[bib]editortypedelim [bib]innametitledelim [bib]nametitledelim incollection
chapter+pages inbook chapter+pages incollection:parent maintitle+booktitle
incollection:maintitle+booktitle inbook:parent maintitle+booktitle
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[1]Justin Huneault [2]Jason Loiseau

[1]Department of Mechanical Engineering, McGill University, Macdonald
Engineering Building, 817 Sherbrooke Street West, Montreal, H3A 0C3, QC,
Canada

2]Department of Chemistry and Chemical Engineering, Royal Military College of
Canada, Sawyer Building, 11 General Crerar Crescent, Kingston, K7K 7B4, ON,
Canada

# An Explosively Driven Launcher Capable of
$10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ Projectile
Velocities

<EMAIL_ADDRESS><EMAIL_ADDRESS>Myles T. Hildebrand
<EMAIL_ADDRESS>Andrew J. Higgins<EMAIL_ADDRESS>*
[

###### Abstract

Launching large (> $1\text{\,}\mathrm{g}$) well-characterized projectiles to
velocities beyond $10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$
is of interest for a number of scientific fields but is beyond the reach of
current hypervelocity launcher technology. This paper reports the development
of an explosively driven light-gas gun that has demonstrated the ability to
launch $8\text{\text{-}}\mathrm{mm}$ diameter, $0.36\text{\,}\mathrm{g}$
magnesium projectiles to
$10.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$. The implosion-
driven launcher (IDL) uses the linear implosion of a pressurized tube to
shock-compress helium gas to a pressure of $5\text{\,}\mathrm{GPa}$, which
then expands to propel a projectile to hypervelocity. The launch cycle of the
IDL is explored with the use of down-bore velocimetry experiments and a quasi-
one-dimensional internal ballistics solver. A detailed overview of the design
of the $8\text{\text{-}}\mathrm{mm}$ launcher is presented, with an emphasis
on the unique considerations which arise from the explosively driven
propellant compression and the resulting extreme pressures and temperatures.
The high average driving pressure results in a launcher that is compact, with
a total length typically less than a meter. The possibility to scale the
design to larger projectile sizes ($25\text{\text{-}}\mathrm{mm}$ diameter) is
demonstrated. Finally, concepts for a modified launch cycle which may allow
the IDL to reach significantly greater projectile velocities are explored
conceptually and with preliminary experiments.

###### keywords:

Down-bore Velocimetry, Light-Gas Gun, Hypervelocity Launcher, Ablation,
Internal Ballistics

##  1 Introduction

The development of hypervelocity launchers based on a gasdynamic cycle have
reached a velocity plateau over the entire projectile mass–velocity spectrum.
The maximum projectile velocity obtainable by hypervelocity launch
technologies is thus insufficient to fully meet orbital debris testing
requirements ($15\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$) or
to probe the behaviour of materials at pressures exceeding 1 TPa. The
existence of the performance envelope is demonstrated by Figure 1, where
launch velocity capability is plotted versus projectile mass for the continuum
of launcher designs, ranging from conventional single-stage guns to multi-
stage light-gas guns. Also included for reference are the results from the
implosion-driven launcher discussed in this work. As can be seen, the ability
to launch well characterized projectiles in the $110\text{\,}\mathrm{g}$ range
to velocities above
$10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ lies outside the
current performance envelope. This combination of projectile mass and velocity
is critical to certify spacecraft shielding against orbital debris that lies
below the detection threshold of ground-based radar NAP13244 (1). It is also
required for the study of materials at high pressure, such as planetary impact
geophysics Ahrens1987 (2, 3, 4) and asteroid deflection RN798 (5).

Figure 1: Projectile velocities as a function of mass for widely used launcher
techniques, showing the envelope of current soft launch capability. Results
for the implosion-driven launcher presented in this work are included for
reference. Based on NAP4765 (6).

The two-stage light-gas gun is the workhorse of hypervelocity research for
launch velocities between
$410\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ Canning1970 (7,
8). Light-gas gun velocity performance is limited by the maximum pressure that
the launcher can contain and the ablation of wall material that results from
the high propellant temperature and flow velocity Bogdanoff1998 (9).
Consequently, light-gas guns are typically operated well below their technical
limits, at velocities of around
$7\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$, in order to
minimize damage to the launcher. Future optimizations promise more routine
operation around $10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$,
but these have yet to be implemented in practice Bogdanoff2016 (10). Because
of the long piston travel distance and large area ratio between piston and
projectile, large facilities are required to launch projectiles to
hypervelocity; large-bore launchers can reach $3050\text{\,}\mathrm{m}$ in
length.

Propellant sound speed can be increased even further by adding a third stage
to the launch cycle. In the three-stage light-gas gun, the high-velocity
projectile from a second stage is used to shock-compress another column of
light gas to greater temperature in order to accelerate a final, smaller
projectile Piekutowski2006 (11). In practice this configuration has exceeded
$10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$, although the
reduced area ratio between successive stages severely limits the mass of
projectile that can be launched Friend1969 (12). Alternatively, a graded-
density impactor can be launched from a two-stage light-gas gun onto a target
flyer plate which is accelerated via the resulting quasi-isentropic impact-
driven compression Chhabildas1995 (13). To obtain significant velocity
enhancement and prevent spalling the projectile, an impact-driven third stage
is necessarily limited to launching thin flyer plates of substantially smaller
mass than the original impactor Chhabildas1995 (13). This technique has been
used to launch a $0.07\text{\,}\mathrm{g}$ titanium flyer plate to
$16\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ Chhabildas1995
(13).

Exceeding the current performance envelope using only gasdynamic stages is
expected to cause irreversible damage to at least part of the launcher
Glenn1990 (14, 15). With the inevitability of launcher damage in this velocity
regime, it becomes economically attractive to use a disposable launch scheme
and harness the power density and driving pressures of high explosives to
exceed $10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$. The
combination of high driving pressures and focusing effects allow explosive
launching techniques to accelerate projectiles to velocities inaccessible by
traditional light-gas guns. The inhibited shaped charge technique permits the
launching of projectiles with a length-to-diameter ratio between 3 and 4 to
$11\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ by interrupting
the formation of a shaped charge jet with a solid die inserted at the mouth of
the cone Walker1993 (16). In another type of energy focusing scheme, a cascade
of flyer plates uses a sequence of explosive charges backing successively
thinner plates to accelerate a final flyer via an over-driven detonation
Ivanov1982 (17). This technique, which is limited to launching thin flyers due
to spallation concerns, has been used to reach velocities beyond
$10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ Ivanov1982 (17,
18). It is also possible to accelerate a projectile without direct contact
with the explosive by using the detonation products or an intermediate gas as
the driver. Examples of such an approach include the UTIAS launcher Glass1972
(19) and the Voitenko compressor Voitenko1964 (20, 21, 22, 23, 24, 25), where
explosive detonation products or an explosively driven flyer plate are used to
compress the driver gas in a hemispherical cavity. Although the hemispherical
focusing used by these techniques can generate large peak gas pressures and
high flow velocities, the intensity and short duration of the impulse results
in an inefficient launch cycle where the projectile driving pressure quickly
decays and the maximum pressure must be maintained well below theoretical
limits of focusing to prevent projectile destruction. Resulting projectile
velocities have been unimpressive Glass1972 (19).

A more attractive option for launching well characterized projectiles with an
explosive driver is to sequentially detonate a hollow cylinder of explosive.
Implosion of the inner surface of the explosive produces a jet at the
centerline, which in turn drives a gradual, linear cumulation of high-pressure
driving gas Merzhievskii1987 (26). Sequential linear implosion does not result
in the same peak pressure as hemispherical or conical focusing but can produce
a longer loading impulse; this is ultimately beneficial for the launching of
intact projectiles to high-speed. An example of this technique is the Titov
launcher, which uses a cumulative jet of detonation products or fill gas
within the cylindrical hollow of a tubular charge of explosive to
aerodynamically drag a projectile to hypervelocity Titov1968 (27, 28, 29, 30,
26). Dust clouds have been accelerated to
$25\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ and micro-
projectiles have been launched to
$14\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ with this
technique, although substantial ablation of projectile mass due to hypersonic
drag is unavoidable Titov1968 (27, 31, 32).

A linear implosion can also be used to compress a light driver gas, similar to
the pump tube of a conventional two-stage light-gas gun. This is accomplished
by using a grazing detonation in an outer cladding of high explosive to
sequentially implode a thin-walled metal tube filled with helium/hydrogen. The
resulting shock-driven compression can generate a propellant with a very high
total enthalpy, which can be expanded to propel a projectile to hypervelocity.
This type of launcher was pioneered in the 1960s by the Physics International
Company (PI), who demonstrated the ability to launch $2\text{\,}\mathrm{g}$
projectiles to velocities exceeding
$12\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ Crosby1967 (33,
34, 35, 36, 37, 38, 39).

##  2 Launch Cycle Overview

The implosion-driven launcher (IDL), shown schematically in Figure 2, is
essentially a light-gas gun in which the propellant is dynamically compressed
by the sequential linear implosion of a pressurized tube. The driver is
composed of a thin-walled steel tube pressurized with helium gas and
surrounded by a thin layer of explosive, which in turn is surrounded by a
thick-walled steel tamper. The explosive is initiated at the end of the tube,
which causes an annular detonation wave to sweep along the tube and
progressively collapse it. The imploding tube wall acts like a piston which
travels at the detonation velocity of the explosive and drives a strong
precursor shock wave (PSW) into the helium driver gas. As the explosively
driven piston travels along the driver, an increasingly long column of shock-
compressed gas is formed. The PSW travels through the chamber and reflects off
the projectile, which stagnates the flow, further increasing its temperature
and pressure. The reflected shock wave travels back into the shock-compressed
flow, forming a reservoir of gas with a high pressure and sound speed which
expands to accelerate the projectile.

Figure 2: Overview of the launch cycle of the implosion-driven launcher.

The launch cycle of the IDL allows the high energy density of high explosives
to be stored in a low molecular-weight gas, resulting in the launch of a
projectile with much lower peak loading and to significantly greater
velocities than can be reached by the direct expansion of detonation products.
The linear implosion gradually focuses energy into the driver gas so that the
peak projectile base pressure is less than for other explosive launcher
schemes, thus allowing the launch of well characterized projectiles Walker1993
(16, 18, 19, 23). The explosively driven piston, which travels into the gas at
the detonation velocity of the high explosive
($59\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ range), causes
the driver gas of the IDL to be compressed by a strong shock wave (Mach 9 for
a $7\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ piston). As the
flow is stagnated behind the projectile, the helium reaches pressures and
temperatures of approximately $5\text{\,}\mathrm{GPa}$ and
$28\,000\text{\,}\mathrm{K}$. The internal energy and speed of sound obtained
by strong-shock-driven compression is much greater than for the nearly
isentropic compression of a typical two-stage light-gas gun pump-tube. Thus,
while the IDL is conceptually similar to a gas gun, the launch cycle also
shows features typical of the acceleration of a flyer plate in contact with an
explosive charge because of the pressures, gas velocities, and shock waves
encountered in the driver.

