MICROWAVE MEASUREMENTS OF PROJECTILE MOTION IN THE BARREL OF THE UTIAS IMPLOSION-DRIVEN HYPERVELOCITY LAUNCHER
by
A. Elsenaar
"
MICROWAVE MEASUREMENTS OF PROJECTILE MOTION IN THE BARREL OF THE UTIAS IMPLOSION-DRIVEN HYPERVELOCITY LAUNCHER
by
A. Elsenaar
Manuscript received July,
1969.
..
•
ACKNOWLEDGEMENT
I wish to express my appreciation to Dr. G. N. Patterson for the
opportunity to conduct this work at the Institute for Aerospace Studies.
I also wish to thank my supervisor, Dr. I. I. Glass, who suggested
this work. Ris critical comments end helpful suggestions are highly appreciated.
Special thanks are due to Wolfgang Graf, Dr. A.
K.
Macpherson,Jean-Claude Poinssot and Dr. D. E. Roberts for the many discussions we had and the
stimulus they provided for this work. The help received from Bill Burgess in
conducting the experiments is very much appreciated .
The research reported herein was supported by the Aerospace Research
Laboratory of the United States Air Force, under Contract No.
AF33(615)-5313
andSUMMARY
A microwave-Doppler method is applied to measure the velocity of a projectile inside the barrel of the UTIAS Implosion-Driven Hypervelocity Launcher. The microwave-Doppler method and its application for this parti-cular case are discussed in detail.
The measurements concentrate on the gas case, in which the driver gas is only a stoichiometrie mixture of hydrogen and oxygen, without
explosive PErN, for initial pressures between 200 and 600 psi. It is clearly shown that the projectile is accelerated by subsequent pressure pulses caused by multiple implosions inside the charnber. The effect of the subsequent
implosions on the motion of the projectile decreases with increasing veloci-ties and for veloeiveloci-ties greater than ~ 8000 ft/sec only the first implosion seems to be important. The muzzle veloeities in this experiment could be compared with earlier measurements and are in good agreement. A numerical calculation, describing the projectile motion only during the first pressure pulse also agrees with the measurements. Finally, earlier results of muzzle velocity for gas and explosive cases are discussed and some general remarks with respect to possible losses in the driving mechanism are made.
1. 2.
3.
4.
TABLE OF CONTENTS NOTATION H-J"TRODUCTIONTHEORY AND APPLICATION OF THE MICROWAVE TECHNIQUE 2.1 Theory of Operation
2.2 Experimental Set-up
2.3
Measurement of Guide Wavelength2.4
Data Red~ction and Accuracy2.5
Reflection from an Ionized Shock Front EXPERIMENTAL RESULTS3.1
Experimental Procedure3.2
Discussion of the Results3.3
Comparison with other Velocity Measurements3.4
Comparison with Numerical Experiments3
.5
Departures from the Ideal Case "and their Fbssible ConsequencesCONCLUSIONS REFERENCES TAB LES FIGURES iv 1 2 2
4
56
7
7 78
1013
15
17
19
NarATION
A Amplitude or barrel area f D Doppler frequency m Projectile mass p Pressure t Time v Velocit-y cp Phase angle
À Cut-off wave length c
À
free Wave length in free space
À Guide wave length g
w Angular frequency
'
1. INTRODUCTION
Only the most important features of the UTIAS Implosion-Driven Hypervelocity Launcher will be considered in the following. An extensive description of this facility can be found elsewhere (Refs. 1,2, and 3). The launcher is basically a hemispherical cavity (see Fig.l) closed by a thick flat plate. At the centre of the hemisphere in the middle of the top plate a barrel is located, containing a small projectile. The hemispherical chamber is filled with a stoichiometric mixture of 2H
2 and O2. Af ter ig-nition by an exploding wire at the origin, a sphericaI detonation wave is formed. This wave rèflects at the outer wall and moves with ever increas-ing strength as an implosion wave towards the origin. There it reflects, leaving behind it a region of high temperature, high-pressure gas. This process repeats itself until viscosity, heat conduction or unstable per-turbations bring it to an end. The high-pressure and hi&h-temperature generated in each cycle just af ter the implosion are applied to accelerate the projectile. The projectile moves down the barrel and travels through a range section where its velocity can be measured. Finally, it impacts on a target at the end of the range.
Temperatures and pressures of an order of magnitude higher can be generated if the outgoing detonation wave is used to initiate a layer of explosive (typically PETN) at the wallof the chamber. This in turn generates a much stronger implosion wave. This is the most important mode of operation of the launcher and it is hoped that with this setup, projectile velocities of 35,000 ft/sec and higher can be generated.
In this report, however, we are mainly concerned with the gas case. This work can be regarded as an extension of the experiment al work of Watson (Ref.2). Watson measured range velocities for different ini~ial pressures and projectile weights. The essential difference is however that by using a microwave technique it was possible to track the projectile right inside the barrel. In this way information is obtained about ~he mechanisms that lead the projectile to its muzzle or range velocity. A better compari-son with the theoretically calculated value is now possible since the vel-ocity af ter the first implosion is more indicative of the driving process than the final velocity that mayor may not be the result of subsequent cycles. The present measurements are in good agre"ement wi th Watson' s resu-lts, as will be shown later. Furthermore, some conclusions can be drawn from a comparison of the measured range velocities for the gas case and the explosive case.
The theoretical model as used by Flagg (Ref.3), Sevray (Ref.4) and Poinssot (Ref.5), using a finite difference scheme and an artificial viscosity technique to describe the shocks, is not completely satisfactory. In general, computed final velocities are about twice as high as the mea-sured ones (Fig.2). The unfavourable comparison between theory and experi-ment was the reason for a critical review of the computer program in the gas case. This review is reported elsewhere (Ref.6). As a result agree-ment between the calculated and measured values is now satisfactory af ter the first implosion wave (see Section 3.4).
