Lightcraft Impulse Measurements Under Vacuum

AFRL-PR-ED-TR-2002-0044 AFRL-PR-ED-TR-2002-0044
Lightcraft Impulse Measurements under

Vacuum
Wolfgang O. Schall
Hans-Albert Eckel
Sebastian Walther
DLR – German Aerospace Center

Institute of Technical Physics
Pfaffenwaldring 38 – 40
D-70569 Stuttgart
Germany
August 2003
Special Report
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1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To)
30-09-2002 Special 01 October 2001 – 30 September 2002
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
EOARD FA8655-02-M4017
Lightcraft Impulse Measurements under Vacuum 5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER

62203F
6. AUTHOR(S) 5d. PROJECT NUMBER
4847
Wolfgang O. Schall; Hans-Albert Eckel; Sebastian Walther 5e. TASK NUMBER
0159
5f. WORK UNIT NUMBER
549907
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT
NO.
Pfaffenwaldring 38 – 40 SPC 02-4017
D-70569 Stuttgart, Germany
9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S)
Air Force Research Laboratory (AFMC)

AFRL/PRSP 11. SPONSOR/MONITOR’S REPORT
10 E. Saturn Blvd. NUMBER(S)
Edwards AFB CA 93524-7680 AFRL-PR-ED-TR-2002-0044
12. DISTRIBUTION / AVAILABILITY STATEMENT
Approved for public release; distribution unlimited.
13. SUPPLEMENTARY NOTES
14. ABSTRACT
Under an EOARD contract, the DLR has conducted a series of comparative impulse measurements for two
different lightcraft configurations with the same nozzle exit diameter of 10 cm: The German design (GL) is of
the more conventional parabolical bell shape with a plasma breakdown region at the focal point of a parabola.
The second lightcraft was supplied by the Air Force Research Laboratory (AFRL), and was designated as model
200-¾. The experiments utilized the DLR multi-gas laser, running in CO2 with a laser wavelength of 10.6µm. It
was the goal of this investigation to extend previous atmospheric impulse measurements to a vacuum
environment and to measure specific propellant consumption of the solid propellant Delrin in order to determine
the exhaust velocity and the specific impulse for both lightcrafts as a function of the laser pulse energy at various
pressures.
15. SUBJECT TERMS

propulsion; lightcraft; impulse; parabola; laser; atmospheric impulse; vacuum; propellant; solid propellant; exhaust velocity;
specific impulse; laser pulse energy
16. SECURITY CLASSIFICATION OF: 17. LIMITATION 18. NUMBER 19a. NAME OF
OF ABSTRACT OF PAGES RESPONSIBLE PERSON
Franklin B. Mead III
a. REPORT b. ABSTRACT c. THIS PAGE 19b. TELEPHONE NO
A 65 (include area code)
Unclassified Unclassified Unclassified (661) 275-5929
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(Rev. 8-98)
Prescribed by ANSI Std.
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NOTICE
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other than a definitely related Government procurement operation, the fact that the Government
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other data, is not to be regarded by implication or otherwise, or in any way licensing the holder
or any other person or corporation, or conveying any rights or permission to manufacture, use or
sell any patented invention that may be related thereto.
FOREWORD
This special technical report, entitled “Lightcraft Impulse Measurements under Vacuum,”
presents the results of an in-house study performed under JON 48470159 by AFRL/PRSP,
Edwards AFB CA. The Principal Investigator/Project Manager for the Air Force Research
Laboratory was Dr. Frank Mead.
This report has been reviewed and is approved for release and distribution in accordance
with the distribution statement on the cover and on the SF Form 298.
This Page Intentionally Left Blank
SPC 02 – 4017
Lightcraft Impulse Measurements under Vacuum
EOARD contract No. FA8655-02-M4017
Report
September 2002
Project officer: Wolfgang O. Schall

Co-authors: Hans-Albert Eckel, Sebastian Walther

Pfaffenwaldring 38 – 40
D-70569 Stuttgart
Germany
1
The Contractor, German Aerospace Center (DLR), Institute of Technical Physics, hereby
declaress that, to the best of its knowledge and belief, the technical data delivered
herewith under Contract No. FA8655-02-MA4017 is complete, accurate, and complies
with all requirements of the contract.
Stuttgart, 30. September 2002
Prof. W.L. Bohn

Director
I certify that there were no subject inventions to declare as defined in FAR 52.227-13,
during the performance of this contact.
Stuttgart, 30. September 2002
Prof. W.L. Bohn

Director
2
Lightcraft Impulse Measurements under Vacuum
1. Introduction
2. Experimental Setup
2.1 Improvements in the experimental setup

2.2 Measurement program
3. Results
3.1 German Lightcraft without and with Delrin

3.1.1 Dependency on pressure with air alone
3.1.2 Dependency on pressure with Delrin added
3.1.3 Dependency on pulse energy in vacuum and atmospheric pressure
3.1.4 Dependency on the intensity at the Delrin surface
3.2 US Lightcraft
3.2.1 Dependency on the ambient pressure
3.2.2 Dependency on the pulse energy in vacuum
4. Discussion of the results
5. Conclusions
References
Appendix
3
List of figures
Fig. 1. German and US lightcraft

Fig. 2. Vacuum test stand
German Lightcraft:
Fig. 3. Impulse vs. pressure with air as propellant
Fig. 4. Coupling coefficient for air and different laser pulse energies vs. ambient
pressure
Fig. 5. Delrin pin inside GL
Fig. 6. Used pin
Fig. 7. Impulse and momentum coupling coefficient for 3 propellant combinations
vs. ambient pressure
Fig. 8. Three successive frames of a movie showing the combustion of Delrin with
the USL
Fig. 9. Mass loss for 3 laser pulses vs. ambient pressure of air or nitrogen
Fig. 10. Average exhaust velocity for air and nitrogen as propellants vs. pressure,
determined according to method 1
Fig. 11. Ratio of air to Delrin for the GL vs. pressure (evaluation method 1)
Fig. 12. Average exhaust velocity according to the second evaluation method
Fig. 13. Mass ratio of the exhaust gas and efficiency increase α due to the
combustion energy (evaluation according to method 2)
Fig. 14. Lightcraft impulse vs. laser pulse energy for 3 cases with and without Delrin
as additional propellant
Fig. 15. Momentum coupling coefficient vs. laser pulse energy for 3 cases with and
without Delrin as additional propellant
Fig. 16. Mass loss of Delrin for 3 laser pulses and specific propellant consumption vs.
pulse energy for 3 cases
Fig. 17 Mass ratio of air to Delrin vapor at atmospheric pressure
Fig. 18. Schematic of irradiation on pin side-on and front-on
Fig. 19. Impulse for different Delrin pin sizes and different irradiation vs. laser pulse
energy
Fig. 20. Mass loss for 3 pulses for different pin irradiations vs. laser pulse energy
Fig. 21. Impulse vs. mass loss
4
Fig. 22. Momentum coupling coefficient for different Delrin pins vs. laser pulse
energy
Fig. 23. Specific propellant consumption for different Delrin pins vs. laser pulse
energy
Fig. 24. Average exhaust velocity for different Delrin pins vs. laser pulse energy
Fig. 25. Jet efficiency for different Delrin pins in vacuum vs. laser pulse energy
US Lightcraft:
Fig. 26. Specific propellant consumption vs. ambient pressure
Fig. 27. Delrin rings
Fig. 28. Coupling coefficient vs. ambient pressure
Fig. 29. Average exhaust velocity vs. ambient pressure
Fig. 30. Mass ratio of exhausted gases vs. ambient pressure
Fig. 31. Lightcraft impulse in vacuum vs. laser pulse energy
Fig. 32. Coupling coefficient in vacuum vs. laser pulse energy
Fig. 33. Mass loss for 3 pulses in vacuum vs. laser pulse energy
Fig. 34. Specific propellant consumption in vacuum vs. laser pulse energy
Fig. 35. Average exhaust velocity in vacuum vs. laser pulse energy
Fig. 36. Jet efficiency in vacuum vs. laser pulse energy
Fig. 37. Momentum coupling coefficient vs. flight altitude (GL)
Fig. 38. Example calculation for the flight velocity vs. altitude where the drag force
assumes the same or the double value of the weight.
5
1. INTRODUCTION
Under its EOARD contract No. F61775-00-WE033 (2001)1 DLR has conducted a series of
comparative impulse measurements for two different lightcraft configurations with the
same nozzle exit diameter of 10 cm: The German design (GL) is of the more
conventional parabolical bell shape with a plasma breakdown region at the focal point
of the parabola. The second lightcraft had been supplied by the Air Force Research
2
Laboratory (USAFRL), Whitesands, NM and was designated as model 200-3/4 . This US
lightcraft (USL) has a configuration similar to a plug nozzle with a ring shaped plasma
formation zone at the circumference of the mirror/nozzle structure. A central parabolic
spike reflects the incoming light radially outward and concentrates it on a ring of solid
propellant. Fig. 1 shows the two lightcrafts together with a sketch of the respective
light paths.
The thrust chamber of the
German lightcraft is made of
aluminum and is polished on
the inside of the parabola. The
height of the parabola is 62.5
mm and the focal distance from
the vertex is 10 mm. A 2 mm
thick metal pin extends about
20 mm from the vertex along
Fig. 1a - German lightcraft
the axis of the parabola through
the focal point and serves as
ignition pin to ensure the
breakdown at the focal point
for all laser pulse energies.
Two figures of merit

characterize the performance
and efficiency of pulsed laser
Fig. 1b - US lightcraft
propulsion: The impulse
coupling coefficient, cm, is the ratio of the mechanical impulse imparted on the lightcraft
and the laser pulse energy. It is a measure for the velocity increase per pulse and
6
together with the pulse repetition frequency determines the thrust. The specific
propellant consumption, µ, is the mass exhausting from the lightcraft divided by the
laser pulse energy. For a solid propellant it can be easily measured by weighing the
propellant before and after a certain number of laser pulses. The ratio of the two
numbers yields the average nozzle exhaust velocity ve = cm / µ. Expressed as the so-called
specific impulse Isp = ve / g0 ( g0 = 9.81 m/s2 is the Earth’s gravity) the fundamental
performance parameters in rocketry are determined. For instance for a non-staged flight
to LEO a specific impulse of greater than 600 s is necessary. In addition, with known
exhaust velocity and mass loss the kinetic energy of the exhausted jet can be calculated
and the jet efficiency (ratio of the kinetic jet energy to the laser pulse energy)
-6 -6
determined. All variables are given in SI units: cm (N/MW = 10 N/W = 10 Ns/J);
µ (µg/J = 10-9 g/J); Isp (s).
In the previous study the impulse measurements have been performed with two
different penduli in order to synchronize the results with each other. The first pendulum
was used in all German measurements and corresponds to a nearly mathematical
pendulum. The second pendulum was supplied by the USAFRL and was of the rigid
type. All the measurements were carried out in air at atmospheric pressure. The GL used
laboratory air as the only propellant. In contrast, most of the measurements with the
USL used Delrin as propellant in addition to the surrounding air. Only the utilisation of
this solid propellant guarantied reproducible impulses with equal or better performance
than the GL. There is a possibility that air and Delrin vapor react chemically and release
additional energy. For a better comparison of the performance data of the two
lightcrafts it is necessary to confirm these results with GL operating with Delrin as well.
An attempt should be made to separate out a possible contribution of a chemical
reaction.
The experiments utilized the DLR multi-gas laser, running in CO2 with a laser wavelength
of 10.6 µm. The typical pulse length was 10 to 12 µs. The laser can be operated with
either a stable resonator, delivering a flat near field intensity distribution, or with an
unstable resonator having a rectangular ring structure in the near field. Because of a
better utilization of the gain medium in the laser higher laser pulse energies could be
obtained with the unstable configuration. However, the experiments showed that these
higher energies do not necessarily increase the imparted impulse on the lightcraft. As a
7
function of the laser pulse energy at least for the GL maximum impulse coupling
coefficients have been found for a laser beam of the stable resonator configuration. For
the USL the pulse energies with the stable resonator remained too low to reach the
point of roll-over. This point was found at lower pulse energies with the unstable
resonator beam. From this point on no further increase in delivered impulse was found.
The experiments of the first study were valuable with respect to the comparison of
different operational and measurement conditions. In the practical application of laser
propulsion they can only describe the propulsion properties in dense air. For flights to
higher altitudes and into low Earth orbits (LEO) most of the propulsive process will occur
outside of the atmosphere under low ambient pressure or even vacuum conditions that
make the utilization of on-board carried propellant indispensable. As the flight altitude
increases the atmospheric pressure decreases and the air density decreases
exponentially. It is therefore essential for any projection of laser propulsion performance
to measure the momentum coupling coefficient as a function of the surrounding air
pressure. The utilization of a solid propellant at various pressures also allows the
separation of the contributions of the two simultaneously propelled matters, air and the
vapor of the solid propellant. While the cessation of air supported thrust at reduced
pressures may lead to a reduction of the impulse coupling coefficient, for the increased
expansion of the additional propellant into vacuum an increase of cm can be expected.
For this reason, it is impossible to predict or extend the present results to the low
pressure and vacuum regime.
It was the goal of this investigation to extend the impulse measurements to a vacuum
environment and, by measuring also the specific propellant consumption of the solid
propellant Delrin, to determine the exhaust velocity and the specific impulse for both
lightcrafts as a function of the laser pulse energy at various pressures.
8
2. EXPERIMENTAL SETUP
2.1 Improvements of the experimental setup
Suspension strings
Swing stop
Laser beam
German lightcraft
Fig. 2a - Side view of open vacuum test stand
Basically the same experimental arrangement with the vacuum vessel has been used as
in the previous study. For all measurements the German pendulum type was employed,
however in a slightly modified version to ease the mounting of the two lightcrafts and
the repositioning after each laser pulse without opening the vacuum vessel. As Fig. 2
shows, the lightcraft was attached to a short profiled aluminum beam. This beam was
fixed at the end of four strings of thin wire in a V-type arrangement. The arrangement
prevented a turning motion of the lightcraft. At its rest point the beam just touched a
motion stopper of soft foam rubber. This acted as strong damper of the lightcraft
oscillations after each laser pulse and brought the lightcraft to a reproducible rest after
only a few swings. The motion was recorded by a diode laser-based distance meter with
an accuracy of the order of 1/10 of a millimeter. The impulse was calculated from the
maximum displacement after the laser pulse. The length of the pendulum for the
German lightcraft was 645 mm.
9
The laser pulse energy was also measured online by the following new method. A small
hole (2 mm diameter) in the center of the metallic resonator back mirror allowed the
outcoupling of a small fraction of the total laser energy. This fraction was directly
measured with an energy meter. The calibration was done by comparing the signal of
Vacuum vessel
German lightcraft Pendulum

