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1
INNOVATIVE UAV PROPULSION-BASED ENGINE DESIGN
Lim Ting Wei
1,Matthew Lo
2, Cui Yong Dong
3
1NUS High School of Mathematics and Science, 20 Clementi Avenue 1, Singapore 129957
2 Dunman High School, 10 Tanjong Rhu Rd, Singapore 436895
2Temasek Laboratories@National University of Singapore, 5A Engineering Drive 1, Singapore 117411
ABSTRACT
In this project, our team proposed two innovative propulsion-based engine design concept
inspired by a vacuum bazooka/cannon and an air rifle respectively with the goal of
eliminating the reliance on combustion for the generation of thrust. Not only could the engine
designs proposed here be a feasible way to eradicate air pollutant emissions in the field of
aeronautics, they can also potentially be much simpler devices compared to conventional
engines, driving production costs down. Here, we developed a theoretical model for the
maximum impulse generated by each proposed engine and compare it with experimental
data. The goal of this study is to investigate the dependence of maximum impulse on several
factors, thus optimise its capability. In the Design 1, the experimental results agreed with
theoretical model and showed that this concept can potentially be feasible. Besides, Design 2
also had a potential for practical applications, even if it was not as efficient as predicted due
to some complications.
Keywords: propulsion-based engine design concept, impulse
INTRODUCTION
Aviation accounts for 2% of all human-induced greenhouse gas emissions, namely CO2 and
NO2 and 12% of all transport sources in 2013 [1]. These pollutants have a profound impact
on global warming. The root cause of these emissions is the reliance of conventional aircraft
on combustion, which we hope to eliminate in our designs without compromising the
efficiency of the engine.
Currently, PDE (pulse detonation engine) is an emerging potential new aerospace engine
actively studied by several countries. However like gas turbine engine, it requires detonation
of a given fuel-oxidizer mixture [3], relying on internal combustion engine to generate
intermittent thrust by detonation waves. Like PDE, our proposed engine also generates
intermittent thrust and is potentially a simpler engine model with few moving parts and
hardware simplicity, however it does not require any combustion and utilizes existing
atmospheric pressure to generate necessary thrust.
We proposed two innovative propulsion-based engine design concepts as possible new types
of aerospace engine. Measurement of maximum impulse is the evaluating criteria of the
performance of each engine concept in this study. In attempt to obtain reliable estimates of
the maximum impulse that can be generated by the proposed engine, we developed a
theoretical model for the maximum impulse generated by proposed engine and compared it
with experimental data for design 1. The goal of this study is to investigate the dependence of
impulse on several factors. Both our propulsion designs are solely be based on the
mechanical, isothermal behaviour of gas and will only require a source of electricity. Taken
together with our preliminary results, we believe that both Design 1 and Design 2 are
plausibility and feasibility.
2
The two proposed design concepts are as follow:
Design 1:
Design 1 is inspired by a vacuum bazooka [9]. In this design, the aircraft is fitted with
one/multiple vacuum cannons each containing a projectile within, as shown in Fig. 1. One
end of the tube is connected to the aircraft while the other end is sealed. When pipe is
unsealed, higher air pressure behind the causes it to accelerate towards the end connected to
the aircraft.
Fig. 1 1) Using control mechanisms, vacuumed tube is unsealed. 2) Atmospheric air
gushes in and exerts force on projectile. 3) Projectile gains kinetic energy and
accelerates forwards. 4) The projectile gains momentum which is transferred to the
aircraft upon collision by conservation of momentum.
Design 2:
Spring-piston airguns are able to achieve muzzle velocities near or greater than the speed of
sound. They operate by means of a coiled steel spring-loaded piston contained within a
compression chamber, and separate from the barrel. Cocking the gun causes the piston
assembly to compress the spring until the rear of the piston engages the sear. The act of
pulling the trigger releases the sear and allows the spring to decompress, pushing the piston
forward, thereby compressing the air in the chamber directly behind the pellet. Once the air
pressure has risen enough to overcome any static friction and/or barrel restriction holding the
pellet, the pellet is propelled forward by an expanding column of air.
This design is inspired by the air piston [5] and modelled after the air cannon [6], but with the
omission of the pellet. Our aim is to optimise the velocity of the air exiting the valve,
simulating the exhaust of a conventional jet engine, except powered with a simpler form of
thrust. In Design 2, air is compressed isothermally to a fraction of its volume. It can be
expected that the air pressure will build up due to compression process. Upon the opening of
a valve, it is then allowed to expand quasi-statically and isothermally, exiting through a
narrow exhaust vent at high velocities.