Since the driver is consumed by the high explosive during its operation and
the helium flow properties are sufficient to cause significant plastic
deformation and ablation of the chamber and launch tube, the IDL is a single-
use device. However, the design of the launcher is both simple: made up
primarily of stock tubing and simple machined components, and very compact:
the launcher presented in this paper is less than $1\text{\,}\mathrm{m}$ in
length, resulting in modest per-shot costs. The high pressures and sound
speeds that are afforded by not being limited by launcher damage and readily
obtained via shock-driven compression enable the IDL to reach projectile
velocities beyond the envelope of other light-gas launchers. By contrast, the
use of an intermediate propellant cumulation cycle yields dramatically better
piezometric efficiency Krier_Ep (40, 41) and propellant sound speeds compared
to direct acceleration by a high explosive, which allows the IDL to actualize
more of the tremendous theoretical potential of explosives.

###  2.1 Explosive Driver

The explosive driver uses the sequential/linear implosion of a thin-walled
steel tube to drive a normal shock wave into the helium gas. In the idealized
case, the implosion pinch forms an impermeable piston that travels into the
driver gas. Thus, the particle velocity behind the shock would be equal to the
detonation velocity of the explosive. The precursor shock-wave (PSW) strength,
described by its Mach number ($M_{\mathrm{s}}$), is then given by the
following equation for a calorically perfect gas (Thompson_fluids, 42, pp.
402):

$\frac{U_{\mathrm{p}}}{c_{\mathrm{o}}}=\frac{2}{\gamma+1}\left(\frac{M_{\mathrm{s}}^{2}-1}{M_{\mathrm{s}}}\right)$
(1)

Where $U_{\mathrm{p}}$ is piston/pinch velocity and is equal to the detonation
velocity of the explosive, $c_{\mathrm{o}}$ is the initial sound speed in the
gas, and $\gamma$ is the ratio of specific heats of the gas.

This equation is obtained from the normal-shock relations, which can be used
to analytically determine the shock-compressed gas properties and the PSW
velocity. For the optimized launcher, Primasheet explosive (63 wt% PETN) was
used, which has a detonation velocity of
$7\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$. This results in an
ideal PSW velocity of
$9.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$; 34% faster than
the detonation velocity. Initial gas tube fill pressures for a typical
launcher range from $37\text{\,}\mathrm{MPa}$, resulting in post-shock
pressures of $300850\text{\,}\mathrm{MPa}$. Since the PSW is continuously
distancing itself from the explosive pinch, it should be possible to produce
arbitrarily long columns of shocked propellant by elongating the gas tube. In
practice, non-ideal effects lead to a decay in the strength of the shock wave
and limit the propellant mass delivered to the chamber.

Driver non-idealities caused by the extreme gas pressures and flow conditions
at the explosive pinch are depicted schematically in Figure 3. Also shown are
representative graphs of the PSW standoff distance from the detonation
position (i.e., the length of the compressed gas column) and PSW velocity as a
function of the detonation position, which show how these parameters evolve
along the length of the driver. Both the shock standoff and the detonation
position are normalized by the driver-tube inner diameter. This data was
obtained from experiments performed by Szirti et al. Szirti2011 (43) using
nitromethane explosive drivers and is compared to the ideal predictions
discussed above. As can be seen in top graph of Figure 3, a certain distance
is required for the explosive piston to form and begin to drive a PSW ahead of
the detonation, causing the standoff distance to initially lag behind ideal
predictions. Approximately 10 tube diameters Moore1968 (34) are needed for the
PSW to emerge from the collapsing tube. Beyond this start-up distance, the PSW
velocity is significantly higher than ideal theory. This is the result of a
cumulative jet composed of metal particulate and helium gas formed at the
central implosion axis Moore1968 (34) and projected forward at approximately
twice the detonation velocity Walsh1953 (44).

Figure 3: Overview of the non-ideal operation of the explosive driver. The
precursor shock-wave standoff and velocity are plotted against the non-
dimensional explosively driven piston position. The non-ideal effects
responsible for observed precursor shock-wave behaviour are sketched below the
plots. Results and figure adapted from Szirti et al. Szirti2011 (43). The
driver explosive was 90% nitromethane sensitized with 10% diethylenetriamine
by mass; pre-compression of the liquid layer from passage of the PSW resulted
in an average detonation velocity of
$6.6\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ and an ideal PSW
velocity of $8.9\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$.

Further along the driver, the PSW velocity decays from thickening of the
boundary layer in the shocked driver gas and expansion of the tube walls from
the intense post-shock pressure. The high-pressure gas in the boundary layer
is nearly quiescent and must be driven forwards by the explosive pinch to
remain in the driver. The resulting stagnation pressures are sufficiently
large to prevent flow turning of the entire volume of gas trapped in the
boundary layer. As a result, an increasing quantity of gas is continuously
lost through the explosively driven piston, leading to a decay in the PSW
velocity. Evidence for this gas loss is provided by Szirti et al., who showed
that imploded pressurized tubes developed a pinhole down their lengths
Szirti2011 (43). As the standoff between the PSW and the detonation increases,
so does the time available for the thin-walled driver tube to expand under the
large pressure of the shock-compressed gas. Szirti et al. developed a
computational model for the expansion of the driver tube, which showed that
expansion contributes to the decay of the PSW velocity, but can be mitigated
by surrounding a thin layer of explosive with a heavy steel tamper Szirti2011
(43). Rapid acoustic reverberations between the tamper inner-surface and the
gas tube outer-surface partially arrest gas tube expansion and prevent
catastrophic bursting. The tamper has the added benefit of focusing the
explosive energy inwards, thus significantly reducing the required mass of
explosive to effectively form the piston. As can be seen in Figure 3 from an
experiment with a nitromethane driver Szirti2011 (43), the combined effects of
boundary layer gas loss and tube expansion lead to a significant decay in the
PSW velocity, which falls well below the ideal model and eventually asymptotes
to the detonation velocity, resulting in a fixed standoff distance. It should
be noted that these effects become more pronounced as the initial pressure of
the helium gas is increased, to the point where at sufficiently high initial
pressures (typically beyond $1015\text{\,}\mathrm{MPa}$) a PSW can no longer
be driven into the gas. The decay in PSW velocity, and thus shock strength, as
a function of normalized driver length, leads to a significant reduction in
the kinetic and internal energy of the shock-compressed gas, which introduces
interesting design compromises that will be discussed in Section 4.2 of this
paper.

###  2.2 Launch Cycle Dynamics

The launch cycle of the IDL is affected by the dynamics of the shock wave as
well as non-ideal effects that result from the high temperature, pressure, and
flow velocity of the driver gas. The main features of the launch cycle
discussed below are illustrated by the time-position schlieren plot of Figure
4, which has been generated using Tecplot 360 to visualize an internal
ballistics simulation. The schlieren image shows the density gradients in the
internal gas flow, which helps identify the key wave-dynamics of the launch
cycle. As the PSW reaches the end of the driver and enters the chamber, it is
amplified by a gradual area reduction section that transitions from the driver
diameter to the s. As a result, the peak pressure on the projectile is not
only affected by the initial driver gas pressure and the strength of the PSW,
but also by the ratio of the driver and launch-tube diameters, or chambrage.
The shock wave then passes through a short constant-diameter section before
reaching the projectile, which allows the PSW to planarize and ensures the
projectile is loaded uniformly. The peak launch cycle pressure occurs as the
PSW reflects off the projectile. Although this pressure is typically much
greater than the tensile strength of the projectile material, confinement from
the launch tube prevents significant plastic deformation as long as the
loading is uniform. Also of concern to projectile integrity is the shock wave
that is transmitted into the projectile upon PSW reflection. It is well known
that shock-wave interactions with free surfaces, in this case the projectile
front face, can lead to tensile spall failure Antoun2003 (45).

Figure 4: Labelled schlieren position–time plot showing the internal gas flow
of the implosion-driven launcher. The density gradients in the flow
demonstrate the main features of the launch cycle.

The reflection of the PSW from the projectile causes a shock wave to travel
back into the chamber. This shock wave essentially stagnates the flow, leading
to a significant increase in the pressure and temperature of the helium gas.
The reservoir that contains the chamber and early launch tube sections is made
very thick such that material strength and more importantly inertia help
contain the gas pressure, which is an order of magnitude greater than the
tensile strength of the wall material. The rapid expansion of the reservoir
inner wall causes the ultimate projectile velocity capability of the IDL to be
very sensitive to the timescale of the launch cycle: heavier projectiles,
which accelerate slower, will reach significantly lower maximum velocities due
to energy loss from reservoir expansion. In an attempt to minimize driver gas
loss through the back of the reservoir, a tapered section is added to the end
of the driver where a thick-walled “sealing cone” section is imploded. The
length of the chamber section is chosen such that the reflected shock wave
approaches the back of the chamber as the detonation in the explosive reaches
the end of the driver and collapses the sealing cone. As the explosively
driven piston effectively stops when reaching the chamber, a strong expansion
front is sent into the flow. While this front causes a significant decrease in
the pressure within the chamber, the launcher is designed such that the
projectile has reached its maximum velocity before the expansion front reaches
the projectile.

Throughout the launch cycle, the walls of the launcher are exposed to hot
high-velocity gas flows. It has been shown that ablation can have a
significant effect on the performance of two-stage light-gas guns, where the
flow through the launch tube and chamber causes ablation and mixing of high-
molecular-weight wall material with the light driver gas, which leads to a
reduction in the maximum projectile velocity Bogdanoff1998 (9). Ablation in
the chamber and launch tube is an even greater concern for the IDL, where the
propellant temperatures caused by the shock-driven compression are much
greater than in a two-stage light-gas gun. For the IDL, ablation is also a
concern in the driver, where the rapid gas flow behind the PSW can cause
ablative mixing of wall material with the light gas Hildebrand2014 (46), which
results in the driver gas being heavily polluted before the projectile begins
accelerating. Experiments performed to quantify the level of ablation by
measuring the mass loss at the driver inner wall showed that the mass of
ablated material is on the order of the total mass of helium gas in the driver
Hildebrand2014 (46). The effects of reservoir expansion and ablation will be
discussed quantitatively later in the manuscript, but the importance of these
effects is illustrated in Figure 5, which shows a cross section of a launcher
reservoir that has been cut in half after being shot. The original cross
section has been traced for reference, with the initial projectile position
indicated by the groove near the reservoir midpoint. The image shows severe
radial expansion of the reservoir walls, especially near the original
projectile position where the diameter has increased by a factor of two. It
should be noted that for this test the first half of the reservoir exterior
was surrounded with explosives that were detonated to mitigate reservoir
expansion, which is why the final outer diameter is smaller than the original
diameter in some areas. Ablative wear and deposited ablated-driver-wall
material can be seen on the inner surface of the reservoir.

Figure 5: Photograph of a launcher reservoir that has been sectioned in half
after being fired. The original profile is shown in the red outline, while the
initial projectile position can be seen by the groove located approximately in
the center of the reservoir. Note that this experiment included explosives on
the exterior of the aft section of the reservoir.

##  3 Down-Bore Velocimetry

Recording the projectile acceleration history via down-bore velocimetry offers
valuable insight into the launch cycle dynamics and a benchmark for internal
ballistic models. The IDL is particularly well suited to performing down-bore
velocimetry, as the high rate of acceleration results in relatively short
projectile acceleration distances: the projectile typically reaches 80% of
maximum velocity at a travel of 10 projectile diameters. Laser interferometry
techniques used in the shock physics community, such as photonic-Doppler
velocimetry (PDV) Strand2006 (47), have the ability to measure kilometer-per-
second free-surface velocities with nanosecond temporal resolution. The
insight gained from down-bore velocimetry is invaluable to the development of
the IDL, since the internal ballistics of the launcher can be resolved
directly in the absence of traditional diagnostic methods such as pressure
transducers, whose use is precluded by the extreme launch cycle conditions.

