Soyuz ("Union") is a series of spacecraft designed for the USSR space
programme by the Korolyov Design Bureau in the 1960s. Soyuz
spacecraf, withsomemodernizations, is
still in service and now produced by RKK Energiain
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 thisarticle,we willstudysometechnical
detailsontheSoyuzmain parachute, anddesign a similar parachute,
total offiveparachutes. Oncethe spacecraftenteredthe atmosphereand at a height about10km,are deployedtwopilotchutes0.6and 4m2,
reducingspeedto 240m/s. Thenopenthe drogue parachute 25
m2 in size, reducing speed to 90-50 m/s. At
the main parachute1000m2, reducing speed to
6-7 m/s If
there isa problem with themain parachute,ata heightbetween 4 and 6km,opens thereserve parachute 574 m2 in size,
reducing speed to 8-11 m/s At1meter above the groundis driven the
fuel rocketsthat slowthe descent rateto 2-3 m/s
6-7 m/s (**)
(*) Probably some TMA and MS models using 590 m2 reserve.
(**) Descent rate at ground level Note:Alldataareunofficial, butobtained frompublic
dataobtained inspecialized sites.
Video TMA-20M landing
let'sanalyzemore data...! Considerthe
beautifulvideo of thelandingof
The medusa effect:
geometrySoyuzTMA-20M parachute.Laboratori d'envol analysisassuminglines40 mlong.
very interesting the "medusa effect" observed
geometryof the dome, varies
periodically in diameterand height. Why? It is probablyan elastic pendulum oscillation,
which ismaintainedinresonancedue tothe changes inthe geometry inthe dome.
periodof oscilation of an elasticpendulumwith an stiffnessconstant
"K" anda mass"m"is: T=sqrt(4 x pi x pi x m / K) In our case,the massis
approximately m= 2500 Kg (capsule without thermic shield). We
can considerthe lines oftheparachute
as an elasticspring. Gores: 80. Lines 80. We
do not know exactly the materialanddiameter ofthe lines,but probablyusing 450kg classic polyamidelineswould 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 =
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 agreesvery wellwithwhat we seein thevideo!
fact theperiod ofoscillationofthe "medusa", itisindicatingthestiffnessof the material used. Other authorsdescribe theoscillationperiodbetween3and 4 seconds,
indicatingprobably the use of lighter
Using 80 lines 450 daN: 80 x 450 Kg = 36000 Kg and considering 3000 Kg
mass: Safety factor=36000/3000= 12 (12g).
is possible tocheck the total weight of theparachute.Ifthe canopyhas anarea
/m2,we have45kgof tissue.If we use80lines
of40 m, is320mwith alinearweight7.88g/ mis25.2kg,total45+25.2=
70.2 Kg + reinforcements = 80 Kg. But why does not stabilize the oscillation?
to theelastic effect,we can
consider thatthe capsuleis subjectedto averticalsinusoidalmovementdescribed by:
where w = 2 x pi / T ; w = angularfrequency;
T = periodof oscillation
Thevertical speed: v(t) = dy/dt = w x cos(wt)
And theacceleration is: a(t) =
dv/dt = - w2 x sin(wt)
according toNewton's law: F=mxa
lowest point, the forceis maximumand
positive.Atthe highest point,force ismaximun
lowest point, the shape of thedomeismore closed anddragareasmaller.Thisincreasesthevertical
speedandpreventsoscillationis extinguished.At the topof
the movement,thetotal vertical forceis reducedandthe shape of thedomeis flattened, increasing itsdragarea.This effectof variable geometry,and the
variation of thevertical speedduringoscillationof the springcausesthepeculiareffect"medusa".However, this effectdoes not seem tohave importantrepercussionsintheaverage speedof descent.
We can estimate the amplitude of the movement. The load intoeachlinein stabilizeddescentis 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%. Andin our
40 m lines, this means 0.61 m totalamplitude. Then ymax = 0.3 m. Probably therealdisplacementsarelarger +-0.5 m, alwaysdepends on thestiffnessof the linesused.
course,we couldchange thelines byothersused inparagliding,Aramid(Kevlar)orDyneema, and the
oscillationswould bemuch smaller,but theinstantaneousloadat
the time oftheopeningcould
materialabsorbsthe oppening shockmuch
We willgraphically representthe movements andforces,
in accordance with theabove formulas.
calculatedas aderivativeposition,acceleration asderived fromthespeed,loadaccording
to the Newton's formula. And parameters:
T = 2.4 s
w = 2.618
ymax = 0.305 m
m = 2500 Kg
Additional load is +- 1700 daN (Kg), it seemsareasonablevalue. However, thevertical
it seemsunacceptablevalue! It isnecessary
to revisethe model,ifthere
For classical parachute calculations read more here.
3. gnuSoyuz parachute
Let's design the gnuSoyuz parachute using LEparachute
program! Version 0.12 does not allowmanyoptions.Sothe shape of thedomecan
not beapproximatedvery accurately,
because currentlyLEparachuteworksbetter with pull down apexparachutes(PDA).Weplan modifythe
programto loaddome profilesof any kind. However, oncein
stabilizein theideal dome shape.So thisparachutewould besafetolandthe
capsule with the astronauts!