At the start of this work it was believed that the microwave technique would be accurate enough to measure the acceleration of the
projectile. Knowing the acceleration and the mass of the projectile its driving base pressure can be calc~lated. In Section 2.4 it is explained why this is not easy tO ,realize. Another technique, involving the Doppler frequency shift of a laser beam is more promising and is now in progress at UTIAS. In this report, however, we will concentrate only on the velocity measurements. 2. THEORY AND APPLICATION OF THE 'MICROWAVE TECHNIQ,UE
2.1 Theory of Operation
The microwave technique is used extensively for velocity measure-ments of projectiles inside a barrel (Refs~
7,8,9),
pistons in light-gas-guns (Ref.10) and shock waves (Refs 11,12). Mîcrowaves are high frequency radio signals, typically 0.1 to 50 Gc. Inside a hollow conductor, the wave guide, they will propagate in certain modes, depending on the frequency of the signal and the geometry of the conductor. The reason for this behaviour is that at the conducting surface the tangential electric field and the normal magnetic field must vanish. Then only a limited number of electro-magpetic fields can be fitted inside a certain geometry. The most commonly used hollow conductors are the rectangular, the circular, and the co-axial wave guides. The applicability of microwaves for velocity measurements lies in the fact th at we can use a tube with a circular cross-section, like a barrel or a shock tube as a waveguide. For a given waveguide, we can choose the frequency and a mode of propagation. The microwaves travel down the tube and reflect from a ëonducting surface, either a projectile or an ionized shock front. Af ter reflection the signal will be shifted in frequency by an amount proportional to the velocity of the moving boundary. The interaction of the incident and reflected wave results in a beat frequency (the Doppler frequency) which can be detected. Two different names are used describing the same technäque; microwave interferometry or microwave-Doppler method. Two different groups of modes of propagation can be distinguished, the TE modes with a transverse electric field (or a longitudinal magnetic field) and the TM-mode with a transverse magnetic field (or a longitudinal electric field). Inside a certain group a particular mode is labelled with a two-number combination. Electromagnetic fields in a cross-section of the wave guide are shown in Fig.3 for a number of modes. The wavelength of a micro-wave signal propagating inside a micro-waveguide is different from the micro-wavelength of a signal propagating in free space. This guide wavelength is given by(Ref .13) .
À
=
gÀ
free ( 1)
where, Àfree is the wavelength in free space (the speed of light divided by the frequency). The so-called cutoff wavelength Àc is a function of the geometry of the waveguides and the particular mode generated (Fig.4).
Some of the cutoff wavelengths for different modes are listed below: Rectangular waveguides: TE10-mode
TliJ 20 -mode T~l-mode À c À c À c 2a
=
a 2ab 2b<
...r
a2+ b2 awhere, a is the longest side, b the shortest.
Circular waveguide: TEll-mode À c 1.706 (2a) TM01-mode À 1.306 (2a)
c TE
21-mode À c t.029 (2a) where, a is the radius of the tube.
As can be seen, Àg becomes imaginary if "rree
>
Àc' Propagation is no.; longer possible and hence, the name cutofif wavelength. The lowest mode (the mode with the lowest frequency or longest guide wavelength) in eachparticular configuration that still can propagate inside a waveguide is cal+ed the dominant mode. This is the TE10-mode for a rectangular waveguide and the TEll-mode for the circular waveguide. If the frequency is chosen so that a particular mode can propagate (say the TE21-mode in a circular waveguide) all the lower modes (the TEll- and TM01-mode) are also physically possible. Which mode will actually be generated depends upon other conditions, i.e., the way in which the microwaves are inserted in the \'laveguide or the pos i tion of a conducting surface (a short) at one of the ends of the waveguide. In practice, we will try to achieve the situation where ohly one or two modes are physically possible in order to be sure which mode is propagating and to hold the mode pure. This means that we are very limited in the choice of frequency or guide wavelength for a particular diameter of the tube.
Let us consider now a waveguide with a wave moving to the left. At the position x
= X, a conducting surface is located with a velocity v. This
can be a projectile or an ionized shock front. The incident wave at the position x= 0 can be represented as:
i (cp
+
wt) ]Re [A.e (2)
where, A is the amplitude, cp the phase, and w the angular frequency. The re-flected wave at x = 0 will have the form:
i( cp + wt+ 7T- 2X /Àg' 27T) ] Re [A.e
since the reflected wave will have travelled over a distance of 2X before arriving again at x
=
O. Furthermore, it is shifted by 1800 because of the reflection.wave or:
In general, we will detect the sum of the inc.ident and reflected
2 A.sin 27TX À g sin (cp + wt)- 27TX ) À g (4 ) ( 27tX )
This represents a high-frequency wave sin cp + wt - --- with an amplitude Àg
2A.sin
-=;::-
27TX gdependent on X.
When we detect the sum of the incident and the reflected wave with a diode
(a
square-law-detect~r)
the high frequency will be filtered out and the result is of the formp
4
... A2 sJ..n . 2If the conducting surface is moving (X is a function of time), P will be a function of time. The distance between two peaks in the output
represents a displacement of the conducting surface over a distance ~ À •
Thus, basically, we measure dis placement . The 'velocity, however, can bg obtained by dividing the displacement by the time interval, or in terms of the frequency of the output signal·(the Doppler frequency) f
D:
v
=
d dt -X-±. 2 Àg (6)
In general, the amplitudes of the incident and the reflected waves will not
be the same because of attenuation inside the waveguide. In that case, ~he
detected signal will be a so-called standing wa~e, with an amplitude os-cillating between the sum and the difference of the amplitudes of incident and reflected wave. The frequency is still the same, however.
2.2 Experimental Setup
With the basic idea of this technique in mind, we will work out
in this section the method in more detail for the case of tracking the pro-jectile in the barrel of the hypervelocity launcher. A microwave source with a frequency of about 34 Gc. was available and it was used. The barrels
of the hypervelocity launcher are made of "high pressure tubing" with inside
diameters of 5/16, 3/16 or 0.22 inches. A diameter of 5/16" was chosen.
The only possible modes with a cutoff wave length greater than the free-space wavelength for this barrel are the TEll-mode and the TMol-mode
(see Fig.4).
Microwave circuits are usually built up from standard rectangular waveguides. The dominant mode is the TE10-mode. The rectangular waveguides of the system had to be connected with the barrel in such a way that only one mode would be generated. There are different ways of making this
connection. The most frequently used is a co-axial transition between the
rectangular waveguide and a small quarter-wave-probe placed inside the
barrel and pointing to the center. In this case, however, the projectile path will be affected by the probe and replacement af ter each run is nece-ssary. Consequently a connection that would not form a physical obstacle
to the projectile was required.
Several methods wére tried and finally one was found to be satis-factory. It is a direct perpendicular connection between the rectangular waveguide and the barrel (see Fig.5). The connection is made on a separate piece of tubing that can be placed at the end of the barrel with clamps.
A reflecting surface , a 11 short'; at the downstream end of this piece is
ad-justed in such a way that only the TEll-mode will be generated. This can be shown as follows (see Fig.5): A wave inserted in A in the circular
waveguide will partly travel to the right, partly to the left. They will
have a phase difference of 1800 The wave travelling to the right will change
its phase over 1800 (half a guide wavelength) when reflected from the
con-ducting surface at B. Af ter reflection it will reinforce or cancel out its
counterpart travelling to the lef~ at A, depending on the distance AB. When
the distance ABA is equal to an even number of half the guide wavelength for
a particular mode, reinforcement will take place. In case of an odd number
the waves will cancel out. So when AB
=
24 mm the TE l-mode (~À=
5.75)will for all practical purposes be reinforced whiié tÊe
TMol-modeg(~À
=8.3)
will be cancelled out. In fact, the optimal position of the end
surf~ce
is adjvsted by inspecting the waveform öf the output signal when we move a
projectile by hand inside the barrel. The reflecting surface at B is made
of a thin piece of aluminum foil. It will be blown away by the shock ahead
of the projectile even before the projectile arrives. There is no indication
that this affects the projectile when it leaves the barrel. Therefore, in the same run the range velocity and impact characteristics could be obtained.