Figure 6: Schematic (left) and photograph (right) of the experimental
arrangement for the down-bore velocimetry experiment.

This section will present a down-bore velocimetry experiment performed using
PDV, in which the velocity history of a $0.1\text{\,}\mathrm{g}$,
$5\text{\text{-}}\mathrm{mm}$-diameter IDL projectile was tracked from 0 to
$7.8\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$. PDV operates by
blending Doppler-shifted laser light reflected from a moving surface with a
source laser signal to extract a beat frequency that is proportional to the
surface velocity. The PDV system uses detectors and a digitizer with
bandwidths of $13\text{\,}\mathrm{GHz}$. The system was operated in a
frequency-shifted mode by using a second, tunable laser as the reference
Dolan_PDV_extreme (48). Offsetting the reference laser frequency relative to
the source laser permits accessing higher surface velocities (in this case
>$10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$).

The experimental arrangement is shown schematically in Figure 6. The PDV
system was coupled to the launcher by threading an aluminum probe holder to
the end of the launch tube, into which an optical collimator was epoxied in
place. Relief ports were milled into the probe holder to allow the gas ahead
of the projectile, air initially at 1 atm, to escape before reaching the
probe. The launch tube length was shortened to a length of 20 projectile
diameters ($100\text{\,}\mathrm{mm}$) in order to limit laser beam divergence
before reaching the projectile. The launcher driver had a length of
$180\text{\,}\mathrm{mm}$ and a diameter of $12.7\text{\,}\mathrm{mm}$. The
cylindrical projectile, which was composed of a magnesium alloy (ZK60-T5), had
a diameter of $5.2\text{\,}\mathrm{mm}$ and a thickness of
$2.5\text{\,}\mathrm{mm}$. The operation of the driver was monitored by
detonation time-of-arrival gauges at the start of the tube and by two
piezoelectric shock pins placed near the entrance to the chamber. The shock
pins pass through the tamper and explosive layer to rest against the driver
tube, leading to a nearly instantaneous voltage rise as the shock wave passed
over their position. The PSW velocity and position can be readily determined
from the pair of shock pins, while the standoff between the detonation and
shock wave can be determined from the self-shorting twisted pairs that record
the arrival of the detonation in the explosives and the known explosive
detonation velocity. These values can be compared with ideal predictions to
ensure the driver operated as expected.

Figure 7: Photonic Doppler velocimetry spectrogram of the down-bore
velocimetry experiment. The light-colored trace shows the evolution of
projectile velocity as a function of time. The color contours show the power
spectral density of a sliding window fast Fourier transform performed on the
PDV data, where the frequency has been converted to velocity using the Doppler
formula.

The PDV data obtained from the experiment was used to construct the
spectrogram shown in Figure 7, in which the lighter portion of the contour
plot indicates the projectile velocity as a function of time. It should be
noted that the time axis zero for the experiment corresponds to the initiation
of the detonation in the driver. The strong return of a single signal in the
spectrogram is indicative of an intact projectile with smooth surface;
significant ejecta or fragmentation of the projectile surface would appear as
broadening of the PDV signal Georges2017 (49). As can be seen in Figure 7, the
PDV signal was lost as the projectile reached a velocity of
$7.8\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$, which is typical
of down bore velocimetry experiments performed on IDLs, and is believed to be
caused by obstruction of the laser signal by driver gas that leaks around the
projectile Hildebrand2017 (50, 51). A comparison of the shock-wave time of
arrival, velocity, and standoff values at the end of the driver obtained from
the shock pins with those of an ideal driver discussed in Section 2.1 is shown
in Table 1. As can be seen, the experimental values were very close to ideal,
as would be expected for a driver with a length-to-diameter ratio of 35.

Table 1: Comparison of the precursor shock-wave time of arrival, velocity, and standoff measured in the down-bore velocimetry experiment to that of an ideal driver. Parameter | Measured | Ideal | % Difference
---|---|---|---
Shock arrival at pin 1 | $37.1\text{\,}\mathrm{\SIUnitSymbolMicro s}$ | $36.3\text{\,}\mathrm{\SIUnitSymbolMicro s}$ | 2.1%
Shock arrival at pin 2 | $39.1\text{\,}\mathrm{\SIUnitSymbolMicro s}$ | $38.3\text{\,}\mathrm{\SIUnitSymbolMicro s}$ | 2.0%
Shock velocity | $9.5\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ | $9.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ | 0.9%
Standoff | 88 mm | 94 mm | 5.7%

Certain key features of the IDL launch cycle are illustrated by the down-bore
velocimetry data. The shock wave transmitted to the projectile caused a nearly
instantaneous jump in projectile velocity to
$1\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$. This shock wave
was followed by release waves that caused the projectile free-surface velocity
to oscillate after the shock. This pullback after the shock indicates the
presence of significant tensile loading within the projectile and that
spallation is an important consideration (discussed in Section 4.1 below).
Another important feature of the launch cycle is the rapid timescale over
which the projectile accelerates. The entire PDV signal lasted
$12\text{\,}\mathrm{\SIUnitSymbolMicro s}$, at which point the projectile had
already reached 80–90% of its maximum velocity. It is instructive to note that
arrival of the detonation at the end of the driver
($54.4\text{\,}\mathrm{\SIUnitSymbolMicro s}$) corresponded to a projectile
velocity of $4.9\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$,
reinforcing the fact that the projectile launch occurs on the same timescale
as the shock-wave reverberations.

###  3.1 Comparison to an Internal Ballistics Model

The experimental results presented above can be compared to a computational
model based on a quasi-one-dimensional Internal Ballistics Solver (IBS)
developed specifically to simulate the IDL HuneaultThesis (52, 53). The model
is based on a second-order-accurate Lagrangian finite difference scheme with
artificial viscosity developed by von Neumann and Richtmyer VonNeumann1950
(54). The IBS treats the projectile as a lumped mass, meaning it cannot
reproduce the initial shock in the projectile seen in the PDV data. The
launcher driver is simulated by moving a planar piston into a rigid tube of
helium gas at the explosive detonation velocity, which is a reasonable
approach given the good agreement between the measured shock velocity and the
ideal driver model shown in Table 1. Due to the simplicity of the solver, it
is possible to add different physical models for non-ideal effects present in
the launch cycle HuneaultThesis (52, 53). A comparison of model results with
the experimental down-bore velocimetry data can be seen in Figure 8. The data
from the spectrogram of Figure 7 has been extracted to form the “Down Bore
Velocimetry” data of Figure 8. The “Ideal Model” curve represents a simulation
where the walls of the launcher have been assumed to be rigid, which would be
expected to provide an upper bound of projectile velocity. The “Expanding
Reservoir Model” curve corresponds to a case where the IBS has been coupled to
a radial hydrocode to simulate the radial expansion of the reservoir under the
high gas pressures. As can be seen in Figure 8, both the ideal and expanding
model significantly under-predict the projectile acceleration for most of the
launch cycle, indicating that there is a non-ideal effect that is offsetting
losses to the point where the driving pressure on the projectile is maintained
above the ideal simulation.

Figure 8: Projectile velocity as a function of time for the down bore
velocimetry experiment. The experimental results are compared to simulations
from an internal ballistics solver with different non-ideal models.

Agreement between IBS simulations and the down-bore velocimetry data is
improved by the addition of an ablation model in which the molecular weight of
the gas is increased due to the mixing of melted wall material with the
helium. The effect of ablation has been simulated using a simplified version
of the model developed by Bogdanoff Bogdanoff1998 (9), where the mass of
melted wall material is determined by calculating the energy deposited to the
launcher walls from convective heat transfer. A tuning parameter is used to
correct for the fact that a portion of the ablated material will be entrained
in the boundary layer and not mix with the bulk driver gas (see Section 2.1).
The IBS simulation incorporating both the ablation model and the expanding
reservoir model is shown in Figure 8 as the “Ablation Model” curve. As can be
seen, the addition of ablation to the simulation increases projectile
acceleration early in the launch cycle and can be further tuned to provide
good agreement with the PDV data. In typical simulations, this tuning
parameter had a value of 8.4; yielding 12% of the ablated mass mixing into the
propellant through the jetting process (see Figure 3). This value is
consistent with the jetted mass in acute-angle shaped charges. Despite the
limitations of this relatively simple model, it provides strong evidence that
ablation is the mechanism responsible for the observed projectile acceleration
exceeding that of the ideal IBS simulation.

Previous ablation studies related to two-stage light-gas guns have focused on
ablation in the launch tube section, where the resulting increase in the
average molecular weight of the gas has a limiting effect on the projectile
velocity, as the driver gas must now accelerate both the projectile and the
ablated wall material Bogdanoff1998 (9). The ablation present in the driver of
the IDL has a significantly different effect on the launch cycle because the
polluted gas has a large initial particle velocity and a non-uniform
distribution along the column of compressed gas. Indeed, the increase in the
molecular weight of the gas within the driver results in the explosive doing
more work on the gas, which leads to an increase in the energy available to
accelerate the projectile. It is also important to consider that the column of
compressed gas between the explosively driven piston and the PSW is expected
to contain a linearly increasing mass of ablated wall material because the gas
near the back of the column has travelled a further distance along the driver
tube. Thus, during the initial stages of projectile acceleration, the
reflected shock wave will stagnate the increasingly heavy gas towards the back
of the compressed gas column, which results in a greater-than-expected
pressure behind the reflected shock wave. This increase in pressure is
transmitted to the projectile by compression waves which help maintain a high
driving pressure. Ablation in the driver therefore produces a mostly favorable
situation in which the helium gas near the projectile, which will be
accelerated to many kilometers-per-second, is initially nearly free of ablated
wall material, while the gas near the back of the compressed gas column sees a
significant increase in molecular weight, which increases the total energy
available to accelerate the projectile. However, it should be noted that the
flow of propellant in the IDL will also cause ablation in the launch tube. The
additional energy needed to accelerate this entrained mass of ablated material
will reduce the maximum velocity that can be achieved by the projectile and
could be a limiting factor in the performance of the launcher. Further
exploration of exploiting this effect by introducing a gradient of molecular
weight in the gas in the driver tube—in order to achieve greater velocities—is
explored in Appendix 2.

##  4 Detailed Launcher Design

This section will present an overview of the design of an 8-mm-bore IDL with a
demonstrated capability to launch a $0.36\text{\,}\mathrm{g}$ projectile to
velocities beyond $10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$.
Results from two experiments performed using the
$8\text{\text{-}}\mathrm{mm}$-dia-bore IDL are presented in Table 2, in which
the launcher was fired into an evacuated test section and observed using a
Photron SA5 video camera. While the image resolution of the projectile was
limited (12 pixels by 6 pixels), the projectiles appeared to be intact, with
no discernible fragments. A witness plate at the end of the target chamber was
also used to ensure the projectile was not fragmented.

