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"gnuSoyuz" parachute

1. Soyuz spacecraft

Soyuz ("Union") is a series of spacecraft designed for the USSR space programme by the Korolyov Design Bureau in the 1960s. Soyuz spacecraf,
with some modernizations, is still in service and now produced by RKK Energia in the Russian Federation. This legendary spacecraft, is currently the only way to access the astronauts on the International Space Station ISS. Although there are other international projects in development, using more modern spacecrafts (NASA Orion, SpaceX Dragon v2, Roscosmos Federation, and others), the wonderful, simple and effective Soyuz design, will remain fully operational many years.

In this article, we will study some technical details on the Soyuz main parachute, and design a similar parachute, which we call "gnuSoyuz".

2. Soyuz parachutes

The Soyuz capsule has a total of five parachutes.
Once the spacecraft entered the atmosphere and at a height about 10 km, are deployed two pilot chutes 0.6 and 4 m2, reducing speed to 240 m/s.
Then open the drogue parachute 25 m2 in size, reducing speed to 90-50 m/s.
At a height of 7 km opens the main parachute 1000 m2, reducing speed to 6-7 m/s
If there is a problem with the main parachute, at a height between 4 and 6 km, opens the reserve parachute 574 m2 in size, reducing speed to 8-11 m/s
At 1 meter above the ground is driven the ignition of six solid fuel rockets that slow the descent rate to 2-3 m/s

Descent rate
Pilot 1
220-270 m/s
Pilot 2
90-50 m/s
6-7 m/s (**)
574 (*)
8-11 m/s
1 m

2-3 m/s

(*) Probably some TMA and MS models using 590 m2 reserve.
(**) Descent rate at ground level
Note: All data are unofficial, but obtained from public data obtained in specialized sites.

Video TMA-20M landing

But let's analyze more data...! Consider the beautiful video of the landing of the Soyuz TMA-20M:

The medusa effect:
Soyux Medusa low
Soyux Medusa top
Changes in geometry Soyuz TMA-20M parachute. Laboratori d'envol analysis assuming lines 40 m long.

Medusa effect

It's very interesting the "medusa effect" observed in the parachute. The geometry of the dome, varies periodically in diameter and height. Why? It is probably an elastic pendulum oscillation, which is maintained in resonance due to the changes in the geometry in the dome.

The period of oscilation of an elastic pendulum with an stiffness constant "K" and a mass "m" is :  T=sqrt(4 x pi x pi x m / K)
In our case, the mass is approximately m= 2500 Kg (capsule without thermic shield).
We can consider the lines of the parachute as an elastic spring. Gores: 80. Lines 80.
We do not know exactly the material and diameter of the lines, but probably using 450 kg classic polyamide lines would suffice.
For example using a 450 daN line 7.3x1.8 mm 24-plaited 7.88 gr/m and 24% of elongation at effective strength of 492 daN...
Hooke's law: F = K x X    K = F / X = 49.2 N / 0.24 m = 205 N/m
And using 80 springs in parallel
stiffness is K= 80 x 205 = 16400 N/m
Then the oscillation period is T = sqrt (4 x pi x pi x 2500 / 16400) = 2.4 s
This agrees very well with what we see in the video! In fact the period of oscillation of the "medusa", it is indicating the stiffness of the material used. Other authors describe the oscillation period between 3 and 4 seconds, indicating probably the use of lighter lines.
Using 80 lines 450 daN: 80 x 450 Kg = 36000 Kg and considering 3000 Kg mass: Safety factor=36000/3000= 12 (12g).

It is possible to check the total weight of the parachute. If the canopy has an area of 1000 m2 using ripstop nylon 45 g / m2, we have 45 kg of tissue. If we use 80 lines of 40 m, is 320 m with a linear weight 7.88 g / m is 25.2 kg, total 45 + 25.2 = 70.2 Kg + reinforcements = 80 Kg.

But why does not stabilize the oscillation?

Due to the elastic effect, we can consider that the capsule is subjected to a vertical sinusoidal movement described by:

(t) = ymax x sin(wt)  

where w = 2 x pi / T  ; w =
angular frequency; T = period of oscillation

The vertical speed: v(t) = dy/dt = w x cos(wt)

And the acceleration is: a(t) = dv/dt = - w2 x sin(wt)

And according to Newton's law: F = m x a

At the lowest point, the force is maximum and positive. At the highest point, force is maximun and negative. So in the lowest point, the shape of the dome is more closed and drag area smaller. This increases the vertical speed and prevents oscillation is extinguished. At the top of the movement, the total vertical force is reduced and the shape of the dome is flattened, increasing its drag area. This effect of variable geometry, and the variation of the vertical speed during oscillation of the spring causes the peculiar effect "medusa". However, this effect does not seem to have important repercussions in the average speed of descent.

We can estimate the
amplitude of the movement. The load into each line in stabilized descent is 2500 Kg/80 = 31.25 kg. Using our 450 daN polyamide lines and considering elongation is about 24% at 492 daN, then elongation at 31.24 Kg is only (31.25/492)x24=1.52%. And in our 40 m lines, this means 0.61 m total amplitude. Then ymax = 0.3 m. Probably the real displacements are larger +-0.5 m, always depends on the stiffness of the lines used.

Of course, we could change the lines by others used in paragliding, Aramid (Kevlar) or Dyneema, and the oscillations would be much smaller, but the instantaneous load at the time of the opening could be very high. The elastic material absorbs the oppening shock much better.

We will graphically represent the movements and forces, in accordance with the above formulas. Speed calculated as a derivative position, acceleration as derived from the speed, load according to the Newton's formula. And parameters:

T = 2.4 s
w = 2.618
ymax = 0.305 m
m = 2500 Kg

gnuplot Medusa analysis
gnuplot script medusa.gnu

Additional load is +- 1700 daN (Kg),
it seems a reasonable value. However, the vertical speed about 3 m/s, it seems unacceptable value!  It is necessary to revise the model, if there is any error.

For classical parachute calculations read more here.

3. gnuSoyuz parachute

Let's design the gnuSoyuz parachute using LEparachute program! Version 0.12
does not allow many options. So the shape of the dome can not be approximated very accurately, because currently LEparachute works better with pull down apex parachutes (PDA). We plan modify the program to load dome profiles of any kind. However, once in flight, the parachute will stabilize in the ideal dome shape. So this parachute would be safe to land the capsule with the astronauts!

We write te data file data.txt:

* Version
* Brand name
"Laboratori d'envol"
* Parachute name
* Scale
* Drawing scale
* Parachute type
* a parameter horizontal axis ellipse (cm)
* b parameter vertical axis ellipse (cm)
* c parameter Apex height (cm)
* ap parameter (cm)
* Apex radius (cm)
* Line height (cm)
* Separation beetwen main karabiners (cm)
* Calage (cm)
* Number of gores
* General ovalizacion factor (%)
* N points used to define meridians

Run the program and we obtain the result file lepc-out.txt:

 Laboratori d'envol
                Version:    .12
                  Brand: Laboratori d'envol                               
                  Model: gnuSoyuz                                         
                N gores:   80
        Main radius (m):   13.29
        Dome height (m):   37.73
    Meridian lenght (m):   18.56
      Surface sail (m2): 1000.00
Surface projection (m2):  554.88
General ovalizacion factor: 6.0 %

 Lines (cm):
     Line   1 to 80 (m): 4000.00

Download here all .txt and .DXF files for the gnuSoyuz!

gnuSoyuz planform
Planform gnuSoyuz (80 gores)

gnuSoyuz 3D
3D view

gnuSoyuz gores
Gore developed geometry

Teiā, 22 September 2016

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