Smithsonian

Contributions to Astrophysics

VOLUME 3, NUMBER 6

A FLUID-DYNAMIC MECHANISM OF

METEORITE PITTING

by DAVID T. WILLIAMS

SMITHSONIAN INSTITUTION

Washington D.C.

1959
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A Fluid-Dynamic Mechanism of

Meteorite Pitting

By DAVID T. WILLIAMS *

The study of meteorite pitting is one part of

the broader subject of meteor (and meteorite)

ablation which has been investigated for many

years. A large number of such studies have

dealt primarily with meteor data obtainable by

photographic and spectrographic methods, and

with analyses designed to aid in interpreting

the results (Whipple, 1943, 1955; Whipple and

Thomas, 1951; Cook, 1954; Cook, Eyring, and

Thomas, 1951; Smith, 1954; Thomas, 1952;

Thomas and Whipple, 1951; Thomas and

White, 1953).

Reasonable and simple theories have been

developed for relating the brightness of meteors

to their masses. These data have been of use

in determining the density of air in the upper

atmosphere at heights between 40 and 120 km.

The details of the processes of ablation of material from meteor surfaces have been of particular concern. Present opinion appears to be

that meteors are sometimes broken up as they

enter the atmosphere (Jacchia, 1955); that

meteorites exhibiting unsteady brightness (or

flaring) emit very small particles of the order

of 10~7 grams, in bursts (Smith, 1954); and that

nonflaring meteorites ablate by vaporization

rather than by melting (Cook, 1954). The

spectrum of a Perseid meteor shows the presence

of atomic spectral lines that support this conclusion (Cook and Millman, 1955).

Data on ablation supplementing those obtained by meteor trail photography have accumulated from experiments using high-speed

pellets (Allen, Rinehart, and White, 1952;

White, Rinehart, and Allen, 1952; Rinehart,

Allen, and White, 1952). Light from the wake

of such bodies shows lines of the elements in

the pellet, as well as bands of the oxides of

> University of Florida, Gainesville, Fla.

those elements. In some cases at least, the

pellet trails show a flashing phenomenon concluded to result from yawing of the pellet.

The light has been identified as coming both

from the shock front and from the trail (Allen

and Mayfield, 1953; Thomas and White, 1953;

White, 1955). The ablation processes acting

on meteors, where very small solid objects are

acted upon by relatively rare gases in the upper

atmosphere, have received particular study.

Of special interest has been the relation of such

processes to the ablation of the larger meteorites that penetrate the denser layers of the

atmosphere without complete disintegration.

Some experiments on high-speed pellets have

been made to correlate the ablation processes

with the resultant shapes of the partly ablated

bodies (Whipple and Thomas, 1951; Whipple,

private communication).

Surface features of meteorites

The nature of the surface features of meteorites

has particular interest. Many rather complete

descriptions of the surfaces of meteoritic stones

and irons are in the literature (e.g., Henderson,

1958; Nininger, 1936a, 1936b, 1952). Outstanding among commonly observed surface

features are evidences of eroding airflow: flow

lines in surfaces of some stone or iron meteorites

with clearly recognizable stagnation points;

frangible crusts of material on some meteorites

so obviously congealed from the molten state

as to require no further proof; shapes that

strongly suggest carving by the action of airflow over the surface. (Pictures are shown in

Nininger, 1952, pis. 31-33, 4(H3.) Not all

meteorites, however, show such clear evidence

of airflow on their surfaces. Another phenomenon, which also is common without being

47
48 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

universal, is that pits appear in the surfaces of

meteorites, both stone and iron. Nininger

(1952) and Henderson (1958) have discussed

these features.

The question whether a direct relation exists

between the pits in meteorite surfaces and the

ablating action of the air on them has been

answered by Nininger in one way and by Henderson in another. Nininger apparently has

concluded that the pits are caused by selective

melting in surfaces that are not chemically

homogeneous. This conclusion is in itself

moderately clearcut. Nininger also suggests,

however, that turbulence of the air flowing into

and around the pits tends to deepen them.

Again he remarks (Nininger 1952, p. 180) that

in certain quite inhomogeneous meteorites

(Pasamonte, Allegin, and Estherville) no pitting is observed, while some homogeneous

meteorites are deeply pitted (Rosebud stone).

Finally, from the frequency of pitting in relation to the probable speed of fall, Nininger

generalizes that pitting is observed more often

in the faster flying bodies. The selective melting of meteorites is still concluded to be the

mechanism of pitting, evidence relating to the

homogeneity of pitted bodies to the contrary

notwithstanding.

Henderson (1958) points out that many

cavities are too intricate or deep to have been

reasonably caused by airflow. Some cavities

might have resulted from influences unspecified

in the early life history of the bodies. Henderson also speculates on the effect of "wave

action" on cavities, and on possible aerodynamic

or thermal mechanisms of formation.

The opinions of Nininger and Henderson are

not necessarily in conflict, in view of the variety

of phenomena to be observed on meteorite surfaces. Obviously, however, there is room for

more evidence on the relation between ablation

and pitting. The present paper is designed to

present such evidence.

Flow patterns on "oriented" meteorites

It is a characteristic of Nininger's (1936a, 1936b,

1952) work that he has deduced the manner of

the airflow over meteorites by direct observation of flow lines in the surface. Rinehart

(1957) has made a similar study. This technique has been recognized as useful for many

years (e.g., Riabouchinsky, 1909; Fales, 1926)

but it has not yet been entirely exploited.

Detailed analyses have not been made of directions of airflow over the surfaces in question so

as to identify in detail not only the nature of

the airflow but the mechanism by which the

flow might have caused the surface peculiarities

of meteorites during their flight through the

atmosphere. That type of analysis is presented

here.

The work began in 1957 under the sponsorship of the Army Ballistic Missile Agency at

Huntsville, Ala., while the author was at

Battelle Memorial Institute in Columbus,

Ohio. It has been continued at the University

of Florida at Gainesville, with some support

from the Engineering Experiment Station of

that institution and from the Smithsonian

Astrophysical Observatory in Cambridge, Mass.

A word of caution" may be appropriate at this

point. The study of flow patterns produces

data relating to the boundary layer of airflow

over solid bodies. Such data are peculiarly

pertinent to ablation since melting occurs

strictly at the surface; but description of the

flow pieced together from such data is far from

complete. The investigator must rely heavily

upon insight gained by experience in aerodynamics in order to interpret and supplement

his direct observations. He must use his imagination, and by that very act he risks being

challenged by other scientists whose insights

are based on other disciplines.

In order to meet possible skepticism on the

part of other investigators in this field, the

present study is supported by many unusually

revealing photographs. The hope is that the

reader may be convinced by the evidence of his

own senses insofar as insight is required to

interpret the data, and that thereby he may

reach the same conclusions as has the author.

Flow patterns from a rocket blast

An unusual feature of flow patterns on meteorites is the fact that the flow speed is initially

supersonic. Whether this circumstance would

have any important effect on the flow patterns

might be questioned. An experiment involving

erosion of a simple model by initially supersonic flow was therefore arranged in order to
METEORITE PITTING 49

discover what might be anticipated under more

complex conditions.

Plate 1 shows the erosion pattern carved on

the flat surface of a ceramic sample by the blast

of an oxygen-hydrogen rocket, incident at an

angle of 30° from the surface. The rocket had a

chamber pressure in excess of 100 psi; the convergent nozzle was a slit one-eighth inch by 1

inch in cross section, the long dimension being

parallel to the plate. Apparently the blast

eroded the plate by melting, carrying streamers

of glassy material straight along the plate in

its main flow but diverging slightly from the

point of initial impact. The flow beneath and

around the main stream was somewhat more

intricate. The erosion was not regular, but was

especially intense at certain points ("A" and

" B" in fig. 1) as though the flow had "bounced"

FIGURE 1.—Schematic version of erosion in a ceramic plate

caused by a rocket blast (see pi. 1). Solid lines indicate

vortex flow in the lee of crests; arrows, flow lines; "A" and

"B", areas of intense erosion; "b", region where gas flow was

reversed; "C", crest.

on the surface, or induced waves on it. At

point "b" (fig. 1) the flow was directly reversed,

carrying glass filaments in a direction opposite

to the main flow. Plate 2a shows an enlargement of region "b." The filaments terminate

in blobs of glass (rounded by surface tension of

the molten glass), indicating the sense of the

airflow.

Region C (fig. 1) is shown enlarged in plate

26. At this point the erosion pattern has a

"crest," like that of a wave about to break.

The crest overhangs the plate beneath. A

vortex is assumed to lie in the lee of the crest,

scrubbing its downstream side and lifting it

above the plate. The air that scrubbed it

obviously left the surface of the sample at the

crest.

The crest at "C" extends along the plate and

veers over toward the center of the plate. An

enlarged photograph (pi. 3) of the region just

upstream of "B" (fig. 1) provides evidence of

the nature of the flow in the lee of the crest.

At the point shown the vortex was a left-hand

spiral. Air from the vortex would leave the

crest at its top on the downstream side, joining the main flow over the crest from the upstream side. A crest showing a sharp edge and

evidence that glass was pulled off the solid

edge (as in pi. 26) is sometimes referred to as

a "skirt" in the following paragraphs.

Figure 1 and plates 1 to 3 are not intended

to prove any explicit characteristics of airflow

around meteorites. The flow in the experiment was from a jet of small size onto a plate

initially flat. Air was drawn into the jet from

the atmosphere, and its characteristic flow

pattern is obviously different from that over

any real meteorite. On the other hand, the

photographs do provide valuable insight for

use in interpreting flow patterns on meteorites.

