Large-Scale Load Stabilization
by
Margarita Dzhalalova
There is an economic necessity in
certain cases of large-scale load transfer (e.g., dwelling houses, industrial
pipes, etc.) by helicopters over long distances sometimes. Very often a
stabilization problem of two connected bodies mechanical systems in airflow
appears. Cases of a load swinging are known when a helicopter develops
a speed of 80-100 km per hour (however a helicopter has a
capacity of going three times as fast). For stabilization of towed loads
different hinge-fairings are used. One may use parachute systems for such
purposes. One part of a parachute application project between Moscow State
University and Academy of Civil Aviation (Saint-Petersburg) for stabilization
of poorly-streamlined loads is considered in this article.
Results of experimental and numerical investigations of a permeable
round parachute with the stripe-stabilizer, the so called "SAL" parachute
- Stabilization of Aerodynamic Loads, are given [1].
Experimental investigations of
a round parachute model with an additional stripe for stabilization have
been carried out in the Grand Aerodynamic Wind Tunnel at the Institute
of Mechanics of the Moscow State University. This parachute model was designed
with 24-triangular gores manufactured of sections cut from woven parachute
cloth of air- permeability parameter l about 800 l/m2s
with a vent and sewed stripe for stabilization (so called stripe-stabilizer)
on the suspension lines (in the same plane), on a short distance from a
canopy edge.
The model has the following parameters:
a number of suspension lines - 24, the vent radius –26 cm, length
distance between canopy edge and stripe-stabilizer – 13 cm, stripe
width – 28 cm, length of lines –175 cm, the total length
of reefing cord, passed through the middle of a stripe, D0=
426
cm. Nine various stages of reefing have been considered
in the course of the tests: (cord of reefing was being shortened up to
length
D with a step of 30 cm). For each reefed parachute
variant all loads were being measured at the confluence point at air flow
velocities V= 10, 15, 20, 25, 30, 35 m/s. The parachute canopy
attained different shapes from each other depending on the value of reefing
(Fig.1).
Fig.1 Parachute model in Grand Aerodynamic Wind Tunnel.
Numbers of the reefing 1, 6 and 9.
|
In Fig.2
values of a drag coefficient are represented by different experimental
symbols according to the upstream flow velocity via various parameters
of reefing
D = Dp/D0.
Drag coefficient Cp = F/(rv2/2)S
is related to a canopy surface area without stripe-stabilizer area, where
F
is the aerodynamic load, acting on the canopy, q = rv2/2
is aerodynamic pressure of the upstream flow, S is
the total area of the main canopy. Values D corresponding to numbers
of reefing variants: D = 0.366 corresponds to number 1; D
= 0.47 - to number 2;…, D = 0.93 - to number 9.
Stable balance of the parachute in
the flow should be specially noted: angle oscillations exceeding a common
pulsations were not discovered. Little vibrations of suspension lines and
the canopy edge were observed at all values of upstream flow velocities
and reefing, but the parachute itself kept a stable position (parachute
axis pole-confluence point was parallel to the vector of the airflow).
As given below some numerical investigations of the stripe-stabilizer
reefing influence on the canopy shape, its aerodynamic drag and the tension
of radial ribbons are considered.
The system of differential equations
for the solution of this problem conformably to the considered parachute
model was used [2]. This system describes the equilibrium of any radial
ribbon element of a round parachute canopy:
(1)
To obtain the solution of this system,
Cartesian coordinate system has been chosen, with the origin on the pole.
The canopy axis is directed along ordinate axis Or, axis OR
is perpendicular to Or (Fig.3). To determine
the point's coordinates on the radial ribbon of inflated canopy this system
is complemented by two more equations
(2)
where T is a tension of the radial ribbon; S is
a coordinate along the radial ribbon from the pole to the edge; q
is the angle between tangent, plotted to meridional section, and the canopy
axis; Rx is the radius curvature
of the canopy element, stretched between the neighbouring radial ribbons
based on the angle 2f. Rx
is in the plane of normals, the angle between them is x.
There is a complete system of differential equations (1) and (2) with unknown
T,
q,
R,
r
and
the following boundary conditions of the problem:
at the coordinate origin, i.e. on the canopy pole, tangent to meridional
section is perpendicular to canopy axis. Therefore q(0)
= p/2; R(0) = 0, r(0) = 0, but
the value of tension T(0) on the pole is unknown. On
the canopy edge the tangent coincides with suspension lines, i.e.
Lsin(q)
+ R = 0, (3)
where L is the given line length, R is the distance between
the canopy edge and the canopy axis. Due to such coordinate system choice
it is more convenient to compute from the pole to the edge along meridional
section S (from 0 to So).
All values are given in dimensionless units
S = Sp/So
, T = Tp/qS2,
Rx
= Rpx/So
, r = rp/So
, R = Rp/So
, Dp= Dpp/q
.
