Encyclopedia of Science & Technology Volume 13.pdf

Parablastoidea — Plants of saline environments

Parablastoidea

A small extinct class of relatively advanced blas-

tozoan echinoderms containing ﬁve genera (three

named), ranging from the middle Early Ordovician

to the early Late Ordovician in eastern Canada;

northeastern, eastern, south-central, and western

United States; south and north Wales; and near St.

Petersburg, western Russia. Parablastoids have a bud-

shaped theca or body with well-developed pentam-

eral symmetry. Thecal plates include basals, small or

large radials, and sometimes other small plates in the

lower theca; large distinctive triangular-to-parabolic

deltoids between the ambulacra in the upper theca

(see illustration ); and small oral plates and an oral

crest surrounding and covering the mouth on the

summit. Parablastoids have single or multiple slits

through the lower deltoids that are connected by in-

ternal folds (cataspires) to pores that open between

the single ambulacral plates at the edge of each am-

bulacrum; presumably they were respiratory organs.

Short-to-long biserial brachioles were attached to the

edges of the ﬁve ambulacra and served as the main

food-gathering structures; when not feeding, the bra-

chioles folded in to lie against a high T-shaped ambu-

lacral crest in the center of each ambulacrum in the

best-known genus. A stem with one-piece columnals

attached the theca to the sea ﬂoor, suggesting that

parablastoids were attached, medium- to high-level,

suspension feeders. Some parablastoids are found in

bank or reef deposits, suggesting they may have been

adapted for rough-water conditions. Although they

converged on blastoids in thecal design and way of

life, parablastoids had differences in their plating,

ambulacra, and respiratory structures that indicate

a separate origin and evolutionary history. This jus-

tiﬁes assigning parablastoids and blastoids to differ-

ent blastozoan classes. See BLASTOIDEA ; ECHINODER-

MATA ; ORDOVICIAN . James Sprinkle

Bibliography. R. O. Fay, Parablastoids, pp. S293–

S296 in R. C. Moore (ed.), Treatise on Inverte-

brate Paleontology, Part S: Echinodermata 1(1) ,

Geological Society of America, Boulder, and Uni-

versity of Kansas, Lawrence, 1968; C. R. C. Paul,

The phylogeny of the cystoids, pp. 199–213 in

C. R. C. Paul and A. B. Smith (eds.), Echinoderm Phy-

logeny and Evolutionary Biology , Clarendon Press,

Oxford, 1988; C. R. C. Paul and J. C. W. Cope, A para-

blastoid from the Arenig of South Wales, Palaeon-

tology , 25(3):499–507, 1982; J. Sprinkle, Morphol-

ogy and Evolution of Blastozoan Echinoderms ,

Museum of Comparative Zoology, Harvard Univer-

sity, Spec. Publ., 1973.

brachioles

deltoid

1 cm

Side view of Blastoidocrinus carchariaedens from the

Middle Ordovician of New York, showing the thecal plating,

large triangular deltoids, and numerous short brachioles

attached to the ambulacra. ( After R. O. Fay, in R. C. Moore,

ed., Treatise on Invertebrate Paleontology, Pt. S, pp.

S293–S296, Geological Society of America and University of

Kansas Press, 1968 )

Parabola

A member of the class of curves that are intersec-

tions of a plane with a cone of revolution. It is ob-

tained (see illus. ) when the cutting plane is parallel

Parachute

of payloads, people, and vehicles since their ﬁrst

recorded use in 1797. Comprising cloth and suspen-

sion lines, their construction is far simpler than that

of aircraft. As a result, parachute construction and

design is a fairly mature art. However, their very “soft-

ness” makes their aerodynamics much more com-

plicated, so complicated in fact that modern super-

computers are not powerful enough to completely

simulate both the evolution of the parachute shape

and the internal and external airﬂows, either during

inﬂation or during rapid ﬂight maneuvers. Indeed,

unlike aircraft, which are solid structures that de-

ﬂect the air around them, parachutes not only de-

ﬂect the surrounding air but also adopt shapes that

are dictated by it. During inﬂation, such feedback

is even more dominant as both shape and ﬂows are

basically unsteady (that is, do not remain constant

in time). Finally, given the lack of streamlining both

c/2

directrix

(a)

(b)

Parabola as ( a ) conic section and ( b ) locus of points.

to an element of the cone. See CONIC SECTION .

In analytic geometry the parabola is deﬁned as the

locus of points (in a plane) equally distant from a

ﬁxed point F (focus) and a ﬁxed line (directrix) not

through the point. It is symmetric about the line

through F perpendicular to the directrix. To con-

struct a parabola, pin one end of a piece of string to

a point F and fasten the other end to one end of a

ruler whose length equals that of the string. If the

other end of the ruler slides along a line, and the

string is kept taut by a pencil, the point of the pencil

will trace an arc of a parabola. Hippocrates of Chios

(about 430 B.C.) showed that one of the three fa-

mous problems of antiquity, duplication of the cube,

can be solved by use of parabolas. The problem is

to construct the edge of a cube whose volume is

twice that of a given cube. If c denotes the edge of

the given cube, then the desired edge is obtained by

considering the two parabolas whose equations in

rectangular cartesian coordinates are x 2

parachute

vent

canopy

2 cx . They intersect at the origin and a point P ( x 0 , y 0 ),

with x 0 3

= cy , y 2

suspension

lines

= 2 c 3 .

