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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.

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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

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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

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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:

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√

(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

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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

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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).

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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

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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.

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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

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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.

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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.

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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

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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,

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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

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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