rig
Fig. 2b - Front view of open vacuum test stand
the energy meter with the more direct measurement of the full laser beam as described
in the previous report. Because of a possible power dependence of this method due to
mode jumps in the resonator as the power input is increased, the calibration has been
performed over the whole energy range of measurements. This procedure resulted in a
linear calibration function that was entered into the computer for immediate
determination of the real pulse energy. The deviation of the linear function from the
actual power dependency was on the order of 1% and thus absolutely sufficient with
respect to the experimental accuracy.
3
The vacuum vessel was connected to a pump of 65 m /h pumping speed. The pressure
in the vessel was measured with two mechanical Wallace&Tiernan vacuum manometers,
one with a pressure range of one bar for moderately reduced pressures and a second
one in the range from 0 to 130 mbar, which allowed the adjustment of the pressure to
10
below 1 mbar. In all vacuum measurements the test was carried out, when the
pressured gauge showed 1 mbar or less.
2.2 Measurement program
Of primary interest was the reduction of the impulse and the coupling coefficient, as the
air pressure was reduced. This has been measured for the GL for various fixed laser pulse
energies. In a further attempt the GL was equipped with the same solid propellant
Delrin, as the USL has been operated with all the time. A cylindrical pin of Delrin was
placed in the focal region of the lightcraft. This enabled a direct performance
comparison between the two lightcraft configurations. These measurements have also
been carried out at various pressure levels from 10-3 to 1 bar at a constant energy level.
The suspicion of a chemical reaction between Delrin vapor and the surrounding air
made it necessary to supplement the measurements in air by similar tests with nitrogen
at various pressure levels. In all experiments with Delrin the amount of evaporated Delrin
has been determined by weighing the propellant probes before and after 3 pulses of
equal voltage setting of the main discharge of the laser. The voltage setting defined the
pulse energy within narrow margins. Finally, the pulse energy has been varied, while
keeping the pressure constant at < 1 mbar and at atmospheric pressure. During the
measurements it had been noted that the intensity of the laser light on the surface of
the Delrin influences amount of evaporated Delrin. Therefore, additional measurements
have been made using a propellant pin of different size and also by changing the
direction of irradiation on the pin.
As far as they are relevant to the USL, the foregoing experiments have been repeated
with the USL; that is the influence of pressure on the performance at constant pulse
energy and varying the pulse energy at vacuum condition. Again, for every parameter
setting a new Delrin ring was used and weighed after every three pulses to determine
the mass loss. Under vacuum condition, when no air can participate at the thrust
process, it is possible to calculate from the measured numbers the exhaust velocity and
the jet efficiency. Based on certain model assumptions an estimate of the air fraction in
the exhaust gas, the velocity and the jet efficiency can be gained for other pressures,
too.
11
3. RESULTS
3.1 German Lighcraft without and with Delrin
3.1.1 Dependency on pressure with air alone
The pendulum mass was found to 438.3 g by weighing and the pendulum length was
645 mm. The ignition pin was always in place. The first experiments at reduced pressure
were carried out in air alone for 4 values of the pulse energy. Every parameter set was
repeated at least two times.
0,10
Air Pulse
0,08
Energy
288 J
Impulse (Ns)
0,06 274 J
203 J
128 J
0,04
0,02
Ser. GL 57 - 506
0,00
0 200 400 600 800 1000 1200 1400
Ambient Pressure (mbar)
Fig. 3 - Impulse vs. pressure with air as propellant
Fig. 3 shows the result for the measured impulse as a function of the pressure in the
vessel. The impulse increases strongly with the energy of the laser pulse up to a certain
threshold level. However, a nearly constant value is found above the threshold pressure.
The threshold pressure depends on the pulse energy and for 128 J is as low as
12
200 mbar. For the high pulse energies at 274 J and 288 J it is reached at 500 mbar. It is
conceivable that for even higher pulse energies the threshold pressure approaches the
atmospheric pressure. While the impulse above the threshold pressure is nearly constant
within the accuracy of the measurement, there seems to be a weak maximum for the
pulse energy of 280 J at 500 mbar.
300
250
Coupling Coefficient (N/MW)
200
Pulse Energy
288 J
150 274 J
203 J
100 128 J
Masse v Druck.data9-graf20
50
Propellant: Air
0
0 200 400 600 800 1000 1200
Fig. 4 - Coupling Coefficient for air and different laser pulse energies vs. ambient
pressure
If the impulse coupling coefficient, cm, is determined from these measurements by

dividing the impulse by the pulse energy, the result in Fig. 4 is obtained. Now the values
of the maximum coupling coefficients differ only little and amount to 250 to
280 N/MW. The low value of 225 N/MW for 128 J and 1 bar corresponds to the general
decrease of cm for lower energies (compare diagram D4 in Sec. 3.1.2.3 of ref. 1). As the
pressure is reduced the curve for this pulse energy increases at first to a value of 260 to
270 N/MW. Although this behaviour has already been noted for the absolute impulse, it
is not understood. A possible explanation could be that the expansion of the accelerated
air goes to a lower pressure, thus reaching a higher exit velocity. This effect is later
13
countered by the reduction of the exhausted air mass in such a way that initially a nearly
balanced situation occurs.
The operation with very low pressures was accompanied by a notable thermal load in
the vertex region of the paraboloid. A yellowish colouring of the aluminum surface
could be seen, indicating the appearance of high temperatures.
3.1.2 Dependency on pressure with Delrin added
Delrin as an additional propellant has been placed in the focal region of the parabolic
thruster mirror. For this purpose Delrin cylinders of 15 mm in length and 8 mm in
diameter were stuck on the ignition pin and pushed to vertex of the paraboloid (Fig. 5).
The light was thus concentrated radially on the cylinder walls with a certain lateral
intensity distribution. A new pin was attached for every new parameter set and hence
after three pulses. It was repetitively observed that the second impulse out of several on
the same target pin was higher than the first and the third. Each pin was weighed
before and after use in order to find the mass loss, m, for the applied laser pulse energy,
E. By this the specific propellant consumption µ = m / E could be determined. Fig. 6
shows an example of a used pin. The groove from the evaporated material follows in its
shape approximately the intensity distribution on the cylinder wall.
Fig. 5 - Delrin pin inside GL Fig. 6 - Used pin
Fig. 7 summarizes the results of the impulse for pulse energies of 252 ± 10 J for the
following 3 different cases: For reference, the black squares represent the already
14
displayed behaviour for air as the only propellant. At pressures below 2 mbar the
impulse is zero. However, with Delrin an impulse of 0.06 Ns has been measured with a
scatter of ± 0.005 Ns (red dots). This value corresponds to 80 % of the maximum
impulse with air alone. As the air pressure is increased in steps to atmospheric pressure
the impulse curve also increases linearly to the same pressure value, where the air curve
0,14
Pulse 500
0,12
Energy

252 +/- 10J
0,10 400
Impulse (Ns)
0,08
300
0,06
200
0,04
Delrin in air
Delrin in nitrogen 100
0,02 Air only
0,00 0
0 200 400 600 800 1000 1200
Fig. 7 - Impulse and momentum coupling coefficient for 3 propellant

combinations vs. ambient pressure
begins to level off. In the range between 100 and 300 mbar the rate of increase of the
Delrin curve is about the same as of the air curve. Surprisingly, from the saturation
pressure of the air curve on, the Delrin curve continues to rise linearly, although with a
different rate. There seems to be no indication of a saturation even at atmospheric
pressure. This latter behaviour can only be explained either if more Delrin vapour is
produced with increasing air pressure, or the Delrin vapour absorbs more energy that is
transformed into kinetic energy, or a combustion reaction of the vapour with the air
takes place, that adds energy to the gas. The latter explanation is the most likely one,
because such a reaction would become stronger with the increasing availability of
oxygen at rising pressure. Furthermore, in video recordings of the laser pulse interaction
with the US lightcraft a flame has been seen developing in front of the lightcraft exit.
15
This is shown in a sequence of three successive video frames in Fig. 8. For the German
lightcraft such a combustion must occur at least to some extend in the inside of the
thruster. Otherwise the reaction energy could not contribute anymore to the impulse.
Fig. 8 - Three successive frames of a movie, showing the combustion of Delrin

with the USL.
This interpretation has been checked by suppressing a possible combustion reaction in a

chemically inert nitrogen atmosphere. The result is displayed in Fig. 7 as blue triangles.
Up to the saturation point in air at 400 mbar the nitrogen (+ Delrin) curve coincides with
the air (+ Delrin) curve. But from this pressure on the impulse in nitrogen saturates also,
obviously because no energy is provided by combustion. The increase of the impulse
with added Delrin over air alone amounts to 16 – 20 % and reaches 0.095 Ns instead of
0.073 Ns. However, another 0.032 Ns are added to this value by the chemical reaction
energy. With this behaviour a hybrid operation has been demonstrated incidently, with
1/3 of the impulse coming from a different energy source.
The fact that the combustion process takes place in the vapor phase of the Delrin and is
not a reaction on the surface of the solid can be proven by the mass loss. For a surface
reaction it is expected that the mass loss would increase with the air pressure. As Fig. 9
shows that, except for the measurement at 0 mbar, the mass loss is independent of the
ambient pressure. For the notably higher values at full vacuum (22 mg per pulse in the
average) no explanation can be given. The mass loss is also independent of the
surrounding gas and amounts to 15 mg per pulse. This is equivalent to an average
specific propellant consumption of 60 µg/J.
Because in these experiments the pulse energy remained constant within the natural
bandwidth of the laser, the coupling coefficient must show exactly the same behaviour
16
as the absolute impulse (Fig. 7 right scale). The numbers are 240 ± 25 N/MW for Delrin
at vacuum, 270 N/MW for air alone at 1 bar, 370 N/MW for Delrin in nitrogen at 1 bar,
and 525 N/MW for Delrin in air at 1 bar.
80
Delrin Mass Loss for 3 Pulses (mg)
Pulse Energy 252 +/- 10 J

60
40
Masse v.Druck.data1-graf19
20
in Air
in N2
0
0 200 400 600 800 1000 1200
Fig. 9 - Mass loss for 3 laser pulses vs. ambient pressure of air or nitrogen
As has been stated in Sec. 1, the knowledge of both, the coupling coefficient, cm, and
the specific propellant consumption, µ, allows the direct determination of the mean
effective exhaust velocity, vj. This determination, however, is only meaningful for the
vacuum case, where solely the measured Delrin mass, but no air, is exhausted. The
effective exhaust or jet velocity is found to be 2.55 ± 0.1 km/s (3.74 km/s). The number
is related to the higher mass loss of Delrin of 22 mg at p = 0 mbar. This mass loss has
been confirmed later on for the measurements with variable pulse energy (Sec. 3.1.3)
and are thus the more conservative data. The number in brackets is for a mass loss that
corresponds to the average value of 15 mg, as found for pressures > 0 mbar.
If the jet velocity is known then the kinetic jet efficiency, η, can also be calculated. In
vacuum it is 0.3 ± 0.03 (0.45). If another 30 % of energy are lost to the wall, as has
been found in very early experiments from measuring the temperature increase of the
17
wall3, then a remainder of 40 % (25 %) is still contained in the jet as inner energy
(sensible heat and excitation) that could not be transformed to kinetic energy during the
expansion process. Again, the numbers in brackets refer to the lower mass loss.
Since the amount of air that is exhausted at the various pressures is a priori unknown, it
is not possible to calculate the common exhaust velocity as a function of the pressure.
However, if one assumes that the efficiency of the energy deposition process is
independent of the mixture ratio and no additional energy is liberated by combustion, as
is the case for nitrogen, then both, the common exhaust velocity, vc, and the mass ratio
between air (index A) and Delrin vapour (index D) can be estimated. In this special case,
the produced kinetic energy in the Delrin vapour under vacuum condition must be the
same as in the mixture of the masses mD and mA that are exhausted with vc :
mD vD2 = 2 η E = ( mD + mA ) vc2
From the measurements is known the ratio of the impulse in vacuum to that at some
pressure: W = ( mD vD ) / [( mD + mA ) vc ]
From these two equations follows the common velocity
vc = W vD
and the mass ratio mA / mD = µA / µD = 1 / W2 - 1 .
The pressure dependence of the common exhaust velocity is shown in Fig. 10.
The velocity drops rapidly to 1.35 km/s at 400 mbar as the amount of exhausted air
increases. While in nitrogen the velocity slightly increases again to 1.5 km/s at 1 bar, it
drops for air to 1.2 km/s. (As before, the numbers are related to the more conservative
mass loss of Delrin measured at p = 0 mbar). The different behaviour must be an artifact
since the combustion effect could not be considered in the above formalism and hence
the effective efficiency has changed. This becomes even more noticeable in the
calculation of the mass ratio air to Delrin, as shown in Fig. 11. With increasing pressure
the ratio grows from 0 to 2.2 at 400 mbar, where the curves begin to separate strongly.
The ratio drops again down to 1.65 for nitrogen at 1 bar, which is correct, and grows at
the same time to 3.7 for air. Since 15 mg of Delrin are exhausted independent of the
pressure, due to the mass ratio of to 2.2 at 400 mbar the mass of air or nitrogen
corresponds 33 mg. This is roughly 30 % of the air contained in the volume of the
thruster and is consistent with derivations from other measurements.
18
3,0
Pulse Energy 252 +/- 10 J in Air