The complete system is shown in Figs.
6,7
and8.
A 15 mW Klystron generatesthe microwave signal that travels down the rectangular waveguides. The
frequency of this signal can be measured with a cavity meter and the power
with a diode on top of a 10 dB directional coupler. At the connection with
the barrel the signal will be converted into the circular TElt-mode, which
propagates inside the barrel. Af ter reflection this signal wlll now be
frequency shifted by the moving projectile. Incident and reflected wave will
interact inside the barrel and the result will finally propagate in opposite
direction through the rectangular waveguides. A second coupler, now pointing
in the other direct ion will subtract a part of this signal and a crystal
detector converts this into an AC signal that can be displayed on one or
more oscilloscopes. An isolator close to the Klystron gives protection against
reflections.
To protect the system against the high-pressure, high-temperature
gas inside the barrel a high-pressure seal is located close to the connection
piece. This consists of a waveguide filled with epoxy over a length of about
10 mmo A vacuum seal in the rectangular waveguide where it is led inside the
dump tank prevents leakage through the waveguide system.
The inside of the barrel is honed before each run and is very smooth. This is quite important especially at the higher frequencies where a small roughness causes severe attenuation. Only in a few cases was the attenuation toa severe and another barrel had to be used. The typical length of the barrels
was about 1500 mmo All the technical specifications of the system.are listed
in Table I.
2.3 Measurement of Guide Wavelengths
To test the system a projectile was moved slowly by hand inside the
barrel and the output signal was recorded. The re sult is shown in Fig.9. As
can be seen, the amplitude of the output signal is fairly constant. When the
short at the end of the connection piece was not properly adjusted, a beat in
the ou~put was noticeable. This is caused by the influence of the second
(TMol) mode. In some cases this effect could not be eliminated at all,
probably due to roughness inside the barrel. Even a very small irregularity
in the barrel surface can cause serias reflections. In Refs.
8
and 9, the samesolution would be to choose a lower frequency, so that only the TE l-mode
.can propagate. Figure 10 shows the output of the signal as a functlon of the
distance over which the projectile is moved. As mentioned before, the distance
between two peaks or troughs correspond to a displacement of the projectile
over half a guide wavelength. The guide wavelength measured in this way
is 11.3 mm + 1%. The calculated value for this diameter and frequency is 11.4 mmo The output follows the pattern of a standing wave as can be cal-culated from the maxima and minima. It is worthwhile to mention here that impurity in the TE11-mode will cause an oscillation of the measured values of
the guide wavelengtfis around theideal value, an effect which is similar to
the effect of adding a wave with an arbitrary frequency and a small amplitude
to a wave with a much greater amplitude. This is shown in Fig.9 where we
note a small variation in.amplitude on the lower picture.
2.4 Data Reduction and Accuracy
The output of the crystal detector was recorded as a function of time on one or several oscilloscopes. The recording could have been dope
more easily with a r.aster-scan oscilloscope (Ref.ll) or a rotating drum
camera (Ref.9) , but the present system proved to be satisfactory and reliable.
The velocity can be derived by measuring the time between peaks and troughs. This time interval corresponds to a dis placement of half a guide wavelength
as calculated from the frequency. A more sophisticated technique, using a
frequency discriminator (which converts the output frequency in~o a voltage)
is of ten used (Ref.ll), but was not applicable in this case since the number
of oscillations was too small during large velocity changes. It was felt
that some information could be lost in the way of analog processing.
In some cases slight oscillations in the velocity profile were
present. It is believed that they are caused by impurity in the TEll-mode.
More serious was an ignition effect, causing a disturbing rise in the signal
during the first 100 ~sec (see Fig.12). This effect may be caused by
radia-tion in the microwave regime of the exploding wire in the center of the chamber. A more powerful microwave source would decrease the influence of this effect considerably.
By measuring the time intervals between subsequent peaks or troughs in the output signal, one poin~ for each· displacement over a distance of
half a guide wavelength is obtained in the time-distance curve. This means
that if an appreciable velocity change takes place inside a distance of a
wavelength (11.4 mm) no accurate results can be obtained. The velocity is
derived by dividing the distance over which the projectile has moved by the time interval. Acceleration can be obtained in principle by differentiating
the time-distance curve twice. But with the limited number of measured
points on this curve no accurate results can be expected. We are interested
in this poi~t since rapid velocity changes are present in this experiment as
will be shown later. It is worthwhile to mention here that by measuring
peaks and troughs in the output signal only a part of the information is"
used. If we recall the expression for the reflected wave, we note that
the phase-shift due to the reflection is equal to:
6. cp 2
1."
' 7r. X + 7T2 g
The rate of phase-shift is then: dep dt 21T 1. À 2 g
.v
( 8)So if we were able to measure the phase shift as a function of time, a real continuous time-velocity curve can be obtained, and the acceleration can be calculated more accurately. The phase shift of a microwave signal can be measured with a so-called phase bridge (Ref.14) provided we are able to separate the reflected wave from the incident wave. In the present set-up
interaction of the reflected and the incident wave takes place inside the barrel and separation was not possible. Several other methods were tried to obtain the preferred separation, without success, but a solution does not seem to be impossible. To the author's knowledge, this refinement of the method has never been applied. In special cases where rapid velocity changes are present, this technique can prove to be useful.
2.5 Reflection from an Ionized Shock-Front
The microwave technique was used both for measuring projectile velocities and shock-wave velocities. However, in the case of projectile motion a bow shock will be formed travelling ahead of the projectile. If
the projectile moves fast enough, the bow shock will be so strong that roicrowaves will be reflected from it. It is interesting to know when this
will happen. The calculation involves the interaction between a plasma and
microwaves (Ref.15). A rough estiroate is obtained if we assume the condition
for reflection to be (Ref.12):
Plasma frequency
>
microwave frequencyIn the actual process, however, there is an intermediate region where a part of the signal is transroitted, a part reflected. The propagation constants of microwaves inside a plasma are a ~unction of the plasma frequency and
the collision frequency. The plasma frequency can readily be obtained as a
function of the electron density. lhe collision frequency is much more
diff-icult to evaluate. To get some estimate of the reflection process data taken from Ref.15 are interpolated and extrapolated for roicrowave frequencies of
2.7 Gc (corresponding to a shock tube wUh 3" dia, Ref.ll) and 34.0 Gc ( in the case of the launcher with a 5/16" barrel), assuroing a shock moving in air at about 1 mm initial pressure. ~he results are shown in Fig.ll. There is a very strong frequency dependence. For the lower frequency the reflected
power increases rapidly af ter a shock speed of 4 mm/~sec, but for the higher frequency only a slow increase is noticeable. This is rather fortunate since shock tubes with diameters of several inches require a low frequency for generating the dominant mode while for projectile velocity measurements with
amuch smaller diameter tube the larger frequencies are necessary. Several experimental data indicate that reflection starts at slightly lower veloci-ties (3.5 mm/~sec). In any case the reflection from the ionized shock would
not be a~problem for the lower velocities.