Table 2: Summary of results for two launcher experiments where the velocity exceeded $10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$. Caliber | Driver Gas | Projectile | Velocity
---|---|---|---
$8\text{\,}\mathrm{mm}$ | He, $4.1\text{\,}\mathrm{MPa}$ | ZK60, $0.36\text{\,}\mathrm{g}$ | $10.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$
$8\text{\,}\mathrm{mm}$ | He, $4.1\text{\,}\mathrm{MPa}$ | ZK60, $0.36\text{\,}\mathrm{g}$ | $10.2\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$

A schematic of the $8\text{\text{-}}\mathrm{mm}$ launcher is shown in Figure
9, which highlights the key details and design parameters that will be
discussed in the following subsections. The total length of the launcher is
$0.91\text{\,}\mathrm{m}$. Values for the design parameters are summarized in
Table 3. The discussion below will focus on the design considerations that
result from the dynamic driver gas compression as well as the extreme
propellant pressures, temperatures, and flow velocities in the IDL. The
$8\text{\text{-}}\mathrm{mm}$ launcher design is based on using helium rather
than hydrogen as the driver gas, a choice which is discussed in detail in
Appendix 1. The design parameters will be discussed in their non-dimensional
form in order to apply to launchers of different sizes.

Figure 9: Overview of the design of the $8\text{\text{-}}\mathrm{mm}$
implosion-driven launcher. Values for the design parameters can be found in
Table 3. Table 3: Main design parameters of the $8\text{\text{-}}\mathrm{mm}$
launcher. Values are presented in non-dimensional form where possible for use
in launcher scaling. Projectile
---
Projectile & Launch Tube Inner Diameter (IDlt) |  $8\text{\,}\mathrm{mm}$
Projectile Thickness to Diameter Ratio (tproj/IDlt) |  0.5
Projectile Material |  ZK60
Projectile Density ($\rho_{\mathrm{proj}}$) |  1.83 g/cm3
Normalized Projectile Mass ($\frac{\rho_{\mathrm{proj}}t_{\mathrm{proj}}}{\mathrm{ID}_{\mathrm{lt}}}$) |  0.92 g/cm3
Driver Design
Driver-Tube Thickness to Outer Diameter Ratio (tdt/ODdt) |  0.065
Explosive Thickness |  $5.6\text{\,}\mathrm{mm}$
Tamper Thickness to Inner Diameter Ratio (ttamp/IDtamp) |  0.55
Explosive Mass to Driver-Tube Mass Ratio (C/M) |  1.1
Driver Geometry
Driver Length to Inner Diameter Ratio (Ldt/IDdt) |  28
Chambrage Ratio (IDdt/IDlt) |  2.1
Driver Fill Pressure |  $4.1\text{\,}\mathrm{MPa}$
Driver Gas Mass to Projectile Mass Ratio (G/M) |  1.9
Reservoir and Launch Tube
Chamber Length to Driver Length Ratio (Lcbr/Ldt) |  0.22
Sealing Cone Length to Driver Inner Diameter Ratio (Lc/IDdt) |  2.2
Shock Planarization Length to Projectile Diameter Ratio (Lpln/IDlt) |  2.8
Area Change Taper Half Angle |  $5\text{\,}\mathrm{\SIUnitSymbolDegree}$
Sealing Cone Taper Half Angle |  $18\text{\,}\mathrm{\SIUnitSymbolDegree}$
Launch Tube Length to Inner Diameter Ratio (Llt/IDlt) |  38

###  4.1 Projectile Considerations

The projectile consists of a ZK60-T5 Magnesium alloy cylinder with a thickness
($4\text{\,}\mathrm{mm}$) equal to half its diameter
($8\text{\,}\mathrm{mm}$). The projectile thickness has been chosen to be as
thin as possible in order to reduce its mass, but sufficiently thick to be
stable within the bore of the launch tube. The projectile is sized such that
it has a tight slip fit into the launch tube. As can be seen in Figure 9, the
projectile has a set of tabs held together by a thin web
($0.2\text{\,}\mathrm{mm}$). The tabs allow the projectile to seal the initial
helium gas pressure with a corner o-ring, while the web is made with a
sufficient thickness to hold the initial driver gas pressure. This self-
sealing projectile arrangement eliminates any flow disturbances or shock
interactions that would otherwise occur with a separate sealing diaphragm and
is easily implemented in the IDL due to the fact that the pressure ramp up
from the reflected shock wave is instantaneous, as opposed to the gradual rise
in pressure encountered in two-stage light-gas guns.

The survivability of the projectile is the limiting factor in the launch cycle
of the IDL. The pressure generated by the explosive driver is not limited by
the capability of the device, but rather by the fracture threshold of the
projectile. Empirical evidence has shown that a reflected shock pressure of
approximately $5\text{\,}\mathrm{GPa}$ corresponds to the limit where the ZK60
magnesium alloy projectiles used in this study can be reliably launched
intact. While the mechanism for projectile failure has not been directly
observed, the two most likely failure mechanisms are uneven loading on the
projectile and shock-wave interactions within the projectile and at the
interface between the projectile and launch tube. While it is possible to
avoid uneven loading on the projectile by ensuring concentricity of mating
parts, allowing the PSW to planarize before reaching the projectile, and
avoiding the use of a diaphragm before the projectile, shock interactions
within the projectile cannot be entirely eliminated. The magnitude of shock-
wave interactions will be proportional to the pressure behind the reflected
shock wave, which explains the dependence of projectile survivability on
maximum pressure. The use of a projectile material whose acoustic impedance
(density multiplied by speed of sound) is closely matched to that of the steel
launch tube prevents significant shock interactions at the interface between
the projectile and launch tube. The projectile material should also have a
sufficiently high spall strength to survive the tensile stresses caused by
wave interactions. The acoustic impedance matching criteria and the need for a
high spall strength precludes the use of plastics as projectile materials due
to their significantly lower speed of sound and spall strength compared to
lightweight metal alloys. We emphasize that the use of a self-sealing
projectile (thus avoiding the use of a diaphragm that would apply uneven
loading to the projectile upon rupture) is critical to operate the launcher
near the limit of projectile survivability and actualize more of the
theoretical potential.

The velocity potential of the IDL is particularly sensitive to the mass of the
projectile due to the radial expansion of the reservoir that results from the
GPa driver-gas pressures. For a fixed launcher geometry and fill pressure, the
projectile acceleration is inversely proportional to its mass. Therefore, as
the mass of the projectile increases, the launch cycle timescale also
increases, which allows for more energy to be lost to radial expansion of the
reservoir, an effect that was demonstrated with the internal ballistics model
of the launcher described in Section 3.1 Loiseau2013_2 (55). Although the
decrease in projectile acceleration can be offset by an increase in the
initial pressure of the driver gas, this also results in an increase in the
rate of radial expansion. In practical terms, this means that an increase in
projectile mass must be accompanied by a proportionally greater increase in
maximum pressure. It is for this reason that ZK60 is chosen as the projectile
material over aluminum or titanium alloys which may have higher strength-to-
weight ratios.

Figure 10: Flash X-ray photography of a $25\text{\,}\mathrm{mm}$ projectile
(right) exiting the launch tube (left) of an implosion-driven launcher.

Despite the large driving pressures and shock loading that result from the
launch cycle, projectiles are routinely launched intact, with no discernible
sign of damage from high-speed video footage, as can be seen in the video
provided in the supplemental material. Experiments have also been performed
where a flash X-ray system imaged the projectile as it exited the launch tube.
The use of a flash X-ray system is needed to image the projectile in the early
stages of flight due to the presence of driver gas that bypasses the
projectile and would obscure an optical camera. The image in Figure 10 was
taken at the muzzle of a $25\text{\text{-}}\mathrm{mm}$-dia-bore IDL in which
the estimated reflected shock pressure was of $5.3\text{\,}\mathrm{GPa}$. The
launcher, which was intended to perform projectile integrity studies, had a
simplified constant area geometry, where the driver and launch tube had the
same inner diameter. As a result, the peak loading is similar to that of
typical IDL, but the measured projectile velocity was only
$5.3\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$, much lower than
would be achieved with a chambered launcher design. The projectile had an
initial diameter (25.4 mm) equal to half the launch tube outer diameter, and a
thickness ($13\text{\,}\mathrm{mm}$) of half its diameter. As can be seen, the
projectile retained its original shape and was relatively planar as it exited
the launch tube.

###  4.2 Driver Design

The driver is composed of a thin-walled steel tube surrounded by a layer of
explosive and a thick-walled tamper made from steel mechanical tubing. The
thickness of the driver tube and explosive layer must be carefully chosen to
ensure the driver operates optimally. As was discussed in Section 2.1,
expansion of the driver tube can cause a significant decay in the PSW
velocity, which lowers the particle velocity and enthalpy behind the shock
wave and results in reduced launcher performance. The magnitude of driver-tube
expansion is mainly determined by the ability of the tamper to provide
confinement to the system, which requires the use of a relatively thin
explosive layer Szirti2011 (43). However, for the explosive driver to operate
properly, the ratio of the detonation velocity of the explosive to the inward
collapse velocity, essentially the aspect ratio of the implosion, must be
sufficiently small in order to prevent excessive driver gas leakage through
the pinch Szirti2011 (43). The inward collapse velocity of the driver tube can
be determined from the Gurney model, which shows that for a given explosive
and tamper thickness, the wall velocity is simply a function of the ratio of
the explosive mass to the driver-tube mass (C/M) LoiseauPEP (56). The
implosion velocity requirement therefore results in the counter-intuitive
outcome that using a _thinner_ driver tube, which allows for the use of a
thinner explosive layer, tends to reduce radial expansion by allowing the
thick-walled tamper to provide confinement to the system. The limit to how
thin the driver tube and explosive layer can be made is determined by the
critical thickness of the explosive, which is the limiting channel size below
which the detonation wave fails to propagate Petel2007 (57). If the initial
explosive layer thickness is too small, expansion of the driver tube can cause
the detonation to fail, which prematurely arrests the explosively driven
piston and essentially terminates the launch cycle. These driver design trade-
offs are illustrated qualitatively via a design parameter map in Figure 11,
where driver performance is described as a function of the driver-tube-
thickness-to-outer-diameter ratio (tdt/ODdt) and explosive-mass-to-driver-
tube-mass ratio (C/M). As can be seen, the optimal driver design uses a
sufficiently thick driver tube and explosive layer to avoid detonation failure
and ensure a prompt implosion. Further increasing the explosive thickness or
driver-tube thickness harms the performance of the driver while simultaneously
increasing the total explosive mass, which may be the limiting factor for the
size of launcher that can be used at a given facility.

Figure 11: Parameter map of the design of the explosive driver showing the
effects of varying the driver-tube thickness and the explosive mass
(thickness).