A fused design of 1 & 2 would be a potential engine in the future:
As showed in Fig. 2a, the piped was split into two parts by piston. At the very beginning, the
valve is closed and vacuum processed was conducted. Once the pressure within the pipe
3
reach to desire value, the valve is opened. As mentioned in Design 1, the higher pressure will
come into the pipe and accelerated the projectile. The projectile will be speeded up and push
against the piston, thereby compression the spring, as shown in Fig. 2b. As air gushed in and
fills the pipe, the valve will be closed. The rest of the steps would follow those of Design 2.
(a)
(b)
Fig. 2 A fused design of 1 and 2
ANALYSIS AND MATHEMATICAL MODEL
Design 1:
1. In the scenario of an empty vacuumed tube (projectile absent), breaking the seal at one
end allows external air to rapidly diffuse in until pressure outside and inside the tube is
equalised, this process is akin to the free expansion of gas in which temperature remains
constant and( )( )=( )( ) under the assumption of ideal gas. By first law of
thermodynamic, internal energy of a closed system is constant ( =0) and only entropy
is changed. Thus, no work is done during free expansion, the history of pressure could be
expected as Fig. 3
Fig. 3 The history of pressure
2. However, by simply adding a projectile at the sealed end of the tube, impulse obtained
can be increased significantly and utilised to do work. The vacuum canon can work in 2
different ways.
In the simplest case scenario, atmospheric air exerts a constant force on the projectile, thus
acceleration is constant and velocity can be given as a function of displacement : √
(1).
Where is pressure inside the pipe, is cross area, m is mass of projectile. However, this
amount of force is exerted only if the ball is not moving faster than the incoming airflow.
Consider the ball moves at the speed of sound, it would move as fast as incoming air and the
4
air would be unable to exert any force. Thus, as velocity increases, the acceleration would
decrease and velocity asymptotically approaches the speed of sound. In this case, Eq. (1) will
no longer be applicable at longer displacement when velocity of projectile is comparable to
that of sound.
Using this first model, we arrive at these calculations,
Displacement of projectile/cm
40 50 60 70
Velocity of a
31.3g projectile
56.67m/s 63.36m/s 69.4m/s 74.97m/s
Velocity of a
85.5g projectile
34.29m/s 38.33m/s 42.11m/s 45.36m/s
Table of velocity of projectile against displacement
In the second case scenario, we assume that incoming airflow forms a stagnant mass of air
behind the projectile, thus atmospheric pressure at one end must not only accelerate the
projectile but also the air column behind it. As displacement x of projectile increases, mass of
air column also increases. Based on the mass of conservation, the mass of air, , can be
expressed as , the Newton’s 2nd
law of motion can be rewritten as:
(m + M) v = P A (2)
Finding Velocity as a function of displacement:
(3)
Solving for x:
Integrating Eq. 2 we can get: (m + pAx) v = PAt
(4)
Since we know that vdt= dx, we multiply both sides by dt and integrate again.
∫ (PAt) dt = ∫ (m + xA) v dt = ∫ (m + xA) dx
=
A+ mx
(5)
Make x the subject by completing the square,
=
+ , we can group the constants, let α =
=
√
–
(6)
Substituting back into equation 3:
(√
– )=
√
(7)
We obtain velocity as a function of time, thus we need time as a function of displacement.
Manipulation of equation 4 will give us:
5
√
(8)
Aiming at more realistic test cases, this study is devoted to examining behaviour of projectile
at shorter lengths for small UAVs. Using this model, we arrive at the following calculations.
Displacement of projectile/cm
40 50 60 70
Velocity of a
31.3g projectile
55.8 m/s 62.13m/s 67.83m/s 72.99m/s
Velocity of a
85.5g projectile
34.1m/s 38.056m/s 41.631m/s 44.9m/s
Table of velocity of projectile against displacement
As t tends to infinity, v approaches √
= 277ms
-1 which is actually the maximum
velocity that can be achieved by such a set up. We can derive this by differentiating Eq. (2):
=
(9)
Terminal velocity is reached when acceleration equates to 0. Substituting
= a = 0, and let
P = 105
Pa and ρ= 1. 3kg/m3, we can predict terminal velocity to be
√
= 277ms
-1
(10)
The theoretical limiting velocity of the projectile is very high and close to sonic speed as
shown in several recent studies[4] [5], but in practice, the actual velocity is lesser.