3. EXPERIMENTAL RESULTS
3.1 Experimental Procedure
magnesium projectile of 0.67 g, driven by a stoichiometrie mixture of oxygen and hydrogen with initial pressures from 200 to 600 psi. A 5/16" barrel di-ameter was selected since it provides an optimal match with the frequency of the microwave source. A magne$±um projectile was used to ins~re reflec-tion of the microwave signal. Titanium or steel projectiles could have been used also bu~ they will give lower veloeities. Several runs with poly-ethylene projectiles, with a conducting surface attached toc'bhe.i front were tried but the output signal was severely d.istorted in these cases. The projectile was held in place before ignition by a small flange at the back of the projectile (see Ref.2); no diaphragm was used. Three different
measurements were made in each run. First the projectile was followed during the first 400 ~sec inside the barrel. Secondly, it was recorded when the projectile left the barrel. This was noticeable on the microwave trace since the rupture of the diaphragm at the end of the barrel changes the output signal. (A typical picture has not been included). Finally, the velocity in the range was measured with the existing equipment. At three stations inside the range a sheet of light was producèd (light screen). The change in light intensity, when the projectile passes the lightscreen is measured with a very sensitive photomultiplier. Two electronic counters measure the transit time between a pair of lightscreens. An accelerometer, mounted on the target, measured the time between ignition and impact.
All the runs were made in an 8t;:-" diameter chamber. Range pressure in all cases was about 1 mm Hg. A view of the experimental setup is shown in Figs. 7 and 8.
3.2 Discussion of the Results
Typical velocity profiles for initial pressures ranging from 200 to 600 psi are shown in Figs. 13 to 17. The results of these runs are also listed in Table 11. A typical oscilloscope record for one of these runs is shown in Fig .12.
In all cases it is very clear that the projectile is accelerated by a series of subsequent pulses (see Fig.19, taken from Ref.4). Each pulse is followed by a much longer period of almost constant velocity during which the reflected wave moves away from the centre, reflects from the hemispherical wall and then moves again towards the centre of the chamber. This causes,
af ter reflection, another sharp ri se in projectile velocity. In most cases at least one subsequent pulse is noticeable. This indicates that the wave system inside the charnber is stable enough to repeat itself. The influence of subsequent pulses is weaker since the projectile has moved away from the orlgln. Each subsequent pressure pulse has to follow a moving projectile with an increased speed af ter each cycle. An additional decrease in strength and probably the most important, is caused by attenuation arising fr om boundary layer effects inside the barrel. The shocks willovertake each other af ter a number of cycles inside the barrel, even before they reach the projectile. Therefore later on the projectile is accelerated in a gradual way. This is
shown more clearly in Fig.18. The velocity is plotted for different initial pressures af ter 150, 250 and 350 microseconds, or roughly af ter the first, second and third implosion. In the same figure the final or muzzle velocity is indicated. It shows clearly that for higher final velocities, the first pressure pulse is more important. We expect this behaviour. In the limit of very high velocities all the acceleration will be caused by one pulse, since
the projectile moves so fast that subsequent pulses can no longer reach the projectile. The velocity af ter the first pressure pulse is the most indicative of the efficiency of the driving process. This velocity varies linearly with the initial pressure in this pressure range. This can be expected since the pressure behind the detonation wave varies also almost linearly with initial pressure. The final velocity varies more as the 0.44 power of initial
pressure, because of the diminishing influence of subsequent pulses. The
spread in the final velocities is rather small as in Watson's measurements. The spread in velocities after·the first pulse is much greater. This diffe-rence may be caused by boundary layer effects inside the barrel. Although most of the acceleration takes place in the first 350 microseconds, it takes another 1000 microseconds before the projectile leaves the barrel. A few runs were made using a 400 psi 2H2 and O2 mixture and approximately 100 g PErN as the explosive driver. A one-calibre titanium projectile (1.74 g) was
used.. The results indicate the same phenomena as is shown in Fig.20 for one of these runs. The reflected signal was so weak that no clear trace could be obtained. However, the part of the velocity profile that could be ob-tained shows a very fast decay. We show in the same figure the velocity profile of a shock tube case ( no projectile but only a diaphragm separating chamber and barrel) under conditions of 400 psi initial pressure, 1 torr
counterpressure~ Similarity between the two curves suggests the possibility of an important leak around the projectile. The high energy gas, in this
way released in front of the projectile, will form a fast decaying shock
wave. Microwaves will reflect fr om this shock front showing us the shock
velocity rather than the projectile velocity. In all cases the impact showed
a small breakup of the projectile. This may be the cause of the leakage.
Another explanation is local expansion of the barrel in the high-pressure
region so that the hot gas can escape around the projectile.
Another indication of leakage around the projectile was obtained more recently from an ionization gauge placed l! ft away from the origin inside the barrel. A 3 foot barrel with 5/16" inner diameter and a titanium
projectile (1.72 g) was used. The ionization gauge will be triggered by the shock wave moving in front of the projectile. This gives us an average value of the shock speed over the first l! feet. The shock speed will differ only slightly from the projectile velocity if there is no leakage around the
projectile. In any case this speed will be smaller than the range velocity.
In case of leakage around the projectile the shock speed will be much higher than the projectile velocity. Oscilloscope traces for three different cases are shown in Fig.21. In Case 1 (200 psi driver gas, no explosive) the ioni-zation gauge was triggered af ter 1180 ~sec (point A) by the projectile or
the shock wave, indicating an average speed over the first 1.5 ft of ~ 1280 ft/sec. The muzzle velocity was 2140 ft/sec. In Case 2 (200 psi driver gas, 85 g of
PErN explosive) the gauge responds af ter 120 and 150 ~sec (point Band C). Possibly point B corresponds to the shock wave and C to the arrival of the contact surface. In any case, an average velocity of ~ 11,500 ft/sec is obtained as compared with a final velocity of 6000 ft/sec. The discrepancy between the shock speed inside the barrel and the muzzle velocity suggests
in this case a strong shock moving far ahead of the projectile caused by
escaping gas. The conditions in Case 3 are similar to those in Case 2, except a small tapered chamber in the back of the projectile was made to provide a better seal. The ionization gauge responds now af ter 760 ~sec (point E) although small oscillations are noticeable af ter 600 ~sec (Point D) that may
be caused by a small amount of escaped gas. The average velocity is now 2400 ft/sec inside the barrel and the muzzle velocity 4500 ftl sec. st,rong leakage is not likely in this case. Strangely enough the range velocity in this case was lower than in the second case, although inside the normal scatter for explosive runs. It is not clear if a we aker pressure pu~se @r the special shaped projectile prevents leakage in Case 3. A further st~dy'
will have to be made to show if leakage has a great influence on perfèrmance or projectile breakup.