The following specific conclusions may be

drawn:

(a) A straight flow over a flat surface produces

erosion that is not necessarily uniform, even though

the flow may be supersonic.

(b) A flow that is initially supersonic becomes subsonic in the boundary layer. Its direction may be at

right angles to or even directly reversed from that of

the main supersonic flow.

(c) At a region where the main flow tends to leave

the surface (at a crest or skirt), a vortex is to be anticipated in the lee of the crest.
50 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

It is notable that the flow in a boundary

layer, in this experiment, showed the same

qualitative characteristics when the flow outside

the layer was initially supersonic as it would

be expected to show below a subsonic flow.

The Estherville meteorites

Nininger (1936b, 1952) has described the small

iron meteorites of the Estherville fall and has

published pictures of some of the specimens.

Photographs of some of these meteorites (pi. 4)

were taken by the author at the Peabody

Museum at Yale University. In order to bring

out the fine detail of the flow patterns, the

surfaces were smoked by use of burning magnesium ribbon. Illumination was from the

side at a grazing incidence.

Plate 4a shows an Estherville oriented

meteorite with a smooth iron surface, coated

with a frangible oxide crust which bears a fine

tracery of flow lines. The smooth iron can be

seen near the top where the crust has been

broken off. The stagnation region is at the

center of the picture, and the direction of airflow was roughly upward. (Note: The term

"stagnation region" or "stagnation point" is

applied to the area on the leading surface from

which all flow lines diverge.)

The meteorite pictured in plate 46 shows

evidence that the iron was once molten; it

has the form of a congealed flow like candle wax.

The meteorite pictured in plate Ac also

shows evidence of having been bathed by a

flow of molten iron. The appearance of the

oxide layer strongly indicates that its flow

was more or less independent of that of the iron

beneath. There is striking evidence that the

oxide layer actually flowed off the irregularities

of the iron flow, as though the iron had congealed somewhat before the oxide. It is interesting in this connection to observe that

pure iron melts at 1535° C; FeO melts at 1420°

C, a temperature some 100° lower. Thus, a

layer of FeO might conceivably still have been

molten on freshly congealed iron. (The fact

that the iron in meteorites is not pure is presumed not to affect this conclusion.) The

oxide Fe2O3 has a melting point of 1565° C.

One would expect to find a thin dust of Fe2O3

floating on the layer of FeO at the time when

the latter congealed. Whether this is in fact

the case cannot be determined clearly from

these pictures.

The pictures shown here demonstrate the

types of flow lines that may be visible on

meteorite surfaces. When present, they provide clear evidence of the direction and sense

of air flow. They may reveal the occurrence of

phenomena, not at first anticipated, during

the atmospheric flight.

The Lafayette meteorite

The delicate structure of the flow lines in iron

oxide on the Estherville irons is in marked contrast to that of the flow lines in some of the

oriented stony meteorites. An example of the

latter is the Lafayette meteorite (USNM 1505)

at the U.S. National Museum. This stone (pi.

5) is roughly hemispherical in shape, some 10

cm in original diameter, with a smooth rounded

surface and a flat back (Nininger, 1952). A

portion of the original stone was sectioned off

and is missing.

The Lafayette meteorite was photographed

by use of an ammonium chloride smoke rather

than the magnesium oxide used on the irons.

The black color of the meteorite is not altogether concealed in plate 5a; there are regions

on the right where it shows through. Smooth

glazed ridges diverge from the stagnation region

on this specimen as rivulets of black slag. The

dimensions of these features appear to be uniform from the stagnation region to the edge of

the front face but as the distance from the stagnation point increases these rivulets possibly

are slightly higher than near where they originate. Also they become more numerous near

the edge of the forward face. The flow pattern strikingly resembles that on a windshield

of a car moving at high speed in the rain.

A relatively heavy deposit of slag, carried by

the wake ring vortex, is to be seen in a broad

region at the center of the trailing face (pi 5b).

This material is full of holes, as though gas

were being evolved in it at the time when it

congealed. The color and luster of the slag

on the rear face are different from the glass on

the forward side of the meteorite.

Out toward the margin of the rear face there

is unmistakable evidence of flow, roughly radial

from the central region. The sense of the flow

is indicated by points where threads of slag
METEORITE PITTING 51

were apparently drawn off outward. At the

margin itself, the slag looks as though it had

been spun off in threads and droplets by the

joining of airflows from the front and rear

surfaces.

Reconstructing the pattern of airflow around

the Lafayette meteorite is reasonablj* simple.

Obviously, the air streamed straight along the

front surface, melting the stone in a thin layer

of slag and sweeping the slag back in straight

lines. At the edge between front and rear, the

flow from the front left the stone, carrying with

it slag from the front surface. In the region

behind, a doughnut-shaped vortex was formed

by the flow, in the manner suggested in the

sketch (fig. 2). By some mechanism, possibly

SKIRT

FIGURE 2.—Flow pattern around the Lafayette meteorite as

deduced from the markings on the surface. The trailing

ring vortex is shown in section as two vortices behind the

stone.

the same vortex, some of the slag was spun off

from the skirt at the margin of the stone and

deposited at the center of the back face. The

holes in the slag layer might be due to air that

was absorbed during flow across the front face,

and released in the relatively low pressure in

the lee of the stone.

According to this interpretation, the airflow

out toward the margin of the trailing face

tended to accelerate, carrying slag along in rivulets. At the edge, air and glass were swept off

by the strong flow from the front face, leaving

some slag behind in the form of the skirt.

It must be recognized that the picture

sketched in this fashion is not the only conceivable one. The conclusion that air leaves the

surface of the meteorite at the skirt is believed

to be much more reasonable than the assumption that air might actually follow the surface

around a sharp edge. This also sometimes happens, as will be made clear later, but when it

does there is no skirt such as is to be seen

around most of the margin of the Lafayette

meteorite (pi. 56). Furthermore, the appearance of the flow lines about half way to the

margin, as revealed on a glossy print, is compatible only with the hypothesis that flow is toward the margin rather than away from it.

The Plainview meteorite

The conclusions relating to the airflow around

the Lafayette stone are strengthened by the

results of a study (Henderson and Williams,

1958) of another oriented stone, the Plainview

meteorite (USNM 521). It appears to have

been altered to only a moderate degree by the

airflow in its flight through the atmosphere.

Plate 6a is a photograph of the front face of

this meteorite. The specimen is a block, shaped

roughly like a keystone. The sides to the left

and lower left of the figure form an obtuse angle

with the face itself, and are therefore scrubbed

directly by the main airflow. The sides at the

top and right of the figure are undercut. Being

shielded from the direct flow, they were washed

by a reversed flow from the back due to a ring

vortex in the rear of the body.

The sketch (fig. 3a) shows the airflow across

the face as deduced by observation of the flow

pattern. The flow lines on the front face (pi.

6a) are easily traced on a glossy print either

with or without a hand lens.

In flight, the leading face was tipped perhaps

20°, the left side being ahead of the right. A

group of shallow pits (in upper right of pi. 6a

and indicated by "2" in fig. 3a) terminate in a

high hornlike projection. In these pits, flow

lines are seen diverging from a stagnation region

at the center. In the side of the pit nearest the

main stagnation point, the flow from area "2"

in figure 3a scours the edge of the pit. The

main flow from "S" leaves the surface of the

stone at the crest shown by the broken line.

Apparently there is actual scrubbing of the

inner walls of the pit. The mechanism by

which the air can flow in opposite or nearly

opposite directions on either side of a crest is,

presumably, a helical vortex inside the pit with

axis parallel to, and just downstream of, the

crest.
52 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

,5

CREST

CREST

a

FIGURE 3.—Flow patterns around the Plainview, Tex., meteorite, a, Leading face: Broken line shows

crest; arrows in shallow pits (2) on right indicate flow lines; larger arrows, flow pattern from the main

stagnation point (S); numbered areas (3, S, 6) are those pictured in plates 11, 13, and 14 (respectively), b, Pit shown in area "2" of a and in plate 10; vortex is shown in section at the deepest portion

of the pit, lying just to the lee of the crest.

The flow in the pit is indicated in figure 36.

The vortex shown in the pit is ascribed to the

aspirating action of the main flow, which generates a relative vacuum in the pit. In reaction, the airflow across the pit is pressed down

by the higher pressure outside, to impinge again

on the stone surface. This impingement, with

the vortex, forms a stagnation region inside the

pit, with airflow diverging outward radially

toward the crest around the depression.

Plate 66 shows the side of Plainview No. 521

that appears on the left in plate 6a ("3" in

fig. 3a). Evidence indicates that this side is

exposed to direct airflow. The pits over the

entire surface are clearly seen to be scoured by

the air. The downstream sides of each pit

show flow lines diverging more or less radially

from the deepest part. Usually the flow marks

are less clear on the inside of the pit nearest

the main upstream direction. In the intricate

shapes on the left of the figure, there is evidence

that molten material has flowed from the bottom of some pits and deposited on the edge on

the downstream side. This region was apparently enough sheltered from the main airflow

so that the crests on the downstream side of

the pits were not swept as clear of slag as in

more exposed areas. The solid glass looks here

like the wavelets on a beach at the point and

moment of the furthest advance of a breaking

wave. The parallel between appearance of the

slag and the form of waves is, of course, not

altogether accidental.

