Skip to main content
SpringerLink
Log in

Oscillations of a wedge in a free stream with particular reference to parachutes

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

The phenomenon of coupled breathing and longitudinal oscillations of a wedge-mass system in a free stream is examined. As a first step the unsteady pressure distribution on the surface of the oscillating wedge is calculated. For dynamic equilibrium of the wedge-mass system, the moment about the apex of the wedge must be zero. This condition establishes the amplitude and phase relation between breathing and longitudinal oscillations. As a final step the equation of motion of the store is used to calculate the frequency of the breathing oscillations. This frequency is shown to be dependent on four parameters. These parameters include the Froude number, the rigging line length to wedge breadth ratio and the rigging line stiffness and damping. Current results are compared with Hume and Stevens [1] experimental results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

a :

constant defined in (1)

c :

breadth of the wedge as shown in Figure 2

C R :

rigging line damping coefficient per unit length of the wedge

D :

drag force

f :

complex variable defined in (4)

g :

acceleration due to gravity

K R :

rigging line stiffness coefficient per unit length of the wedge

L :

length of the rigging lines

M :

mass of the store per unit length of the wedge

n :

nondimensional number (α S/π)

N D :

damping number

N F :

Froude number (2U 2/gc)

N S :

stiffness number

p :

pressure

q :

velocity of fluid

s :

distance measured along the wetted surface

t :

time

T :

tension in the rigging lines

U :

mean fluid velocity

v t, v n :

tangential and normal velocities of a point on the wetted surface

V :

velocity of the store

W :

complex plane (φ+iψ)

Z :

complex variable defining the physical plane such that Z=(x+iy)

α :

wedge angle as shown in Fig. 2

β :

phase angle between breathing and longitudinal oscillations

δ :

drag phase angle

ε :

displacement of the store due to ε R

ε R :

rigging line elongation as shown in Fig. 9

ζ :

an independent complex plane (γ+iη)

θ :

angle between the rigging lines and the symmetric axis of the wedge

Θ :

angle between q and x-axis

K :

complex plane

λ, Λ :

frequency parameters (Λ=λ/I 1 λ=cω/2U)

μ :

amplitude ratio of breathing and longitudinal oscillations \((2\hat x/c\hat a)\)

ν :

phase angle of the displacement ε

ρ :

density

ω :

frequency of oscillations

Ω :

velocity ratio equal to log(U/q)

s:

steady

u:

unsteady

References

  1. Hume, R. G. and G. W. H. Stevens, Proc. Symp. on Parachutes and Related Technology, Royal Aeronautical Society, London, 1971.

    Google Scholar 

  2. Woods, L. C., University Press, Cambridge, 1961.

  3. Roberts, B. W., J. of Aircraft, II (1974) 736.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mech. Eng., Univ. of Sydney, 2006, Australia

    K. R. Reddy & B. W. Roberts

Authors
  1. K. R. Reddy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. W. Roberts
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reddy, K.R., Roberts, B.W. Oscillations of a wedge in a free stream with particular reference to parachutes. Appl. Sci. Res. 31, 279–308 (1975). https://doi.org/10.1007/BF00389220

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00389220

Keywords

Search

Navigation