2,5 in Nitrogen
Exhaust velocity (km/s)
2,0
1,5
Lightcraft/Masse v.Druck.graf10-data1
1,0
0,5
Determination: Method 1 Ser. GL 610-802

0,0
0 200 400 600 800 1000 1200
Fig. 10 - Average exhaust velocity for air and nitrogen as propellants vs.
pressure, determined according to method 1
4,0
3,5
Pulse Energy 274.7 +/- 4.5 J
3,0 Air
2,5
mAir / mDelrin
2,0
1,5
N2
Lightcraft/Masse v. Druck.graf25-data1
30% of total air

1,0 in volume
0,5
0,0
0 200 400 600 800 1000 1200
Fig. 11 - Ratio of air to Delrin for the GL vs. pressure (evaluation method 1)
19
The assumption of equal efficiency is doubtful for air at pressures ≥ 400 mbar, where
the combustion energy acts as if the efficiency of the laser interaction would increase by
an amount α. With an assumption of η + α a new derivation is possible. Let ID, IN, IA be
the measured absolute impulse values for Delrin, Delrin + nitrogen and Delrin + air,
respectively, and with the same indices the exhaust velocity, v. For the exhausted gas
mass we have to introduce another assumption, namely that the exhausted gas mass is
the same for nitrogen and for air, mg = mN = mA, irrespective of a different energy
production and neglecting the small difference in molecular weight. The following
equations can be set up from the definition of the momentum and the balance of
energy:
vD = ID / mD
2 η E = ID vD ⇒ η = ID vD / 2 E
2 η E = IN vN ⇒ vN = 2 η E / IN
2 (η + α) E = IA vA
IN = (mD + mg) vN ⇒ mg = IN / vN - mD
IN / IA = WNA = IN / (mD +mg) vA
⇒ vA = IN / (mD + mg) WNA
⇒ α = IA vA / 2 E - η
The new result for the velocities vN and vA is given in Fig. 12 for both values of the Delrin
mass loss. Similarly, the mass ratio mg / mD, and the combustion efficiency term α are
shown in Fig. 13. The values are calculated only for the mean values of the impulses and
the masses. While the exhaust velocity of nitrogen continues to drop as the pressure is
raised to 1 bar, the exhaust velocity of air goes up again for pressures of 400 mbar and
higher. This is in fact expected as being the consequence of an additional heating by the
chemical reaction. In contrast to the earlier assumption, the exhausted mass fraction of
either nitrogen or air rises steeply in the low pressure regime and becomes constant in
the high pressure regime because the impulse with nitrogen has saturated. In this
regime the combustion efficiency term α grows to 24 % (35 %) at the pressure of
1 bar.
20
4000
N2 Air
3500 mD for p > 0 mbar*

Exhaust Velocity (m/s) mD for p = 0 mbar
3000
2500
eigene dateien/lightcraft/origin-diagramme/exhaust veloc.graf1

2000
1500
*Optimistic evaluation
1000
0 200 400 600 800 1000 1200
Fig. 12 - Average exhaust velocity according to the second evaluation method
2,0
1,8
1,6
mgas / mD
1,4
mgas / mD ; α
1,2
Eigene Dateien/Lightcraft/Origin-Diagramme/exhaust veloc.graf2
1,0
0,8 Pulse Energy 274.7 +/- 4.5 J
0,6
α
0,4
0,2
0,0
0 200 400 600 800 1000 1200
Fig. 13 - Mass ratio of the exhaust gas and efficiency increase α due to the
combustion energy (according evaluation method 2)
21
Note, that both considerations rely on some extreme assumptions and do not describe
the reality in a correct way, because one number is missing, i.e. the fraction of the
combustion energy. The combustion energy only manifests itself in the increase of the
impulse. The reality is certainly found somewhere in between of the results from the
two models. Hence, at atmospheric pressure the numbers are to expected in the range
as given in the following table for air ( E = 258.7 J)
1st method 2nd method

Assumption ηN = ηA mN = mA
vA (m/s) 1180 2150
mA (mg) 85.4 37.0
ηA ( + α) 0.30 0.54
The values for nitrogen are the same for both methods: vN = 1590 m/s and mN = 37 mg.
3.1.3 Dependency on the pulse energy in vacuum and atmospheric pressure
0,14
0,12
0,10
Impulse (Ns)
0,08
0,06
Origindiagramme/lightcraft/Massv.Druck.Graf14-data6
0,04
Delrin in air at 1 bar
0,02 air only at 1 bar
Ser. Gl 33-59, 810-952
Delrin in vacuum
0,00
100 150 200 250 300
Pulse Energy (J)
Fig. 14 - Lightcraft impulse vs. laser pulse energy for 3 cases with and without
Delrin as additional propellant
22
Fig. 14 shows the measured impulse as a function of the laser pulse energy for 3 cases:
The black squares represent the impulse at a pressure of 1 bar, when air is the only
propellant. In comparison, the green triangles show the result when Delrin is added as a
second propellant. While the impulse in air alone grows linearly with the pulse energy
and achieves a maximum value 0.083 Ns for 251 J the values with Delrin at first grow
more rapidly, but then begin to saturate for the highest energies. The maximum
achieved value is 0.12 Ns and thus 50 % higher then without Delrin. If the air is now
omitted by operating in vacuum (red circles), a dependency is found with a much slower
growth and a fairly early saturation. Although for 126 J the impulse is still higher than
with atmospheric air (0.045 Ns), at the maximum energy of 251 J it ends up lower than
air (0.06 Ns).
700
600
500
400
Origindiagramme/Lightcraft/Mass v.Druck.graf30-data3
300
200
Delrin in air at 1 bar
100 Delrin in vacuum
Air alone at 1 bar
0
100 120 140 160 180 200 220 240 260 280 300
Pulse Energy (J)
Fig. 15 - Momentum coupling coefficient vs. laser pulse energy for 3 cases with and
without Delrin as additional propellant
Because the rise of the impulse is slower than the energy increase, the coupling
coefficient must fall in all cases where Delrin is applied. This is indeed so, as Fig. 15
shows. The decrease for cases with Delrin is comparable and linear, only at a different
level. Now the highest coupling coefficients are found for the lowest pulse energies. The
23
maximum values are roughly 400 N/MW for Delrin in vacuum and 650 N/MW at
p = 1 bar. In atmospheric air alone there is a slight increase for low energies with a rapid
saturation at about 275 N/MW. Some mechanism seems to prevent the deposition of
the full energy into the Delrin. Such a mechanism could be plasma absorption in a laser
supported detonation wave (LSD-wave) running towards the laser beam, that does not
interact with the thruster walls to produce thrust. Or, the index of refraction changes in
the shock wave front that emanates from the breakdown plasma and reduces the focal
intensity by bending the light away from the focal point. The created Delrin vapour, on
the other hand, seems to be transparent to the incoming light, because an absorption
would raise the enthalpy of the vapor and result in a higher expansion velocity. The
consequence would be a higher measured impulse. The fact that the process is more
efficient when the thrust is actually lower requires a higher repetition rate of the laser if
the same propulsion power is to be obtained.
200
180
Specific Mass Consumption (µg/J)
Vacuum
160 Atmosphere
140
Spec. Mass consumption
120
100
80
60
40
Mass Loss
20
Ser GL 810-952
0
100 120 140 160 180 200 220 240 260 280 300
Pulse Energy (J)
Fig. 16 - Mass loss of Delrin for 3 laser pulses (open symbols) and specific
propellant consumption (full symbols) vs. pulse energy for 3 cases.
Of particular interest is now the result for the mass loss of Delrin. This is shown in
Fig. 16. It is found that the mass loss is nearly independent of the pulse energy. In
atmospheric air it even slightly decreases with increasing pulse energy. Consequently,
24
the specific mass consumption must decrease inversely proportional to the pulse energy.
A possible explanation is again the creation of an LSD-wave, a travelling plasma zone
that absorbs all the subsequently delivered energy.
Due to the similar decrease of both cm and µ with increasing energy, the ratio between
the two quantities, expressing the exhaust velocity, stays nearly constant. For the
vacuum condition the exhaust velocity, v, can be determined directly and without any
further assumption. With increasing pulse energy the exhaust velocity goes up from
2.25 km/s to 2.65 km/s only (see Fig. 24 Sec. 3.1.4). The calculation for the Delrin / air
mixture according to method 1 (equal jet efficiency for operation with and without
Delrin) yields a velocity of 1.3 km/s, which is within experimental error constant over the
energy range. The jet efficiency, η, however decreases with increasing energy from
43 % at 125 J down to about 30 % at 250 J (Fig. 25 Sec. 3.1.4). The fraction of
exhausted air to Delrin vapor, mA/mD, increases from 2 to 3.5 over the same range
(Fig. 17). The additional energy seems to end up only in the air. A more ideal propellant
should absorb all the energy in the vapor. The derived numbers for air (v, η, and mA/mD)
are approximations within the limits of method 1. Since the corresponding dependence
in nitrogen has not been measured, the other limit cannot be calculated.
4,0
3,5
3,0
mAir / mDelrin
Origindiagramme/Lightcraft/Masse v.Druck.graf26-data11
2,5
2,0
1,5
Ambient pressure 1 bar
1,0
100 150 200 250 300
Pulse Energy (J)
Fig. 17 - Mass ratio of air to Delrin vapor at atmospheric pressure
25
3.1.4 Dependency on the intensity at the Delrin surface.
Sine there is an obvious blocking of the energy delivered to the target, a lower intensity
distribution at the target surface may lead to different results. The simplest way to
decrease the energy distribution was to enlarge the diameter of the Delrin pin, for
instance from 8 to 10 mm. This reduces the fluence level on the surface by a factor of
0.65. For a 100 J pulse the peak intensity would go down from 3⋅107 W/cm2 to
1.9⋅107 W/cm2 (for comparison the peak intensity on the ignition needle is
8 2
7.3⋅10 W/cm ). Associated with the reduction in intensity was an enlargement of the
irradiated area.
F F
Fig. 18 - Schematic of irradiation on pin (green) side-on (left) and front-on (right)
A second test has been made going in the opposite direction: The 8 mm diameter pin
was shortened to a length of 8.5 mm. In this case the light was focused on the circular
front side of the cylinder with a several times higher fluence level than for the cylinder
circumference of the same diameter. The two possibilities for the target irradiation are
shown schematically in Fig. 18. As this figure shows, not all of the incoming light for the
front side irradiation is actually concentrated on the surface. There was a second
purpose for this experiment. In the case of radial irradiation the produced Delrin also
expands radially. However, the thruster walls enforce an overall axial flow. Thus by
turning the flow the propulsive force acts primarily against the thruster walls. In the case
of the front side irradiation the Delrin vapor expands primarily in the axial direction and
the thrust acts at first on the pin surface itself. This could simulate the mechanics of a
direct ablation plasma thruster. Because the produced impulse on the lightcraft was so
poor and because the pin was pressed on the needle so firmly by the high force that it
26
was difficult to remove and replace it, these experiments were only carried out for one
value of the pulse energy.
The results for all experiments with a different pin size are displayed in the following
figures. In addition to showing the absolute impulse of the 8 mm pin the impulse for the
10 mm pin and the impulse for the front side irradiation are displayed in Fig. 19 also.
0,14
Pin 8 mm dia (1 bar)

0,12
0,10
Impulse (Ns)
0,08
0,06
Origindiagramme/Lightcraft/Masse v.Druck.graf32
0,04
0,02 Pin 8 mm dia (0 bar)
Focus on front end (0 bar) Ser. GL 810-952
0,00
100 150 200 250 300
Pulse Energy (J)
Fig. 19 - Impulse for different Delrin pin sizes and different irradiation vs. laser
pulse energy
Although starting at nearly the same value at the low energies the impulse for the
10 mm pin increases significantly faster than the impulse for the 8 mm pin. At the
maximum pulse energy it ends up with a 50 % higher value. This corresponds to the
fact that also more Delrin mass has been vaporized (Fig. 20). In contrast, the vaporized
mass in the case of the front side irradiation amounts to only 40 % of the side wall
irradiation value. If now the impulse is plotted versus the evaporated mass a completely
proportional relationship is found (Fig. 21). This means that the increase in impulse for
higher laser pulse energies is only due to the increased in exhausted Delrin vapor mass.
The Delrin vapor does not absorb any additional energy and therefore the exhaust
velocity cannot increase as desired. So, the specific impulse is practically fixed.
27
120
100
80
60
40
Pin 10 mm Diam. (0 bar)
Pin 8 mm Diam. (0 bar)
20
Pin 8 mm Diam. (1bar)
Focus on Front End (0 bar)
0
100 150 200 250 300
Pulse Energy (J)
Fig. 20 - Mass loss for 3 pulses for different pin irradiations vs. laser pulse
energy
0,10
Delrin pin 10 mm dia