The mottled appearance of the trailing face

(pi. 6c) of Plainview No. 521 is due to the

presence of broad, shallow depressions, and is

strikingly typical of trailing faces of bodies

eroded by any fluid flow. The streamers of

slag radial from the center of the face are quite

different in appearance from those on the leading face; there are fewer of them, and they tend

to lie straight across the surface irregularities

instead of being turned or reversed as was found

in the front surface pit of plate 6a. No evidence

of bubbling is found here, such as appears on

the trailing face of the Lafayette meteorite.

The edge of the trailing face shown in plate 6c

would be expected to be the location of a skirt,

if the Lafayette stone (pi. 56) is a reasonable

criterion. In contrast, however, Plainview No.

521 (pi. 6c) shows a skirt over less than half of

the periphery of the trailing face. On the edge

to the left there is a skirt as far around as the

point at the bottom. The rest of the edge is

smoothed, indicating neither crest nor skirt,

although the edge is a region of sharp change in

plane orientation. The nature of the airflow

across this edge is clarified in figure 4a and in

plate 7a,6.

The question has been posed whether the

slag deposited on the back face of meteorites

may not have resulted from the deceleration of

the meteorite, the slag in the wake making a

rear-end collision with the stone. Such a

mechanism, however, would apparently not

change the nature of the conclusions regarding
METEORITE PITTING 53

FIGURE 4.—Sketches of sides of the Plainview, Tex., meteorite, a, Side 5 shown in plate 13: This face was in the lee of the relative

wind, so that airflow left the surface near the bottom and formed a crest roughly along the broken line; the trailing face in this

region showed no edge skirt, confirming the interpretation made here, b, Side 6 shown in plate 14: Location of the crest region

near bottom of this face is readily accounted for by presence of the projection there;^the flow was forward, induced by the trailing

vortex system behind the stone.

the airflow around the meteorite. Thus, in still

air the deceleration —dv/dt of any object of

given shape would increase as its size decreased,

because the drag would decrease as its diameter

squared, whereas its mass would decrease as its

diameter cubed. That is,

dv d2 1

— -77 « -j | o r OC -r

dt d3 d

Here d is the diameter. This means that slag

particles could overtake the parent meteorite

only if the air in the wake had some forward

velocity. As shown in plate 6c, the air must

have had enough forward velocity actually to

overtake the stone, i.e., to form a trailing

toroidal vortex, for there is a stagnation point

at the center of the face and there are streamers

of slag radial from that point.

If small particles of slag can overtake the

stone because of its deceleration in flight they

might conceivably be observed as solid chunks

which had time to congeal before striking and

sticking to the back face. Furthermore, they

would presumably be more widely distributed

in the point of impact than would slag drawn

along primarily by the trailing toroidal vortex.

On careful examination of the photographs

of the front (pi. 6a) and back (pi. 6c) surfaces,

small particles of material are seen that look as

though they might indeed have been deposited

directly on the surfaces, in the solid state. The

distribution of the particles is more or less

random, and the little heaps of material are

larger in size on the back face than on the front.

Mr. E. P. Henderson, associate curator of

mineralogy at the U.S. National Museum,

examined these particles and concluded they

are pieces of sand stuck to the surface by alterations that occurred after the meteorite had

fallen to the ground. It therefore is concluded

that even granting the possibility of solid slag

particles overtaking the meteorite in flight, no

data supporting such a speculation have been

identified by this author.2

The presence of a sharply overhanging region

on the side of the meteorite has been mentioned. Observe the flow on side 5 in figure 3a

(shown also in pi. la and sketched in fig. 4a).

This side was enough behind the stone so that

the airflow broke away near the bottom of this

face. In plate la, the heavy slag deposit was

scoured forward from the trailing face. The

shadowed region at the top is the back face of

the stone. In the center of the picture, sharply

etched flow lines diverge downward from the

' Note added In proof: Mr. Henderson has forwarded to the author a

picture of the trailing face of the Pasamonte, New Mexico, meteorite.

This picture shows droplets of once-niolten slag that would seem to have

been carried away from the edge of the stone and been redeposited on Its

rear by the trailing vortex In the wake behind the meteorite. It Is not

altogether clear from this photograph that the droplets were free of the

stone, rather than streamers from the skirt, when the deposition occurred.

Furthermore, flow lines revealing any significant detail of the air currents

across this face do not show in the photograph, if they are in fact present.

It Is nevertheless concluded by this author that slag may be deposited

from the wake after enough cooling has taken place to cause some degree

of solidification. To what extent deceleration of the parent stone was

the proximate cause of the rear-end collision on the Pasamonte stone Is a

matter on which no conclusion has been drawn here.
54 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

back face. These flow lines indicate back flow

from the back face toward the front, as can be

verified by careful examination of plate la and

of the stone itself. Lines of airflow from the

front face toward the back can be seen also at

the bottom of the photograph. The airflow

collides with that from the trailing face in the

region of the crest (shown as a dotted line in

fig. 4a) where both airflows abruptly leave

the stone surface. There is no skirt of slag

here because the stone has no sharp edge at

the line where the airflow leaves the stone.

It may seem a little surprising, at first, to see

such sharply visible flow lines in the lee of a

meteorite, indicating reversed flow. They do

not necessarily mean that the surface was

heavily eroded there; on the contrary, they

simply mean that much slag was left by the

slow-moving air.

Adjacent to this overhanging side 5 is region

6 of figure 3a (shown in pi. 76 and also sketched

in fig. 46) .This region is also overhanging, and

lies in the lee of flow over the leading face of

the stone, just as for the face shown in figure

4a and plate 7a. As is to be expected, reversed

flow is seen here, with a clearly visible crest

area near the bottom, accounted for by the

presence of the projection visible at the bottom

of the figure. This put the face in the lee of

the flow, so that the airflow from the leading

face left the surface instead of following it

beyond the crest.

Study of the flow patterns on Plainview

meteorite No. 521 led to a consistent and rational picture that agrees with the qualitative

laws of aerodynamic flow. Airflow over the

front face of this meteorite, much like that on

the Lafayette, broke away from the body in a

crest belt surrounding the stone. The Plainview stone was irregular in shape and tilted a

little in the airflow, so that the crest did not

coincide at every point with a sharp edge of the

stone, to form a skirt. In this respect, the

Lafayette and the Plainview specimens apparently differed, but the difference is strictly

predictable from the nature of airflow and the

shapes of the stones.

The Olivenza fragment

A fragment (in the Peabody Museum at Yale

University) from one of the Olivenza, Spain,

meteorites was smoked with magnesium oxide

and photographed (pi. 7c). This heavily pitted

fragment of a stony meteorite is surmised to

have been originally on the side of the main

body, well back from the stagnation region.

The extraordinary clarity of the flow patterns

in the pits presumably results from the fact

that the region shown was not so vigorously

scoured as were areas on the leading face; more

slag is left to show how the air flowed. Stagnation regions are visible at the bottom of the

pits. Flow lines stream away from the stagnation points in directions more or less normal

to the crests around the pits but flying downstream a little with the main wind. As in some

of the Plainview pictures, there are many crests

where slag has deposited, as though swept up

from the bottom of neighboring pits.

The perfect whorl in the center of the picture

is unusual in that its axis is normal to the

surface rather than parallel to it.

The Miller meteorite

A photograph (pi. 8) of the leading face of the

Miller, Arkansas, meteorite (in the American

Museum of Natural History) shows how pits in

meteorites may be oriented with reference to

the stagnation region. Flow lines appear inside the pits as well as elsewhere on the surface.

These lines are difficult to see in the photograph because the stone was not smoked before

the picture was taken. The pits themselves

are clearly arrayed radially around the stagnation region. In shape they are elongated, with

their long axes radiating from the stagnation

region.

General conclusions

The series of photographs presented here were

intended to establish certain general conclusions

relating to airflow over the surfaces of meteorites:

(a) The surfaces can bear clear evidence of the

nature of airflow over a melting meteorite, stone or

iron. When flow lines are found, evidence of the

direction of the flow can be persuasive if not decisive,

both as to line and sense.

(b) The pattern of airflow as observed is characterized by reversed flow in the lee of bluff objects. A

band marking the position of a crest will form a continuous ring around any bluff meteorite shape.
METEORITE PITTING 55

(c) Flow lines inside of pits in the surface indicate

a stagnation point at the deepest point, with flow diverging toward the edge of the pits. Such flow might

be caused, for example, by a vortex with axis having a

hairpin shape, lying in the pit straddling the stagnation

point in the pit. The ends of the vortex would then

trail off to infinity downstream in the wake, much as

the tip vortices of wings in the conventional vortex

theory of lift.

There are certain further possible conclusions

that the foregoing observations did not establish entirely:

(a) Thus far no clear evidence exists that any pits are

of aerodynamic origin, even though the appearance of

the Miller meteorite strongly suggests such a mechanism.

(b) In general, the presence of flow lines inside the

pits on a congealing meteorite surface proves only that

air will flow inside the pits. Since it does, a conceivable

mechanism for pit formation exists in the airflow, but

the assertion that such a mechanism did actually operate to deepen pits has not been made as yet.

The main point of this discussion is that the

conclusions listed above resulted from a study

of the flow lines on meteorites; they are precisely what one might have expected from a

study of ablation of a body subjected to a subsonic liquid flow. Neither the vortices in the

lee of bluff objects nor the reversed flow due to

a vortex in a steep-walled depression depend

specifically on the supersonic nature of the flow,

except insofar as such a flow is required to produce the melting temperatures of stone. The

obviously subsonic speed of the flow over meteorites is, of course, not altogether unexpected,

since the flow that is mainly effective in producing flow lines is that at the bottom of a

boundary layer. The subsonic speed does suggest, however, that one need not be limited to

supersonic flows in searching for an aerodynamic mechanism for meteorite pitting.

