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The Theory of Fabric Porosity as Applied to Parachutes in Incompressible Flow

Published online by Cambridge University Press:  07 June 2016

Peter R. Payne
Peter R. Payne*
Affiliation:
(Payne inc., Annapolis, U.S.A.)
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Summary

Many aspects of parachute behaviour are dominated by the permeability of the canopy cloth. Techniques employing kinematic principles to predict parachute opening behaviour, for example, must first be able to predict the air flow through the canopy material. This paper is concerned with the development of such a predictive capability.

The flow of air through cloth of gauze has been studied by many workers; since the 1850’s, in connection with filters; and since the early twenties, in connection with parachutes. Workers in each of these disciplines seemed unaware of the work being done in the other.

In the case of parachute cloth permeability we find the foundations being laid down by such eminent workers as Glauert in 1932 and Taylor in 1944. Yet most subsequent writers seem not to be aware of this, and since World War II, there have been many papers “rediscovering” basic principles; often with errors which could have been corrected by reference to the earlier authorities.

In this paper we attempt to bring together all the work which has been done in this field, and to rationalize the data by simple mathematical modelling. Individual elements of the model have been proposed before, of course.

We then examine the effect of tension on the geometric porosity of fabric, and hence the pressure loss Ap. A theoretical analysis shows that tension is likely to be a major factor. For cloths which have low porosity when unloaded our simple mathematical model shows that, for a given Ap, a stress equal to 50% of ultimate can increase the air volume flow Q by an order of magnitude. In general, the increase in permeability is greatest at the lower values of Ap, indicating that the viscous term is more influenced by tension than the dynamic term. This theoretical result is confirmed by some rather limited experiments carried out by Lashbrook and Marby. But their data also shows that a cloth made from relatively stiff glass fibers can experience a reduction in permeability when loaded, due to a “closing up” of the weave. The reasons for this are discussed.

Type
Research Article
Information
Aeronautical Quarterly , Volume 29 , Issue 3 , August 1978 , pp. 175 - 206
Copyright
Copyright © Royal Aeronautical Society. 1978