0,09
0,08
Impulse (Ns)
0,07
Origindiagramme/Lightcraft/Imp von m.graf1-data1
0,06
0,05
Vers. 1400-1452
0,04
60 70 80 90 100 110 120
Mass Loss (mg)
Fig. 21 - Impulse vs. mass loss
If the energy specific quantities, the coupling coefficient cm and the specific mass
consumption are derived, it is found that for the thicker pin cm decreases much less with
increasing energy than for the 8 mm pin (Fig. 22): From 420 N/MW to 370 N/MW,
28
corresponding to 12 % as compared to 44 % (390 N/MW to 220 N/MW). In the same
manner, the specific propellant consumption decreases much less for 10 mm pin
compared to the 8 mm pin (Fig. 23). The values are 195 µg/J for the lowest energy and
158 µg/J for the highest. As expected the exhaust velocities show comparably little
differences. Starting from about 2.2 km/s they increase to 2.6 km/s for the 8 mm pin
and to 2.35 km/s for the 10 mm pin (Fig. 24). The velocity value for the front side
irradiation is similar to that of the 8 mm pin. The jet efficiency also decreases only
marginally (Fig. 25) from 42 % to 37 % (compared to 43 % and 28 % for the 8 mm
pin).
700
Propellant: Delrin
600
500
400
300
200 Pin 8 mm dia (1 bar)

Focus on front end (0 bar)
Ser. GL 810-952, 1210-1452
0
100 150 200 250 300
Pulse Energy (J)
Fig. 22 - Momentum coupling coefficient for different Delrin pins vs. laser
pulse energy
29
200
Specific Propellant Consumption (µg/J)

180
160
140
120
100
Origindiagramme/Lightcraft/Masse v.Druck.graf33-data2
80

40
20 Focus on front end (0 bar)
Ser. GL 810-952, 1210-1452
0
100 120 140 160 180 200 220 240 260 280 300
Pulse Energy (J)
Fig. 23 - Specific propellant consumption for different Delrin pins vs. laser
pulse energy
3,0
2,5
Exhaust Velocity (km/s)
2,0 0 bar
1,5
1,0 1 bar
Pin 8 mm diameter
Pin 10 mm diameter
0,5
Pin 8 mm diameter
Focus on front end
0,0
100 150 200 250 300
Pulse Energy (J)
Fig. 24 - Average exhaust velocity for different Delrin pins vs. laser pulse
energy
30
0,5
Propellant: Delrin
0,4
Jet Efficiency
0,3
Vacuum
Origindiagramme/Lightcraft/Masse von Druck.graf24-data5

0,2
Pin 10 mm diameter
0,1 Pin 8 mm diameter
Focus on front end
0,0
100 150 200 250 300
Pulse Energy (J)
Fig. 25 - Jet efficiency for different Delrin propellant pins in vacuum vs. laser
pulse energy
3.2 US-Lightcraft
3.2.1 Dependency on the ambient pressure
Leaving everything else unchanged the GL has been exchanged for the USL. The
pendulum mass was 494 g and the pendulum length 645 mm. In this series the pulse
energy was kept constant during the change of the ambient pressure in the vessel. The
pressure was changed from below 1 mbar in several steps to approx. 970 mbar (local
pressure for the open vessel). In contrast to the GL, the measurements have been carried
out only with the additional propellant Delrin, since measurements in air alone did not
result in reproducible and meaningful impulses with the stable resonator. The Delrin ring
was exchanged after every 3 pulses and the mass loss was determined by weighing.
Besides air as the ambient gas, a control value was determined in a nitrogen atmosphere
at environmental pressure. For a better comparison in all diagrams to follow the
equivalent data for the GL are shown as well. The data for the GL are those with a
Delrin pin of 15 mm length and 8 mm in diameter, if not specified otherwise.
31
250
Spec. Propellant Consumption (µg/J)
200
US-Lightcraft
150 Pulse Energy 236.7 +/- 4.7 J
100
G-Lightcraft
US-Lcvacuum.graf8-data4
50
Open symbols: N2
Ser. GLc 620-722 USLc 1060-1152
0
0 200 400 600 800 1000 1200
Fig. 26 - Specific propellant consumption vs. ambient pressure
Analogously to the findings for the GL the specific propellant consumption for the USL is
independent of the pressure (Fig. 26). The value is 208 ± 2 µg/J. A chemical reaction
with air on the Delrin surface can be excluded. This is also supported by the comparable
value in the nitrogen atmosphere. However, the mass loss is more than 3 times higher
than for the GL at the tested pulse energy level. This is attributed to the lower intensity
on the long focal line, allowing the evaporation of more Delrin before the surface is
shielded from the laser light. Because the pulse energy was equal for all data, the
absolute mass loss has the same behavior. It can be re-calculated by multiplication with
the pulse energy of 236.7 J. Note, that in contrast to the GL at pressures ≤ 50 mbar no
increase in the vaporized Delrin mass has been observed.
32
An inspection of the used Delrin
rings showed that the material is
ablated not only along the focal
line but over a considerable
fraction of the exposed surface.
(Fig. 27). It is also not
homogenously removed but
unveils a series of parallel
circumferential lines that can be
felt easily as tiny grooves. Before
use the surface was smooth.
Fig. 27 - Used Delrin rings. The lowest ring is
unused .
600
G-Lightcraft
500
400
300
US-Lightcraft
200
100
Open symbols: N2
Ser. GLc 601-722, USLc 1010, 1060-1152
0
0 200 400 600 800 1000 1200
Fig. 28 - Coupling coefficient vs. ambient pressure
Quite in contrast to the GL the coupling coefficient cm is also fairly independent of the
ambient pressure (Fig. 28). There is a small increase in the pressure range below
400 mbar of 15 % from 300 N/MW to 345 N/MW. With this value about the same
impulse is produced as with the GL in a nitrogen atmosphere of 1 bar. The nitrogen
value for the USL at 1 bar is within experimental error comparable to the vacuum values.
33
As the control value in nitrogen suggests, only a slight effect of the reaction enthalpy of
the Delrin vapor burning in air is found. Although movie pictures have shown a
considerable cloud emanating from the lightcraft (see Fig. 8), most of the reaction
apparently takes place outside of the range of the lightcraft and does not contribute to
the thrust. In vacuum the coupling coefficient is higher than for the GL, probably a
direct consequence of the higher evaporated mass.
3,0

2,5
Exhaust velocity (km/s)
2,0
US-Lightcraft
1,5
1,0
G-Lightcraft
0,5
Ser GLC 620-722, USLc 1052-1152

0,0
0 200 400 600 800 1000 1200
Fig. 29 - Average exhaust velocity vs. ambient pressure
The jet exhaust velocity can be exactly determined under vacuum conditions. A value of
1.5 km/s is derived (Fig. 29). As soon as residual air participates in the thrust process
only approximate values can be determined, as shown in the evaluations for the GL.
Because of the minor dependence of both, specific mass loss and coupling coefficient
on pressure, the jet velocity also shows little dependence. Above 400 mbar it is virtually
constant within experimental error and surpasses the value for the GL at atmospheric
pressure. The jet efficiency in vacuum is ηj = 21.4 %.
34
4,0
3,5 Pulse Energy 236.7 +/- 4.7 J

3,0
2,5
G-Lightcraft
2,0
µAir/µDelrin
1,5
1,0
US-Lightcraft
0,5
0,0
Ser. GLC 610-722, USLc 1060-1142
-0,5
0 200 400 600 800 1000 1200
Fig. 30 - Mass ratio of exhausted gases vs. ambient pressure
The amount of participating air in the thrust mechanism is apparently small and does
not exceed 25 % of the Delrin vapor mass (Fig. 30). This is very different from the GL.
One reason for this discrepancy may be found in the radically different structure of the
two lightcrafts. In the semi-closed bell shape a considerable amount of the enclosed air
is accelerated and pushed out of the exit of the nozzle. In the open plug nozzle perhaps
less volume is accelerated.
3.2.2 Dependency on the pulse energy in vacuum
In the experiments with the GL it has been found, that there is a marked difference
whether the Delrin pin has a diameter of 8 or of 10 mm. The reason is probably the
lower intensity on the surface and a wider illuminated area. This allows the evaporation
over a broader area before the shielding effect sets in. Because this situation is closer to
that encountered with the USL, both results for the GL have been enclosed in the
following diagrams.
As Fig. 31 shows the absolute impulse for the USL is strictly linear and can be described
as
-4
I = 3.5⋅10 E – 0.01 (Ns)
35
There is a minimum energy of 30 J necessary to induce any impulse at all. Because of
the linear nature of the impulse, the coupling coefficient must approach a finite value as
E → ∞. This value is 350 N/MW and cannot be surpassed.
0,10
G-Lightcraft
10 mm dia
0,08
Lightcraft Impulse (Ns)
US-Lightcraft
0,06
G-Lightcraft
0,04 8 mm dia
0,02 Vacuum
Ser. GLc 810-862, USLc 1000-1052
0,00
100 120 140 160 180 200 220 240 260 280 300
Pulse Energy (J)
Fig. 31 - Lightcraft impulse in vacuum vs. laser pulse energy
Hence, the behavior of the two lightcrafts with respect to the coupling coefficient is very
different (Fig. 32), if the 8 mm pin for the GL is considered: While for the USL the
coupling coefficient starts for low energies with a relatively low value and then increases
with the pulse energy (red dots), the GL shows the opposite behavior and for the 8 mm
pin drops by almost a factor of two over the investigated energy range.
We believe, that the intensity in the focal region of the GL is already so high, that a
substantial shielding effect occurs, that increases with the pulse energy. On the other
hand, because of the much larger focal region in the USL the cut-off energy is not yet
reached and only approached for the higher pulse energies. As the energy of the USL is
increased to numbers, where the intensity on the Delrin surface reaches comparable
36
values as for the GL, then the same shielding effect is expected to set in and the
coupling coefficient should then decrease again.
450
G-Lightcraft
400 10 mm dia
350
US limit
300
250 US-Lightcraft
Lightcraft/US-Lc vacuum.graf1-data1
G-Lightcraft
8 mm dia
200 Vacuum
Ser. GLc 810-862, USLc 1000-1052

150
100 120 140 160 180 200 220 240 260 280
Pulse Energy (J)
Fig. 32 – Coupling coefficient in vacuum vs. laser pulse energy
The assumption that the cut-off energy has not been reached yet for the USL is
supported by the observed mass loss (Fig. 33). For the 8 mm pin the GL exhibits
practically no change of the amount of produced Delrin vapor as the pulse energy is
raised. So only a certain fixed fraction of the incoming laser light is actually dumped into
the Delrin. In contrast, for the USL the mass loss increases proportionally to the pulse
energy. Thus all the incident energy seems to be transfered into vapor. The functional
dependence can be described as
-6
m = (0.213 E – 0.33)⋅ 10 (kg)
37
200
Vacuum
Mass Loss for 3 Pulses (mg)
150 US-Lightcraft
10 mm dia
100
G-Lightcraft
Lightcraft/USLc vacuum.graf2-data2
50 8 mm dia
Ser. GLc 810-862, USLc 1000-1052

0
100 120 140 160 180 200 220 240 260 280 300
Pulses Energy (J)
Fig. 33 - Mass loss for 3 pulses in vacuum vs. laser pulse energy
250
US limit
Specific Mass Consumption (µg/J)
200
US-Lightcraft
150 10 mm dia
G-Lightcraft
Lightcraft/Diagramme Origin/USLcvacuum.graf3-data2
100
Vacuum 8 mm dia
50
Ser. GLc 810-862, USLc 1000-1052

0
100 120 140 160 180 200 220 240 260 280 300
Pulse Energy (J)
Fig. 34 - Specific propellant consumption in vacuum vs. laser pulse energy
Due to the linearity of the impulse and the mass loss with the pulse energy, the impulse
38
can be directly written as a function of the mass loss
I = 1.64 ⋅103 m – 9.46⋅10-3
In this and all the following diagrams the pulse energy is always the mean value of all 3
energies that acted on the Delrin ring before it was taken of, weighed and replaced by a
new one for the next pulse energy level.
Because the mass loss is proportional to the pulse energy for the USL, the specific mass
loss, µ, must be nearly independent and it must decrease for the GL. This is actually so,
as seen in Fig. 34. The limiting value for µ = 213 µg/J.
A low mass loss supports a high exhaust velocity, because of vex = cm/ µ. Therefore, the
exhaust velocity is higher for the GL (Fig. 35). The analytical function for the USL is also
plotted in the diagram. The exhaust velocity barely reaches 1.5 km/s.
Because of this low exhaust velocity the jet efficiency for the USL is low, too (Fig. 36).
3,0
8 mm dia
2,5
10 mm dia
Exhaust Velocity (km/s)
2,0 G-Lightcraft
1,5
US-Lightcraft
1,0
Vacuum
0,5
Ser. GLc 810-862, USLc 1000-1052

0,0
100 120 140 160 180 200 220 240 260 280 300
Pulse Energy (J)
Fig. 35 - Average exhaust velocity in vacuum vs. laser pulse energy
39
0,5
G-Lightcraft
0,4
10 mm dia
8 mm dia
Jet Efficiency
0,3
0,2
US-Lightcraft
0,1
Vacuum
Ser. GLc 810-862, USLc 1000-1052