The driver for the $8\text{\text{-}}\mathrm{mm}$ launcher used an inner tube
with a thickness-to-outer-diameter (tdt/ODdt) ratio of 0.065 and an explosive
thickness (te) corresponding to a C/M ratio of 1.1. Designs which
approximately satisfy these ratios are expected to drive a nearly ideal PSW
for the driver lengths and initial helium fill pressures of interest for the
IDL. The tamper is typically made of the thickest, readily available and
affordable mechanical tubing, which for the $8\text{\text{-}}\mathrm{mm}$
launcher corresponded to a thickness-to-inner-diameter ratio (tt/IDt) of 0.55.
The explosive layer was formed by wrapping layers of Primasheet 1000, a PETN
based sheet explosive whose properties are summarized in Table 4. The C/M
ratio, tamper thickness, and the Gurney energy of the explosive, an empirical
measurement of an explosive’s efficacy in launching flyers, determine the
implosion velocity of the driver-tube wall. The $8\text{\text{-}}\mathrm{mm}$
launcher had a calculated implosion velocity of
$2.1\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$, which, for a
detonation velocity of
$7\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$, gives an implosion
aspect ratio of 3.3. Driver designs should seek to approximately match or
exceed this value to prevent gas loss through the explosive pinch. Any
explosive that can be layered, cast, poured, or pressed into a thin annulus
could be used for the driver, although care must be taken to ensure gaps
within the explosive assembly are minimized as this can prevent the tamper
from confining the driver tube111Considerable development of the launcher
reported in this study was performed with amine-sensitized liquid nitromethane
as the explosive. Nitromethane was replaced with Primasheet to permit simpler
evacuation of the entire chamber containing the launcher, and for launcher use
on field sites that did not permit liquid explosives. The main selection
requirements for a driver explosive are that it have a high detonation
velocity, density, and Gurney energy, as well as a small critical thickness.
The high detonation velocity maximizes the strength of the PSW, and therefore
the speed of sound of the propellant. Increasing the explosive density and
Gurney energy allows for a thinner explosive layer while maintaining the
desired C/M ratio, and decreasing the critical thickness helps prevent
detonation failure.

Table 4: Properties of Primasheet 1000. Density | $1.44\text{\,}\mathrm{g}\text{${}\cdot{}$}{\mathrm{cm}}^{-3}$
---|---
Detonation velocity | $7\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$
Gurney energy | $2.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$
Critical thickness | <$1\text{\,}\mathrm{mm}$

###  4.3 Driver Geometry

The diameter, length, and initial helium fill pressure of the driver determine
the total amount of gas available to accelerate the projectile. nn that the
ratio of driver gas mass to projectile mass (G/M) is a critical design
parameter in gasdynamic launchers Seigel1965 (58). In maximizing launcher
velocity potential, the goal is often to design the launcher such that it has
an effectively infinite G/M, which for the IDL means that the driver is
sufficiently long such that the projectile never experiences the strong
rarefaction front produced when the explosively driven piston stops. While in
theory this would require an impractically long driver, reservoir expansion
and ablation cause the projectile driving pressure in the IDL to decay much
faster near its maximum velocity than an ideal launcher, making it possible to
design the launcher such that further velocity gains from increasing driver
length are negligible.

Launcher performance is also affected by the chambrage ratio, which is the
ratio of the driver diameter (IDdt) to the launch-tube diameter (IDlt). For
gasdynamic launchers, increasing the chambrage ratio leads to a higher average
driving pressure on the projectile as the expansion front generated by the
acceleration of the projectile partially reflects from the area change section
as compression waves that increase the pressure acting on the projectile
Seigel1965 (58). For the IDL, the chambrage ratio and the geometry of the area
reduction section, or chamber, that connects the driver and launch tube have
an additional influence on the launch cycle because they affect the strength
of the PSW and induce a relatively complex flow with significant density and
velocity gradients behind the PSW Watson1970_1 (35). Studies of shock-wave
travel through tapered area change sections have shown that the degree of
shock amplification increases with increasing area ratio and with more gradual
nozzle shapes Russell1967 (59); the chamber taper angle is a critical
optimization parameter in light-gas guns Bogdanoff2016 (10). The chambrage
ratio and nozzle shape also influence the uniformity of the PSW wave when it
reaches the projectile and the magnitude of density gradients in the flow
behind the shock. As the PSW reflects from the projectile and travels towards
the chamber, it will interact with these density gradients and cause
compression waves to reflect towards the projectile, which will increase the
driving pressure.

Although G/M and chambrage considerations would typically suggest that the
length (Ldt) and diameter (IDdt) of the driver should be maximized, five
factors unique to the IDL must be considered in determining ideal driver
geometry:

  1. 1.

The strength of the PSW decreases with increasing normalized driver length
(Ldt/IDdt) and increasing initial helium fill pressure.

  2. 2.

Projectile survivability places a limit on the maximum allowable PSW strength,
which therefore limits the initial driver fill pressure.

  3. 3.

As the driver diameter is increased, the magnitude of PSW focusing through the
chamber is increased, requiring a lower initial fill pressure to match the PSW
strength at the projectile.

  4. 4.

The maximum pressure of the driver gas in the chamber of a chambered launcher
is not uniform due to shock focusing effects. The stagnated gas near the back
of the chamber is at lower pressure than the gas near the projectile.

  5. 5.

Increasing the chambrage ratio drastically increases the cost and explosive
mass requirement of the IDL.

Taking these factors into consideration, the ideal driver design will have a
small normalized length in order to prevent PSW decay, but a sufficiently
large physical length to provide an effectively infinite G/M. For the
$8\text{\text{-}}\mathrm{mm}$ launcher, this is achieved by using a driver
length (Ldt/IDdt) of 28 diameters, with a sufficiently large chambrage ratio
(IDdt/IDlt=2.1) to reach a driver length that approaches the infinite G/M
criteria. For this geometry, an initial helium fill pressure of
$4\text{\,}\mathrm{MPa}$ is required to generate a reflected shock pressure of
$5\text{\,}\mathrm{GPa}$, which is well within the pressure limit of the
driver. A further increase in the chambrage ratio is not expected to result in
a significant increase in launcher performance. This is mainly because an
increase in the chambrage ratio must be accompanied by a decrease in the
initial helium fill pressure of the driver to maintain a constant shock
loading on the projectile. This compensatory reduction in helium fill pressure
not only provides diminishing returns for increasing G/M, but can also cause a
reduction in projectile driving pressure later in the launch cycle. The
maximum pressure in the IDL chamber, obtained as the flow is stagnated by the
reflected shock wave, is not spatially uniform for a chambered launcher: the
maximum pressure decreases with increasing diameter due to shock focusing. If
the maximum pressure at the projectile is held constant for projectile
integrity reasons, then the average pressure in the chamber decreases as the
chambrage ratio is increased. This results in a trade-off where launchers with
large chambrage ratios eventually see a faster decay in the projectile driving
pressure because of the lower overall chamber pressure. The design trade-offs
involved in determining the driver geometry are illustrated in a parameter map
shown in Figure 12.

Figure 12: Parameter map showing the effect of varying the length and diameter
of the explosive driver.

The effect of increasing the chambrage ratio discussed above is illustrated in
Figure 13, which shows the projectile driving pressure as a function of
velocity for a series of ideal 1-D simulations, where ablation, reservoir
expansion, and non-ideal driver-tube effects have been neglected. The
simulations are based on the geometry of the $8\text{\text{-}}\mathrm{mm}$
launcher presented above, with the driver and chamber length scaled by the
chambrage ratio. Launchers with higher chambrage ratios maintain a larger
pressure initially, mainly due to interactions between the reflected shock
wave and density gradients in the flow. The effect of not having sufficient
G/M is clearly illustrated by the constant diameter launcher (chambrage
ratio=1), where a steep decrease in the projectile driving pressure is seen
beyond $4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ due to the
arrival of the expansion front originating from the stopped driver piston. The
effect of reduced chamber pressures at high values of chambrage is slightly
more subtle, but is illustrated by the fact that in the range of
$47\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$, the projectile
driving pressure decays much faster at the highest value of chambrage than in
less chambered launchers. It should be noted that the optimum driver
normalized length and chambrage chosen for the $8\text{\text{-}}\mathrm{mm}$
launcher are specific to the normalized mass
($\frac{\rho_{\mathrm{proj}}t_{\mathrm{proj}}}{ID_{\mathrm{lt}}}$) of the
projectile used in this study. It should be expected that an increase in
normalized mass, caused either by higher projectile material density
($\rho_{\mathrm{proj}}$) or thickness ($t_{\mathrm{proj}}$), would be
accompanied by an increase in optimum driver size.

Figure 13: Projectile driving pressure as a function of velocity for internal
ballistics simulations in which the chambrage ratio was varied. The length of
the driver was scaled with its diameter.

The area reduction section between the driver and launch tube is made gradual
($5\text{\,}\mathrm{\SIUnitSymbolDegree}$ straight taper) to minimize flow
disturbances behind the PSW. As was discussed in Section 4.1, a length of 2.8
launch-tube diameters was given between the end of the area change section and
the back of the projectile to allow the PSW to planarize before reaching the
projectile. Choosing this length was a compromise between ensuring uniform
loading on the projectile and maximizing projectile velocity by ensuring a
short communication time between the projectile and the area change section.
The effect of the internal chamber geometry has not been studied
computationally, which would require a two-dimensional solver, or
experimentally, and it may be possible that it could be optimized to maintain
a satisfactorily uniform loading on the projectile while increasing the
driving pressure through the interaction of the reflected shock wave with
density gradients in the flow. The authors of the present study largely
adopted the convergence angles and planarization lengths established by PI
Watson1970_1 (35).

###  4.4 Reservoir and Launch Tube

The reservoir is a thick-walled steel vessel which transitions between the
driver and the launch tube and is designed to contain the high-pressure driver
gas during projectile acceleration. The driver tube is welded to the
reservoir, while the launch tube is threaded in to allow the projectile to be
inserted and the sealing o-ring to be compressed. The length of the chamber
($L_{\mathrm{cbr}}$), which corresponds to the distance between the end of the
driver and the initial position of the projectile, is chosen such that the
explosively driven piston and the reflected shock wave reach the start of the
chamber, or equivalently the end of the driver, at approximately the same
time. This timing criteria, which is illustrated schematically on the third
image of Figure 2, is dictated by the ratio of the chamber length to the
driver length (Lcbr/Ldt), which was set to 0.22 for the
$8\text{\text{-}}\mathrm{mm}$ launcher. If the chamber is made longer, the
driver compression will end prematurely, forming an expansion front that will
decrease the chamber pressure. Conversely, if the chamber is made shorter, the
reflected shock will enter the driver tube, which can disrupt the explosively
driven piston and again cause a strong expansion front to originate from the
back of the chamber due to the loss of driver gas. Although it may seem
possible to improve launcher performance by reducing the chamber length in an
attempt to further compress the driver gas, similar to increasing the
compression ratio in a two-stage light-gas gun, the pressures required to
drive the explosively driven piston into the stagnated flow behind the
reflected shock wave are much greater than explosive detonation pressures,
which makes such an approach seemingly non-viable. The back of the reservoir
contains a tapered conical section with an increased explosive mass thickness,
which implodes to form a plug that minimizes the loss of driver gas from the
back of the reservoir as the explosively driven piston reaches the end of the
driver. This “sealing cone” section (see Figure 2), which has a length of 2.2
internal driver diameters and a taper angle of
$18\text{\,}\mathrm{\SIUnitSymbolDegree}$, also provides a gradual transition
from the very thin driver tube to the thick-walled reservoir, which reduces
the likelihood of tube fracture and gas loss at the interface between the
driver tube and the reservoir as the tube expands due to the high-pressure gas
behind the PSW.