Erosion of salt cakes

The preceding discussion leads directly to the

conclusion that if an aerodynamic mechanism

does produce pitting in meteorites, then laboratory experiments should be able to demonstrate

a similar pitting in objects subjected to erosion

by fluid flow, at subsonic speeds. A program

was therefore carried out to investigate in a

strictly exploratory manner the erosion in water

of salt blocks such as are used in Florida and

elsewhere for supplementing the diet of cattle.

Cakes were purchased and mounted on a

"stinger," or short iron rod, supported on a

framework mounted on the prow of a skiff (see

fig. 5). The framework was hinged so that the

FIGURE 5.—Diagram of rig for holding salt cakes in water of

lake during erosion tests. Framework holding stinger with

salt cake is hinged at the boat prow, so the cake can be

lifted from the water by the block and tackle attached to

top of frame. Both depth and attitude of stinger are adjustable.

salt blocks could be immersed or withdrawn

from the water while the boat was in motion.

The attitude of the blocks and the depth of submersion were adjustable, between runs.

As the boat was driven by an outboard motor, its speed was measured by use of a water

manometer on a float (pi. 9a) towed behind a

light boom, well away from the bow waves of

the boat. The operator read the dynamic

pressure directly on the meter stick alongside

the manometer, and could thus regulate the

speed of the motor to maintain constant water

speed. In later tests a level was used in the

boat so that reproducible trim could be maintained by shifting the positions of the crew

during the tests.

Tests were made on salt cakes of five different

chemical compositions during the fall, winter,

and spring of 1957-58 in Lake Wauberg near

Gainesville. The five types were pure white

salt; yellow salt containing 98 percent salt and

2 percent sulfur; a brown cake of pure salt with
56 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

about 2 percent of iodine in it; a blue salt cake

with a trace of copper sulfate or carbonate;

and a deep red salt cake containing 2 percent

of impurities including iron, manganese, copper,

cobalt, and iodine. Water erosion produced

results that were qualitatively much the same

on all cakes, regardless of chemical composition;

however, the pure salt tended to be more pitted

and irregular in its erosion.

Observations

A series of runs at various speeds and lengths

were made on salt cakes having various initial

shapes. Plates 9-14 illustrate the results.

The salt cakes as purchased (pi. 96) were

rectangular blocks 12 inches long and 8 inches

square, weighing 50 pounds. The depression

at each end was made by the form in which the

kiln-dried salt was pressed. The depression,

usually saucer-shaped, was I-shaped in the

iodine salt cakes. To mount a cake on the

stinger, a 2-inch hole was drilled in one end of

the salt cake. The stinger, fitted with a pair

of soft rubber stoppers between washers at its

tip, was slipped easily into the hole. The

rubber stoppers were compressed by a nut, and

expanded sidewise enough to hold the block

firmly on the stinger.

Some runs used salt blocks shaped like that

shown in plate 96. Others used circular cylinders 8 inches in diameter and 10 inches long,

machined from the salt blocks as purchased.

Still other blocks were machined into the shape

of an ogive, or pointed arch (pi. 9c). Machining was done on a Shop Smith, by a wood lathe

technique. Various salt compositions differ

considerably in ease of machining; their durability under erosion seems to bear no relation

to hardness in the machining process.

The forms resulting from erosion varied

greatly. White salt cakes in their original

form eroded very irregularly (pi. 10a). Iodine

salt eroded in a somewhat more orderly fashion

(pi. 106). A hairpin-shaped pit is clearly

visible just upstream of the corner of the cake

in the center of the figure (pi. 106). An apparent break in the center of the pit results from

the presence of another pit of the same type

just above it, with a high ridge at its center

just upstream of the break. Two pits near the

top of the cake are in the process of fusing.

The one on the left is seen in profile; its location

just upstream of the corner on the left is quite

analogous to the pit in the center of the figure.

The neighboring pit with which it is combining

is visible above the center one. Flow lines are

clearly visible in each pit, running in directions

normal to the pit edge, from the high point in

the center. The pits shown obviously tend to

erode back toward the point of the cake.

If the mechanism of pit erosion is assumed to

be a hairpin-shaped vortex with axis lying in

the pit, the directions of the flow lines are properly rationalized. The legs of the vortex trail

downstream, as indicated by corresponding

grooves that become shallower downstream.

Where two pits are so near as to begin to fuse,

the neighboring legs of their generating vortices

should cancel out, since they would be rotations

in opposite sense. The tendency to cancel is

recognizable in the two fusing vortices of plate

106. In the salt cakes, many pits may appear in

which one leg of the vortex is altogether missing;

ordinarily a canceling vortex leg can be found to

account for the disappearance.

Plate 106 also shows many small pits on the

side of the cake far from the tip. These bear a

superficial resemblance to pitting on meteorites;

however, that fact is not particularly significant

and the pits display no recognizable erosion

pattern beyond the apparent evidence of

turbulence.

A striking characteristic of the iodine salt

cake shown in plate 10c is the presence of many

small pits near the tip without any easily recognizable pattern of shape or arrangement. Obviously the block is tending toward a more pointed

shape than it had originally. During erosion

the block was moving at a speed somewhat less

than that of most of the other blocks shown in

the photographs.

A more orderly and recognizable pattern of

erosion than that provided by the iodine cakes

was observed on cakes of blue salt (pi. lla,b).

Plate ll a shows an extraordinarily well developed pit with the expected hairpin shape of the

generating vortex. The pit straddles the corner,

but not sj-mmetrically; the flow lines inside the

pit run from the high point in the center normally to the pit edge. The right leg of the

generating vortex is indicated by the groove

carved on the cake on the right; the other leg of
METEORITE PITTING 57

the vortex is hardly detectable. Immediately

above the large pit shown, another rather similar one is visible, with less typical shape and less

striking flow lines. The left leg of the pit is

present as a groove not easily visible in the highlighted side on the left; the right leg is missing.

On the other side of this cake are two pits,

neither one straddling a corner, but located on

the flat side.

Plate 116 shows a block of blue salt whose

pitting pattern, in spite of apparent differences,

resembles that of the block in plate lla. The

large and well-formed pits on the two corners

shown in plate 116 have enlarged and receded

toward the point of the cake so far that they are

close to fusing, and about to remove the tip of

the cake. The pit on the left is visible almost in

profile. Both pits are far enough up on the

shoulder of the cake so that the legs are not

visible as grooves, although the low ridge running down on the left of the face may be a

remnant. A pit is also visible in the middle of

the face, somewhat downstream of the shoulder.

The stagnation point at the center of the pit is

a high point rather than a low one as in meteorite pits.

Before erosion, the three iodine salt cakes

shown in plate lie were right or flat-ended

circular cylinders obtained by machining the

purchased blocks. Cakes of this shape were

not expected to pit during erosion. The first

two samples on the left in the photograph were

not carefully oriented; the third was alined with

the boat axis and kept level. The deep pit just

downstream of the point in the first sample

is believed to have been favored by an angle of

pitch in the attitude of the cake. Although the

shape is not typical of those formed by a hairpin

vortex, a high point occurs below the deepest

part of the pit, and ridges down the side mark

the location of the vortex legs. Presumably

the pit was in the lee of the point, which was

cocked a little with respect to the flow. The

middle block has a small pit, also just downstream from the point, that shows flow lines

and the typical hairpin shape. A tendency to

pit is evident near the point of the third sample,

but some reduction in pitting seemed to result

from the care taken in maintaining the attitude

of this salt cake.

A more dramatic demonstration of the

influence of attitude on tendency to pit is

presented in plates 12 and 13. The attitude

of the blue salt cake shown in plate 12a (initially

a right circular cylinder) was not checked or

maintained, and the block is deeply pitted.

The thin hook at the tip is the relic of a large

pit quite similar to that near the tip of the cake

in plate 116, but it represents a later stage in

erosion. One well-formed pit lies just downstream of that in the hook; and to the left are

two overlapping "half-pits," showing only one

leg of the hairpin vortex. The lack of a leg

on the upper "half-pit" might be accounted for

by the observation that the leg should cancel

with one leg of the vortex in the hook. The

absence of the left leg of the lower pit has not

been explained so far. The deep pitting on the

shoulder probably was favored by a chance

pitching angle of the cake to the relative motion

of the water.

The blue salt cake shown in plate 126 also

started as a right circular cylinder. The axis

of the cylinder was carefully adjusted to be

parallel to the motion of the boat, and this

attitude was maintained during the run by use

of a level in the boat. It is clear that there is

no trace of a pit anywhere on the surface.

This result was demonstrated repeatedly by

use of sulfur (pi. 12c) and other salt (pis. 13a,

14a) cakes whose initial shapes were right

circular cylinders, ogives, and cones.

In plate 14a, the first two blue salt cakes on

the left (shown earlier in pi. 11 a,6) started as

rectangular blocks. The other four were cylindrically symmetrical; only the first of these four

is pitted, and it was the shape of the cake in

plate 12c, which was presumed cocked to the

flow since no effort was made to adjust its

attitude. The second and third shapes from

the right initially were ogives; the one at the

far right was a right circular cylinder. These

last three were adjusted to be straight with

respect to the boat's motion.