0,0
100 120 140 160 180 200 220 240 260 280 300
Pulse Energy (J)
Fig. 36 - Jet efficiency in vacuum vs. laser pulse energy
40
4. DISCUSSION OF THE RESULTS
Several experimental results can serve as a basis for extrapolations and have
consequences with respect to future investigations. The measurements described in this
report are the only one at reduced environmental pressures and at vacuum in the recent
past since the pioneering work in the USA of Pirri and Weiss in 19724 and in Russia by
Ageev in 19805 .
1) The result of the measurements with the GL in air without additional propellant
(Fig. 4) has an important consequence for the launching of lightcrafts. If the pressure is
translated into values of altitude corresponding to the variation of the pressure in the
normal atmosphere, the surprising result of Fig. 37 becomes apparent (in this diagram
the curve for 128 J has been plotted): For an airbreathing propulsion the cm-value and
thus the thrust remains constant to an altitude of 11.2 km, before it begins to decrease.
But at 20 km still half of the thrust is available. Finally, between 25 and 30 km it
becomes so low that it can just about compensate the weight force and the acceleration
goes to zero. It is thus possible to lift a lightcraft without using on-board propellant to
an altitude where the air density is reduced considerably. The air density is responsible
for the drag force and would require additional propellant. At the maximum altitude the
propulsion must switch over to the rocket mode, utilizing propellant carried on board.
Also a moderate acceleration can be applied now, as the lightcraft gains altitude and
the drag force is further reduced. This launch procedure with a pure air breathing mode
is impossible with the shape of the USL because no reproducible breakdown of air with
sufficient impulse can be achieved, especially at lower pulse powers.
2) At very low pressures (≤ 100 mbar) the use of an additional on-board propellant is
indispensable. With an appropriate laser pulse that allows to dump the pulse energy
fully into the propellant, i.e. a matched intensity at the surface of a solid propellant, a
coupling coefficient of 400 N/MW for Delrin could be achieved in vacuum with the GL.
The USL showed a definite upper limit at the slightly lower value of 350 N/MW.
3) Since the coupling coefficient with Delrin propellant in the GL decreases with
2
increasing fluence (J/cm ) at the target a threshold fluence must exist that is not yet
reached for the USL with its much larger focal area. The physical mechanism that limits
41
300
100%
250
Normal Atmosphere
200
cm data for pulse
energy of 128 J
150
50%
100
Minimum cm
for positive acceleration
50
cm(h).graf1
10%
1%
0
0 10 20 30 40 50
Altitude (km)
Fig. 37 - Coupling coefficient vs. flight altitude
the deposition of energy into the propellant is most likely the creation of LSD-waves
(Laser Supported Detonation waves). LSD-waves absorb a certain fraction of the pulse
energy at a location where it cannot contribute to the thrust. It has been found that the
created impulse is directly proportional to the evaporated Delrin mass. Therefore, the
vapor itself must be transparent to the laser radiation. Both properties, the cut-off of the
laser beam after a certain time and the impossibility to deposit energy in the vapor call
for a different laser radiation with respect to wavelength and pulse duration and for a
different propellant material. To resolve the problem of inappropriate energy deposition
investigations using short time imaging techniques should be carried out.
4) If instead of air alone another propellant is used during the ascent in the denser air a
considerable increase in impulse can be obtained. At a pressure of 1 bar the coupling
coefficient (for low pulse energy) in the bell shaped GL is increased by a factor of 2.7
(Fig. 15). A significant fraction of this increase is most likely associated with the
combustion of propellant vapor in air (Fig. 7). Since this combustion occurs inside the
thrust chamber of the GL it can contribute to the impulse. This effect is much less
pronounced in the USL with its open thruster structure (Fig. 28). In the USL less air can
be accelerated together with the Delrin as the air pressure increases (Fig. 30). It needs to
42
be found out by mission calculations which propulsion mode is more efficient in the
overall transportation balance. Too high an acceleration in the denser atmosphere is
uneconomical because of the quadratic increase of the drag force with the velocity.
Fig. 38 shows the velocity vs. the altitude where the drag force becomes equal or twice
as high as the weight force. If for the rise through the atmosphere the air breathing
mode is preferred, then a bell shaped nozzle must be utilized. In addition, propellants
should be investigated for their efficiency that release additional energy for instance by
6
decomposition or by a combustion process with air for a hybrid propulsion mode. The
combustion of Delrin vapor with air delivered an additional propulsive effect down to a
pressure of 400 mbar, corresponding to an altitude of 7 km in the normal atmosphere.
5) Due to the combustion effect the exact exhaust conditions could not be determined,
except for full vacuum. Some means to determine the fraction of air in the exhaust gas
should be developed. Independent of this deficiency it is clear that the obtained exhaust
10000
m = 20 kg orbital velocity
2
A=1m cw = 0.15
M > 4.8
1000
Velocity (m/s)
speed of sound
cw =0.43
100
cw = 0.15 D=1G
M < 0.6 D=2G
3
ρ0 = 1.225 kg/m -5
ρ80 = 1.57 10 kg/m
3
10
0 20 40 60 80
Altitude (km)
Fig. 38 - Example calculation for the flight velocity vs. altitude where the drag
force assumes the same or the double value of the weight. The dip is due to an
increase of the drag coefficient in the vicinity of Mach 1.
43
velocity in vacuum with a maximum of 2.6 km/s for the GL and only 1.5 km/s for the
USL is entirely insufficient for launching satellites (Fig. 35). For such a mission a
minimum of 6 km/s should be obtained. Again, for this purpose a different propellant is
required that needs a higher energy for ablation / evaporation and allows the deposition
of additional energy in the gaseous state.
6) The jet efficiency is an important quantity that defines the size of the laser for a
certain flight application. It should be as high as possible for an effective propulsion as
well as for the reduction of heat losses to the thrust chamber. A maximum value of
40 % has been found for the GL (Fig. 36), while for the USL an efficiency in excess of
25 % would require very high pulse energies. On the other hand, higher gas
temperatures in the thrust chamber will lead to a higher non-recoverable inner energy in
the gas (excitation, ionization …) and to increased radiation and thus reduce the
efficiency again. A loss of about 30 % of the pulse energy to the wall by convection
and radiation leaves another 30 % for non-recoverable losses.
7) The specific propellant consumption for Delrin seems to be limited to 213 µg/J and is
a property of the particular propellant (Fig. 34). Lower values are apparently due to
other effects. The specific propellant consumption is obviously independent of the
ambient pressure, except for an unresolved increase at pressure below 50 mbar in the
GL (Fig. 26).
8) It should be reminded that a decreasing tendency of the cm-value with pulse energy
does not necessarily mean that a higher energy does no more produce a higher impulse.
It actually depends on the rate of decrease of cm. For a constant cm the impulse still
grows in proportion to the pulse energy.
5. CONCLUSIONS
The goal of this study was the determination of the propulsive properties of a lightcraft
in vacuum. Two lightcrafts of similar size but very different geometry have been
successfully tested for the first time at pressures below the atmospheric pressure. With a
pendulum in a vacuum tank the impulse on the lightcrafts has been determined for a
variety of conditions: The ambient gas, air or nitrogen, has been used as the only
44
propellant and it has been supplemented or substituted with Delrin as a solid propellant.
Various geometries for the propellant irradiation with the laser light have been
investigated as well and showed the necessity to tailor the laser pulse to the propellant
or vice versa for maximum performance. In particular, test with shorter pulse durations
should be attempted and other wavelengths with sufficient pulse energy would be of
interest as well. It has been found that with a proper shape of the light concentrating
thrust chamber a launch with propelled altitudes up to 25 km can be performed in an
air breathing propulsion mode. The consequent monitoring of the Delrin loss
throughout the test sequences with solid propellant allowed the derivation of the
exhaust properties, and hence the specific impulse, and the jet efficiency at least for full
vacuum conditions (p ≤ 1 mbar). For intermediate pressure conditions a certain range of
the exhaust properties could be given. The derived exhaust velocities have not exceeded
2.6 km/s and therefore the specific impulse of 265 s falls short of the requirements for a
satellite launch. Other propellants must be tested for better performance and it is
adviced to look more deeply into the physical mechanisms that are associated with the
breakdown process and the formation of thrust. The investigated propellant Delrin was
ideal for the experiments, because it did not produce any depositions. In that respect
other propellants may be less convenient. Hybrid propulsion with a chemical energy
component may considerably enhance the performance in the operating regime for
satellite launches. Only two shapes of a thruster have been tested in this study. Other
geometries should be looked at in more detail, too. It has been noticed several times
that a more slender geometry of the bell-shaped lightcrafts could still improve the
3,5,7
coupling coefficient .
Acknowledgement
The authors express their gratitude to Dr. Ingrid Wysong for her engagement to make
this study possible at last.
45
References
1. W.O. Schall, W.L. Bohn, H.-A. Eckel, W. Mayerhofer, W. Riede, S. Walther, E.

Zeyfang, "US German lightcraft impulse measurements", EOARD Report under contract
no. F61775-00-WE033, April 2001.
2. C.W. Larson, F.B. Mead Jr., W.M. Kalliomaa, "Energy conversion in laser propulsion
II", paper AIAA 2002-0632, January 2002.
3. W.O. Schall, W.L. Bohn, H.-A. Eckel, W. Mayerhofer, W. Riede, E. Zeyfang,
"Lightcraft experiments in Germany", High-Power Laser Ablation III, Proc. SPIE Vol.4065,
pp. 472-481, 2000.
4. A.N. Pirri, R.F. Weiss, "Laser propulsion", paper AIAA 72-719, June 1972.
5. V.P. Ageev, A.I. Barchukov, F.V. Bunkin, V.I. Konov, V.P. Korobeinikov, B.V. Butjatin,
V.M. Hudjakov, "Experimental and theoretical modeling of laser propulsion", Acta
Astronautica, Vol. 7, pp. 79-90, 1980.
6. R.A. Liukonen, " Laser jet propulsion", Proc. SPIE Vol. 3574, pp. 470-474, 1998
7. L.N. Myrabo, M.A. Libeau, E.D. Meloney, R.L. Bracken, "Pulsed Laser propulsion
performance of 11-cm parabolic "Bell" engines within the atmosphere", paper AIAA
2002-2206, May 2002.
46
Appendix
Tables of measurements and evaluation.
Table A – German Lightcraft