Design 2:
Fig. 4. Simplified sketch of our experimentation model
As seen in Figure 4, air is manually compressed by a piston into the truncated portion with
Volume 142.5cm3.
Pressure in tube after manual compression is:
where is the length of
compression and is the cross-sectional area of the compression tube. Hence, it is easy to
6
see that the longer the length of compression, the larger the reduction in volume and the
greater the pressure built up.
By assuming isothermal compression, the energy stored in the compressed air, which is the
work done on the gas, is:
According to ideal gas law, PV = nRT where P is pressure, V is volume, n is moles of gas, R
is the universal gas constant and T is temperature in Kelvins which remains constant here.
Therefore energy stored in compressed gas
∫
= ∫
= nRT
= nRT ( ( (
Thus, the larger is, the larger
and thus the larger the energy stored in the gas since
nRT is constant. Thus when the valve is manually released, the air will exit from the exhaust
with more kinetic energy and thus higher velocity.
EXPERIMENTAL SETUP AND PROCEDURE
Design 1:
1. Test 1: Analysis of airflow into pipe
The pipe is 40 mm in diameter. One PCB dynamic pressure sensor was installed at the
closed end of pipe and was used to measure shock wave pressure generated by
compressed air. The pressure sensor is connected to an oscilloscope with level set at 100
mV. Data processed was carried out using Matlab version R2010b. Impulse, , is the
integral of force over a time interval, which can be obtained by the following equation:
∫
∫
, (11)
where is force exerted by incoming airflow. In Design 1, the experimental variables were
focused on pipe length and pressure differential.
Fig. 5 Schematic diagram of test 1 of Design 1
2. Test 2: Analysis of terminal velocity of projectile in vacuumed tube.
To measure the terminal velocity of projectile using photogate, one transparent pipe 40 mm
in diameter was used and was sealed with aluminium foil at the closed end. The pipe is
vacuumed. 1 pressure gauge was used to monitor the pressure within the pipe. The aluminium
7
seal is broken when pressure reaches to absolute vacuum. As can be expected, the projectile
will be accelerated and the photogate can measure the time for which projectile obscures the
light. The diameter of the projectile (39 mm) is then divided by this time to calculate to
velocity. The pipe length ranged from 70 cm to 40 cm with an interval of 10 cm. Two distinct
projectile mass of 31.3 g and 85.5 g were employed to investigate the mass effect on the
velocity.
Fig. 6 Schematic diagram of test 2 of Design 1
Design 2:
A pipe of internal diameter 50 mm (main chamber) is connected to a ball valve which leads
to a pipe of internal diameter 1.5 mm (exhaust pipe). A piston compatible with the interior of
the tube is attached to a 1.0 m long rod. When the valve is opened, the rod is pulled back at
different lengths to allow air to gush in. Then the valve is closed and piston is moved back to
its original position, manually compressing the volume of air in front. A Pitot tube was used
to measure the velocity of the air rushing out of the exhaust pipe once valve is opened.
Fig.7 Schematic diagram of test 3 of Design 1
RESULTS DISCUSSION AND ANALYSIS
Design 1:
1. Test 1: Analysis of airflow into pipe
In the test cases of pressure differential of 30 inHg, the pressure histories with pipe lengths of
70 cm and 60 cm were shown in Fig. 8 and Fig. 9, respectively. As can be seen in Figs. 8 and
9, there is a sharp increase in pressure recorded upon unsealing of pipe, followed by another
increase before it slowly decreases to equilibrium at atmospheric pressure (1498.596 mV).
8
Fig.8 Pressure history for 70 cm-long pipe with pressure differential (between external
and internal of pipe) of 30 inHg.
Fig. 9 Pressure history for 60 cm-long pipe with pressure differential (between external
and internal of pipe) of 30 inHg.
Please refer to appendix section A for the rest of graphical details.
The graph shape is similar to that of the pressure-time profile during a shock tube experiment
[2]. When the diaphragm separating the driver gas (high pressure) and the test gas (low
pressure) breaks, a shock wave is formed and propagates down the tube at supersonic speed,
compressing the test gas (incident shock wave). The shock wave is reflected at the end wall
and the test gas is compressed again (reflected shock wave). In this experiment, external air
acts was driver gas while vacuum acts as test gas, the two steps can be simply due to the
pressure wave propagating down tube and reflected by end wall. The experimental results
were summarised and shown in Table 1.