So is the radius of a round
canopy in the plane of cutting out, index “p” means
just “parachute”. Angles f, y,
x
and
the radius curvature Rx
are determined
from the algebraic equations:
f = p/n, Rsin(f)
= Rxsin(y),
fS
=
yRx
,
sin(x) = sin(f)cos(q).
The formulated one-parameter boundary
value problem has been solved by Newton's method [3]. Tension value T(0)
is selected on the pole so that a given value of the line length would
be obtained on the canopy edge. For a numerical integration of differential
equations Runge-Kutta's method of the fourth order precision [4] has been
used.
This problem was solved assuming
Dp
= const over the total canopy of parachute. The value of Dp
for the considered parachute model with the known value of air-permeability
was assigned by the constant value along the radial ribbon equal to 1.2.
But as the tested parachute differs
essentially from the usual round parachute by its geometric parameters,
then obviously, the boundary conditions (3) in view of such writing are
not suitable to our variant. Knowing the exact diameter of the stripe (i.e.
the reefing-line-length), tightened by a reefed cord, and taken into consideration
the fact that the diameter of the stripe does not exceed f the diameter
of the canopy inlet (if they are equal to each other, then short lines
between the stripe and the canopy edge would be parallel to the canopy
axis OQ - pole-confluence point), one may deduce the relationship
between the values of the reefing D
and the "imaginary" suspension
lines (Fig.4):
from which one can see that D asymptotically tends to 1 (one),
when L tends to infinity (that is the case when the diameter of
stripe, tightened by the reefed cord, is equal to the diameter of the inlet).
This relation was being put into boundary condition (3). Then the problem
was being solved as if for an usual round parachute.
The values of the drag coefficient
Cp
have been obtained at all values of the reefing D as a result of
the numerical solution of equations taking into account the above relation
- the solid curve in Fig.2. One can see that
scattering between numerical and experimental data of
Cp
is within by 3 - 8%.
Reefed canopy profiles obtained
from the solution of the differential equations are shown in Fig.5
for parameters of the reefing 0.2 < D < 0.85 (with a step
of the reefing 0.05). Having compared these profiles with photos of the
corresponding canopies, one can notice their qualitative correspondence.
For the quantitative comparison of experimental and numerical profiles
the table of the ratio of S radial ribbon length divided by inlet
radius R is shown below.
reef.# |
D |
V, m/s |
Snum/Rnum |
Sexp/Rexp |
% |
1 |
0.40 |
25 |
2.07 |
2.17 |
4.8 |
2 |
0.50 |
15 |
1.96 |
1.91 |
3.0 |
3
|
0.55
|
20
|
1.63
|
1.60
|
1.8
|
4
|
0.60
|
35
|
1.59
|
1.62
|
1.9
|
5
|
0.70
|
20
|
1.50
|
1.54
|
3.0
|
6
|
0.75
|
35
|
1.45
|
1.46
|
0.7
|
7
|
0.80
|
35
|
1.43
|
1.50
|
4.9
|
9
|
0.95
|
10
|
1.38
|
1.42
|
2.9
|
One can see from the right column
that the ratio of numerical S/R to experimental, does not exceed
5%. Satisfactory agreement of the experimental and numerical values of
Cp
and also the shape parameters of considered parachute indicates that one
may use the developed computer program.
Numerical distributions of radial
ribbon tension T are shown in Fig.6 within
0.2 < D < 0.8.
Fig.5 Profiles of the parachute model depending on the parameters
of reefing.
|
Fig.6 Distribution of radial ribbon tension T along meridian
S from the pole to the edge depending on the parameters of reefing.
|
CONCLUSION
As a result of experiments carrying out for the permeable parachute
model with the stripe-stabilizer at different values of reefing and
upstream flow velocities v = 10 - 35 m/s , the following
is achieved:
-
first, to find out that the availability of the stripe-stabilizer
(sewed fabric stripe on suspension lines) provides a good stable behaviour
of the model in the flow;
-
second, to determine the optimum value of reefing D = 0.648
for that average value of drag coefficient equal to 0.55;
-
third, to reveal that drag coefficient Cp
is practically invariable when value of reefing increases from D
= 0.648; within 0.366 < D < 0.577 values of Cp
are considerably smaller: 0.28 < D < 0.5.
Program for computation of drag coefficient, tension of the radial ribbon
and profiles of the tested parachute model has been developed. The results
of computation, brought out due to this program for all values of reefing
(even up to D = 0.1), are confirmed by experimental data both for
Cp
(a difference is 3 - 8 per cent) and for parameters of the canopy shape
(a difference does not exceed 5 per cent).
REFERENCES
- M.V. Dzhalalova, A.F. Zubkov “Numerical and Experimental Research
of Permeable Parachute - SAL”, Report #4400, MSU, Institute of Mechanics,1995,
p.42.
- Kh.A. Rakhmatulin “Theory of Axisymmetric Parachute”, Transactions
#35, Moscow State University, 1975.
- B.P. Demidovich, I.A. Maron “Foundation of Computational Mathematics”,
Moscow, 1960.
- N.S. Bakhvalov “Numerical Methods”, Moscow, 1973.
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