Stable resonator
Total pendulum mass: 438.3 g
Pendulum length (center of mass): 645 mm
47
# Comment Press. Energy Displace- Laser Angle Height Energy Velocity Impulse Coupling Mass
(mbar) (V) ment Energy (°) (mm) (J) (m/s) (N*s) (N/MW) loss
(mm) (J) (mg)
20 no vessel 960 0.0779 42.2 238.2 3.750 1.381 0.005939 1.65E-01 7.22E-02 302.94
21 no vessel 960 0.0788 42.8 240.5 3.805 1.422 0.006114 1.67E-01 7.32E-02 304.45
30 no vessel 960 0.0947 43.5 284.8 3.867 1.468 0.006313 1.70E-01 7.44E-02 261.18
31 no vessel 960 0.0946 43.7 284.7 3.884 1.481 0.006368 1.70E-01 7.47E-02 262.47
32 no vessel 960 0.0935 43.1 281.6 3.830 1.441 0.006195 1.68E-01 7.37E-02 261.67
33 no vessel 960 0.1041 47.9 310.4 4.260 1.782 0.007660 1.87E-01 8.19E-02 263.98
34 no vessel 960 0.1045 48.3 311.5 4.293 1.810 0.007782 1.88E-01 8.26E-02 265.16
35 no vessel 960 0.1047 47.6 312.0 4.231 1.758 0.007558 1.86E-01 8.14E-02 260.87
36 no vessel 960 0.0785 35.9 239.8 3.186 0.997 0.004286 1.40E-01 6.13E-02 255.60
37 no vessel 960 0.0788 36.2 240.6 3.212 1.013 0.004356 1.41E-01 6.18E-02 256.79
38 no vessel 960 0.0782 35.8 239.0 3.183 0.995 0.004279 1.40E-01 6.12E-02 256.23
39 no vessel 960 0.0673 30.5 207.6 2.711 0.722 0.003105 1.19E-01 5.22E-02 251.30
40 no vessel 960 0.0677 30.8 208.7 2.738 0.736 0.003166 1.20E-01 5.27E-02 252.40
41 no vessel 960 0.0675 31.0 208.4 2.753 0.744 0.003201 1.21E-01 5.30E-02 254.22
42 no vessel 960 0.0553 25.2 172.5 2.241 0.493 0.002122 9.84E-02 4.31E-02 250.06
43 no vessel 960 0.0555 25.3 173.1 2.249 0.497 0.002137 9.87E-02 4.33E-02 250.01
44 no vessel 960 0.0556 25.3 173.5 2.243 0.494 0.002125 9.85E-02 4.32E-02 248.80
45 no vessel 960 0.0417 17.6 131.7 1.565 0.241 0.001035 6.87E-02 3.01E-02 228.64
46 no vessel 960 0.0415 17.8 131.1 1.578 0.245 0.001051 6.93E-02 3.04E-02 231.53
47 no vessel 960 0.0418 17.8 131.8 1.581 0.246 0.001056 6.94E-02 3.04E-02 230.76
50 960 0.0420 16.5 132.7 1.463 0.210 0.000904 6.42E-02 2.82E-02 212.15
51 960 0.0392 15.9 124.0 1.412 0.196 0.000843 6.20E-02 2.72E-02 219.20
52 960 0.0394 16.6 124.8 1.474 0.213 0.000917 6.47E-02 2.84E-02 227.26
53 960 0.0397 17.2 125.5 1.530 0.230 0.000988 6.72E-02 2.94E-02 234.63
48
(mm) (J) (mg)
54 960 0.0650 31.1 201.1 2.760 0.748 0.003218 1.21E-01 5.31E-02 264.09
55 960 0.0641 30.0 198.2 2.666 0.698 0.003002 1.17E-01 5.13E-02 258.76
56 960 0.0645 30.4 199.6 2.698 0.715 0.003074 1.18E-01 5.19E-02 260.11
57 960 0.0880 44.4 266.4 3.943 1.527 0.006565 1.73E-01 7.59E-02 284.75
58 960 0.0890 43.0 269.0 3.824 1.436 0.006174 1.68E-01 7.36E-02 273.44
59 960 0.0885 43.2 267.8 3.841 1.449 0.006229 1.69E-01 7.39E-02 275.93
60 Air 0 0.0917 7.4 276.6 0.660 0.043 0.000184 2.90E-02 1.27E-02 45.91
61 Air 0 0.0896 1.9 270.8 0.171 0.003 0.000012 7.50E-03 3.29E-03 12.13
62 Air 0 0.0902 0.8 272.4 0.075 0.001 0.000002 3.31E-03 1.45E-03 5.33
70 Air 200 0.0906 34.0 273.5 3.023 0.898 0.003860 1.33E-01 5.82E-02 212.68
71 Air 200 0.0894 34.0 270.3 3.023 0.898 0.003860 1.33E-01 5.82E-02 215.18
72 Air 200 0.0912 34.1 275.1 3.031 0.902 0.003880 1.33E-01 5.83E-02 211.98
80 Air 400 0.0919 43.5 277.1 3.868 1.470 0.006319 1.70E-01 7.44E-02 268.56
82 Air 400 0.0905 43.4 273.3 3.852 1.457 0.006264 1.69E-01 7.41E-02 271.09
84 Air 400 0.0925 42.4 279.0 3.767 1.394 0.005992 1.65E-01 7.25E-02 259.80
90 Air 600 0.0925 42.3 278.9 3.761 1.389 0.005972 1.65E-01 7.24E-02 259.47
92 Air 600 0.0909 42.3 274.4 3.762 1.390 0.005975 1.65E-01 7.24E-02 263.71
93 Air 600 0.0923 46.4 278.2 4.122 1.668 0.007173 1.81E-01 7.93E-02 285.06
100 Air 800 0.0896 40.7 270.8 3.616 1.284 0.005521 1.59E-01 6.96E-02 256.94
102 Air 800 0.0918 41.5 276.8 3.687 1.335 0.005740 1.62E-01 7.09E-02 256.28
103 Air 800 0.0915 41.4 276.0 3.679 1.329 0.005716 1.61E-01 7.08E-02 256.49
110 Air 50 0.0908 18.6 274.1 1.653 0.268 0.001154 7.26E-02 3.18E-02 116.07
111 Air 50 0.0903 18.8 272.8 1.671 0.274 0.001179 7.34E-02 3.22E-02 117.87
112 Air 50 0.0916 18.5 276.2 1.641 0.264 0.001137 7.20E-02 3.16E-02 114.29
49
(mm) (J) (mg)
120 Air 100 0.0913 25.6 275.5 2.270 0.506 0.002176 9.96E-02 4.37E-02 158.51
121 Air 100 0.0918 25.6 277.0 2.276 0.509 0.002188 9.99E-02 4.38E-02 158.12
122 Air 100 0.0915 26.0 276.1 2.312 0.525 0.002258 1.02E-01 4.45E-02 161.13
130 Air 150 0.0919 31.3 277.3 2.783 0.761 0.003272 1.22E-01 5.36E-02 193.13
131 Air 150 0.0916 31.2 276.5 2.769 0.753 0.003238 1.22E-01 5.33E-02 192.72
132 Air 150 0.0905 31.0 273.2 2.751 0.744 0.003197 1.21E-01 5.29E-02 193.75
140 Air 300 0.0915 39.1 276.1 3.474 1.185 0.005096 1.52E-01 6.68E-02 242.09
141 Air 300 0.0911 40.3 274.9 3.582 1.260 0.005419 1.57E-01 6.89E-02 250.72
142 Air 300 0.0908 38.8 274.2 3.451 1.169 0.005028 1.51E-01 6.64E-02 242.15
150 Air 25 0.0892 12.3 269.8 1.090 0.117 0.000502 4.79E-02 2.10E-02 77.75
151 Air 25 0.0904 12.5 273.0 1.107 0.120 0.000517 4.86E-02 2.13E-02 78.03
152 Air 25 0.0904 12.2 273.1 1.086 0.116 0.000499 4.77E-02 2.09E-02 76.56
160 Air 25 0.0669 10.2 206.4 0.903 0.080 0.000344 3.96E-02 1.74E-02 84.13
161 Air 25 0.0656 9.8 202.8 0.870 0.074 0.000319 3.82E-02 1.67E-02 82.51
162 Air 25 0.0646 9.4 199.8 0.832 0.068 0.000292 3.65E-02 1.60E-02 80.11
170 Air 50 0.0658 14.6 203.3 1.299 0.166 0.000712 5.70E-02 2.50E-02 122.94
171 Air 50 0.0657 14.1 203.1 1.254 0.155 0.000665 5.51E-02 2.41E-02 118.84
172 Air 50 0.0652 14.3 201.7 1.270 0.159 0.000682 5.58E-02 2.44E-02 121.19
180 Air 100 0.0665 20.1 205.2 1.782 0.312 0.001341 7.82E-02 3.43E-02 167.09
181 Air 100 0.0655 20.6 202.4 1.832 0.330 0.001417 8.04E-02 3.52E-02 174.14
182 Air 100 0.0650 20.0 201.1 1.774 0.309 0.001329 7.79E-02 3.41E-02 169.73
191 Air 150 0.0653 24.1 201.9 2.144 0.451 0.001941 9.41E-02 4.12E-02 204.31
192 Air 150 0.0653 24.0 201.9 2.130 0.446 0.001917 9.35E-02 4.10E-02 203.04
193 Air 150 0.0662 24.5 204.5 2.172 0.463 0.001993 9.54E-02 4.18E-02 204.41
50
(mm) (J) (mg)
200 Air 200 0.0661 26.6 204.1 2.360 0.547 0.002353 1.04E-01 4.54E-02 222.48
201 Air 200 0.0653 26.4 201.8 2.344 0.539 0.002320 1.03E-01 4.51E-02 223.49
202 Air 200 0.0652 26.8 201.6 2.377 0.555 0.002387 1.04E-01 4.57E-02 226.84
210 Air 300 0.0659 29.4 203.7 2.613 0.671 0.002883 1.15E-01 5.03E-02 246.82
211 Air 300 0.0655 30.8 202.5 2.739 0.737 0.003168 1.20E-01 5.27E-02 260.22
212 Air 300 0.0659 29.2 203.7 2.592 0.660 0.002838 1.14E-01 4.99E-02 244.89
220 Air 400 0.0659 31.2 203.5 2.769 0.753 0.003238 1.22E-01 5.33E-02 261.81
221 Air 400 0.0655 30.4 202.5 2.702 0.717 0.003084 1.19E-01 5.20E-02 256.83
222 Air 400 0.0651 29.8 201.2 2.651 0.690 0.002968 1.16E-01 5.10E-02 253.46
230 Air 600 0.0658 30.3 203.3 2.694 0.713 0.003064 1.18E-01 5.18E-02 254.96
231 Air 600 0.0654 29.9 202.2 2.659 0.694 0.002986 1.17E-01 5.12E-02 252.99
232 Air 600 0.0653 30.0 201.8 2.667 0.699 0.003004 1.17E-01 5.13E-02 254.33
240 Air 800 0.0665 29.7 205.3 2.642 0.686 0.002948 1.16E-01 5.08E-02 247.58
241 Air 800 0.0658 30.7 203.2 2.723 0.728 0.003131 1.20E-01 5.24E-02 257.81
242 Air 800 0.0661 30.8 204.3 2.737 0.736 0.003164 1.20E-01 5.27E-02 257.80
250 Air 960 0.0668 30.5 206.2 2.708 0.720 0.003097 1.19E-01 5.21E-02 252.67
251 Air 960 0.0657 29.4 203.2 2.608 0.668 0.002873 1.15E-01 5.02E-02 247.03
252 Air 960 0.0656 30.1 202.6 2.672 0.701 0.003016 1.17E-01 5.14E-02 253.74
260 Air 25 0.0408 6.3 129.1 0.557 0.031 0.000131 2.45E-02 1.07E-02 83.10
261 Air 25 0.0408 5.6 129.0 0.497 0.024 0.000105 2.18E-02 9.57E-03 74.23
262 Air 25 0.0406 5.8 128.3 0.513 0.026 0.000111 2.25E-02 9.88E-03 76.96
270 Air 50 0.0412 9.9 130.0 0.876 0.075 0.000324 3.84E-02 1.69E-02 129.60
271 Air 50 0.0397 9.6 125.7 0.851 0.071 0.000306 3.74E-02 1.64E-02 130.30
272 Air 50 0.0404 9.7 127.7 0.859 0.073 0.000312 3.77E-02 1.65E-02 129.44
51
(mm) (J) (mg)
280 Air 100 0.0412 13.9 130.3 1.238 0.151 0.000648 5.44E-02 2.38E-02 182.92
281 Air 100 0.0406 14.1 128.3 1.253 0.154 0.000663 5.50E-02 2.41E-02 187.87
282 Air 100 0.0406 13.8 128.3 1.229 0.148 0.000638 5.40E-02 2.37E-02 184.32
290 Air 150 0.0408 17.0 128.9 1.512 0.225 0.000966 6.64E-02 2.91E-02 225.71
291 Air 150 0.0413 16.8 130.4 1.492 0.219 0.000941 6.55E-02 2.87E-02 220.14
292 Air 150 0.0412 17.3 130.0 1.532 0.231 0.000992 6.73E-02 2.95E-02 226.77
300 Air 200 0.0427 18.6 134.6 1.648 0.267 0.001147 7.23E-02 3.17E-02 235.55
301 Air 200 0.0406 18.9 128.2 1.677 0.276 0.001188 7.36E-02 3.23E-02 251.68
302 Air 200 0.0410 18.8 129.6 1.672 0.275 0.001181 7.34E-02 3.22E-02 248.17
310 Air 300 0.0404 18.2 127.9 1.614 0.256 0.001100 7.09E-02 3.11E-02 242.91
312 Air 300 0.0402 18.9 127.3 1.680 0.277 0.001192 7.37E-02 3.23E-02 254.01
313 Air 300 0.0406 18.8 128.3 1.672 0.275 0.001181 7.34E-02 3.22E-02 250.76
320 Air 400 0.0412 18.5 130.1 1.643 0.265 0.001141 7.21E-02 3.16E-02 242.98
321 Air 400 0.0404 18.3 127.7 1.621 0.258 0.001110 7.12E-02 3.12E-02 244.21
322 Air 400 0.0410 18.0 129.6 1.601 0.252 0.001082 7.03E-02 3.08E-02 237.62
330 Air 600 0.0414 18.7 130.7 1.659 0.270 0.001162 7.28E-02 3.19E-02 244.18
331 Air 600 0.0413 18.5 130.4 1.640 0.264 0.001136 7.20E-02 3.16E-02 242.00
332 Air 600 0.0409 18.9 129.3 1.675 0.276 0.001186 7.36E-02 3.22E-02 249.28
340 Air 800 0.0411 19.5 130.0 1.736 0.296 0.001273 7.62E-02 3.34E-02 257.00
341 Air 800 0.0404 18.6 127.8 1.651 0.268 0.001151 7.25E-02 3.18E-02 248.51
342 Air 800 0.0411 19.1 130.0 1.695 0.282 0.001213 7.44E-02 3.26E-02 250.95
350 Air 960 0.0416 16.4 131.2 1.460 0.209 0.000900 6.41E-02 2.81E-02 213.99
351 Air 960 0.0415 16.7 131.1 1.479 0.215 0.000924 6.49E-02 2.85E-02 217.06
352 Air 960 0.0413 16.3 130.6 1.449 0.206 0.000887 6.36E-02 2.79E-02 213.52
52
(mm) (J) (mg)
360 Air 25 0.0982 12.7 294.5 1.127 0.125 0.000537 4.95E-02 2.17E-02 73.66
361 Air 25 0.0997 12.9 298.6 1.141 0.128 0.000550 5.01E-02 2.20E-02 73.56
362 Air 25 0.0995 12.6 297.9 1.117 0.122 0.000527 4.90E-02 2.15E-02 72.14
370 Air 50 0.0964 18.6 289.5 1.654 0.269 0.001156 7.26E-02 3.18E-02 109.93
371 Air 50 0.0984 18.9 295.0 1.677 0.276 0.001188 7.36E-02 3.23E-02 109.40
372 Air 50 0.0994 18.9 297.7 1.676 0.276 0.001187 7.36E-02 3.23E-02 108.33
380 Air 100 0.1009 26.4 301.8 2.343 0.539 0.002318 1.03E-01 4.51E-02 149.36
381 Air 100 0.1002 26.4 299.9 2.348 0.542 0.002328 1.03E-01 4.52E-02 150.65
382 Air 100 0.0937 25.6 282.1 2.272 0.507 0.002179 9.97E-02 4.37E-02 154.95
390 Air 150 0.1003 31.1 300.2 2.760 0.748 0.003218 1.21E-01 5.31E-02 176.93
391 Air 150 0.0990 30.8 296.7 2.740 0.737 0.003170 1.20E-01 5.27E-02 177.66
392 Air 150 0.0958 30.8 287.8 2.737 0.736 0.003164 1.20E-01 5.27E-02 182.99
400 Air 200 0.1002 34.7 299.9 3.079 0.931 0.004004 1.35E-01 5.92E-02 197.56
401 Air 200 0.0961 34.8 288.7 3.088 0.937 0.004027 1.36E-01 5.94E-02 205.82
402 Air 200 0.0991 34.9 296.8 3.099 0.943 0.004055 1.36E-01 5.96E-02 200.86
410 Air 300 0.0995 40.0 297.9 3.554 1.240 0.005333 1.56E-01 6.84E-02 229.55
411 Air 300 0.0993 40.2 297.4 3.570 1.251 0.005381 1.57E-01 6.87E-02 230.96
412 Air 300 0.0988 40.0 296.1 3.556 1.242 0.005341 1.56E-01 6.84E-02 231.11
420 Air 400 0.1006 43.3 301.0 3.849 1.455 0.006255 1.69E-01 7.40E-02 246.03
421 Air 400 0.0966 42.9 290.0 3.812 1.427 0.006137 1.67E-01 7.33E-02 252.91
422 Air 400 0.1007 43.6 301.2 3.873 1.473 0.006333 1.70E-01 7.45E-02 247.34
430 Air 500 0.0928 45.3 279.6 4.026 1.591 0.006843 1.77E-01 7.74E-02 277.03
431 Air 500 0.0960 43.5 288.5 3.864 1.466 0.006304 1.70E-01 7.43E-02 257.71
432 Air 500 0.1001 48.5 299.6 4.308 1.823 0.007837 1.89E-01 8.29E-02 276.63
53
(mm) (J) (mg)
440 Air 600 0.1015 47.4 303.4 4.209 1.739 0.007479 1.85E-01 8.10E-02 266.87
444 Air 600 0.0950 43.9 285.7 3.902 1.495 0.006429 1.71E-01 7.51E-02 262.75
447 Air 600 0.0937 46.5 282.2 4.131 1.675 0.007204 1.81E-01 7.95E-02 281.56
452 Air 800 0.0864 41.3 262.0 3.669 1.322 0.005685 1.61E-01 7.06E-02 269.41
453 Air 800 0.0956 43.0 287.3 3.823 1.435 0.006172 1.68E-01 7.36E-02 256.05
454 Air 800 0.0985 44.4 295.3 3.942 1.526 0.006562 1.73E-01 7.58E-02 256.81
455 Air 800 0.0904 40.4 273.0 3.590 1.266 0.005443 1.58E-01 6.91E-02 253.01
460 Air 960 0.0913 42.1 275.5 3.743 1.376 0.005916 1.64E-01 7.20E-02 261.42
461 Air 960 0.0977 42.5 293.2 3.773 1.398 0.006012 1.66E-01 7.26E-02 247.59
462 Air 960 0.0934 42.0 281.4 3.729 1.365 0.005871 1.64E-01 7.17E-02 254.95
463 Air 960 0.0914 41.0 275.8 3.642 1.302 0.005600 1.60E-01 7.01E-02 254.05
501 Delrin 0 0.0907 30.7 273.9 2.724 0.729 0.003133 1.20E-01 5.24E-02 191.31
502 Delrin 0 0.0923 31.5 278.4 2.795 0.767 0.003299 1.23E-01 5.38E-02 193.17
503 Delrin 0 0.0909 29.7 274.4 2.642 0.686 0.002948 1.16E-01 5.08E-02 185.27
504 Delrin 0 0.0908 29.6 274.2 2.631 0.680 0.002922 1.15E-01 5.06E-02 184.57
505 Delrin 0 0.0914 28.2 275.7 2.503 0.615 0.002645 1.10E-01 4.82E-02 174.63 102.3
601 Delrin 0 0.0849 34.3 257.8 3.047 0.912 0.003921 1.34E-01 5.86E-02 227.40
602 Delrin 0 0.0800 34.0 244.0 3.018 0.895 0.003846 1.32E-01 5.81E-02 237.98
603 Delrin 0 0.0792 32.5 241.6 2.887 0.819 0.003521 1.27E-01 5.56E-02 229.94 69.3
610 Delrin 50 0.0800 34.6 243.9 3.072 0.927 0.003986 1.35E-01 5.91E-02 242.36
612 Delrin 50 0.0802 35.6 244.6 3.165 0.984 0.004231 1.39E-01 6.09E-02 249.03