In short, these experiments gave ample proof

that pitting is complete^ suppressed, or at

least substantially reduced, whenever the initial

shape of the salt cake is cylindrically symmetrical around a line that is parallel with the

direction of motion of the boat. However,
58

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

even when all controllable conditions are the

same there may be considerable differences in

pitting. The white salt ogive on the right in

plate 13a was not pitted, but its surface was

not as regular as those of blue salt cakes subjected to the same erosion conditions.

Reference has been made to the characteristic appearance of the trailing surfaces of

meteorites (p. 52). A similar appearance is

characteristic also of trailing faces of salt

blocks, as shown in plate 136. The iodine salt

cake was chosen arbitrarily from among

eroded blocks having the same type of carving

on the rear. The appearance, referred to as

"mottled," is due to broad and shallow depressions. Notice that the edge of the face has a

shairp skirt. A corresponding view of a meteorite's trailing face appears in plate 6c.

Pit formation in salt cakes

The photographs of eroded salt cakes in plates

10 to 14 show the following general features:

Pitting of surfaces usually occurs. The degree of pitting varies greatly, depending on

the sample's material, and attitude to the fluid

motion.

The detailed geometry of pit arrangement is

not precisely reproducible from sample to

sample. However, pits appear at a number of

typical locations:

(1) In the lee of a projection such as an ogive point

cocked to the water flow. (PI. 12a shows one such pit

in its last stage before disappearance, another example

appears in the left cake in pi. lie.)

(2) Upstream of projections, such as the corners of

square blocks. (Examples occur in several figures,

notably pi. lla.)

(3) Downstream of a sharp shoulder. (Lower pit

of pi. 116 is an example.)

(4) On a face parallel to the water flow, far from the

front tip. (PI. 106.)

(5) On the base of eroding bodies. (PL 136.)

Pitting either does not occur at all or occurs

much less frequently on objects having a

cylindrical symmetry around an axis parallel

to the direction of water flow (pi. 14a). A

right circular cylinder is a little less pit-resistant than an ogive. A small yawing angle

causes a pit in the lee of the tip of an ogive

(pis. 12, 13a).

The centers of the pits in salt cakes tend to

show high points rather than low points. In

meteorites, the flow lines suggest the presence

of a hairpin-shaped vortex lying in the lee of

the upstream edge of the pit, straddling a

stagnation point at the deepest point of the pit.

In the salt cakes exactly the same type of

vortex is evident, similarly hairpin-shaped, and

lying in the pit straddling the stagnation point

in the pit. But since the stagnation point in

salt cakes is a high point rather than a low one,

it indicates a minimum rate of erosion, rather

than a maximum rate at the stagnation region,

as in meteorites.

The mechanism of pit-formation in salt cakes

was in most cases quite recognizably a vortex.

Plate ll a shows perhaps the most convincing

evidence of the nature of the flow. The flow

lines in the pit are here normal to the edge,

which is so sharp as effectively to preclude

serious consideration of any but vortex flow

inside the pit.

The nature of water flow over the surface of

the pitting cakes obviously changes with time—

pits form and deepen; they may be intersected

by competing pits; and they may be erased.

The same flow patterns first observed on

meteorite surfaces are recognized also on the

surfaces of salt cakes subjected to erosion by

flowing water. It has not been determined

whether differences in detail may exist due to

the supersonic speed of the meteorites as compared to the low speed of the salt cakes. Since

the pits in the salt were formed by vortices

identified by their carving action, it seems a reasonable hypothesis that the pits on meteorites

were formed similarly by vortices, identified by

their flow lines in the pits.

Cavitation

The process of cavitation, often observed to

effect dramatic erosion of solids in motion under

water, can hardly be a factor in the experiments

under discussion here. Cavitation is known to

occur when dynamic pressures are of the same

magnitude as the static pressure on the submerged body. Thus cavitation would be expected on an object at a depth of 1 foot of water

at sea level, at speeds such that the dynamic

head would be about 35 feet of water. This

would be at a speed of 28 knots, larger by »

factor of 6 than the speeds used in the tests.
METEORITE PITTING 59

The vortex mechanism of pit formation

The following analysis proposes to rationalize,

as far as possible, the hypothesis of a vortex

mechanism of pit formation in salt cakes.

This hypothesis will be supported if

(a) the existence of vortices at places where pits are

formed can be shown to result reasonably from the

principles of fluid physics; and

(b) if it can be demonstrated that the presence of a

vortex would set up a velocity distribution such as

would be expected to increase the erosion rate.

The introduction of the idea of vortex motion

as a phenomenon of fluid dynamics is generally

credited to Helmholtz (1858) (see Durand,

1934, p. 330). He pointed out that whereas

ideal fluids that can be described by a potential

function possess no rotary motion, nonideal

fluids in which no potential exists are found to

be characterized by rotation in some parts.

Rotation is consequently found in connection

with flow of viscous fluids across solid surfaces.

The use of the concept of rotation in describing the lift of an airfoil is familiar. In

this discussion the problem is to connect the

formation of vortices with erosion, which is

already presumably related in some way to

drag forces on a solid in a fluid stream. The

classical work on trailing vortices by von Karman (von Kannan and Rubach, 1912; Durand,

1935, p. 346) extended as far as the computation

of the drag on a bluff body, from the geometry

of the vortex array in the wake. However,

the theory was not capable of predicting the

geometry of the trailing vortex array from the

shape of the body (Prandtl, 1952).

The requirement in establishing the vortex

mechanism of pitting is precisely to predict

the conditions under which a stable vortex

will form in the boundary layer of a flow near

the surface of a solid body. In this discussion

no theory of any great scope is developed;

however, qualitative considerations are used

to predict how and where vortices will form.

A subsonic flow over a curved body tends to

follow the body, as is well known from theory

and experiment. In this process the pressure

of the potential flow outside the boundary

layer will increase, and the velocity will decrease in any region where the normal to the

solid surface has a component parallel to and

in the same sense as the free stream velocity.

It is known that the boundary laj'er will tend

to thicken in such a region.

A flow tends to separate from a curved body

with cylindrical (or spherical) symmetry in the

presence of a positive pressure gradient (Green,

1937; Prandtl and Tietjens, 1934). The pressure gradient, parallel to the flow, causes deceleration and reversed flow in the boundary

layer. Such a mechanism can be used to

account for the trailing toroidal-type vortex

anticipated in the wake of any bluff object

(pis. 56, 6c). The same assumed mechanism

can be used to lead to the conclusion that no

pitting is possible in regions where the curvature of the surface is small or negative, as

long as pressure gradients have no component

normal to the initial direction of flow. Qualitatively, the argument is that in a two-dimensional boundary layer any tendency of the

flow to stop and reverse, due to a pressure

gradient parallel to the two-dimensional potential flow, will at once thicken the boundary

layer. This conclusion results directly from

the continuity relation for two-dimensional

incompressible flow: if the x- and y-components

of the velocity are u and v respectively, a

reduction of u along the surface in question,

—du= — bu/bx dx,

must result directly in an increase in the normal

component of velocity. By the continuity

relation for two-dimensional incompressible

flow, we obtain the relation

__bu do

dx by

The consequence of such normal motion is

that the flow outside the boundary layer must

be deflected outward to cause a relative increase

in vm and a reduction in the pressure, i.e.,

a decrease in bpfbx which was the initial cause

of the deceleration. This change would

promptly erase the tendency to form a stable

vortex as long as the gradient bp/bx is always

parallel to the two-dimensional flow.

An attempt at a mathematical description of

this type of flow has been put forward as an

initial value problem by Prandtl (1940). It

led to the conclusion that at the point where

bp the pressure gradient ^r^O there are restric-
60 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

tions on dufdx, d2ufox2, and ZPufdx3 wherever

u=0, if du/dx is not to become infinite. Consequently, reversed flow could not be rigorously

demonstrated by the analysis. This finding is

suggested as supporting the conclusion that

pits cannot in fact form, because vortex flow

is not stable, even in the presence of a pressure

gradient, as long as that gradient is parallel

to the direction of flow.

Pursuing this line of thought suggests that

we might avoid the difficulty encountered in

this initial-value boundary-layer problem in

two-dimensional flow if three-dimensional flow

were assumed or if the reaction of the boundary

layer on the external potential flow were considered. We might then be able to demonstrate the stability of a hairpin-shaped vortex

straddling a pressure "hill" in a boundary

layer even in a region where the pressure nearby tends to decrease downstream. For the

present, the evidence that stable vortices occur

upstream of a projection on an eroding body

must remain empirical.

Some conclusions might be drawn relating

to the vortex motion in a pit during erosion.

The existence of a vortex inside the pit must

depend on the existence of a permanent pressure gradient holding the fluid in the vortex

stationary with reference to translation downstream. The equation for the x-component of

the forces, i.e., in the direction of the main

flow, might be derived as follows:

Suppose a vortex exists in a pit in such a

way that the fluid stays in it for a period that

is long, compared to the time required for fluid

in the exterior flow to pass across the pit. In

cross section, the vortex might appear like that

sketched in figure 6. The section is made by a

vertical plane parallel to the potential flow,

along the axis of symmetry of the pit. The

dotted line is a flow line for the fluid in the

vortex. Inside the dotted line, the velocity

might be assumed to vary inversely with the

distance from the vortex center, as might be

assumed for a vortex in general. Outside the

dotted line bounding the vortex, one might

assume a boundary layer in which viscous

forces are predominant. The dotted perimeter

might be considered to be divided into two

portions. The part designated by Ao in the

figure represents the portion adjacent to a

FIGURE 6.—Longitudinal section showing a vortex (dotted

line) lying in a pit. Due to the flow outside the pit, there

is a velocity gradient over half of the perimeter that exerts

a downstream force on the vortex. Over the other half

(Ao) of the perimeter the drag force between the vortex

and the pit surface also is in the downstream direction.