3.3 Comparison with other Velocity Measurements
,,' .
! ~",~., \
In this section we will compare the results of the present éxperi-ments with the final velocity measureéxperi-ments of Watson (Ref.3), Flagg (Ref.4) and Graf (Ref.16). As mentioned already, Watson measured the muzzle v~lecity
of one-calibre, 0.22 lightweight projectiles, driven by a mixture .of 2H2 aml O2 only. Some of his results are shown in Fig.22 for a projectile mass (lèxan) of 0.126 g and initial pressures from 100 to 500 psi. In the same figure are indicated the results for final velocity in the present experiments, using a one-calibre
5/16"
diameter projectile of 0.67 g (magnesium).The two curves have a similar shape. In Watson's experiments, the muzzle velocity varied as the 0.42 power (for lower pressures) and the 0.31 power (for higher pressures) of the initial pressure, whereaS3iào.the present results a power of 0.44 gives the best fit. This power cannot be ~elated te the kinematic solution, indicating a power of 0.5, as will be shown .. It is interesting to note that for approximately five-times lighter projectiles only an increase of 30% in final velocity is obtained. To make a better comparison possible we will first assume the same pressure history at the base of the projectile for the two cases. This seems a reasonable assumption
since the wave system inside the chamber that generates these pressures is nearly independent of the weight of the projectile. The velocity is then given by:
v
constant. dt
A for a certain initial pressure.
m
The velocities for two cases with different masses ml and ~ and areas of the barrel Al and A
2 can then be related as:
(10).
In the present case, the ratio is 2.63. The measured ratio is ab0ut, 1.4. This difference is caused by the dominant importance of the first implosien wave that reaches the projectile as we will see. We have indicated in Fig.22 the velocity af ter the first implosion (roughly 150 j.lsec af ter ig;niti~n}.i;n the case of the heavy projectile as measured with the microwave teçhnique. During this phase the projectile has not moved far away from the origin, aml the pressure at the origin will be the same as the base pressure of.tb,e prE>-jectile. When the projectile has moved away from the origin, iN the' cá:~e of subsequent implosions , this will no longer be the case. The preSs<ure ]>ulse
may well be attenuated inside the barrel because of boundary layer effects and the projectile is now moving with an increased speed aft er each cycle giving a further drop in base pressure. This means that the assumption
J
p. dt=
constant is only valid for the first implosion. Consequently we can find the velocity af ter the first implosion for the light projectile from the heavier one by multiplication using a factor of 2.6. This scaled value is also indicated in Fig.22.Consider now the light projectile for an initial pressure of 200 psi (point a) and a heavy one for 500 psi (point b). They have af ter the first implosion the same velocity and have consequently travelled over the same distance. A drop in base pressure because of the expansion behind the projectile is maihly dependent on the projectile velocity and will also be the same for the two cases. Although the pressure will be higher for the 500 psi case, the effect of the pressure on the velocity will be the same for these cases since the ratio m/A is smaller by the same ratio. Boundary layer.effects inside the barrel will depend on pressure and density but are also strongly dependent on the distance over which the projectile has travelled inside the barrel. This suggests that if the velocity af ter the first pulse is the same for two cases (a and b), the muzzle velocity will also be approxi-mately the same for these case? (a' and b' in Fig.22). This agrees very well indeed with the measured values and Watson's results are in good agreement with the measurements for the heavier projectile. This leads to two con-clusions for the gas case:
- the velocity aft er the first implosion can be scaled with respect to the ratio of mass over area;
the increase in velocity af ter the first implosion is only a function of the velocity af ter the first implosion
This function is plotted in Fig.23. Note that for velocities of 8000 ft/sec and higher only one pressure pulse is important.
Next we will compare final velocities for the gas case and the
explosive case. For this we consider Fig.24 where a sample of range velocities is plotted for a great number of runs, made in the last two years by Flagg and Graf (Refs. 3 and 16). These runs were made under a variety of conditions and we have plotted the muzzle velocity as function of projectile mass in the range of 0.1 till 1.68. The explosive weight was 100 + 30 g PETN. Initial gas pressures were kept at 400 psi. The scatter in tbe results is partly due to differences in projectile location, projectile sizes, barrel lengths,
ignition systems but will also be caused by variations in the driving mechanism itself like off-centered and non-symmetrical implosions. This point will be discussed later. In any case, a clear trend in the results is present if we plot range velocities against projectile masses. Two things are worthwhile noticing:
- the dependence on projectile mass is for the explosive case much stronger than for the gas case;
the addition of explosive gives only a small increase in velocity for the larger masses
Ideally, the projectile velocity will be proportional to the inverse of the
projectile mass for a constant charnber-barrel configuration and the same
initial conditions. ~or very high velocities, say greater than 15,000 ft/sec,
the effect of a finite escape speed and hence a drop in base pressure because
of expansion becomes increasingly important. For velocities smaller than
~ 8000 ft/sec subsequent pulses give a substantial contribution to the velocity
of the projectile. This contribution becomes increasingly important for lower
projectile velocities (see Fig.23). Therefore, there is only a small dependence
on projectile mass in the gas case where the velocities for an initial condition
of 400 psi gas are smaller than 6000 ft/sec. In the explosive case, we can
eipect astrong dependence on the projectile mass for velocities greater than
8000 ft/sec, since th en only the first pulse is important. But for velocities
smaller than ~ 8000 ft/sec we expect the performance curve to level off similar
to the gas case since then subsequent implosions become increasingly important.
This is not the,case and this might indicate that in the explosive case, for
all projectile masses, the first implosion always gives the greatest
contri-bution to the final velocity. This means that in the explosive case multiple
implosions are less likely to happen. This also explains why there is such
a small difference between the explosive and the gas case for a 1.72 g
pro-jectile. The projectile attains its final velocity in a different way for
these two cases. In the explosive case one pulse is dominant, while in the gas
case a great nurnber of cycles is required. A physical explanation for this
different behaviour in the gas and the explosive cases might be sought in
the presence of the explosive itself. In the gas case, the wave system inside
the charnber repeats itself till instabilities, viscosity, and heat conduction
become dominant. The movement of the shock or shocks in the explosive case
is much more complex. Inside the charnber we can distinguish two regions af ter
the detonation of the explosive. An inner region, filled with the cornbustion
products of hydrogen and oxygen and an outer region with the cornbustion products
of the PETN. The two regions are separated by an interface. An imploding
shock is formed inside the "gas region" just af ter the detonation of the
ex-plosive. This shock moves ideally af ter reflection from the origin, where it
gives the first pressure pulse to the projectile, through the interface into
the "explosive gas region". Then i t reflects from the outer wall, moves
towards the centre, again passing the interface, before it implodes in the
centre. From this picture it is clear that the symmetry in this process is
easily lost if the flow in the "explosive gas region" is not symmetrical. This can be caused by non-uniform det9nation generating contact-front-ripples in
all directions. The first impl~ding shock may very well not be effected too
much since it starts off as a reflected detonation wave and moves away,
al-though reinforced by the explosive, from the distur~ances. The subsequent imploding shocks, already very weak at the wall because of the expansion
process, will move through a non-uniform region and may easily lose their
symmetry, prohibiting any further focussed implosions. Some increase in
velocity af ter the first implosion, however, can still be expected for the
heavier projectiles since the charnber is filled with a pressure,
high-temperature gas, although no focussed implosions may occur afterwards.
