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Dept. of Agricultural & Biological EngineeringUniversity of Illinois

ABE223: ABE Principles – Machine Systems

Air cannon as a pneumatic safety

testing device

Tony Grift

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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

• Derivation of dynamics in equation form: • What happens to a flying projectile

in air? • Solving non-linear equations in

MatLab®

• Linking MatLab and Excel

ConstantkpV

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The piston design allows for very fast air release

• Drawings in SolidWorks®

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Air cannon used for high speed cutting of Miscanthus Giganteus

Swing arm Cutting blade

Lower bearing

Upper bearing

Cover plate

Laser transmitter

Laser receiver

Cannon barrel

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Air cannon used for high speed cutting of Miscanthus Giganteus

Cutting blade

Miscanthus mount

Laser transmitters

Cannon barrel

Laser receivers

Swing arm

Bearings

Damper

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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

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The air while expanding has no time to transfer energy to the environment: Adiabatic expansion

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Thermodynamics 101

• Ideal gas law:

• First law of thermodynamics: Internal energy is composed of heat and work performed on or by the gas

• Processes:• Isochoric (constant volume)• Isothermal (constant temperature)• Adiabatic (no heat exchange with environment)

nRTpV

32

* **

N Jp V m n mol R T Km mol K

VpqWqU

pdVdqdWdqdU

Internal energy = Heat + Work

Enthalpy

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Three possible processes:

Isochoric (const. volume) Isothermal (const. temperature)

Adiabatic (no heat exchange with environment: fast processes!)

dq

dU

pdVdWdq

0dU dW

0dq

dU

pdVdWdU

0dW

pdVdqdWdqdU

dq

dW

dTncdqdU v

Kmol

Jcv *

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Isochoric (constant volume) process

dq

00

dWdV

pdVdW

dU

12

2

1

TTncdTncU

dTncdqdU

v

TT

TT

v

v

kc

c

ccR

nRTpV

v

p

vp

Kmol

Jcv *

pdVdqdWdqdU

0dW

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Isothermal (constant Temperature) process

dq

00 dTcdUdT v

0dU

1

212 lnlnln

1

1

2

1V

VnRTVVnRTdV

VnRTq

dVV

nRTdq

pdVdq

CC

VV

VVC

C

pdVdW

nRTpV

kc

c

ccR

nRTpV

v

p

vp

pdVdqdWdqdU

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Adiabatic process: No heat exchange with the environment

0dqpdVdWdUdq 0

dU

k

kkk

v

vp

vvv

v

p

p

V

V

T

T

V

V

T

T

V

Vk

T

T

kc

cc

c

R

V

V

c

R

T

TdV

Vc

RdT

T

dVV

nRdTT

ncpdVdU

1

1

2

1

2

1

1

2

1

2

1

1

2

2

1

1

2

2

1

1

2

lnln

ln1ln

1 wherelnln11

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pdVdW

kc

c

ccR

nRTpV

v

p

vp

pdVdqdWdqdU

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11

2 1 2

1 2 1

kk

kT V p

T V p

1

1 1 2 2 2 2 2 1

1 2 1 1 1 2

1 1 2 2

k

k k

pV p V T p V V

T T T pV V

pV p V

1 1 2 2

1 2

constantpV

pV nRT nRT

pV p V

T T

1 1 2 2k kpV p V• Adiabatic equation

Adiabatic process: No heat exchange with the environment

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How much work do we get from the gas that is expanding adiabatically?

• Work is Force through a distance change or Pressure through a Volume change

k

VVCdV

VCW

kkVV

VVk 1

1 11

12

2

1

k

VpVpW

1

1122

constant2211 kk VpVp

kk

VV

VV

VV

VVk

VpVpC

dVV

CpdVW

2211 where

2

1

2

1

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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:

• The exit velocity of the projectile would now be:

21122

2

1

1 ppvmk

VpVpW

21

1122

1

2

k

VpVp

mv

pp

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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