The pressure gradient balances the sum of the two viscous

forces. Arrows indicate airflow; cross-hatching indicates

surface.

boundary layer between the vortex and the

surface of the pit. The remainder of the

vortex surface is adjacent to the potential flow.

The assumption that air stays in the vortex

for a relatively long time requires that the

resultant of the forces acting on the vortex—

due to both the pressure gradient and the

viscous drag over the vortex surface—must be

equal to zero:

fP+f,=o.

Here tp is the resultant of the pressure gradient

forces, acting on the vortex element, and f, is

the resultant of the forces due to viscous drag

on the vortex, i.e., due to the velocity gradients

at the vortex boundary.

Suppose now that the area Ao of the vortex

is described in terms of the element of length,

dz, of the vortex and that central angles a and

j8 are measured as positive clockwise irom the

pole, which is parallel to the negative z-direction. The force on an element r dO dz of area

on the periphery of the vortex has a component

in the x-direction given by

dzdf=fij-rddsin ddz. (1)

The gradient bv/dr is that at the boundary of

the vortex at a distance r from its center. This

gradient reverses direction at the points corresponding to central angles a and £, the bounds

of the area Ao. It is therefore proper to write

(2)
METEORITE PITTING 61

Here (dp/dr^ is the gradient in the boundary

layer between vortex and pit surface, (dp/dr)3

is that in the boundary layer between vortex

and external potential flow.

Suppose (dr/dr)! and (dy/dr)2 have constant

mean values over the respective ranges of 8

in which they act. The resultant f, is then

computed to yield the value,

f

.=,r(cosa-cos,){-(|)+(|)J. (3)

According to the sign convention (dy/dr)! is

negative so that equation (3) represents a force

downstream of magnitude

(4)

(5)

The equilibrium condition is then

2r

Equation (5) states one of the conditions

necessary for a vortex to remain stationary on

the surface of a solid over which fluid is flowing.

Another condition is that the rotary motion of

the vortex should continue for a time, t, long

compared to the time for fluid in the external

flow to cross the pit (t»2r/vm). The energy

fed into the rotation of fluid in the vortex by

the external flow should be equal to that

absorbed by friction on the pit wall. If the

energy imparted to the vortex were in the form

of work done by viscous forces, and if the velocity

of the fluid at the vortex boundary is assumed

uniform, the energy conservation law is given

by the equation

A * r ^

That

dr|, dr 2 \a+/3 /

(6)

(7)

Brief consideration of equation (7) is sufficient to demonstrate that the model thus far

developed cannot possibly account for the deepening of a pit by erosion, if the erosion rate

499091—69 2

increases with the fluid velocity. (That such

an increase in fact takes place is demonstrated

later; increase in erosion rate with increase in

velocity is in any case a reasonable assumption.) Suppose, for example, that in equation

(7), a+/3=x radians. For such a case

The erosion rate might be presumed proportional, more or less, to |dtf/dr|,. But the erosion

rate inside the pit must then be less than that

outside the pit just upstream, where the velocity

gradient is |do/dy'|0, say. For |dp/dr]2 must be

less than \dv/dy\0 because \dv/dr\2 is due to a

boundary layer between flows having speeds of

vm and tWtex^O whereas the \dvjdy\o is due to

a boundary layer between fluid with the speed

vm and the wall where the speed is zero. If the

boundary layers are of equal thickness inside

and outside the pit, it follows that

and hence the erosion rate inside the pit would

be less than that outside, as was stated.

It should be emphasized that there is no

assurance that the boundary layers have equal

thicknesses inside and outside the pit. Hence

the question as to how large the velocity gradients may be in various boundary layers cannot

be answered at present.

An alternative viewpoint relating to the conservation law for energy may be somewhat

more promising for rationalizing the observations. Consider the following argument: In

the analysis thus far made, no account has been

taken of the continuity relation. It has been

suggested in the preceding discussion that to

apply that relation to the case under discussion

would require some flow normal to the plane

of the section shown in figure 6; that is, fluid is

continually fed into the pit from the boundary

layer upstream. In order that the vortex

should remain constant in size, there must be a

continuous outward flow of fluid in a direction

normal to the section of vortex considered. If

the boundary layer upstream has a depth 8 and

a mean velocity c/2, the mass flow into the

vortex would be pcm Sdz/2 where p is the fluid
62 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS TOL.S

density. This must be equal to the net outward flow of fluid, 2-K r

2

 pwX2 where w is the outward axial flow at distance dz/2 from the plane

of figure 6. That is,

tangential velocity increases inversely with ?•*, as

shown by the relation

It is not difficult to work up an expression

based on the force law relating w with the axial

component of pressure gradient. However, this

discussion intends rather to draw some qualitative conclusions relating to the energy of fluid

circulation inside the vortex. The model here

described, of course, has more than a passing

resemblance to the so-called vortex or Hilsch

tube (see Scheper, 1951, for a discussion of the

characteristics of the Hilsch tube). That is,

fluid is fed into a vortex from the periphery with

some kinetic energy and, hence, some moment

of momentum; fluid is removed along the axis,

or at least in the axial direction. In such a

vortex tube there may be a redistribution of

energy such that the energy relation of equation

(7) is not valid. Itispossible that the deepening

of pits in erosion may be shown to be reasonable

by virtue of that redistribution, in contrast with

the conclusions based on the equation.

Rotational energy in a vortex

The literature dealing with analysis of flow in

vortex tubes has been concerned mainly with

heat flow or the separation of gases (Pohlhausen,

1921; Elser and Hoch, 1951). It is not intended

at this point to discuss those characteristics of

the vortex tube or to derive the dynamic characteristics of the device. However, the qualitative picture of vortex flow in a vortex tube

suggests a mechanism capable of accounting

for pit formation by vortices.

Consider a vortex in which the circulation

is constant. Such a flow is a reasonable first

approximation to a real vortex, and is characteristic of a frictionless fluid. In such a vortex,

the tangential velocity v at each point is inversely proportional to the distance r of the

point from the vortex center:

(8)

Here r is the constant circulation. For such

a vortex in a perfect fluid, the gradient of the

dv

~dt (8a)

If a vortex exists in a gas having a small

viscosity, the flow will tend to depart from the

pattern of a free vortex. In effect, the inner

layers would tend to do work on the outer

layers of fluid; the velocity gradients would

tend to decrease. In time the vortex would

change toward the state in which the angular

velocity v/r is constant.

Suppose that fluid is brought into the vortex

with a rotation r, and that it stays for a while,

being removed from the vortex axially. For

some period of operation with this type of flow,

the fluid should have less vorticity as it leaves

than it had as it entered, vorticity being defined

as the product 2rvr. In other words, vorticity,

according to this picture, should tend to accumulate in the vortex until the velocity at the

periphery of the vortex is as great as or even

greater than that of the fluid entering the vortex.

This behavior of fluids may be observed in

the manner of operation of the cyclone separator

for removing dust from air. It can be observed

also in the bath tub when the water is running

out the drain. And it would appear that the

thermal phenomena in the Hilsch tube might

be explained by use of the same model. Since

a detailed analysis of the mechanism as it

applies to the pitting phenomenon has not been

made, the model is proposed at this time only

as a possible means of rationalizing the observation that pits do form where vortices are found.

That is, if an accumulation of vorticity can be

demonstrated in a pit vortex, the requisite

mechanism for rationalizing pit formation would

be established, subject only to the further condition that the rate of erosion increase with

speed of the fluid.

Variation of erosion rate

The dependence of the rate of erosion on

flow speed is not difficult to demonstrate.

Several series of runs were made in which the

time and speed were observed as they affect

the weight loss of salt cakes.

It is to be expected that erosion of a body

subject to fluid flow would be proportional to
METEORITE PITTING 63

the surface area exposed to the flow. That is,

dm . . . .

~~odt ' ^

where m is the mass of the eroded body, A is its

surface area, k is the linear rate of erosion per

unit time and per unit exposed area, and p is the

density of the solid.

Suppose the shape is not greatly changed as

erosion proceeds; that is, suppose mlp^at3,

A=bri, where a and 6 are constants, and r is

some characteristic dimension of the body.

Then

(10)

(11)

(Ha)

A=b ( —pa

and equation (9) yields the value

fa u(m\*m

pat \pfl/

This equation may be integrated to yield

—3roM=/> ,Mt-(-constant.

(pa)"

If t is measured from the time when m = mfl, the

equation can be written as

mon-mH=aW>t (nb)

(

m

\"-i Pkb

 { no)

U o / ~ 3(pa)WTOoK*' V*)

or

Equation (12) states that the ratio of salt

cake weight at any time t to its initial weight,

raised to the % power, is a linear function of

time, the slope being proportional to the linear

erosion rate k, and inversely proportional to the

H power of the initial weight. It should be

noticed that shape factors also enter into the

slope.

If the eroded bod}T changes in shape with

time, the slope of the erosion curve as derived

should also change with time. However the

form in which the data are presented might

reasonably still be a plot of (TO/TOO)** as a function of time.