Therefore, if we want to compare.the explosives case with the gas case, we should rather compare the final velo city in the explosive case with the
velocity af ter the first implosión in the gas case (see Fig.24). We then find
that the addition of explosive improves the velocit~, generally speaking, by
a factor of five. This is a bit lower (3.5) for the light projectile.
How-ever, there. is a pressure drop at the base of the projectile because of rapid
pressure and hence a smaller velocity increase.
3.4 Comparison with Numerical Experiments
A computer program based on a finite difference scheme in Lagrangian co-ordinates is used for the first time to describe the launcher process by Brode and Flagg (Ref.3). Sevray (Ref.4) has extended this code including barrel processes resulting in a code that could be used both for gas and ex-plosive cases. Flagg and Mitchell (Ref.17) modified this program slightly
with respect to zoning and chamber barrel transition. Optimization of a
bigger scale model is made with this code. Finally Poinssot adopted this code (Ref.5) to study the use of the launcher chamber as a driver for a shock tube facility.
All these programs describe a spherical symmetrie motion of a non-viscous, non-heat conducting gas, using fairly realistic equations of state for the gas and the explosive. Shocks are represented in this code by an
artificial viscosity or pressure term, the so-called q-method dueto von Neumann and Richtmyer (Ref.18) causing abrupt changes in parameters across
the shock to be 'smeared out over a number of zones. Because this technique does not represent an exact solution of the hydrodynamic equations but rather a numerical simulation of the physical process we call it a numerical
experi-ment. This code predicts in general for the explosive case veloeities twice the measured values (Fig.2). It is, however, difficult to compare the experi-mental final velocities, especially in the gas case, with the calculated ones, since af ter the first implosion other processes like attenuation of pressure pulses, dissipation inside the barrel, and a decrease in strength of
subsequent implosions, become increasingly important. These processes are
not accounted for in the ideal calculations. With the microwave measurements,
a time history of the velocity could be obtained and a better comparison is now possible.
Using Sevray's code, velocities af ter the first implosion could be calculated. The measured values appeared to be twice as high. The discrep-ancy between measured and calculated performances for the shock tube case as found by Poinssot, raised some further doubts regarding the validity of these numerical experiments.
The main problems with the computer code are: application of the q-method i~ a spherical geometry
difficulties with the zoning scheme to get op~imal definition near the wall and near the origin
divergence in pressure at the origin proof of convergence
coupling of chamber and barrel processes
A separate investigation of the application of this technique was therefore necessary, the results of which are reported in \Ref.6~ .
This work has resulted in a computer code, similar to the previous ones but with improved zoning. The program treats only the implbsion in a
closed sphere. The results have been tested regarding convergence, although
this point could not be proven conclusively because of limitations inherent in this technique. Where possible comparisons with "exact" solutions are
made. The projectile velocity can be obtained from this program by
inte-gration in time of the average origin pressure over the barrel area. This
origin pressure is an average pressure, weighted with respect to area, of the
zones th at have collapsed to a radius smaller than the barrel radius. The
assumption that the origin pressure is equal to the base pressure on the pro
-jectile is only valid if the projectile has not moved far away from the origin
and if the projectile velocity is small compared with the local sound speed
of the gas. This is clearly the case in gas runs, but only during the first
cycle. Rence, the program will only describe the projectile motion during the rise and the decay of the first pressure pulse.
Figures 25 to 28 show some results of this program compared with
measured values. An 8t" diameter chamber and a 5/16" diameter one-calibre projectile of 0.67 g was used in all cases. Figure 25 shows for gener al
interest an x-t diagram for this case. The calculated time for the detonation
wave to reach the wall is about 10% higher than measured by Watson and Robetts
(Refs. 2 and 9). This may be caused by the unrealistic representation of the initial stage of the detonation process. In the program a detonation wave is set up at the time of ignition (t
=
0), whereas the exploding wire will starta strong blast wave changing at a later stage into a detonation.
Figures 26 and 27 show velocity profiles during the first 150 ~sec
for different gas pressures. Figure 28 shows the experimental and computed velocities aft er 150 ~sec.
The agreement is reasonable, although the experimental values are
sometimes higher than the computed ones, which is not what we would expect from an ideal calculation. There is a very good possibility that the computed values are too low because of the limited convergence of this technique.
Another possibility, first indicated by Roberts (Ref.19) is that the pressure pulse at the origin lasts long er than the one calculated for ideal implosions. Figure 29 shows the calculated base pressure on the projectile for a 400 psi case. The width of the pressure pulse here is 2.5 ~sec, where Roberts measured
a duration of the high-pressure, high-temperature regiqn at the origin of the order of 5 ~sec. In addition there is some evidence that the implosion
coll-apses to a final radius, typically about .6 mm although greater and smaller
values are observed. I~ is also worthwhile mentioning that the actual geo-metry near the origin is different from the plane wall, with the projectile in the centre, as assumed in the calculations. Chamber and barrel are conne-cted by a small nozzle, placing the projectile about 5 mm away from the centre. It is not clear what effect this has on projectile velocity. Clearly, the.
symmetrical ideal calculations are not adequate to describe the final stage
of collapse.
Roberts also did some calculations on velocity, assuming a so-called classical behaviour (see Ref.3) and using the empirical duration of
5 ~sec for the pressure pulse. Ris results indicate veloeities not far from
the measured values. The assumption of classical implosions and others that
his conclusions, however, are confirmed by the present numerical results.
3.5 Departures from the Ideal Case and their Possible Consequences
The ideal model of a spherical symmetric pr0cess without energy losses
does obviously not describe the actual physical process. For some of these
departures, experimental evidence is available; others can only be estimated
theoretically. We will try in this section to comment on these and estimate their possible consequences.
(A) Processes influencing the symmetry of the wave system
Under certain conditions the exploding wire will start a detonation
wave (see' Benoit, Ref.22). With an exploding wire, dumping ~ 25 Joules into
the gas at initial pressures of 200 psi and up, this will always be the case.