The driver gas pressures are sufficient to yield the reservoir, which must be
made sufficiently thick such that its inertia provides confinement and
prevents fracture within the timescale of projectile launch. A ratio of
reservoir outer diameter to projectile diameter of 11 has been used for the
$8\text{\text{-}}\mathrm{mm}$ launcher and is a reasonable design guideline.
The reservoir must also extend sufficiently far ahead of the projectile to
confine the launch tube until the driving pressure has decayed. The reservoir
of the $8\text{\text{-}}\mathrm{mm}$ launcher extends 10 launch-tube inner
diameters past the initial projectile position. A launch tube sleeve, which
slides onto the launch tube, is added to provide additional confinement while
minimizing the cost (material and machining time) of the reservoir. The sleeve
has a diameter of four projectile diameters and extends 25 projectile
diameters ahead of the initial projectile position.

Attempts have been made to mitigate reservoir expansion and even re-compress
the driver gas by surrounding the reservoir by a thick layer of explosives. To
meaningfully influence projectile maximum velocity, these explosives must be
detonated early in the launch cycle, typically even before the projectile
begins to accelerate. In doing so, a shock wave is driven into the steel
reservoir that can fracture the projectile. Although modest velocity gains
have been demonstrated using reservoir explosives Loiseau2013_2 (55), the
additional risk to projectile integrity and the significant increase in
explosive mass requirements (typically many times the explosive mass required
for the driver) has precluded the use of reservoir explosives with the
$8\text{\text{-}}\mathrm{mm}$ launcher. Nevertheless, PI demonstrated an
increase of $2\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ (from
$8\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ to
$10.2\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$) using reservoir
explosives Watson1970_1 (35). More recently Wang et al. have demonstrated a
$1\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ increase (from
$10.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ to
$11.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$) using the
launcher described in the present study as a baseline Wang2019 (60, 61, 62).

The launch tube is made from 4130 mechanical tubing having a length of 38
projectile diameters that has been honed smooth. The launch cycle of the IDL
is sufficiently dynamic that further increases in launch tube length do not
improve launcher performance and may actually decrease the exit velocity if
the launch tube has not been evacuated Huneault2015 (63). While evacuating the
launch tube is common practice for light-gas gun facilities, the use of
explosives in the IDL launch cycle can make it challenging to evacuate the
launch tube and target chamber, as most explosive testing facilities are
either outdoors, or in large indoor blast chambers that are difficult to
evacuate. Nonetheless, it is highly recommended that the launch tube and
target chamber be evacuated, either by evacuating the entire blast chamber or
fitting the launch tube to a one-time-use sealed target assembly which can be
evacuated. A compromise solution adopted through much of the development
program in this paper used a helium flush at 1 atm to remove residual air from
the launch tube and target chamber.

##  5 Discussion

The above sections presented a detailed overview of the launch cycle and
design considerations of an explosively driven light-gas launcher capable of
reaching velocities currently inaccessible to other gasdynamic launchers. Of
particular interest is the fact that the compact $8\text{\text{-}}\mathrm{mm}$
launcher presented in this study could readily be scaled-up to launch more
massive projectiles. It is well known that gasdynamic launchers should be
expected to reach nearly the same projectile velocity regardless of size, as
long as all proportions of the launcher are uniformly scaled (Cooper1996, 64,
p. 376). Using either simulations or geometric scaling, it is readily
demonstrated that the ideal launch cycle of the IDL scales perfectly, as long
as the normalized size of the driver, reservoir, launch tube, and projectile
are held constant Loiseau2013_1 (65, 52). The effect of launcher size on non-
ideal effects must also be considered. Simple analytical treatments and
simulations have been used to show that the effect of radial expansion of the
reservoir on the launch cycle is independent of scale HuneaultThesis (52).
While the timescale of projectile acceleration increases proportionally to the
diameter of the projectile, allowing more time for radial expansion to occur,
the relative rate of change in volume from radial expansion is inversely
proportional to launcher size. Similarly, driver non-ideal effects (PSW
formation distance, driver-tube expansion, and boundary layer growth, see
Section 2.1) are also expected to be unaffected by driver size, a fact that
was experimentally verified during an extensive experimental campaign
undertaken by the Physics International Company which compared the PSW
velocity and standoff of a $3.5\text{\text{-}}\mathrm{cm}$-diameter driver
with that of a $200\text{\text{-}}\mathrm{cm}$-driver Watson1970_1 (35, 36).
Losses that depend on surface area, such as gas friction, heat transfer, and
ablation become less significant as the launcher size is increased due to the
decrease in the surface-area-to-volume ratio. Of particular interest is
ablation which plays a significant role in the launch cycle of the IDL, as was
shown in Section 3. While ablation in the driver leads to an increase in
projectile driving pressure early in the launch cycle, ablation in the launch
tube increases the molecular weight of the driver gas and is likely an
important factor in limiting the velocity potential of the IDL.

The scaling considerations discussed above indicate that the projectile
velocity capability of the IDL is generally independent of launcher size, and
that larger launchers may be expected to outperform the
$8\text{\text{-}}\mathrm{mm}$ results presented above due to a reduction in
surface area losses. Tests with older generation designs of the IDL have been
performed on launchers ranging from $5\text{\,}\mathrm{mm}$
($0.1\text{\,}\mathrm{g}$ projectile mass) to $25\text{\,}\mathrm{mm}$
($15\text{\,}\mathrm{g}$ projectile mass), demonstrating velocities of
$9.5\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ and
$7.6\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ respectively
Loiseau2013_2 (55, 63). The variation in projectile velocity between these
launchers and the $8\text{\text{-}}\mathrm{mm}$ launcher presented in this
work can be attributed to evolutions in the design rather than effects of
scale. The authors are confident that the $8\text{\text{-}}\mathrm{mm}$
design, capable of achieving
$10.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ projectile
velocity as presented in Section 4, could be successfully scaled to launch
projectiles of $25\text{\,}\mathrm{mm}$ or even larger to the same velocity.
Unfortunately, lack of access to outdoor ranges necessitated by the mass of
explosive required when scaling-up has precluded our testing of large-caliber
launchers since 2011 (when the
$7.6\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ was demonstrated
with an earlier, non-optimized design). The $8\text{\text{-}}\mathrm{mm}$ IDL
design can be used as a baseline to estimate the requirements of large-scale
launchers. Table 5 presents an overview of expected explosive mass and
launcher size for different projectile sizes, as well as an indication of the
facility required to operate the launcher.

Table 5: Predicted launcher size and explosive mass requirements for larger scale implosion-driven launchers obtained by scaling the 8-mm design. Projectile | Projectile | Explosive | Launcher | Launcher |  Facility Requirements
---|---|---|---|---|---
Diameter | Mass | Mass | Mass | Length
(mm) | (g) | (kg) | (kg) | (m)
8 | 0.36 | 0.24 | 18 | 0.84 | small indoor facility
12 | 1.2 | 0.82 | 62 | 1.3 | large indoor facility
16 | 2.9 | 1.90 | 150 | 1.7 | small outdoor test site
25 | 11.0 | 7.40 | 560 | 2.6 | large outdoor range
50 | 90.0 | 59.00 | 4500 | 5.3 | large outdoor range

The numerous design parameters and the significant cost and preparation time
in developing new launchers has made it difficult to conduct parametric
studies of the IDL to experimentally determine the effect of design changes on
the projectile exit velocity. Additionally, conclusions drawn from parametric
studies performed in one area of the parameter space do not necessarily apply
when changes are made to key parameters such as the normalized projectile
mass. Although the development of the IDL may appear to lend itself to
hydrocode simulation, numerous challenges exist that complicate the modelling
of the launch cycle. Some examples include: the converging geometry of the
explosively driven piston leads to singularities in two-dimensional
axisymmetric simulations, modelling ablation and the resulting two-phase flow,
modelling of boundary layer growth and gas loss in the driver, modelling of
projectile fracture, etc. For these reasons, the development approach taken in
this work has been to focus on launcher experiments guided by a simple one-
dimensional internal ballistics model to which physical models for non-ideal
effects were added. The design presented in Section 4 is the result of
numerous design iterations, and while the entire design parameter space has
not been explored experimentally, it seems unlikely that significant velocity
increments could be made by varying the design of the driver or the launcher
geometry.

Significant improvements in the projectile velocity of the IDL may be possible
by changing the way in which the explosive driver operates. In the
$8\text{\text{-}}\mathrm{mm}$ launcher design presented above, the driver is
operated at a helium fill pressure that is approximately three times lower
than the experimentally determined limit due to projectile integrity concerns.
This indicates that there is unused potential in the driver that may be
harnessed if the launch cycle can be designed to provide additional
compression to the propellant without increasing the loading on the
projectile.

The launch cycle presented in this work provides no additional compression to
the driver gas once the projectile has been set in motion, which results in a
rapid monotonic pressure decay and a relatively inefficient launch cycle.
However, it is possible to maintain a high driving pressure on the projectile
in a gasdynamic launcher by continuously increasing propellant compression
after the projectile has begun to accelerate, as is accomplished with the
accelerated reservoir technique of conventional two-stage light-gas guns
Charters1987 (66). Simulations have been used to demonstrate that when the
explosively driven piston is accelerated near the end of the driver of the
IDL, compression waves travel into the chamber and increase the pressure such
that a nearly constant driving pressure can be maintained on the projectile
Huneault2014 (67). Accelerating the explosively driven piston, which can be
accomplished using phase velocity methods such as a wave shaper or an
explosive lens LoiseauThesis (68, 69, 70, 67), poses a significant challenge
as any loss of driver gas will offset the benefit of the increased piston
velocity. Another possibility is to design the driver such that there is an
initial density discontinuity in gas, either by varying the pressure or
molecular weight of the propellant HildebrandThesis (51). The gas near the
projectile is initially held at a lower density, while the gas at the back of
the driver is at a higher density that will result in the driver operating
close to its pressure limit. The density discontinuity forms a high impedance
contact surface that travels into the chamber. When reflected shock waves
originating from the area change section and the projectile reach the contact
surface, they are partially reflected as shock waves that travel towards the
projectile, further compressing the gas. With this approach, the driver can be
designed such that the initial projectile shock-loading is the same or even
lower than with the standard launcher, but ramps up due to the aforementioned
shock interactions. The velocity benefits that result from the higher density
gas at the back of the driver are based on the same effect that was seen in
Section 3.1, where ablation in the driver leads to higher than anticipated
projectile acceleration. Simulations indicate that successful implementation
of the density discontinuity launch cycle may allow for a significant (many
km/s) increase in projectile velocity. This technique is discussed in more
detail in Appendix 2.

##  6 Conclusion

This work has demonstrated that the implosion-driven launcher (IDL) has the
potential to address the need for hypervelocity testing beyond
$10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$. The extreme
projectile loading and strong sensitivity to projectile mass mean that the IDL
will likely never be a viable option for launching the types of elaborate
aeroballistic packages that can be used with two-stage light-gas guns.
However, tests requiring simpler projectiles, such as impact testing (orbital
debris, geophysics, asteroid deflection) or flyer plate-based equation of
state testing are well suited to the IDL. The projectile launched from the IDL
could also be combined with the density-gradient impactor technique
Chhabildas1995 (13) to in-turn drive thinner projectiles to even greater
velocities, or be used to effect quasi-isentropic compression to previously
inaccessible densities and pressures. Moreover, the use of precision-timed
explosives (low jitter) and the disposable nature of the launcher offer
interesting opportunities that would otherwise require massive capital
investments, such as using two counter-firing launchers to double the impact
velocity, or performing one-off tests of larger launchers. While the material
cost of the IDL is quite low, the cost of the explosive facility and technical
expertise needed to perform the testing is substantial. However, where these
facilities and expertise exist, the IDL offers a very accessible avenue to
performing hypervelocity impact testing. Given the velocity capability
demonstrated by the IDL over a short and limited development period, as well
as the apparent inevitability that any launcher routinely reaching velocities
well above $10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ will
be, at least in part, non-reusable, further development of the IDL may offer
the most promising avenue to reaching velocities well above
$10\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ with large
($110\text{\,}\mathrm{g}$), well characterized projectiles.