Figure 7a presents a graph showing how the

rate of erosion of two blue salt cakes varied

with time of running; the relative mass to the

one-third power is considered proportional to

the linear size. One cake was originally an

ogive; its data are well represented by a

straight line throughout the experiment. The

other cake was a right circular cylinder, whose

data may also be represented by a straight

line except for the first 6 minutes of running

time, when the erosion rate was relatively small.

The slopes of the two lines are equal, but the

significance of that fact is not clear, because of

the difference in original shape and size of the

blocks. The final shapes of the two blocks,

after erosion, are found in plate 14a, on the

extreme right; they are remarkably similar in

shape, and quite free of pits.

Figure 7b shows a set of curves representing

the data on erosion of three right circular

cylinders of salt cakes of different compositions.

The curves are rather close together, and all

three are well represented by straight lines

throughout most of the running time. During

the first six minutes, the blue cake was relatively more durable; the sulfur cake was slightly

less so, and the iodine cake was the least durable

of the three.

At 3-minute intervals during erosion, successive changes in the shape of a right circular

cylinder of blue salt occur (fig. 8). Clearly the

leading face of the cylinder is first rounded.

The shape becomes somewhat bulbous for a

period, but later the typical ogive is formed.

In many salt cakes, large pits were formed

throughout the run, generally on the shoulder

and near the tip. None appeared on the blue

cake.

These preliminary data are presented as a

background for the data on erosion rate as a

function of the water speed. Two series of tests

were made in which salt cakes shaped as purchased (pi. 96) were subjected to erosion at

different speeds. That the erosion rate increases

with speed is immediately made clear by a

glance at plate 146, showing four iodine salt

cakes which were eroded for 16 minutes at different speeds. The differences in size of the

cakes are clear and direct evidence, albeit not

very quantitative, that erosion rate increases

with water speed.

A more quantitative measure of the erosion

rate would be the slope of the curve of (m/mo)1"

against t, a slope presumably proportional to
64

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

a

RIGHT CIRCULAR CYLINDER Z. A •

6 9 12 15

RUNNING TIME, MINUTES.

18 21

1.0

C

.2

BLUE

6 9 12 15

RUNNING TIME, MINUTES

18 21 2 4

FIGURE 7.—Erosion as a function of running time; water speed, 4.8 knots. One-third power of cake

weight is considered proportional to the linear size; presumably, the slopes of these curves are

proportional to the linear erosion rate, a, Ogive and right circular cylinder, blue salt cakes, b,

Right circular cylinders, salt cakes of various compositions.
METEORITE PITTING 65

FIGURE 8.—Successive shapes at 3-minute intervals of a

blue salt cylinder during erosion. Erosion begins as a

rounding of the cylinder edge. A tendency to form a

bulbous shape quickly gives way to the typical ogive shape.

Erosion of base proceeds relatively slowly.

the linear erosion rate k (see equation (12)).

The slopes for the iodine salt cake tests were

computed from the initial and final weights for

the four iodine salt cakes shown in plate 146

that were eroded at different water speeds.

The results, in the form of two different curves,

are presented in figure 9. The solid curve shows

pkb/Zipay^W* as a function of speed; the

dashed curve shows the same quantity as a

function of dynamic head. Both curves are

valid measures of the relative erosion rate as a

function of water speed, because the composition, original shape, and original size were the

same for the four blocks of iodine salt. The

linear erosion rate, as measured, clearly varies

as a smooth function of speed. When dynamic

head is used as the independent variable, the

points lie on a straight line which has an intercept above the time axis. Such a variation

implies an erosion rate at zero speed, and an

additional rate proportional to the square of

the water speed.

Pitting of salt cakes and meteorites

The experiments on salt cakes were designed

to show that the bound vortex mechanism of

pit formation, as first suggested by the flow

marks on meteorites, docs actually operate to

produce pits on eroding salt cakes; and hence,

presumably, on any ablating solid body. The

tests established empirically that salt cakes are

pitted, exactly as predicted. The shapes and

locations of the pits support the conclusion

that bound vortices are responsible for the erosion. A possible mechanism was suggested

which might cause higher velocity gradients in

pits than in the area nearby outside the pits.

Although the existence of this mechanism was

not established by any complete theory, the

tests provide experimental proof that an increased erosion rate in the pits would result if

higher velocity gradients do exist inside the

pits.

None of this evidence is, strictly speaking, a

"proof"; and of course a rigorous proof is out

of the question since no tests can be made on

the pitting of meteorites during astroballistic

flight. It is considered desirable to marshall

the empirical evidence as it stands:

(a) Direct observation has proved that vortices of

the same type as are detected on salt cakes in water

existed on meteorites during a period when airflow was

hot enough to melt them.

(b) Pits occur on meteorites at points that are altogether analogous to the position of pits on salt cake.

Specifically:

(1) A meteorite like the Lafayette, which is symmetrical enough to show no pressure gradients transverse to the airflow, did not pit; similarly, the

axially symmetrical salt cakes showed a reduced

tendency to pit (pis. 5a, 126).

(2) Pits are found on and near the shoulders of

axially nonsymmetrical meteorites; similarly, they

are found on and near the shoulders of axially nonsymmetrical salt cakes (pis. 8,1 la).

(3) On trailing faces of meteorites the pits bear a

striking visual resemblance to those on the trailing

faces of eroded salt blocks (pis. 6c, 13b).

(4) Small pita on the sides of salt cakes far from

the leading face resemble meteorite pits seen on

many meteorites. (Data supporting this point are

not presented in any detail here, but see pis. 7c, 106.)

(c) An increased erosion rate for salt cakes due to

higher water speeds was experimentally established.

If the mechanisms of pitting on meteorites and on salt

cakes are similarly affected by fluid dynamic influences,

presumably the effect of increased velocity in the
66

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

CO

H

Z

as

£.04

A

ac

*

ui

z

o

5

o

ae

ui

IE

<

KVS DYNAMIC

HEAD

KVS SPEED

DYNAMIC HEAD, IN. H2O

5 10 15

SPEED, KNOTS

FIGURE 9.—Variation of linear erosion rate of iodine salt cake with water speed. Dashed line shows

curve of linear erosion rate as a function of dynamic head. Since this line is straight, it indicates

a variation proportional to the speed squared. The intercept of this line suggests that erosion

would occur at zero speed.

boundary layer on erosion rate should be at least

qualitatively similar for meteorites and salt cakes.

That is, the erosion rate could be expected to increase

with fluid speed on bodies ablating in a hot air blast,

a fact that has been generally observed. To give one

of many possible examples: a plate of refractory material was highly resistant to erosion when heated by a

gas-oxygen torch for several tens of seconds. The

same material tested in a hydrogen-peroxide kerosene

rocket eroded to a depth of about an inch in somewhat

less than 2 seconds. The difficulties encountered in

the search for lining materials for rocket nozzles and

jet vanes are well known. Thus the dependence of

erosion rate on fluid speed, which is observed on salt

cakes in water, is the same qualitatively as that observed

for solids subject to aerothermodynamic ablation.

The evidence just summarized has convinced this author that pitting on meteorites

is caused by the fluid dynamic mechanism of

bound vortices. It should be pointed out that

this conclusion is not affected in any way by

the following facts:

(a) The detailed processes involved in erosion on salt

cakes and on meteorites are quite different.

(b) The meteorites were subject to supersonic flow,

and the salt cakes to subsonic flow.

(c) The materials, sizes, and Reynolds numbers of the

flows over meteorites and over salt cakes are different.

(d) The detailed dependence of erosion rate on fluid

speed presumably differs in meteorites and in salt cakes.

(e) As far as any conclusions drawn here are concerned, erosion and possibly pitting of meteorites might

also be effected without the presence of vortices, or

even in the absence of enough air to form a shock wave.

That is, no assertion is made here that all pits in meteorites are due to vortices.

The arguments summarized here have led

the author to conclude also that pitting of the

same type may be studied on erosion models

subjected to subsonic flows. The model

chosen for the research presented here is, of

course, not the only one possible. Specifically)

the conclusions reached here might be supported by detailed measurement of flow speeds
METEORITE PITTING 67

inside such pits as are actually formed by water

erosion. A hot wire anemometer could be

used in a low-speed wind tunnel to test salt

cakes previously pitted in the manner described in this paper. The same type of study

might be made also of plaster casts of meteorites. Such a program of studies might greatly

advance the detailed theory of ablation and

pitting of coatings for vehicles designed for

reentry from outer space.

The type of study suggested here, of course,

is not at all new, though the application to

pitting may be. Work reported by Berman

(1955) presents a theory that would be useful

in developing a proper analogy between ablation and heat transfer. The experimental

study that served as a background for that

work was the ablation of icicles in a wind

tunnel.

References

ALLEN, W. A., AND MAYFIELD, E. B.

1953. Journ. Appl. Phys., vol. 24, p. 131.

ALLEN, W. A.; RINEHAHT, J. S.; AND WHITE, W. C.

1952. Journ. Appl. Phys., vol. 23, p. 132.

BERMAN, K.

1955. Journ. Appl. Mech., vol. 22, p. 196.

COOK, A. F.

1954. Astrophys. Journ., vol. 120, p. 572.

COOK, A. F., AND MILLMAN, P. M.

1955. Astrophys. Journ., vol. 121, p. 250.

COOK, M. A.; ETBING, H.; AND THOMAS, R. N.

1951. Astrophys. Journ., vol. 113, p. 475.

DUBAND, W. F.

1934. Aerodynamic theory. Vol. 1, 398 pp.

1935. Aerodynamic theory. Vol. 2, 367 pp.

ELSER, K., AND HOCH, M.