Tube length (cm)
70 60 50 40
Impulse obtained for
set up with pressure
differential of 30 inHg
1.407N*s 1.255N*s Resultant
pressure is
below trigger
level
Resultant
pressure is
below trigger
level
Table 1. Impulse exerted by air on the end wall of tubes of different length
For test cases with pressure differential of 20inHg, resultant pressure was below trigger level
(100 mV), thus no data was obtained for these variables. It should be noted that lowering
trigger level risks inaccurate result due to noise triggering. Impulse recorded is very weak as
9
predicted and can be increased by increasing tube length and diameter, however it cannot be
utilised to do work.
2. For projectile of mass with 85.5 g and 31.3 g, the experimental results were summarised
in Table 2.
Displacement (x) of
projectile (cm)
Projectile of mass 85.5 g
Velocity (m/s)
Projectile of mass 31.1 g
Velocity (m/s)
70.0 39.00 46.43
60.0 33.19 47.27
50.0 27.08 39.00
40.0 26.17 31.33
Table 2. Velocity of projectile against displacement.
For data details, refer to Appendix section B.
The velocity of the lightweight ball (31.1 g) is about 63.1% of the predicted values, while that
of the heavy ball (85.5 g) is about 78.2%. The discrepancies in values can be attributed to
several factors. There is friction between the projectile and inner surface of tube which slows
the projectile. Also, aluminium foil may partially obstruct the incoming airflow. Besides, the
projectile does not fit the tube exactly, leaving a gap of 1mm around the edge, this allows air
to flow beyond the projectile. The pressure built up in front of the projectile decelerates it
significantly.
The two arrows in Fig. 10 showed where the 60 cm and 70 cm reading are taken. There is a
shorter remaining tube length after 70 cm mark than the 60 cm mark, this means compression
effect of air by ping pong ball at the 70 cm will be higher than at the 60 cm mark, the
compressed air slows down the ball significantly. This likely explains why the lightweight
projectile has a higher velocity when x=60 cm then when x= 70 cm.
The maximum impulse generated by the lightweight ball within a short displacement of 70cm
is (39.00m/s * 0.0855kg) 3.3345Ns. That of the lightweight ball is (47.27m/s * 0.0313kg)
1.48Ns. Although seemingly very less, impulse can be increased by multiple folds by
increasing the cross sectional area of the tube, mass of the projectile and displacement
travelled. It is also much greater than impulse obtained with the same set up but without the
projectile in test 1, showing how this design successfully utilises existing atmospheric
pressure to generate thrust. We can increase efficiency of this model by changing the shape of
the projectile to be more aerodynamic and allowing it to fit more tightly within the tube while
decreasing friction in between surfaces. The final velocity of the projectile just before
collision can be raised to as high as 277m/s as calculated. However, we are aware of potential
problems, such as damage done during collision, and instability of such a design, which can
be tackle in the future.
10
Fig. 10
Design 2:
The results agreed with the trend we predicted with our theoretical model.
Length of
compression / m
0.05 0.10
0.15 0.20 0.25 0.30 0.35 0.40
Average exit
velocity of air /
ms^-1
10.540 16.175
26.385 37.130 41.405 45.175 49.400 52.810
Table 2. Exit velocity of air against compression length.
For the rest of the data details, refer to Appendix under section C.
One key factor that could have compromised the exhaust air velocity was air viscosity and
pipe resistance, which could have had a large effect given the relatively diminutive opening
of the exhaust valve and the high air velocity.
Another important source of error could be leakage of air from the set-up as the air was being
manually compressed, especially for longer lengths of compression (more time taken to
compress) causing the pressure built up in the set-up before the manual releasing of the valve
to be lower than expected, thus reducing the exit velocity of the air.
Areas to improve upon:
If this design were to be incorporated into a real-life aircraft, such leakages must be
prevented. As for the source of compression, we have two suggestions for improvement. A
spring could be compressed by a motor and then released to provide the source of
compression. A solenoid-actuated valve could replace the manual valve in our set-up. Just
when the pressure built up to a certain value, a static pressure-voltage transducer would then
tip the circuit and trigger a lever to open the solenoid-actuated valve.