Acknowledgments The authors would like to thank Vincent Tanguay, Daniel
Szirti, Matthew Serge, and Patrick Bachelor for their help in conducting
experiments and useful input during the early development of the launcher.
This work was supported by the Canadian Space Agency (CSA) [Contracts No.
9F028-064201/A and 64/7012003]; Defense Research and Development Canada (DRDC)
[Contract No. W7701-82047]; the Fonds de Recherche du Quebec Nature et
Technologies (FRQNT) [Grant 2012-PR-148696]; and the Natural Sciences and
Engineering Research Council of Canada (NSERC) [Grant 2014-06258].

Data Availability Data included in this paper is available upon reasonable
request.

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##  Appendix 1 Hydrogen as a Driver Gas

The choice of propellant for the IDL is somewhat more nuanced than for two-
stage light-gas guns, where using hydrogen instead of helium provides a
significant advantage due to reduced launcher wear from ablation Charters1987
(66). The lower ablation rates that result from using hydrogen allow the
launcher to be operated at greater compression ratios, resulting in higher
launch cycle pressures and propellant sound speed. Although launcher wear is
not a concern for the IDL, the effect of driver gas choice on ablation rates
must still be considered due to the fact that mixing of the heavy ablated wall
material with the light gas can lead to significant reductions in the speed of
sound of the propellant and ultimately limit the velocity potential of the
launcher.

The rate of ablation in a hypervelocity launcher is determined by the rate of
convective heat transfer to the launcher walls from the hot driver gas flow.
Using Reynold’s analogy Bogdanoff1995 (71), it is possible to relate the rate
of convective heat transfer ($\dot{Q}$) to the frictional fluid shear force
($F_{\mathrm{r}}$) at the launcher walls, the flow velocity ($u$) and the
difference between the total flow enthalpy ($h+\frac{1}{2}u^{2}$) and the
static enthalpy at the wall ($h_{\mathrm{w}}$):

$\dot{Q}=\frac{F_{\mathrm{r}}}{u}\left(h+\frac{1}{2}u^{2}-h_{\mathrm{w}}\right)$
(2)

The fluid shear force can be expressed in terms of the wall surface area
($A_{\mathrm{w}}$), the density ($\rho$), the flow velocity ($u$), and the
skin friction coefficient ($C_{f}$):

$F_{\mathrm{r}}=\frac{1}{2}A_{\mathrm{w}}C_{f}\rho u^{2}$ (3)

The rate of heat transfer per unit mass ($\dot{q}$) of gas can then be
expressed as follows, where $D$ is the diameter of the channel:

$\dot{q}=\frac{2uC_{f}}{D}\left(h+\frac{1}{2}u^{2}-h_{\mathrm{w}}\right)$ (4)

As can be seen from Equation 4, for similar flow velocities (i.e., comparable
projectile velocities) the key fluid parameter that determines the rate of
heat transfer is the difference between the static flow enthalpy ($h$) and the
wall enthalpy ($h_{\mathrm{w}}$). In a two-stage light-gas gun, the lower
specific-heat ratio of hydrogen ($\gamma_{\mathrm{H_{2}}}=1.4$,
$\gamma_{\mathrm{He}}=1.667$) as well as dissociation of hydrogen molecules
make it possible to maintain maximum propellant temperatures below or near the
melting point of steel ($\approx$ $1720\text{\,}\mathrm{K}$), whereas
comparable helium launch cycles would generate propellant temperatures beyond
$6000\text{\,}\mathrm{K}$ Glenn1997 (15). The advantage of hydrogen as a two-
stage light-gas gun propellant can mainly be attributed to the fact that the
enthalpy of hydrogen at $1720\text{\,}\mathrm{K}$ is much greater than that of
helium at the same temperature.

For the IDL, maximum launch cycle temperatures, estimated from ideal launcher
simulations with the SESAME tabulated equation of state SESAME_1992 (72), in
both hydrogen ($6500\text{\,}\mathrm{K}$) and helium
($27\,800\text{\,}\mathrm{K}$) are significantly above the melting point of
steel HuneaultThesis (52). As a result, the wall enthalpy, which plays an
important role in determining the rate of heat transfer in the two-stage
light-gas gun has little effect at IDL propellant conditions because it is
negligible compared to the total enthalpy of the flow for both helium and
hydrogen. Table 6 gives a comparison of the difference between the wall
enthalpy and the enthalpy behind the reflected shock wave in a helium and
hydrogen IDL using the SESAME equation of state to capture real gas effects
SESAME_1992 (72). Despite having a much lower reflected shock temperature, the
static enthalpy difference for hydrogen is only 24% smaller than for helium.
The considerable contribution of flow velocity to the total flow enthalpy will
further reduce the proportional difference between ablation rates in helium
and hydrogen launchers. This simple analysis indicates that while ablation
rates are predicted to be larger with a helium propellant, the difference may
not be as significant as might be expected and might be sufficiently small
such that it is not the determining factor in the choice of propellant.

Table 6: Comparison of the difference between the reflected shock enthalpy and the wall enthalpy for helium and hydrogen launchers with matched reflected shock pressures. Driver Gas |  Reflected Shock Temperature |  Reflected Shock Enthalpy | Wall Enthalpy | Enthalpy Difference
---|---|---|---|---
(K) | ($\text{\,}\mathrm{MJ}\text{${}\cdot{}$}{\mathrm{kg}}^{-1}$) | ($\text{\,}\mathrm{MJ}\text{${}\cdot{}$}{\mathrm{kg}}^{-1}$) | ($\text{\,}\mathrm{MJ}\text{${}\cdot{}$}{\mathrm{kg}}^{-1}$)
He, $4.0\text{\,}\mathrm{MPa}$ | 27800 | 179 | 9.3 | 170
H2, $5.7\text{\,}\mathrm{MPa}$ | 6500 | 158 | 28.6 | 129
Table 7: Summary of experiments performed to determine the effect of the driver gas on the performance of the implosion-driven launcher. Driver Gas |  Driver Length (Ldt/IDdt) |  Chambrage Ratio (IDdt/IDlt) |  Area Change Taper |  Launch Tube Inner Diameter | Projectile | Velocity
---|---|---|---|---|---|---
He, $3.5\text{\,}\mathrm{MPa}$ | 28 | 2.3 | $4.5\text{\,}\mathrm{\SIUnitSymbolDegree}$ | $8.5\text{\,}\mathrm{mm}$ | Al7075, $0.68\text{\,}\mathrm{g}$ | $6.8\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$
H2, $5.4\text{\,}\mathrm{MPa}$ | 28 | 2.3 | $6.5\text{\,}\mathrm{\SIUnitSymbolDegree}$ | $8.5\text{\,}\mathrm{mm}$ | Al7075, $0.68\text{\,}\mathrm{g}$ | $5.7\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$

Consideration must be given to the effect of hydrogen on the launch cycle of
the IDL. Ideal IDL simulations show that for a properly sized driver and
matching reflected shock pressures, helium and hydrogen launchers should be
expected to reach similar velocities. This is shown in Figure 14, where the
projectile driving pressure as a function of velocity is plotted for identical
helium and hydrogen launchers. The $8\text{\text{-}}\mathrm{mm}$ launcher
design was used for the simulations, while the driver fill pressure was
adjusted to obtain matching reflected shock pressures. The ideal simulations
(impermeable piston, rigid launcher walls, no ablation) used the SESAME
equation of state SESAME_1992 (72) for both helium and hydrogen.

Figure 14: Projectile driving pressure as a function of velocity for internal
ballistics simulations in which the $8\text{\text{-}}\mathrm{mm}$ helium-
driven launcher is compared to hydrogen-driven launchers with different driver
and chamber geometries.

The most significant difference between hydrogen and helium in the IDL launch
cycle is the effect of the specific-heat ratio on the shock-wave dynamics (see
Equation 1). The use of hydrogen, which has a lower specific-heat ratio and
lower molecular weight, results in a reduced precursor shock-wave velocity
(PSW) and pressure increase across the shock. As a result, a hydrogen launcher
requires a higher initial driver fill pressure to reach the same reflected
shock pressure as a helium launcher. Ideal simulations also indicate that in
order to meet the effectively infinite G/M criteria discussed in Section 4.3,
a hydrogen launcher requires a larger driver. This can be seen in Figure 14,
where the inflection point from the stopped piston arrives significantly
earlier for the hydrogen launcher
($6.2\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$) than with
helium ($7.8\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$). Also
shown in Figure 14 is the driving pressure as a function of velocity for a
hydrogen launcher with a larger driver: chambrage ratio (IDdt/IDlt) of 3,
normalized driver length (Ldt/IDdt) of 28. The significant improvement in
projectile driving pressure as a function of velocity that results from the
increase in driver size indicates that the hydrogen IDL requires a larger
driver than a comparable helium launcher in order to maximize projectile
velocity.

The lower PSW velocity in the hydrogen propellant also affects the choice of
chamber length, because the shock timing criteria discussed in Section 4.4
(the chamber length is chosen such that the explosively driven piston reaches
the transition section between the driver and the chamber at the same time as
the reflected shock wave) would require a chamber length that is less than
half the length of a comparable helium chamber. However, the increase in the
area change angle that would result from shortening the chamber may have a
significant effect on the PSW as it travels through the area change section,
influencing density gradients in the flow and the uniformity of projectile
loading. The effect of shortening the chamber is shown in Figure 14, where the
“$8\text{\,}\mathrm{\SIUnitSymbolDegree}$ taper” curve corresponds to a
simulation where the taper angle was increased from
$5\text{\,}\mathrm{\SIUnitSymbolDegree}$ to
$8\text{\,}\mathrm{\SIUnitSymbolDegree}$ to meet the shock timing criteria. As
can be seen, shortening the chamber does not appear to be beneficial, and
projectile driving pressure is improved by keeping a longer area change
section which does not meet the shock timing criteria, but maintains a very
gradual taper. This effect would need to be further studied either
experimentally or with two-dimensional simulations in order to properly
capture the shock interactions in the area change section.