614 Delrin 50 0.0799 31.8 243.6 2.822 0.782 0.003364 1.24E-01 5.43E-02 222.95 79
620 Delrin 100 0.0787 37.3 240.4 3.314 1.079 0.004637 1.45E-01 6.38E-02 265.27
621 Delrin 100 0.0810 43.1 246.8 3.828 1.439 0.006186 1.68E-01 7.36E-02 298.41
54
(mm) (J) (mg)
622 Delrin 100 0.0801 41.8 244.3 3.713 1.354 0.005821 1.63E-01 7.14E-02 292.42 44
630 Delrin 200 0.0792 46.1 241.7 4.092 1.644 0.007068 1.80E-01 7.87E-02 325.73
631 Delrin 200 0.0792 51.6 241.8 4.585 2.064 0.008875 2.01E-01 8.82E-02 364.73
632 Delrin 200 0.0804 51.8 245.2 4.604 2.081 0.008947 2.02E-01 8.86E-02 361.11 43
640 Delrin 400 0.0807 60.0 245.9 5.331 2.790 0.011995 2.34E-01 1.03E-01 416.98
641 Delrin 400 0.0791 60.6 241.5 5.385 2.847 0.012240 2.36E-01 1.04E-01 428.95
642 Delrin 400 0.0804 59.8 245.0 5.311 2.769 0.011907 2.33E-01 1.02E-01 416.98 47.5
651 Delrin 600 0.0807 64.2 245.9 5.703 3.192 0.013725 2.50E-01 1.10E-01 446.13
652 Delrin 600 0.0796 67.0 242.7 5.957 3.483 0.014976 2.61E-01 1.15E-01 472.04
653 Delrin 600 0.0798 64.5 243.5 5.728 3.220 0.013845 2.51E-01 1.10E-01 452.50 44.9
660 Delrin 800 0.0796 68.2 242.9 6.058 3.601 0.015485 2.66E-01 1.17E-01 479.66
661 Delrin 800 0.0816 71.0 248.6 6.308 3.906 0.016793 2.77E-01 1.21E-01 488.05
662 Delrin 800 0.0801 70.1 244.3 6.226 3.804 0.016356 2.73E-01 1.20E-01 490.05 47.4
670 Delrin 970 0.0811 72.4 247.2 6.432 4.060 0.017457 2.82E-01 1.24E-01 500.50
671 Delrin 970 0.0811 74.9 247.1 6.654 4.345 0.018684 2.92E-01 1.28E-01 517.91
672 Delrin 970 0.0806 72.0 245.6 6.396 4.014 0.017260 2.81E-01 1.23E-01 500.87 47.2
701 Delrin 0 0.0859 33.7 260.5 2.991 0.879 0.003779 1.31E-01 5.76E-02 220.97
710 Delrin 0 0.0841 31.3 255.6 2.777 0.758 0.003257 1.22E-01 5.34E-02 209.04
711 Delrin 0 0.0850 33.0 257.9 2.934 0.845 0.003634 1.29E-01 5.64E-02 218.82
712 Delrin 0 0.0853 32.5 258.9 2.883 0.816 0.003510 1.27E-01 5.55E-02 214.25 67.6
720 Delrin 50 0.0846 27.4 257.0 2.432 0.581 0.002499 1.07E-01 4.68E-02 182.14
721 Delrin 50 0.0851 33.7 258.4 2.994 0.880 0.003785 1.31E-01 5.76E-02 222.89
722 Delrin 50 0.0850 31.2 258.0 2.772 0.755 0.003245 1.22E-01 5.33E-02 206.67 38.9
730 Delrin, N2 960 0.0851 53.7 258.3 4.767 2.231 0.009594 2.09E-01 9.17E-02 355.00
55
(mm) (J) (mg)
731 Delrin, N2 960 0.0844 55.5 256.4 4.930 2.386 0.010259 2.16E-01 9.48E-02 369.87
732 Delrin, N2 960 0.0834 54.3 253.6 4.825 2.286 0.009828 2.12E-01 9.28E-02 366.00 43.8
740 Delrin, N2 800 0.0876 53.0 265.2 4.708 2.176 0.009356 2.07E-01 9.06E-02 341.42
741 Delrin, N2 800 0.0847 56.6 257.2 5.027 2.481 0.010667 2.21E-01 9.67E-02 375.99
742 Delrin, N2 800 0.0857 56.4 260.1 5.014 2.468 0.010614 2.20E-01 9.65E-02 370.82 44
750 Delrin, N2 600 0.0854 54.4 259.1 4.836 2.296 0.009871 2.12E-01 9.30E-02 359.08
751 Delrin, N2 600 0.0844 61.4 256.2 5.452 2.918 0.012545 2.39E-01 1.05E-01 409.27
752 Delrin, N2 600 0.0862 62.4 261.5 5.544 3.017 0.012974 2.43E-01 1.07E-01 407.85 76.1
760 Delrin, N2 400 0.0865 53.4 262.2 4.740 2.206 0.009487 2.08E-01 9.12E-02 347.79
761 Delrin, N2 400 0.0840 54.8 255.3 4.865 2.324 0.009991 2.14E-01 9.36E-02 366.60
762 Delrin, N2 400 0.0838 70.1 254.7 6.233 3.813 0.016393 2.74E-01 1.20E-01 470.62 50.3
770 Delrin, N2 200 0.0878 40.4 265.8 3.588 1.264 0.005435 1.57E-01 6.90E-02 259.68
771 Delrin, N2 200 0.0843 47.2 256.2 4.194 1.727 0.007426 1.84E-01 8.07E-02 314.94
772 Delrin, N2 200 0.0850 47.1 258.0 4.188 1.723 0.007407 1.84E-01 8.06E-02 312.33 38.8
800 Delrin, N2 100 0.0814 36.9 248.0 3.275 1.053 0.004529 1.44E-01 6.30E-02 254.08
801 Delrin, N2 100 0.0809 40.1 246.7 3.564 1.247 0.005362 1.56E-01 6.86E-02 277.97
802 Delrin, N2 100 0.0809 39.9 246.7 3.548 1.237 0.005317 1.56E-01 6.83E-02 276.79 36.6
810 Delrin 0 0.0812 37.1 247.2 3.297 1.068 0.004590 1.45E-01 6.34E-02 256.56
811 Delrin 0 0.0813 35.9 247.7 3.193 1.001 0.004305 1.40E-01 6.14E-02 248.02
812 Delrin 0 0.0813 33.4 247.6 2.967 0.865 0.003718 1.30E-01 5.71E-02 230.60 68.6
820 Delrin 0 0.0853 33.4 258.8 2.965 0.864 0.003714 1.30E-01 5.71E-02 220.44
821 Delrin 0 0.0823 32.8 250.5 2.911 0.832 0.003579 1.28E-01 5.60E-02 223.65
822 Delrin 0 0.0878 33.1 265.9 2.942 0.850 0.003656 1.29E-01 5.66E-02 212.95 66.4
830 Delrin 0 0.0703 34.4 216.5 3.060 0.919 0.003953 1.34E-01 5.89E-02 271.97
56
(mm) (J) (mg)
831 Delrin 0 0.0686 32.5 211.4 2.889 0.820 0.003525 1.27E-01 5.56E-02 262.97
832 Delrin 0 0.0694 32.4 213.7 2.882 0.816 0.003508 1.27E-01 5.55E-02 259.46 68.4
840 Delrin 0 0.0609 32.6 189.1 2.898 0.825 0.003547 1.27E-01 5.58E-02 294.88
841 Delrin 0 0.0614 32.2 190.3 2.856 0.801 0.003445 1.25E-01 5.50E-02 288.71
842 Delrin 0 0.0607 31.0 188.4 2.754 0.745 0.003203 1.21E-01 5.30E-02 281.28 67.6
850 Delrin 0 0.0509 31.9 159.5 2.834 0.789 0.003392 1.24E-01 5.45E-02 341.89
851 Delrin 0 0.0501 31.1 157.0 2.764 0.750 0.003226 1.21E-01 5.32E-02 338.63
852 Delrin 0 0.0509 29.4 159.4 2.608 0.668 0.002873 1.15E-01 5.02E-02 314.78 67.2
860 Delrin 0 0.0388 25.7 122.9 2.281 0.511 0.002198 1.00E-01 4.39E-02 357.03
861 Delrin 0 0.0381 25.4 120.7 2.259 0.501 0.002155 9.92E-02 4.35E-02 360.09
862 Delrin 0 0.0380 26.2 120.4 2.331 0.534 0.002295 1.02E-01 4.49E-02 372.50 59.2
900 Delrin 960 0.0400 44.6 126.4 3.965 1.544 0.006639 1.74E-01 7.63E-02 603.55
901 Delrin 960 0.0397 44.9 125.6 3.989 1.563 0.006720 1.75E-01 7.67E-02 611.18
902 Delrin 960 0.0396 43.6 125.3 3.876 1.476 0.006345 1.70E-01 7.46E-02 595.05 56.8
910 Delrin 960 0.0524 56.8 163.9 5.045 2.499 0.010746 2.21E-01 9.71E-02 592.14
911 Delrin 960 0.0528 57.6 165.2 5.117 2.570 0.011051 2.25E-01 9.84E-02 595.94
912 Delrin 960 0.0524 56.6 164.0 5.029 2.483 0.010678 2.21E-01 9.67E-02 590.05 54.5
920 Delrin 960 0.0615 57.8 190.9 5.133 2.587 0.011124 2.25E-01 9.87E-02 517.34
921 Delrin 960 0.0613 63.8 190.2 5.667 3.152 0.013555 2.49E-01 1.09E-01 573.18
922 Delrin 960 0.0611 62.2 189.6 5.527 2.999 0.012895 2.43E-01 1.06E-01 560.88 46.9
930 Delrin 960 0.0712 64.2 218.8 5.709 3.199 0.013755 2.51E-01 1.10E-01 501.76
931 Delrin 960 0.0697 67.8 214.5 6.025 3.563 0.015322 2.64E-01 1.16E-01 540.37
932 Delrin 960 0.0701 67.3 215.9 5.979 3.509 0.015088 2.62E-01 1.15E-01 532.72 44
940 Delrin 960 0.0828 68.0 252.0 6.039 3.579 0.015390 2.65E-01 1.16E-01 460.91
57
(mm) (J) (mg)
941 Delrin 960 0.0825 72.4 251.0 6.432 4.060 0.017457 2.82E-01 1.24E-01 492.76
942 Delrin 960 0.0807 71.1 246.1 6.320 3.920 0.016854 2.77E-01 1.22E-01 493.93 41.7
950 Delrin 960 0.0836 68.2 254.1 6.058 3.602 0.015489 2.66E-01 1.17E-01 458.53
951 Delrin 960 0.0817 72.0 248.9 6.400 4.020 0.017284 2.81E-01 1.23E-01 494.58
952 Delrin 960 0.0824 71.3 250.8 6.332 3.935 0.016921 2.78E-01 1.22E-01 485.68 42.2
1201 0 0.0791 40.4 241.5 3.588 1.264 0.005435 1.57E-01 6.90E-02 285.76
1202 0 0.0793 47.1 242.1 4.187 1.721 0.007401 1.84E-01 8.05E-02 332.76
1203 0 0.0787 52.2 240.2 4.636 2.111 0.009075 2.03E-01 8.92E-02 371.35
1204 0 0.0779 45.8 238.2 4.073 1.629 0.007004 1.79E-01 7.84E-02 328.99
1205 0 0.0787 2.8 240.4 0.253 0.006 0.000027 1.11E-02 4.86E-03 20.22
1210 0 0.0791 10.2 241.3 0.902 0.080 0.000343 3.96E-02 1.73E-02 71.90
1211 0 0.0772 16.7 236.2 1.486 0.217 0.000933 6.52E-02 2.86E-02 121.09
1212 0 0.0784 15.7 239.5 1.390 0.190 0.000816 6.10E-02 2.68E-02 111.71 28.4
1300 0 0.0797 10.0 243.1 0.888 0.078 0.000333 3.90E-02 1.71E-02 70.31
1301 0 0.0802 11.8 244.6 1.046 0.108 0.000463 4.59E-02 2.01E-02 82.31
1302 0 0.0797 11.5 243.1 1.021 0.102 0.000440 4.48E-02 1.96E-02 80.78 18.1
1400 0 0.0807 49.0 246.0 4.350 1.858 0.007990 1.91E-01 8.37E-02 340.23
1401 0 0.0790 52.5 241.1 4.665 2.137 0.009187 2.05E-01 8.97E-02 372.14
1402 0 0.0798 53.8 243.3 4.776 2.240 0.009630 2.10E-01 9.19E-02 377.64 113.3
1410 0 0.0821 52.5 249.9 4.663 2.135 0.009180 2.05E-01 8.97E-02 358.90
1411 0 0.0792 50.2 241.8 4.464 1.957 0.008413 1.96E-01 8.59E-02 355.12
1412 0 0.0736 51.1 225.9 4.542 2.026 0.008710 1.99E-01 8.74E-02 386.82 112.6
1420 0 0.0701 45.3 215.8 4.020 1.587 0.006825 1.76E-01 7.73E-02 358.38
1421 0 0.0684 46.4 210.8 4.119 1.666 0.007164 1.81E-01 7.92E-02 375.92
1422 0 0.0687 48.2 211.8 4.279 1.798 0.007731 1.88E-01 8.23E-02 388.75 104.3
58
(mm) (J) (mg)
1430 0 0.0591 41.4 183.7 3.678 1.329 0.005713 1.61E-01 7.08E-02 385.20
1431 0 0.0604 42.6 187.4 3.788 1.409 0.006057 1.66E-01 7.29E-02 388.74
1432 0 0.0592 42.4 184.1 3.765 1.392 0.005986 1.65E-01 7.24E-02 393.43 94.2
1440 0 0.0504 35.5 157.8 3.157 0.979 0.004208 1.39E-01 6.07E-02 384.83
1441 0 0.0502 36.0 157.4 3.197 1.004 0.004317 1.40E-01 6.15E-02 390.85
1442 0 0.0498 36.2 156.2 3.219 1.018 0.004375 1.41E-01 6.19E-02 396.40 82.3
1450 0 0.0383 28.1 121.3 2.497 0.613 0.002634 1.10E-01 4.80E-02 396.03
1451 0 0.0386 28.2 122.2 2.501 0.614 0.002641 1.10E-01 4.81E-02 393.82
1452 0 0.0380 28.1 120.3 2.496 0.612 0.002632 1.10E-01 4.80E-02 399.11 66.8
59
This Page Intentionally Left Blank
Table B – US Lightcraft
Stable resonator
Total pendulum mass: 494.0 g
Pendulum length (center of mass): 645 mm
61
(mm) (J) (mg)
1000 Delrin 0 0.0842 39.7 255.8 3.526 1.221 0.005918 1.55E-01 7.65E-02 298.94
1001 Delrin 0 0.0771 38.5 235.9 3.423 1.151 0.005577 1.50E-01 7.42E-02 314.71
1002 Delrin 0 0.0779 38.5 238.2 3.418 1.147 0.005560 1.50E-01 7.41E-02 311.18 154.9
1010 Delrin 0 0.0776 37.8 237.3 3.357 1.106 0.005362 1.47E-01 7.28E-02 306.70
1011 Delrin 0 0.0770 37.6 235.4 3.339 1.095 0.005305 1.47E-01 7.24E-02 307.54
1012 Delrin 0 0.0779 38.7 238.1 3.438 1.161 0.005626 1.51E-01 7.46E-02 313.19 148.4
1020 Delrin 0 0.0671 32.3 207.2 2.867 0.807 0.003912 1.26E-01 6.22E-02 300.07
1021 Delrin 0 0.0673 33.5 207.7 2.974 0.869 0.004211 1.31E-01 6.45E-02 310.54
1022 Delrin 0 0.0666 33.0 205.7 2.930 0.843 0.004086 1.29E-01 6.35E-02 308.92 131.4
1030 Delrin 0 0.0580 28.1 180.4 2.492 0.610 0.002956 1.09E-01 5.40E-02 299.58
1031 Delrin 0 0.0586 28.4 182.3 2.521 0.624 0.003026 1.11E-01 5.47E-02 299.97
1032 Delrin 0 0.0583 28.4 181.5 2.527 0.627 0.003039 1.11E-01 5.48E-02 301.87 115.2
1040 Delrin 0 0.0493 23.1 154.6 2.048 0.412 0.001996 8.99E-02 4.44E-02 287.33
1041 Delrin 0 0.0503 23.2 157.5 2.059 0.417 0.002019 9.04E-02 4.47E-02 283.51
1042 Delrin 0 0.0492 23.0 154.2 2.045 0.411 0.001991 8.98E-02 4.43E-02 287.63 98.1
1050 Delrin 0 0.0375 16.4 119.0 1.458 0.209 0.001012 6.40E-02 3.16E-02 265.67
1051 Delrin 0 0.0380 17.1 120.3 1.515 0.226 0.001093 6.65E-02 3.29E-02 273.10
1052 Delrin 0 0.0382 17.4 120.9 1.542 0.234 0.001132 6.77E-02 3.34E-02 276.64 75.1
1060 Delrin 50 0.0775 36.4 236.9 3.235 1.028 0.004980 1.42E-01 7.01E-02 296.14
1061 Delrin 50 0.0758 35.9 232.1 3.189 0.999 0.004842 1.40E-01 6.92E-02 297.93
1062 Delrin 50 0.0775 36.2 236.9 3.215 1.015 0.004920 1.41E-01 6.97E-02 294.35 146.6
1070 Delrin 100 0.0774 38.1 236.5 3.388 1.128 0.005465 1.49E-01 7.35E-02 310.70
1071 Delrin 100 0.0777 38.0 237.4 3.380 1.122 0.005436 1.48E-01 7.33E-02 308.73
1072 Delrin 100 0.0777 38.0 237.5 3.372 1.116 0.005410 1.48E-01 7.31E-02 307.78 149.2
62
(mm) (J) (mg)
1080 Delrin 150 0.0789 38.4 240.8 3.408 1.141 0.005528 1.50E-01 7.39E-02 306.90
1081 Delrin 150 0.0780 39.0 238.5 3.465 1.179 0.005714 1.52E-01 7.51E-02 315.09
1082 Delrin 150 0.0774 38.7 236.5 3.440 1.162 0.005632 1.51E-01 7.46E-02 315.42 146.5
1090 Delrin 200 0.0782 39.3 239.0 3.487 1.194 0.005787 1.53E-01 7.56E-02 316.44
1091 Delrin 200 0.0780 38.9 238.2 3.460 1.175 0.005696 1.52E-01 7.50E-02 314.91
1092 Delrin 200 0.0777 39.5 237.6 3.505 1.206 0.005847 1.54E-01 7.60E-02 319.87 146.8
1100 Delrin 300 0.0780 40.5 238.4 3.602 1.274 0.006174 1.58E-01 7.81E-02 327.62
1101 Delrin 300 0.0772 41.1 236.1 3.647 1.306 0.006330 1.60E-01 7.91E-02 334.97
1102 Delrin 300 0.0762 40.5 233.1 3.599 1.272 0.006165 1.58E-01 7.80E-02 334.83 147.6
1110 Delrin 400 0.0783 42.1 239.1 3.741 1.375 0.006662 1.64E-01 8.11E-02 339.25
1111 Delrin 400 0.0787 42.9 240.4 3.808 1.424 0.006901 1.67E-01 8.26E-02 343.47
1112 Delrin 400 0.0789 43.9 240.9 3.900 1.493 0.007237 1.71E-01 8.46E-02 351.06 150.6
1120 Delrin 600 0.0775 42.4 237.0 3.767 1.394 0.006754 1.65E-01 8.17E-02 344.70
1121 Delrin 600 0.0775 42.3 236.9 3.761 1.389 0.006731 1.65E-01 8.16E-02 344.29
1122 Delrin 600 0.0779 42.5 238.1 3.774 1.399 0.006779 1.66E-01 8.18E-02 343.70 148.1
1130 Delrin 800 0.0778 42.6 237.8 3.788 1.409 0.006830 1.66E-01 8.21E-02 345.41
1131 Delrin 800 0.0776 42.6 237.3 3.780 1.403 0.006802 1.66E-01 8.20E-02 345.50
1132 Delrin 800 0.0783 42.8 239.1 3.801 1.419 0.006875 1.67E-01 8.24E-02 344.73 149.3
1140 Delrin 980 0.0771 41.9 235.7 3.718 1.358 0.006580 1.63E-01 8.06E-02 342.07
1141 Delrin 980 0.0786 43.1 239.9 3.827 1.438 0.006969 1.68E-01 8.30E-02 345.84
1142 Delrin 980 0.0791 44.2 241.4 3.929 1.516 0.007346 1.72E-01 8.52E-02 352.95 149.4
1150 Delrin, N2 980 0.0790 35.6 241.1 3.165 0.984 0.004769 1.39E-01 6.86E-02 284.72
1151 Delrin, N2 980 0.0784 35.8 239.6 3.183 0.995 0.004823 1.40E-01 6.90E-02 288.11
1152 Delrin, N2 980 0.0775 34.8 236.8 3.087 0.936 0.004536 1.36E-01 6.69E-02 282.71 147.6
63
64
AFRL-PR-ED-TR-2002-0044 Dr. Jim Benford (1 CD)
Primary Distribution of this Report: Microwave Sciences, Inc.
1041 Los Arabis Ln.
Lafayette, CA 94549
AFRL/PRSP (15 CD)

