ABE223: ABE Principles – Machine Systems
Air cannon as a
pneumatic safety
testing device
Tony Grift
Dept. of Agricultural & Biological Engineering
University of Illinois
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Agenda
• Introduction to cannon function
• Adiabatic expansion theory:
• What happens inside the cannon when
you fire it?
• Build an Excel spreadsheet to deal with
ANY air cannon
pV k  Constant
• Derivation of dynamics in equation form:
• What happens to a flying projectile in air?
• Solving non-linear equations in MatLab®
• Linking MatLab and Excel
2
The piston design allows for very
fast air release
• Drawings in SolidWorks®
3
Air cannon used for high speed cutting of Miscanthus Giganteus
Laser receiver
Laser
transmitter
Cannon barrel
Upper bearing
Cover plate
Cutting blade
Swing arm
Lower bearing
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Air cannon used for high speed cutting of Miscanthus Giganteus
Laser
receivers
Cannon
barrel
Laser
transmitters
Cutting
blade
Damper
Swing arm
Bearings
Miscanthus
mount
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Air cannon used for high speed cutting of Miscanthus Giganteus
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Charging the reservoir takes place while the piston seals the
barrel
• Open main valve
• Piston is pushed against barrel with great force sealing the
barrel (pressure inside barrel is atmospheric)
• Pressure rises until the main chamber pressure equals the feed
line pressure
• Close main valve
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The cannon is fired by dropping the pressure behind the piston
instantaneously
• Disconnect feed line
• Quickly open main valve
• Pressure drops behind piston
• Piston slams back REALLY fast
• Projectile is accelerated and released from the barrel
8
The air while expanding has no time to transfer energy to the
environment: Adiabatic expansion
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Thermodynamics 101
• Ideal gas law:
pV  nRT
N
 J 
3
p  2  *V  m   n  mol  R 
*T  K 

m 
 mol * K 
• First law of thermodynamics: Internal energy is composed of
heat and work performed on or by the gas
Internal energy = Heat + Work
U  q  W  q  pV
• Processes:
Enthalpy
dU  dq  dW  dq  pdV
• Isochoric (constant volume)
• Isothermal (constant temperature)
• Adiabatic (no heat exchange with environment)
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Three possible processes:
Isochoric (const. volume)
dU
dU  dq  dW  dq  pdV
Isothermal (const. temperature)
dW  0
 J 
cv 

dq
 mol * K 
dU  dq  ncv dT
dU  0
dW
dq
dq  dW  pdV
Adiabatic (no heat exchange with environment: fast processes!)
dU
dq  0
dW
dU  dW   pdV
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pV  nRT
R  c p  cv
Isochoric (constant volume) process
dU  dq  dW  dq  pdV
cp
cv
dW   pdV 
dW  0
dV  0

dU
k
dW  0
dq
dU  dq  ncv dT
U  ncv
T T2
 dT  nc T
v
T T1
2
 T1 
 J 
cv 

 mol * K 
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Isothermal (constant Temperature) process
dU  dq  dW  dq  pdV
dT  0  dU  cv dT  0
dU  0
pV  nRT
R  c p  cv
cp
cv
k
dW   pdV
dq
dq  pdV
dq  nRT

C
pV  nRT
1
dV
V
V V2
 V2 
1
q  nRT
dV  nRT
 
ln V2  ln V1   nRT
 ln  
C V V1 V
C
C
 V1 
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Adiabatic process: No heat exchange with the environment
dU  dq  dW  dq  pdV
dq  0  dU  dW   pdV
dU
dW  pdV
pV  nRT
R  c p  cv
dq  0
cp
k
1
1
dT  nR dV
cv
T
V
1
R 1
T2 R V1
R c p  cv
dT  
dV  ln  ln
where 
 k  1
T
cv V
T1 cv V2
cv
cv
dU   pdV  ncv
T2
V1
ln  k  1 ln
T1
V2
 V1 
T2
ln  ln  
T1
 V2 
 k 1
T2  V1 
   
T1  V2 
k 1
 p2 
  
 p1 
k 1
k
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Adiabatic process: No heat exchange with the environment
pV
pV  nRT 
 nR  constant
T
p1V1 p2V2

T1
T2
T2  V1 
 
T1  V2 
k 1
 p2 
 
 p1 
k 1
k
p1V1 p2V2
T2 p2V2  V1 

 
 
T1
T2
T1
p1V1  V2 
p1V1k  p2V2 k
• Adiabatic equation
k 1
p1V1k  p2V2 k
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How much work do we get from the gas that is expanding
adiabatically?
p1V1  p2V2  constant
k
k
• Work is Force through a distance change or Pressure through a
Volume change
V V
V V
W

2
V V1
2
C
pdV   k dV
V
V V1
where C  p1V1  p2V2
k
V V2
k
 V21 k  V11 k
1
W  C  k dV C 
V
V V1
 1 k




p2V2  p1V1
W
1 k
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This work is (at least partially) used to accelerate our projectile
• Assuming that all energy from the gas is converted into kinetic
energy of the projectile (this is a major assumption) we get:
W
p2V2  p1V1 1
2
 mpv p
1 k
2
• The exit velocity of the projectile would now be:
 2 p2V2  p1V1 
vp  

1 k
 m p

1
2
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In the computer lab we will develop a spread sheet for the
complete cannon
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Keep things safe during the lab!
•
Your assignment
• Think of everything that could go wrong
• Make a safety procedure sheet for the test cannon before and after we fire it
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Lab
• Outdoor part
• Fire the cannon with various pressure settings and various
projectile
• Indoor part
• Build complete Excel spreadsheet from a template to model the
cannon assuming adiabatic expansion
• Use MatLab to simulate a ballistic model
• Connect MatLab and Excel using a Dynamic Data Exchange (DDE)
link and make them work together
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Air cannon as a safety testing device:
The End
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