The results of two early launcher experiments which were performed to compare
the performance of helium and hydrogen in the IDL are presented in Table 7.
The two launchers had the same driver geometry, as well as an identical
projectile and launch tube. The chamber of the hydrogen launcher was made
shorter to meet the shock timing criteria discussed above. As a result, the
area change taper angle was of $4.5\text{\,}\mathrm{\SIUnitSymbolDegree}$ for
the helium launcher and $6.5\text{\,}\mathrm{\SIUnitSymbolDegree}$ for the
hydrogen launcher. The driver fill pressure was chosen such that both
launchers would have a similar reflected shock pressure. As can be seen, the
projectile velocity from the hydrogen launcher was
$1.2\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ (17%) slower than
for the helium launcher. The projectile velocities are much lower than those
of current launcher designs, mainly from changes in the projectile material
and design, as well as reducing the launch tube length and evacuating the
launch tube and projectile flight path. Although it is certainly possible that
the hydrogen launcher’s velocity deficit may be overcome by changes in design,
notably by increasing the chambrage and the chamber taper angle, it seems
unlikely that a hydrogen launcher would significantly surpass velocities
obtained with helium propellant. The authors acknowledge that it may be of
interest to re-visit the comparison given the recent improvements in launcher
design and understanding of the launch cycle.

##  Appendix 2 Advanced Launch Cycle Concepts

A significant increase in the maximum projectile velocity of the IDL may be
possible with modifications to the launch cycle such that additional
compression is provided to the driver gas during projectile acceleration. This
was recognized in the initial development of the IDL by Physics International,
where a technique was proposed in which a second explosively driven piston
would collapse the launch tube behind the projectile Moore1968 (34, 35). The
explosively driven pinch would be accelerated using explosive lensing
techniques such that it kept a constant standoff with the projectile, thus
preventing the driver gas from expanding. Correctly setting the timing and
rate of the launch tube implosion as to obtain a meaningful velocity increase
without damaging the projectile is a significant challenge Moore1968 (34, 35).
Moreover, very large pressures are required to reach the implosion velocities
needed to prevent the driver gas from leaking past the explosive pinch due to
the high driver gas pressures in the launch tube and the development of a
boundary layer behind the projectile Baum1973_1 (37, 38). Although it is
possible to achieve such implosion velocities via the impact of explosively
driven flyers, the cumulative jet that results from the implosion may threaten
to damage the projectile Baum1973_1 (37, 38).

A more practical approach may be to modify the design of the driver such that
the launch cycle maintains a high driving pressure on the projectile. As will
be shown, this can be accomplished by having a discontinuity in the initial
density of the driver gas, meaning that either the molecular weight or
pressure of the gas at the start of the driver is larger than the gas near the
projectile. The initial propellant density at the start of the driver can be
set such that the driver operates near its limiting pressure, which
corresponds to a post-shock pressure of approximately
$1.2\text{\,}\mathrm{GPa}$, while the gas near the projectile is at a much
lower density in order to maintain a reflected shock pressure that is near
that of the standard launcher. The initial contact surface (density
discontinuity) travels with the flow and acts much like a piston: shock waves
formed by the reflection of the PSW from the area change section and the
projectile are partially reflected by the high impedance contact surface
towards the projectile, which re-compresses the expanding flow. The operation
of the density discontinuity launch cycle is depicted in the schlieren
position–time plot of Figure 15, which was produced using an ideal IDL
simulation in which there was a pressure discontinuity in the driver. The
density gradients in the flow show the shock reflections responsible for
maintaining a high driving pressure on the projectile.

Figure 15: Labelled schlieren position–time plot showing the internal gas flow
for a launcher with a pressure discontinuity in the driver. The density
gradients show the shock-wave reflections responsible for maintaining a high
driving pressure on the projectile.

The potential benefit of the density discontinuity technique is best
illustrated by observing the evolution in the projectile driving pressure as a
function of velocity using simulations. Figure 16 shows the predicted
evolution in driving pressure for two variations of the density discontinuity
technique along with that of the standard $8\text{\text{-}}\mathrm{mm}$
launcher. All three simulations were performed with the ideal solver
(impermeable piston, rigid launcher walls, no ablation) and the geometry of
the $8\text{\text{-}}\mathrm{mm}$ launcher presented in this work. The “two-
pressure launcher” simulation had helium at a pressure of
$8.8\text{\,}\mathrm{MPa}$ at the start of the driver and
$0.5\text{\,}\mathrm{MPa}$ on the projectile side, with the initial
discontinuity located at 24 inner diameters ($39\text{\,}\mathrm{cm}$) from
the start of the driver. The “molecular weight discontinuity” simulation had a
helium-argon mixture of 60% by volume helium (mixture molecular weight of
$18.4\text{\,}\mathrm{kmol}\text{${}\cdot{}$}{\mathrm{kg}}^{-1}$) at the start
of the driver and pure helium near the projectile, both at a pressure of
$2.1\text{\,}\mathrm{MPa}$ and with the discontinuity located at 22 inner
diameters ($36\text{\,}\mathrm{cm}$) from the start of the driver. The initial
conditions in both cases ensured that the pressure in the driver never
exceeded $1.1\text{\,}\mathrm{GPa}$, which is below its established limit of
operation. The traces of Figure 16 clearly demonstrate that the interactions
between the contact surface and shock waves in the flow maintain a high
driving pressure on the projectile. This results in a much more efficient
launch cycle where the average driving pressure on the projectile is
significantly increased without increasing the initial shock loading. In
particular, a driver with a pressure discontinuity can be tailored to give a
much lower reflected shock pressure ($1.8\text{\,}\mathrm{GPa}$ in this
simulation), while allowing the pressure to ramp up beyond
$5\text{\,}\mathrm{GPa}$ in order to reach the velocities of interest. The
reduction in the strength of the shock wave transmitted into the projectile is
expected to significantly reduce the likelihood of projectile damage. As can
be seen in Figure 16, both density discontinuity techniques may allow for a
projectile velocity increase of several km/s using the standard
$8\text{\text{-}}\mathrm{mm}$ IDL geometry simply by modifying the initial
conditions in the driver.

Figure 16: Projectile driving pressure as a function of velocity for internal
ballistics simulations comparing the standard $8\text{\text{-}}\mathrm{mm}$
design presented in this work to two variations of the density discontinuity
launcher technique. Figure 17: Schematic of the design of the two-pressure
launcher used in the experiments presented in Figure 18. Figure 18: Results of
down-bore velocimetry experiments performed on the
$8\text{\text{-}}\mathrm{mm}$ implosion-driven launcher. The performance of
the standard $8\text{\text{-}}\mathrm{mm}$ launcher is compared to that of a
two-pressure launcher.

Although the density discontinuity launch cycle should be relatively easy to
implement, creating the initial conditions in the driver presents a challenge.
In the case of a pressure discontinuity, a diaphragm must be used to hold the
initial pressure differential (approximately $8\text{\,}\mathrm{MPa}$). The
pressures and flow velocities behind the PSW are sufficiently large that the
diaphragm will shear off upon impact of the PSW, much like a very thin
projectile. The finite time needed to accelerate the diaphragm will disrupt
the flow and cause the PSW to partially reflect, which will generate large
pressures that could cause significant loss of driver gas, failure of the
detonation front, or pre-detonation of the explosive. Moreover, creating a
mechanical assembly that holds the diaphragm in place and seals the driver gas
while not disrupting the implosion of the driver tube is troublesome.

The advantage of varying the molecular weight of the gas is that the density
discontinuity can be established without a pressure gradient so that a very
thin diaphragm could be used or be removed altogether. For example, by
extending the driver tube well beyond the start of the explosives, it would be
possible to arrange an auxiliary shock tube where the initial conditions are
such that the desired gas distribution (pressure and contact surface location)
is achieved once the wave dynamics have decayed and the gasses are stationary.
The shock tube diaphragm would be located before the start of the explosives,
such that it does not disturb the operation of the driver. Although there
would certainly be some smearing of the contact surface during the shock tube
flow, the main features of the launch cycle described above would still be
present. More importantly, without the diaphragm the driver would operate
exactly as it would in a standard launcher, eliminating any possibility of
driver gas loss or disruption of the explosively driven piston.

Preliminary experiments were performed to attempt the pressure discontinuity
technique on launchers with the same geometry and projectile design as the
$8\text{\text{-}}\mathrm{mm}$ IDL presented in Section 4. The two-pressure
launcher and standard launcher were compared with down bore velocimetry
experiments and high-speed photography experiments that measured the exit
velocity and condition of the projectile. A schematic of the two-pressure
launcher can be seen in Figure 17. The driver was filled with helium at
$9.0\text{\,}\mathrm{MPa}$ in the high-pressure section and
$1.0\text{\,}\mathrm{MPa}$ near the projectile. A
$0.25\text{\text{-}}\mathrm{mm}$-thick 7075 aluminum diaphragm separated the
two sections and was coupled to the driver with threads that were sealed with
epoxy. The diaphragm was located $39\text{\,}\mathrm{cm}$ (24 inner diameters)
from the start of the driver. The thickness of the explosive layer near the
diaphragm was increased from $5.6\text{\,}\mathrm{mm}$ to
$10.8\text{\,}\mathrm{mm}$ in order to accommodate the expected increase in
driver-tube expansion and prevent failure of the detonation front. All other
launcher parameters were identical to the $8\text{\text{-}}\mathrm{mm}$
launcher presented in Section 4. The parameters for the standard launcher were
the same as those presented in Table 2.

The results of down-bore velocimetry experiments comparing the early
projectile acceleration history of the two-pressure launcher with that of the
standard $8\text{\text{-}}\mathrm{mm}$ IDL is presented in the velocity–time
plot of Figure 18. The experimental arrangement for the PDV down bore
experiments was nearly identical to that of Section 3, with the only notable
difference being that the PDV probe holder was sealed in order to draw vacuum
on the launch tube. As can be seen in Figure 18, the strength of the shock
wave initially transmitted into the projectile for the pressure gradient
launch cycle was significantly less than for the standard launcher. As
expected, the projectile base pressure for the pressure gradient launcher
gradually increased to the point where acceleration exceeded that of the
standard launcher. Unfortunately, the PDV signal was lost early in the launch
cycle (at $5.5\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$), so it
is not possible to examine how the projectile acceleration was affected later
in the launch cycle. The muzzle velocity of the pressure gradient launcher was
measured to be $8.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ in
a follow-on experiment with high-speed videography, with the projectile being
in good condition. This velocity is significantly less than the results for
the standard $8\text{\text{-}}\mathrm{mm}$ launcher presented in Table 2
($10.4\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$ and
$10.2\text{\,}\mathrm{km}\text{${}\cdot{}$}{\mathrm{s}}^{-1}$) and suggests
that the presence of a diaphragm affected the launch cycle. Indeed,
preliminary internal ballistics simulations that included the mass of the
diaphragm (treated as a lumped mass) have shown that the diaphragm has a
significant effect on the internal ballistics and ultimately leads to lower
projectile exit velocities HildebrandThesis (51). This effect, combined with
the expected disruption of the driver due to the large transient pressures
near the diaphragm are the most likely cause of the unexpectedly low
projectile exit velocity.

Preliminary tests have clearly demonstrated the ability of the density
gradient launch cycle to apply a more gentle initial shock loading on the
projectile while allowing the pressure to progressively increase such that the
projectile acceleration matches or exceeds that of the standard launcher.
However, these tests have revealed the need for minimizing the mass of the
diaphragm or eliminating it entirely in order to achieve the full potential of
the density discontinuity launch cycle. Manipulating the molecular weight of
the gas rather than the initial pressure in order to establish a density
discontinuity in the driver would significantly reduce the thickness
requirement of the diaphragm or even eliminate the need for one altogether.
This approach is seen as the most promising strategy for achieving the
potential improvements in projectile velocity that the simulations using the
internal ballistics solver suggest are possible.