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References

1 Glauert, H., Hirst, D.M. and Hartshorn, A.S. “The Induced Flow Through a Partially Choked Pipe With Axis Along the Wind Stream.” Reports and Memoranda No. 14-69 (March 1932)Google Scholar
2 Taylor, G.I. “Air Resistance of a Flat Plate of Very Porous Material.” A.R.C. R&M No. 2236, (January 1944), ATI 97321Google Scholar
3 Taylor, G.I., and Davies, R.M. “The Aerodynamics of Porous Sheets.” ARC R&M No. 2237, April 1944, ATI 50554Google Scholar
4 Lashbrook, R.V., and Marby, C.M. “An Investigation of Low Permability Fabrics and of Suspension and Control Lines for the All Flexible Parawing.” AIAA Paper Preprint No. 68-593 presented at AIAA Second Aerodynamic Deceleration Systems Conference, El Centro, California (September 1968), A68–42033 Google Scholar
5 Darcy, H.P.G. Les Foutaines Publiques de la Ville de Digon. Victor Dalmont: Paris (1856)Google Scholar
6 Davies, C.N. Air Filtration. Academic Press, New York, (1973)Google Scholar
7 Phillip, J.R. “Flow in Porous Media” in Annual Review of Fluid Mechanics, Vol. II (1970), Annual Reviews, Inc., Palo Alto, California Google Scholar
8 Walker, D.A., and Gloor, W.H. “Fiber and Yarn Density Determination.” AFML TR 68-74 (AD 675 142), Wright-Patterson Air Force Base, Ohio (July 1968)Google Scholar
9 Annand, W.J.D. “The Resistance to Air Flow of Wire Gauzes.” Journal of the Royal Aeronautical Society, Vol. 57, (March 1953)CrossRefGoogle Scholar
10 Grootenhuis, P. “A Correlation of the Resistance to Air Flow of Wire Gauzes.” Proceedings of the Institute of Mechanical Engineers, Vol. 68, No. 34, (1954)Google Scholar
11 Morgan, P.G. “Fluid Flow Through Screens of Low Solidity.” Journal of the Royal Aeronautical Society, Vol. 66, (January 1962)Google Scholar
12 Baines, W.D., and Peterson, E.G. “An Investigation of Flow Through Screens.” Transactions of the ASME, 73, p.467, (1951)Google Scholar
13 Rainard, L.W. “Air Permeability of Fabrics, II.” Textile Research Journal, (March 1947)CrossRefGoogle Scholar
14 Goglia, M.J., LaVier, H.W.S., and Brown, C.D. “Air Permeability of Parachute Cloths.” Textile Research Journal, (April 1955)CrossRefGoogle Scholar
15 Goglia, M.J. “Air Permeability of Parachute Cloths.” Wright Air Development Center Rept. 52-283, (November 1952), AD 3890Google Scholar
16 Green, L., and Duwez, P. “Fluid Flow Through Porous Media.” Journal of Applied Mechanics, Vol. 18:1, 39–45, (March 1951)Google Scholar
17 Pinker, R.A., and Herbert, M.V. “Pressure Loss Associated with Compressible Flow Through Square-Mesh Wire Gauzes.” Journal Mechanical Engineering Science, Vol. 9, No. 1, (1967)Google Scholar
18 Backer, S. “The Relationship Between the Structural Geometry of a Textile Fabric and its Physical Properties, Part IV-Interstice Geometry and Air Permeability.” Textile Research Journal XXI, 703 (1951)Google Scholar
19 Hoerner, S.F. “Fluid Dynamic Drag.” Published by the Author, (1958)Google Scholar
20 Ludtke, W.P. “A Technique for the Calculation of the Opening-Shock Forces for Several Types of Solid Cloth Parachutes.” NDTR 72-146, (June 1972)Google Scholar
21 Simmons, L.F.G., Gould, R.F.W. and Cowdray, C.F. “Wind Tunnel Experiments on the Squidding of Parachutes.” ARC 7062 (October 1943) ATI 99897Google Scholar
22 Duncan, W.J. “The Cause of the Spontaneous Opening and Closing of Parachutes (The Phenomena of ‘Squidding’).” ARC R&M No. 2119, (December 1943), ATI 101577Google Scholar
23 O’Hara, F. “Notes on the Opening Behaviour and the Opening Forces of Parachutes.” Royal Aeronautical Society Journal, Vol. 53, pp. 1054–1062, (November 1949)Google Scholar
24 Smetana, F.O., and Williams, J.C. “Aerodynamic Characteristics of Representative Parachute Fabrics at Simulated High Altitudes.” in International Symposium on Space Technology and Science (AIAA Technical Information Service A68-10195) (December 1968)Google Scholar
25 Ingmanson, W.L., Han, S.T., Widler, H.D., and Myers, W.T. Jr. “Resistance of Wire Screens to Flow of Water”. Tappe, Vol. 44, No. 1 (January 1961)Google Scholar
26 Reynolds, O. Papers on Mechanical and Physical Subjects. Cambridge, Mass., Cambridge University Press (1900)Google Scholar
27 Batchelor, G.K. An Introduction of Fluid Dynamics. Cambridge University Press (1967)Google Scholar
28 Baine’s, W.D., and Peterson, E.G. “An Investigation of Flow Through Screens.” Transactions of the ASME, pp. 467, (July 1951)Google Scholar