All parabolas are similar; they differ only in scale.

Foradiscussion of the optical property of parabolas

see ANALYTIC GEOMETRY .

The curve has numerous other properties of in-

terest in both pure and applied mathematics. (For

example, the trajectory of an artillery shell, assumed

to be acted upon only by the force of gravity, is a

parabola; and the circle that circumscribes the tri-

angle formed by any three tangents of a parabola

goes through the focus.) Archimedes found the area

bounded by an arc of a parabola and its chord; for

example, the area bounded by the parabola y 2

parachute

harness

= 2 cx

and its latus rectum (the chord through F perpendic-

ular to the axis) is 2

arc t h at is cut off by the latus rectum is [ √ 2 +

/ 3 c 2 . The length of the para bo lic

(a)

ln ( √ 2 + 1)] c . The volume obtained by revolving this

about the axi s of the parabola is π c 3 /4, and the sur-

face is 2

/ 3 (2 √ 2 − 1) π c 2 .

Leonard M. Blumenthal

Parachute

Aﬂexible, lightweight structure, generally intended

to retard the passage of an object through the at-

mosphere by materially increasing the resistive sur-

face. Parachutes have continued to be the sim-

plest and cheapest devices for the deceleration

(b)

Fig. 1. Hemispherical parachutes. ( a )T-10 parachute, used

for airborne troop insertion. ( b ) Parachute with gaps to

enhance stability.

Parachute

during and after inﬂation, turbulent ﬂow rather than

laminar ﬂow controls the aerodynamics. See AERO-

DYNAMICS ; LAMINAR FLOW ; SUPERCOMPUTER ; TURBU-

LENT FLOW .

Types. Parachutes come in two basic shapes: a

near-hemispherical cup ( Fig. 1 )orawing ( Fig. 2 ).

Most are made of nylon fabric. When fully inﬂated,

some hemispherical parachutes have a slight coni-

cal shape, while in others slots, vents, or concen-

tric gaps are cut to enhance stability (Fig. 1 b and

Fig. 3 ). Winglike parachutes, also commonly know

as parafoils or ram-air parachutes, are made of bags or

cells sewn together to form a wing. They maintain

this shape via the wind entering inlets cut on the

leading edge of the parachute, thereby pressurizing

each cell.

Figure 3 shows several versions of so-called slot-

ted canopies which, by virtue of having concentric

rings of small slots, are considered to be the most sta-

ble hemispherical parachutes. By stability is meant a

reduced propensity to oscillate, that is, to swing the

payload sideways, in a direction that is perpendicular

to the direction of fall. During their steady descent

through the air, stability or lack thereof is caused by

the fact that all parachutes accumulate air and build

up internal pressure. Parachutes without slots or

gaps (such as the parachute in Fig. 1 a ) allow the

accumulating internal air to escape by periodically

spilling it to one side by the parachute’s mouth. Like

thrust coming out of a jet engine, such spilling in-

duces motions in directions opposite to the spill,

namely sideways. Slotted canopies achieve stability

by allowing this accumulating air to ﬂow through a

large number of gaps distributed symmetrically over

the entire surface of the cloth. But the drawback

is that introducing slots and vents yields a lower

deceleration capacity—that is, an overall loss of

drag-creation performance. Thus the parachute de-

signer must ﬁnd a compromise between two desired

qualities—stability and drag generation—which un-

fortunately work in opposition. See AERODYNAMIC

FORCE .

The ribbon parachute (Fig. 3 a )isconstructed by

using many ribbons, usually 2-in-wide (5-cm) nylon,

arranged in concentric circles from the center (vent)

of the parachute to the skirt. Between the ribbons

are the slots. Similarly, a ring-slot parachute (Fig. 3 b )

is constructed from wider rings of cloth with slots

between the rings. For a given size, a ribbon

parachute would have perhaps 40 ribbons and slots,

and a ring-slot parachute would have 10 rings and

slots. A ring-sail parachute (Fig. 3 c )issimilar to a

ring-slot parachute, but with the lower rings having

added fullness (that is, extra cloth). Such fullness al-

lows the lower edge of each ring of cloth to bulge out

and vent air downward, thereby giving the parachute

agreater drag-producing capability than a ring-slot

parachute.