However, the detonation wave may not be spherical symmetric in its init.ial
stages due to the elongated shape of the wire (2 mm long, 2 ml thick) and
the influence of directional electromagnetic fields set up by the discharge.
Macpherson (Ref.20) observed photographically irregularities on the outgoing
detonation wave even far away from the centre (see Fig.30). Also observed is an off-centering of the implosion wave, as indicated by a dip in the so-called
witnesss plugs, that is, copper plugs, mounted in the centre of the chamber
(see Figs. 31 and 32). The off-centering appears always on the vertical axis,
to the bo~tom side. This strongly suggests a gravitational effect in the time
during which the chamber is filled, or afterwards. The position of the
ig-nition wire and the position of the chamber itself (unless horizontal) does
not seem to have any influence. The position of the gas inlet may have some
influence. Recently Chan (Ref.23) obtained centered implosions, by stimulating turbulent mixing during the filling process. The imprint itself on the witness
plugs is quite sharp, indicating well focussed implosion. Photographic
ob-servations by Roberts indicate also a well focussed implosion (see Fig.30).
This seems to suggest that small perturbations on the outgoing detonation wave does not influence the implosion to a great extent in the gas case. Butler
(Ref.24) proved that imploding shocks tend to be unstable. This can only be
proven in the limit for very strong shocks. In the gas case the shock Mach
number at the barrel radius (4 mm) is about 3.5. Based on the experimental results it is therefore likely that the imp loding shock can be regarded over
most of its distance as stable. Only in its final stage, at a very small
distance away from the centre, instabilities may become important, limiting the theoretically infinite accumulation of energy at the centre(Ref.21) and causing different degrees of collapse, as observed by Roberts (Ref.19). But even if the imploding shock is not perfectly focussed or centered, the effect on the projectile velocity will be small. This is explained in Fig.29 where the average base pressure on the projectile is shown as calculated with the
finite difference technique. Indicated are the times t
l , when the incoming
shock passes the barrel radius, t2, the instant of implosion and t
3, when the
outgoing or reflected shock passes the barrel radius. These times are app-roximate times since the q-method smoothes out the position of the shock wave. The areas I, 11 and 111 under the curve represent the contribution to the total impulse between these different times. Their ratios are about 1:2:5, or
in other terms, more than
60%
of the projectile velocity is obtained af terthe reflected shock passes the barrel radius. This shows very clearly that
the details of the implosion process are not very important. The same
(B) Viscosity, Heat-Conduction and Radiation
Roberts (Ref.19) showed that these losses are in th
5
gas case un-important. Radiation losses will prohibit temperatures of 10 OK, but these temperatures can theoretically only be reached at a very small distance awayfrom the centre. Therefore, it is more likely that instabilities in the final
stage of the implosion will limit the temperature. This may have its effect
on the escape speed. Roberts measured an average temperature of ~ 50000K
for the gas case (200 psi 2H2 + O2 ), An increase of this temperature by a
factor of 3 for the explosive case, gives already an escape speed close to
100,000 ft/sec, still appreciably higher than the anticipated projectile
velocities. However, it is difficult to estimate what effect a rapidly
de-caying pressure and temperature at the origin, af ter the peak-pressure is reached, will have on the projectile velocity and some further study on this point seems worthwhile.
(c) Barrel Processes
Barrel processes like ablation and boundary layer effects in the
flow behind the projectile are only important if the projectile has moved
away from the origin. This is not the case during the first implosion. In
the gas case the projectile has then moved over a distance of the otder of 10 mmo In the explosive case, for an assumed projectile velocity of 50,000
ft/sec this will be ~ 100 mm, and boundary layer effects may become increas-ingly important. The short duration of the implosion phase (~10 ~sec) makes
the importance of ablation very unlikely. This will be more important for
subsequent implosions.
Boundary layer effects are believed to be the main reason for the
weakening of subsequent pressure pulses in the gas case. For projectile velocities higher than 8000 ft/sec subsequent implosions are no longer
im-portant (see Fig.22). The projectile has then moved over a distance of
~ 200 mm or 25 barrel diameter s . This is about the order of magnitude for
which boundary layer closure can be expected (see Ref.25). But as we have
shcwn, subsequent implosions are not important in the explosive case. Pro-jectile friction and counterpressure can be neglected compared with the gen-erated base pressures. The influence of leakage around the projectile is not yet known (see Section 3.2), but it seems that a proper projectile shape
and barrel entrance configuration can prevent any leakage. (D) Detonation of the Explosive
Non-uniform detonation of the explosive caused by either a
non-pherical detonation wave, as observed or a non-uniform layer of PErN is
likely. The process of detonation of explosives itself by means of a gaseous detonation wave is still very much unknown. In Section 3.3 it is mentioned that non-uniform detonation may very well have only a slight effect on the
focussing of the first implosion wave, since this wave moves away from the
region of disturbances. This is substantiated by the witness plugs (Fig.31).
Subsequent implosions will be affected. The strength of the first imploding
shock mayalso be affected. (E) Projectile Integrity
The projectile integrity problem is one of the major difficulties
for an implosion driven launcher. The fracture is caused mainly by an
inter-action of two expansion waves inside the projectile. One expansion wave is caused by the reflection of the shock at the front of the projectile. The other one is a result of the rapid decrease in pressure at the origin and is inherent to the launcher process. For higher velocities this decrease is still further accentuated by the expansion because of the movement of the projectile itself. This problem is presently under study by Graf (Ref.16).
4. CONCLUSIONS
Microwave measurements of projectile velocities during the first the launching process in the UTIAS Implosion Driven Hypervelocity are made to show the mechanisms by which the projectile is acce
le-stage of
Launcher
rate.d. A microwave system, operating in the TEll-circular mode with a fre-quency
mm and enough
of 34 Gc was used. The guide-wavelength under these conditions is 11.4 the accuracy was acceptable for velocity measurements but not accurate to measure acceleration.