Another possible source of compression could come from magnets. The walls of the tube
would be made of a good insulator, while the piston and truncated part (facing the valve)
would be made of magnetic material. The magnets would attract each other to provide the
force for compression and upon the opening of the valve, the piston flips and repels back to
its original position. Another way would be to induce opposite magnetic fields in the two
magnetised surfaces with a circuit.
CONCLUSION
While both designs potential to energy efficient and environmentally friendly engines in the
future. Design 1 is shown to be more feasible as it was generally more successful both in
11
terms of theoretical model and practical testing, Design 2 however ran into a few
complications. Although practical results were not as high as predicted, it still suggest that
Design 2 is plausible in the future.
ACKNOWLEDGMENT
We would like to express our gratitude towards our mentors, Dr Chang Po Hsiung and Dr Cui
Yong Dong, for their guidance and constant supervision. We would also like to thank Mr
Bernard Lee for his assistance in woodwork and the interns, Desmond, Clark and Wee Kian
for their guidance throughout the project. Mr Jonathan Peh was also there to assist us in
certain experimental procedures. This project would not be possible without their help.
12
REFERENCES
1. Air Transport Action Group, http://www.atag.org/facts-and-figures.html.
2. Gernot Friedriches.,“Thermal Decomposition Mechanism of Formaldehyde:
Shock Tube Investigations of High Temperature Reaction Kinetics” Institute of Physical
Chemistry, Kiel University.
3. Matthew Lam Daniel Tillie Timothy Leaver Brian McFadden.,” Pulse Detonation
Engine Technology: An overview” University of British Columbia November 26, 2004.
4. The vacuum canon equation,
http://www.phys.utk.edu/demoroom/MECH/The%20Vacuum%20Canon.pdf.
5. Eric Ayars and Louis Buch holtz “Analysis of the Vacuum Cannon” Department of
Physics California State University, CA95929-0202, January 6,2004.
6. Stephen J. Compton, “Internal Ballistics of a Spring-Air Pellet Gun”, May 18, 2007.
7. Z. J. Rohrbach, T. R. Buresh, and M. J. Madsen, “The Projectile Velocity of an Air
Cannon”, May 6, 2001.
8. http://www.insula.com.au/physics/1279/L7.html.
9. https://www.youtube.com/watch?v=CVL99yIB3NQ.
13
APPENDIX A
Results of Design 1: Momentum of air rushing into tube
70cm-long tube with
pressure differential
of 30 inHg
Area under graph:
1.0632kPa*s,
70cm-long tube with
pressure differential
of 30 inHg
Area under graph:
1.0436kPa*s
70cm-long tube with
pressure differential
of 30 inHg
Area under graph:
1.2301kPa*s
14
70cm-long tube with
pressure differential
of 30 inHg
Area under graph:
1.1443kPa*s
60cm-long tube with
pressure differential
of 30inHg
Area under graph:
1.0088kPa*s,
15
60cm-long tube with
pressure differential
of 30inHg
Area under graph:
0.9889kPa*s,
Appendix B
Results of Design 1 (velocity of projectile)
Length of
Tube (cm)
Pressure
(inHg)
Mass of
Projectile(g)
Data Time
(ms)
Average
Time for
which
projectile
blocked the
photogate
(ms)
Velocity
(m/s)
70.0
-30 85.5 0.90
1.10
1.00 39.000
60.0
-30 85.5 1.35
1.00
1.175 33.191
50.0 -30 85.5 1.49
1.39
1.44 27.08
40.0 -30 85.5 1.49
1.49
1.490 26.174
16
Length of
Tube
(cm)/cm
Pressure
(inHg)
Mass of
Projectile
(g)
Data Time
(ms)
Average
Time for
which
projectile
blocked the
photogate
(ms)
Velocity
(m/s)
70.0
-30 31.3 0.90
0.78
0.84 46.43
60.0
-30 31.3 0.80
0.85
0.825 47.27
50.0 -30 31.3 0.90
1.10
1.00
1.000 39.00
40.0 -30 31.3 1.49
1.00
1.245 31.3
Appendix C
Results of Design 2
Length of compression
(m)
Exit velocity of air 1st and
2nd readings
(m/s)
Average exit velocity of air
(m/s)
0.05 10.02, 11.06 10.540
0.10 16.02, 16.33 16.175
0.15 25.59, 27.18 26.385
0.20 36.95, 37.31 37.130
0.25 40.86, 41.95 41.405
0.30 44.96, 45.39 45.175
0.35 49.13, 49.67 49.400
0.40 52.50, 53.12 52.810