Deployment and inﬂation stages. All parachutes are

packed into a small container prior to actual use,

and therefore require hardware that will extract the

parachute out of its container and deploy it into the

wind. The initial deployment stages of hemispherical

parachutes and parafoils are similar. Both begin with

the extraction of the bag containing the folded

parachute from the harness-container assembly (or

vehicle). The extraction is normally carried out with

either a lanyard attached to the aircraft (that is, the

so-called static line), or with a “pilot” or “extraction”

chute, usually a small hemispherical parachute that

is previously deployed into the airstream by a latch

and ejection spring mechanism (Fig. 2 c ). As the bag

separates from the harness or vehicle, the suspen-

sion lines unfold ﬁrst. Only when these lines are

completely stretched is the parachute allowed to un-

furl out of the bag and begin inﬂating. Inﬂation is

typically characterized by several stages whose dura-

tion depends on the speciﬁc design of the parachute

(or parafoil) and on whether the parachute is

reefed.

Reeﬁng systems. If not controlled, the opening

forces that accompany the inﬂation process may

(a)

cell

leading edge

half cell

right

side

left

side

stabilizer

cascade

lines

trailing

edge

slider lower

control lines

upper

control lines

risers

toggles

(b)

pilot chute

(free)bag

(c)

bridle

Fig. 2. Wing-shaped parachutes (parafoils). ( a ) Deployed

parafoil descending. ( b ) Components of deployed parafoil.

( c ) Deployment mechanism.

Parachute

(a)

(b)

(c)

Fig. 3. Slotted canopy parachutes. ( a ) Ribbon parachute. ( b ) Ring-slot parachute. ( c ) Ring-sail parachute. ( After Recovery

Systems Design Guide, Irvin Industries Inc., Air Force Flight Dynamics Laboratory, Tech. Rep. AFFDL-TR-78-151, 1978 )

be large enough to destroy the parachute or damage

its payload. Typically, the inﬂation forces are large

when a parachute inﬂates too quickly. In this case the

parachute and its payload still travel at high speeds by

the time the parachute has spread open, thereby gen-

erating a very large amount of drag. Reeﬁng devices

are designed to limit the rate of canopy expansion

during the early phase of inﬂation, allowing enough

time for the parachute-payload system to reduce its

speed with the help of the small but sufﬁcient drag

provided by the partially opened parachute. With

some hemispherical parachutes, for example, a line

routed around the skirt limits the canopy expansion

by constraining the parachute’s mouth (or skirt) to

a small-diameter circle. Usually, a mechanical or py-

rotechnic device cuts this line at a preset time or al-

titude to allow full canopy inﬂation, albeit at a lower

speed. On parafoils, a slider is used to achieve the

same result (Fig. 2 b ). Here, a square of nylon fabric

is allowed to slide freely and slowly down the suspen-

sion lines at a rate that is controlled by the slider’s

owndrag and by the tension of the lines that fan out

of the slider.

Pressure dynamics during inﬂation. The inﬂation

stages of a hemispherical parachute without reef-

ing are shown in Fig. 4 . After unfurling out of its

container, the parachute adopts a rather elongated

shape, resembling a vertical tube opened at its lower

end (Fig. 4 a ). Because of the system’s rapid descent,

air rushes in through the tube’s opening and ac-

cumulates at the apex of the canopy to create a

high-pressure “bubble.” Continuous inﬂow builds up

internal pressure, allowing the bubble’s volume to

expand horizontally as well as vertically (Fig. 4 b ).

Early in the inﬂation process, the expansion is more

along the vertical; later it is mostly along the hori-

zontal. This expansion continues until the bubble is

large enough to occupy the entire “design” volume

of the parachute, the size of which is determined by

the system’s descent rate, by the presence of vents

or gaps, and by the balance of pressure outside and

inside the parachute (Fig. 4 c ).

The shape of the expanding air bubble trapped in

the canopy is dictated by the balance of the aero-

dynamic forces that act in opposite directions along

the boundary deﬁned by the parachute’s fabric. The

bubble’s expansion rate ﬁrst depends on the pres-

sure differential between the outside and inside of

the parachute. As for any object moving through air,

wake turbulence generated on the downwind side

causes the external pressure to be lower near the

apex than the pressure inside the parachute. The

faster the parachute, the larger this pressure differ-

ential, and the faster the bubble’s expansion. How-

ever, such rapid expansion generates a large exter-

nal pressure which squeezes the bubble on its up-

wind side, thereby slowing down its expansion. This

external pressure arises because the bubble de-

ﬂects outside air sideways, thereby increasing the

resistance of the air to the deﬂection. This balancing

act between the bubble’s expansion and the resulting

external air deﬂection results in the bubble expand-

ing more along the vertical than the horizontal at

ﬁrst. Only when internal pressure is high enough to

overcome the effects of air deﬂection will the bub-

bleexpand along the horizontal. Finally, because the

parachute-payload system decelerates during inﬂa-

tion, this pressure and force balance is continuously

readjusted as the inﬂow becomes slower. See WAKE

FLOW .

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