29 Schutt, H.C. “Losses of Pressure Head Due to a Sudden Enlargement of a Flow Cross Section.” Paper HYD-51;10, pp. 83–87, (1929)Google Scholar
30 Peters, H. “Conversion of Energy in Cross-Sectional Divergence Under Different Conditions of Inflow.” NACA Tech. Memor. 737, (1934) (Translation from Ing. Archiv., Vol. 2, pp. 92–107, (1931).)Google Scholar
31 Patterson, G.N. “Modern Diffuser Design.” Aircraft Engng., Vol. 10, pp. 267–273, (1938)Google Scholar
32 Cole, B.N., and Mills, B. “Theory of Sudden Enlargements Applied to the Poppet Exhaust-Valve, With Special Reference to Exhaust-Pulse Scavenging.” Proc. Instn. Mech. Engrs., Vol. IB, No. 8, pp. 364–378, (1952-53)Google Scholar
33 Benson, R.C.J. Communication on Reference 34, Proc. Instn. Mech. Engrs., Vol. 169, p. 1016, (1955)Google Scholar
34 Hall, W.B., and Orme, E.M. “Flow of a Compressible Fluid Through a Sudden Enlargement in a Pipe.” Proc. Instn. Mech. Engrs., Vol. 169, No. 49, pp. 1007–1020, (1955)Google Scholar
35 Benedict, P.R., Carlucci, N.A., and Swetz, S.D. “Flow Losses in Abrupt Enlargements and Contractions.” J. Engng. Pwr., Vol. 88, No. 1, pp. 73–81, (1966)Google Scholar
36 Idel’chik, I.E. Handbook of Hydraulic Resistance. Coefficients of Local Resistance and of Friction. A.E.C.-tr-6630. U.S. Atomic Energy Commission, (1966) (Available from U.S. Dept. Commerce, Springfield, Va. Translation from Spravochnik po gidravlicheskim soprotivleniyam. Gos. Energ. Izd., Moscow, 1960)Google Scholar
37 Tyler, R.A., and Williamson, R.G. “Sudden Area Enlargement Pressure Recovery with Inflow Distortion.” Aeronautical Journal, Vol. 72, No. 687, pp. 243–244, (1968)Google Scholar
38 Eckert, B., and Pfluger, F. “The Resistance Coefficient of Commercial Round Wire Grids.” NACA Technical Memo. No. 1003, ARC 7466, (January 1942)Google Scholar
39 Hoerner, S.F. Pressure Losses Across Screens and Grids. AFTR 6289, (Date Unknown)Google Scholar
40 Cornell, W.G. “Losses in Flow Normal to Plane Screens.” Transactions of the ASME, Vol. 80, p. 791 (1958)Google Scholar
41 Rainard, L.W. “Air Permeability of Fabrics.” Textile Research Journal, Vol. 16, No. 10, (October 1946)Google Scholar
42 Robertson, A.F. Textile Research Journal, 20, pp. 838–857 (1950)Google Scholar
43 Penner, S.E., and Robertson, A.F. “Flow Through Fabric-Like Structures.” Textile Research Journal, (November 1951)Google Scholar
44 Schubauer, G.B., Spangenberg, W.G., and Klebanoff, P.S. “Aerodynamic Characteristics of Damping Screens.” NACA Technical Note No. 2001 (January 1950)Google Scholar
45 Crane, J.F.W. “The Use of Woollen Felt Screens as Air Cleaners for Supersonic Wind Tunnels.” ARC C.P. No. 538, (October 1960)Google Scholar
46 Perry, W.O. “Study of the Effects of Fabric Geometry Variables on Air Permeability.” WADC Tech. Report 54-574, (AD 920 30), Wright Patterson Air Force Base, Ohio, (November 1955)Google Scholar
47 Brown, W.D. “The Effect of Tension on the Porosity of a Parachute Fabric.” Rept. 7 Memo No. 2325 (RAE Tn Aero. 1356), ATI 103 793 (Also ATI 96439, (January 1944))Google Scholar
48 Klein, W.G., Lermond, C.A., and Piatt, M.M. Development of Design Data on the Mechanics of Air Flow Through Parachute Fabrics. WADC Technical Report TR 56-576, (September 1967), AD 131055Google Scholar
49 Klein, W.G., Lermond, C.A., and Piatt, M.M. Research Program for the Development of a Design Procedure to Engineer Parachute Fabrics. WADC Technical Report TR 58-65 (May 1958), AD 155517Google Scholar
50 Krizik, J.G., Victory, E., Cheatham, J., and Backer, S. Design Data on Biaxial Forces Developed in Parachute Fabrics. WADC Technical Report TR 57-443, (December 1957) AD 142208Google Scholar
51 Seshadri, C.V., Brown, G.A., Backer, S., Krizik, J.G., and Mellen, D.M. Air Flow Characteristics of Parachute Fabrics at Simulated High Altitudes. WADC TR 59-374 (AD 270 928), (March 1960)Google Scholar
52 Baker, A. “The Mechanical Properties and Porosity of Parachute Fabrics.” RAE Report No. Chem 507 (AD 123 193), (September 1956)Google Scholar
53 Baker, W., and Mikolajewski, E. “Effect of Angular Deformation on Porosity of Nylon Parachute Fabrics.” RAE Tech. Note Chem 1198 (AD 14515) (May 1953)Google Scholar
54 Skelton, J., and Abbott, N.J. “Development of Stretch Fabric for Parachute Canopies.” Technical Report ASD-TR-74-26, Wright-Patterson Air Force Base, Ohio (AD 785 195), (August 1974)Google Scholar