1 R E P O R T G72!I

Before a load analysis of an elastic structure can be made, the shape that the structure assumes under load must be determined. Inasmuch as neither the radial lines nor the horizontal ribbons have any bending stiffness, the outward acting pressure field can be supported only by the curvature of the chute surface. The pressure surface is generated by rotating a radial line about the chute centerline. In general, part of the outward acting pressure is supported by the curvature of the surface in the direction of the horizon-tal ribbons and part by the curvature in the direction of the radial lines. A general expression relating the curvature in the two directions and the tangential forces in these directions is:

•P = Pressure differential (Force per unit area). Fjl Z The component of force in the direction of a

radial line (Per unit width). Rg z The local radius of curvature of the radial line. F}j s The horizontal component of force (Per unit width)

tangent to the surface defined above. Rj£ Z The local radius of curvature of the generated

FR fH RR + %

Where:

surface in a horizontal plane /

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L O C K H E E D A I R C R A F T C O R P O R A T I O N 1 R E P O R T G72!I

Forr ̂ 7(7

In a conical chute, the horizontal ribbons stabilize the radial lines and the conical shape is maintained near the top. But, moving downward from the top, a point is reached where the chute departs from its true conical shape, resulting in a variation in the loads carried by the horizontal ribbons.

Step §\ The following analysis will show the high rate at which the radial lines

pick up the support of the pressure field as the horizontal ribbons become slack.

The diagram below illustrates the section used for the analysis. The distance between the points U represents the true length (no slack) of the horizontal ribbon in the undeformed cone. Section A - A shows the relocation of these points to U', placing them in a plane normal to the chute surface and in true relationship to the shortened (slack) distance between the same points (3) with a departure from the conical surface.

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L O C K H E E D A I R C R A F T C O R P O R A T I O N 1 R E P O R T G72!I

The following explanation of the same thing from a slightly different viewpoint may help to clarify the picture.

If axial symmetry is assumed, then a gore is enclosed within a three-dimensional segment with an angle of ^ T. .

The distance between the planes of the angle is proportional to the horizontal distance from the £ .

"X" is proportional to "y".

Therefore, the length ratio of a horizontal ribbon is equal to D ' "1

which is also equal to (_jL_) • A Rz £

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LOCKHEED AIRCRAFT C O R P O R A T I O N REPORT 85U.

Using Section Ik -A, notations are made as shown in the diagram. Lets = K

r 2

s : R 2 o c - - (L)

From (1) r z & Prom (2) t ^ s / ^ ) W

f ) 2.

R i ^ S/'/c ~ <o

&2 S/n.

Since for values of <K~ from 0° to 20° (chutes with 18 gores or more) we can say (approximately), ̂ C (radians) Z S ,

Then: K

R2 ' For a -given angle oC > & can be found for ratios of — . Angle <=C R 2

is a function of the number of gores and the geometry of the parachute under consideration.

For illustrative purposes, assume a 20°. Then Z and ribbon hoop tension The component of force normal to R^ is

prcos(-j - and the percent of the pressure carried by the ribbons for small

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L O C K H E E D A I R C R A F T C O R P O R A T I O N 1 R E P O R T G72!I

deviations from the true cone is .pT. ^ ^ • relationship is shewn in Figure 1, Values of the ratio £ Vs. K are also plotted. The error due to the assumption that AngleoC is constant for a given parachute is small, and the actual percent load curve will fall somewhere between the two curves shown. True, oC remains constant for a given parachute as long as the true conical shape is followed, but as the shape departs from the cone and wraps dowiward, oC increases until it becomes equal to 6̂0

N

maximum inflated radius (RINF)«

Step #2

Before further analysis can be made, the relationship that exists be-tween the maximum inflated radius of the chute and the radius of curvature of the radial lines at that point must be determined.

From the diagram: Hjjjp Z Maximum inflated radius (Flan

View). RJJT a Radius of curvature of the

radlais at RjNF* PG = -p- (Rinf)2 TT - Axial load

N per radial at RIM?.

Where: •p z Pressure differential N Z Number of radial lines

At the maximum inflated diameter, the horizontal ribbons are scalloped and carry no appreciable portion of the hoop tension, and it follows that the maximum axial load in the radial lines occurs at this point.

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L O C K H E E D A i R C R A F Y C © R P O R A Y 8 O N R E P O R T 85 ill

So: P0 = -p Rht (2 77 ̂ ), and ̂ ('Wjj 7T = * Rht (2 TT RlNF ) N r N jj

Reducing, RINF Z Z ®HT

The radius of curvature of the radial lines at the maxinum inflated diameter is half the maximum inflated radius of the chute.

Step 13 From the foregoing relationship, graphic derivations of inflated radius

as a function of cone angle may be made for chutes of various shroud line and gore lengths. The construction consists of laying out the cone angle and torus for given shroud line and gore lengths so that two points of tangency to the torus are obtained.

The derivation for conical parachutes having shroud line lengths 1.7 times the conical radius is given in Figure 2. The values shown are consider-ed accurate for cone angles of 30° and greater. For angles less than 15°, the curve is only approximate. Corrections for elasticity of the lines can be applied when the drag load is known and load-deflection characteristics of the lines are determined.

Step From observations of photographs of parachutes taken during test drops,

and from the curves of Figure 1, a rapid transition from horizontal ribbon support to pure radial line support of the pressure field was indicated. Two approaches to the problem of analysis were made in order to better evaluate the assumptions which would have to be made for parachutes with small cone angles.

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L O C K H E E D AiRCRAFT C O R P O R A T I O N REPORT 85hl

SOLUTION A

Assume that the load in the radial lines is zero at the apex of the parachute cone, but at some point a distance "X" from the apex the load has increased to the same value required for equilibrium at the maximum inflated radius. Through distance "X", the horizontal ribbons are tight and support the pressure field, but as the radial lines depart from the cone and move around the radius (ROT r ^JF), the horizontal ribbons start to slacken and the load from the pressure field is progressively transferred from the hori-zontal ribbons to the radial lines until it becomes a constant axial load on the radials.

R1 - X Cfs/S , and Rg = taryS

Radial Line Load at Max. R^- r 77<RINF)̂ t> N

Radial Line Load at "X" distance from the Apex = TTVU 2?

N S/nyS

To satisfy the assumptions:

7T(RINF)2^ N

Or: (RINF)2

TT ( V ?

N Sj'lyS

W 2

S/rlyg

Substituting for R^ ai*3 inverting; X s R INF Cos, os4d

3y comparisons of geometrical layouts and solutions for the above equa-tion, the tangency point between the torus and cone was in agreement for angles of^? equal to and greater. To determine the critical value of

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LOCKHEED AIRCRAFT C O R P O R A T I O N R E P O R T 8 & 1

"X" for cone angles less than Li5°, a second solution to the problem is neces-sary.

SOLUTION B

Assume that the departure from the conical surface is an approximate ellipse, rather than circular in shape. The assumed shape is constructed from 2 radii with the point of tangency at U5°, as shown in the diagram.

, R j r X C O ^ G

Also I z

1.207 RxNF

And:

X cos/3

1.207 Rjnf

1.20?

Solutions of this equation for values of cone angle <y* ) of hf and less gave the corresponding values of critical —2L . The plotted data are

RINF

shown on Figure 3» and represent the location of the maximum loaded horizon, tal ribbon.

Step #5

The variation of axial load in a radial line can now be predicted by using the probable values given in Figure 3. Since the tension load

INF

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