1951. Zeitschr. Naturf., vol. 6a, p. 25.

FALES, E. N.

1926. Visible study of flow. McCook Field Rep.,

Serial No. 2635. Published by Chief of

Air Service, Washington, D.C.

GBEEN, S. L.

1937. Hydro- and aeromechanics. 166 pp.

HELMHOLTZ, H.

1858. Journ. Reine Angew. Math., vol. 55, p. 25.

HENDERSON, E. P.

1958. Proc. U.S. Nat. Museum, vol. 107, p. 339.

HENDEBSON, E. P., AND WILLIAMS, D. T.

1958. Techn. Rep. No. 9, Smithsonian Inst.

Astrophys. Obs.

JACCHIA, L. G.

1955. Astrophys. Journ., vol. 121, p. 521.

NININGEB, H. H.

1936a. Amer. Journ. Sci., vol. 31, p. 209.

1936b. Amer. Journ. Sci., vol. 32, p. 1.

1952. Out of the Sky. 336 pp.

POHLHAUSEN, E.

1921. Zeitschr. Angew. Math. Mech., vol. 1, p.

115.

PRANDTL, L.

1940. Tech. Mem. No. 959, National Advisory

Committee for Aeronautics.

1952. Essentials of fluid dynamics. 452 pp.

PBANDTL, L., AND TIETJENS, O. G.

1934. Applied hydro- and aeromechanics. 311

pp.

RlABOUCHINSKT, D .

1909. Bull. Inst. Ae'rodyn., Koutchino, vol. 3, p.

59.

RlNEHART, J. S.

1957. Bull. Amer. Phys. Soc., ser. 2, vol. 2, p. 45.

RINEHART, J. S.; ALLEN, W. A.; AND WHITE, W. C.

1952. Journ. Appl. Phys., vol. 23, p. 297.

SCHEPER. G. W., JR.

1951. Refrig. Eng., vol. 59, p. 985.

SMITH, H. J.

1954. Astrophys. Journ., vol. 119, p. 438.

THOMAS, R. N.

1952. Astrophys. Journ., vol. 116, p. 203.

THOMAS, R. N., AND WHIPPLE, F. L.

1951. Astrophys. Journ., vol. 114, p. 448.

THOMAS, R. N.f AND WHITE, W. C.

1953. Astrophys. Journ., vol. 118, p. 555.

VON KABMAN, T., AND RUBACH, H.

1912. Phys. Zeitschr., vol. 13, p. 49.

WHIPPLE, F. L.

1943. Rev. Mod. Phys., vol. 15, p. 246.

1955. Astrophys. Journ., voL 121, p. 241.

WHIPPLE, F. L., AND THOMAS, R. N.

1951. Journ. Aeron. Sci., vol. 18, p. 636.

WHITE, W. C.

1955. Astrophys. Journ., vol. 121, p. 271.

WHITE, W. C; RINEHABT, J. S.; AND ALLEN, W. A.

1952. Journ. Appl. Phys., vol. 23, p. 198.

Abstract

Flow lines on meteorites were photographed to determine the nature of airflow inside the "thumb pits" in the

surface. The flow is shown to be consistent with that occurring if a hairpin-shaped vortex were lying with bent portion in the pits, with vortex legs trailing off to infinity downstream. Since such a flow is not unique to supersonic

fluid speeds, the prediction is made that pits similar to those on meteorites would be observed on salt cakes pushed

through a lake. Experiments demonstrated that salt cake erosion may indeed be accompanied by pit formation due

to vortices precisely like those detected in meteorite pits. The evidence, supplied by photographs, leads to the conclusion that pitting is a general phenomenon in eroding fluid flow, and that tests at low speeds may provide valuable

information regarding certain problems in astroballistic ablation.

WILLIAMS PLATE 1

Erosion pattern carved in a ceramic plate by a rocket blast, with evidence of reversed flow at the bottom. As the blast "bounced'1

along the surface, it created vortices in the boundary layer between the plate and the blast.

499091—59 3
WILLIAMS

PLATE 2

a, Enlargement of region "b" of text figure 1, showing

reversed flow just upstream of point of impingement of

rocket blast. Flow direction is marked by a streamer of

glass terminating in a knob formed by surface tension.

b, Enlargement of region "C" of text figure 1, showing

crest region above the plate surface. Main flow, marked

by glass streamers, is upward and toward the left.
WILLIAMS

r

PLATE 3

Enlargement of a crest region in the eroded ceramic plate pictured in plates 1 and 2. The main flow is upward. Due to a vortex

in the boundary layer the flow in the lee of the crest is roughly at right angles to the main flow, as indicated by the glass rivulets

terminating in a knob.
WILLIAMS PLATE 4

Estherville oriented iron meteorites. All photos same scale.

a, Stagnation point is in the center. Airflow was upward.

Flow lines appear in the oxide layer, which has broken off

near the top, showing the smooth iron beneath.

b, Stagnation point is at bottom. Airflow was upward.

Flow lines on the oxide layer are finer than the carved features

in the once molten iron.

c, Stagnation point is at bottom. Airflow was upward.

Oxide crust has broken off near the top.
WILLIAMS PLATE 5

a, Leading face of the Lafayette stone, with stagnation region near the bottom. The

airflow, smooth and producing no pitting, is clearly marked by flow lines. Flow left the

stone where the top edge of the face is marked by a skirt of slag.

n

\

P

L

*

".s

,: \ i

\ . s

I

<

_

i .

i

_

1

 A

•I

i, Trailing face of the Lafayette stone, with stagnation point at lower center. Flow

outward toward the edge is indicated by a skirt of slag, where airflow left the stone.
WILLIAMS PLATE 6

a, Leading face. Flow lines diverge from stagnation point, just left of center. Pits on right show

flow lines inside.

b, Side 3 (text fig. 3a), full face view. Front face

is at bottom. Airflow was upward. Flow lines are

visible inside all pits, but vortices not evident.

c, Trailing face. Characteristic mottled appearance is caused by broad, shallow pits in surface.

Flow lines radiate from center. A distinct skirt is

observable only on edge to the left and as far around

as the point at the bottom.

Faces of the Plainview, Tex., meteorite (No. 521). This stone is fiat on front and rear.
WILLIAMS PLATE 7

a, Side 5 (text fig. 3a) of Plainview si

meteorite, with stagnation region toward

the bottom.

b, Region 6 (text fig. 3d) of Plainview

meteorite. This face is adjacent to side 5,

on the left; the trailing face is toward the

top, the leading face toward the bottom.

c, The Olivenza fragment. The flow

lines inside the pits are unusually clear; in

each pit is a stagnation point with flow lines

diverging more or less directly toward the

edges.
WILLIAMS PLATE 8

. - , ._ • •- •

-*?>•

-..|,,n),,,r.Tn,j,i,.-|...,

Leading face of the Miller meteorite, with the stagnation region at the center. Note radial orientation of the pits on the shoulder.
WILLIAMS PLATE 9

a, Speedometer used when towing salt

cakes.

c, Ogive machined from salt block (b).
WILLIAMS PLATE 10

a, White salt block after erosion for 8 minutes at 4.1 knots,

showing irregular erosion and deep pitting. Eroded shapes

are so intricate that interpretation of water flow is difficult.

b, Iodine salt block after erosion for 8 minutes at 4.1 knots.

Note orderly pit system on the leading end and the small pits

near the base, far from the tip.

c, Iodine salt block after erosion for 16 minutes at 3.1 knots.

Pitting is extensive on the leading face, a characteristic of low

speed erosion on bluff objects.
WILLIAMS PLATE 11

a

 A

a, Blue salt block after continuous run for 16 minutes at

4.8 knots.

b, Blue salt cake after intermittent run for 16 minutes at

k8 knots. The run was intermittent to permit successive

veighings.

c, Iodine- salt cakes (initially right circular cylinders) after

erosion at 4.8 knots for (left to right) 18 minutes, intermittent;

16 minutes, steady; and 21 minutes, intermittent.
WILLIAMS PLATE 12

a, Blue salt cake (initially a right circular cylinder)

after^erosion at 4.8 knots for 16 minutes with attitude not

adjusted.

b, Blue salt cake (initially a right circular cylinder)

after erosion at 4.8 knots for 21 minutes with attitude

adjusted.

c, Sulfur cakes after erosion at 4.8 knots. First two cakes (initially rectangular

blocks) ran 16 minutes; the third"(initially a right circular cylinder) and fourth (initially

an ogive) ran 12 minutes. Only the fourth cake, the only one with attitude adjusted,

shows no pitting.
WILLIAMS PLATE 13

a, White salt cakes (initially symmetrical) after erosion at 4.8 knots for (left to right) 14,

14, 8, and 12 minutes. The first block on the left was the only one not adjusted as to attitude. The first two cakes on the left were right circular cylinders; the other two were ogives.

b, Base of an iodine salt cake after erosion at 5.5 knots for 16 minutes, typical of all base

areas on eroded bodies. Note the broad and shallow depressions and striking resemblance to

meteorite trailing faces.
WILLIAMS PLATE 14

a, Blue salt cakes after erosion at different lengths of time and speeds. Only the three

unpitted shapes on the right were both symmetrical initially and adjusted as to attitude;

of these, the cake at the far right was a right circular cylinder and the other two were ogives.

The difference in color of the cake furthest right suggests variation in composition.

b, Iodine salt cakes (initially rectangular blocks) after 16 minutes at (left to right) 3.1,4.1,

4.8, and 5.5 knots.