The measurements concentrate on the gas case, when only a stoichio-metric mixture of hydrogen and oxygen is used as the dr-iver gas, for initial pressures between 200 and 600 psi and a one calibre 5/16" diameter magnesium projectile of 0.67 g. It is shown th at under these conditions the projectile
is accelerated by a number of pulses, caused by multiple implosions inside
the hemispherical chamber. fhe first pressure pulse is dominant, whereas the
subsequent pressure pulses become less and less important for higher projectile
velocities. For velocities greater than ~ 8000 ft/sec the projectile is
accelerated in one single pulse. The velocity af ter the first pulse is linearly dependent on the initial gas pressure. The tot al effect of subsequent pulses
appears to be a function of the velocity af ter the first implosion only. The
measurements of muzzle velocity are in good agreement with earlier experiments. A camparison of the measurements with a numerical experiment ( a modification of a UTIAS-developed, fini te difference scheme), and describing the projectile motion only during the first pressure pulse, showed reasonable agreement. Since the same applies for temperature measurements done by
Roberts, the conclusion seems to be justified that the launcher behaves in the
gas case as can be expected fram an idealized ~heory. Asymmetries in the wave
process and losses do not appear to affect the performance in the gas case to a great extent. Following the calcul~tions, a peak pressure and temperature, averaged over the barrel area (0.5 cm ) of respectively 430 times the initial gas pressure and 50000 K are reached at the origine
Microwave measurements in the explosive driven mode of operation failed since a strong shock, caused by leakage around the projectile prohibited proper reflection of the microwaves from the front of the projectile. A
comparison of the final velocities in the gas and the explosive cases, however, might indicate that in the explosive cases the first implosion is always the most important with respect to the final velocity and that multiple implosions
are n~l likely to occur. If this is the case, the addition of 100 g PETN
explosive in the chamber improves the velocity af ter the first implosion roughly by a factor of five.
Previous numerical experiments for the explosive case predicted velo-cities about twice as high as the measured values. In an attempt to explain this difference a review was made of the most likely departures from the ideal
behaviour. None of these, however, seems very critical, with the exception of the detonation process of the layer of explosive which is not yet known. Another reason for the discrepancy between theory and experiment may be an
over-estimation by the theory. Some aspects of the numerical calculations
are not satisfactory and a different treatment of the flow at the origin (as done for the gas case in more recent calculations) may change the results considerably. An analytical approach to the theory mayalso be useful. Further work in this direction may lead to a bet ter understanding of the experimental results.
1. Glass, 1. 1. 2. Watson, J. D. 3. Flagg, R. F. 4. Sevray, P.A. L. 5. Poinssot, J. C. 6. Elsenaar, A. 7. Smith, N. M. Jr., Crocker, J. A. 8. Hendrix, R. E, It 9. M Konig et al. 10. Pennelegion, L. 11. Dunn, M. G. Blum, R. J. 12. Anderson, F. G. Kelly, J. G. ) 13· Montgomery, C .G. et al. REFERENCES
Research Frontiers at Hypervelocity, Can. Aero Jl, VOl.13, Nos 8 and 9, pp 347-426, 1967. Implosion Driven Hypervelocity Launcher Per-formance Using Gaseous Detonation Waves. UTIAS Tech.Note No.hl3, 1967.
The Application of Implosion Wave Dynamics to a
Hypervelocity Launcher, UTIAS Report No. 125, 1967.
Performance Analysis of UTIAS Implosion Driven
Hypervelocity Launcher. UTIAS Tech.Note No.121,
1968.
A Preliminary Investigation of a UTIAS Implosion Driven Shock Tube, UTIAS Tech.Note No.136, 1969. A Numerical Model for a Cornbustion-Driven
Spherical Implosion Wave. UTIAS Tech.Note No.144,
1969.
Measurements of Various Quantities on a Projectile Moving in the Bore of a Gun. NDRC Report A-259,
(OSRIlJ-3376), March, 1944.
Microwave Measurements of Projectile Kinematics
Within Launcher Barrels. von Karman Gas Dynamics Facility, ARO Inc. Report No. AEDC-TDR-62-213, November, 1962.
Berechnung der Geschossbeschleunigung im Rohr aus
Radioelektrischen Weg-Zeit Messungen.
Deutsch-Franzosisches Forchungsinstitut Saint-Louis
Aktennotiz Nl.67, February, 1967.
A Microwave Method of Determining the Displacement and Velocity of a Piston in a Hypersonic Gun
Tunnel. Nature, Vol.183, p.246, January, 1959.
Continuous Measurement of Shock Velocity Using a
Microwave Technique. NASA CR-490, May, 1966.
Continuous Measurement of Shock and Contact
Dis-continuities Velocity. IEEE Transactions on
Aero-space and Electronic Systems. Vol. AES-3, No,4.
July, 1967.
Principlessof Microwave Circuits. Radiation Laboratory Series, VOl.8, McGraw-Hill, 1948.
14. Ginzton, L. E. 15. Bachynski et al. 16. Graf, W. O. lV'i. Flagg, R. F. Mitchell, G. P. 18. Von Neumann, J. Richtmyer, R. D. 19. Roberts, D. E. 20. Macpherson, A. K. 21. Zab ab akhin, E. I. 22. Benoit, A. 23. Chan, S. K. 24. Butler, D. S. 25. Glass, I. I. Hall, J. G.
Microwave Measurements. McGraw-Hill, 1957. Electromagnetic Properties of High-Temperature Air. Proc. of the IRE, p.347, Mareh, 1960. Work in Progress. University of Toronto, Ph.D. Thesis.
An Optimization Study of the UTIAS Implosion Driven Hypervelocity Launcher MK 11.. UTIAS Tech. Note No.130, November, 1968.
A Method for the Numerical Calculation of Hydro-dynamic Shocks. Journal of Applied Physics, p.232, VOl.21, Mareh, 1950.
A Spectroscopie Investigation of Combustion-Driven Spherical Implosion Waves. UTIAS Tech. Note No.140, September, 1969.
Work in Progess.
Cumulation of Energy and lts Limits. Soviet Physics USPEKHI 8, No,2. p.295, 1965.
An Experimental Investigation of Spherical C~ ustion for the UTIAS Implosion Driven Launcher. UTIAS Tech.Note No.71, September, 1963.
Work in Progress, University of Toronto, Ph.D. Thesis. The Stability of Converging Spherical and Cylind-rical Shock Waves. ARDE Report (B) 18.56, August, 1956.
Handbook of Supersonic Aerodynamics, Section 8, Shock Tubes. NAVORD Report 1488 (Vol.6), December, 1959·
I
TABLE I
SPECIFICATION OF MICROWAVE EQUIPMENT
Klystron Raytheon QK-291 - power
beam voltage - cathode current - reflector voltage
18
mW 2500 V DC 15 mAmp -15/-400 V - frequency of operation 34 Gc Crystal DetectorCoaxial Silicon Mixer Diode
lN5
3
TABLE II
Results of Microwave Measurements. Diameter- Chamber 8~". 1 Calibre long, 5/16" diameter Magnesium Projectile. Projectile position 5 mm away from origin.
~un Initial Gas Proj. Barrel Time of Time of C onnt er 3 iNumber Pressure (psi) Weight Length exit l impact 2 (J.lsec)
2H 2 + O2 (g) (mm) (J.lsec) (J.lsec) 325 200 0.66 2153 2010 7010 329 300 0.67 1790 1560 6000 790 286 400 0.67 1780 1230 690 287 400 0.67 2250 1500 5200 690 328 500 0.67 1790 4650 630 326 600 0.66 1790 1160 4500 327 600 0.61 1790 4400
1) Projectile leaves the barrel 2) Length of range section 24 feet.