Dr. Gary L. Bennett (1 CD)
Dr. Frank Mead
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Lightcraft Impulse Measurements Under Vacuum

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AFRL-PR-ED-TR-2002-0044 AFRL-PR-ED-TR-2002-0044

Lightcraft Impulse Measurements under

DLR – German Aerospace Center

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED.

AIR FORCE RESEARCH LABORATORY

5c. PROGRAM ELEMENT NUMBER

Air Force Research Laboratory (AFMC)

Approved for public release; distribution unlimited.

13. SUPPLEMENTARY NOTES

15. SUBJECT TERMS

Lightcraft Impulse Measurements under Vacuum

EOARD contract No. FA8655-02-M4017

Project officer: Wolfgang O. Schall

DLR – German Aerospace Center

Stuttgart, 30. September 2002

Prof. W.L. Bohn

Stuttgart, 30. September 2002

Prof. W.L. Bohn

2.1 Improvements in the experimental setup

3.1 German Lightcraft without and with Delrin

4. Discussion of the results

Fig. 1. German and US lightcraft

Two figures of merit

2.1 Improvements of the experimental setup

Fig. 2a - Side view of open vacuum test stand

German lightcraft Pendulum

Fig. 2b - Front view of open vacuum test stand

2.2 Measurement program

3.1 German Lighcraft without and with Delrin

3.1.1 Dependency on pressure with air alone

Fig. 3 - Impulse vs. pressure with air as propellant

If the impulse coupling coefficient, cm, is determined from these measurements by

3.1.2 Dependency on pressure with Delrin added

Fig. 5 - Delrin pin inside GL Fig. 6 - Used pin

Coupling Coefficient (N/MW)

Fig. 7 - Impulse and momentum coupling coefficient for 3 propellant

Fig. 8 - Three successive frames of a movie, showing the combustion of Delrin

This interpretation has been checked by suppressing a possible combustion reaction in a

Pulse Energy 252 +/- 10 J

Pulse Energy 252 +/- 10 J in Air

Determination: Method 1 Ser. GL 610-802

30% of total air

3500 mD for p > 0 mbar*

eigene dateien/lightcraft/origin-diagramme/exhaust veloc.graf1

Fig. 12 - Average exhaust velocity according to the second evaluation method

0,8 Pulse Energy 274.7 +/- 4.5 J

1st method 2nd method

3.1.3 Dependency on the pulse energy in vacuum and atmospheric pressure

Pulse Energy (J)

Fig. 17 - Mass ratio of air to Delrin vapor at atmospheric pressure

Pin 8 mm dia (1 bar)

Delrin pin 10 mm dia

Fig. 21 - Impulse vs. mass loss

200 Pin 8 mm dia (1 bar)

Specific Propellant Consumption (µg/J)

60 Pin 10 mm dia (0 bar)

Origindiagramme/Lightcraft/Masse von Druck.graf24-data5

3.2.1 Dependency on the ambient pressure