Engineering of Distributed Systems

1
Engineering of Distributed Systems

• Coil Gun Lecture 2

2
How do we Design it?

• Easy answer
• Use a much current as possible
• Use as many turns of wire as possible
• But
• Every turn of wire adds resistance (consuming
  power)
• Making the coil longer may not help much
• Harder Answer
• Optimize coil size, shape before building it
• First step Understand how to quantitatively
  model propulsion force as a function of coil
  current and distance to magnet

3
What does this have to do with our coil gun?

• If we know how the magnetic field of the magnet
  decreases with axial distance, then we know how
  much must be going out perpendicular to the axis
• Diagram

4
Maxwells Equations

• Gauss's Law for Electricity.
• The surface integral of electric field over any
  closed surface is proportional to the enclosed
  charge.
• Gauss's Law for Magnetism.
• The integral of magnetic flux density over any
  closed surface is zero.
• Faraday's Law of Induction.
• The line integral of electric field over any
  closed path is proportional to the rate of change
  of magnetic flux in the enclosed region.
• Ampere's Law (as extended by Maxwell).
• The line integral of magnetic flux density over
  any closed path is proportional to the rate of
  change of electric field and electric current in
  the enclosed region.

5
Gausss law

• Total field (a.k.a. flux) going through a surface
  surrounding sources of flux is equal to (within a
  constant factor) the flux generated by the
  enclosed flux sources.
• For electric fields

6
Hydraulic Analogy of Gausss Law

• Garden Hose Outlet in Bag

7
What if we enclose a volume with no (or balance
/-) flux sources?

• Divergence Free Field
• What goes in must come out

8
From radial field strength to force

• F I x B
• Axial force current x radial field
• Problems
• Magnet has non-zero length
• Coil has non-zero length

9
Force on magnet is due togradient of coils
axial field coils radial field
x
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Is there another way to approach this problem?

• How about treating the coil gun as a black box,
  i.e. a LINEAR MOTOR

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This weeks lab

• Drop a magnet through a series of coils
• Measure voltage V(t)

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Review Why does Faradays Law of Induction Work?

• Sliding Bar thought experiment

Result Voltage generated is proportional to
CHANGE in flux through surface
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This weeks lab

• Drop a magnet through a series of coils
• Measure voltage V(t)

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Last Semester

• Electromagnetic Transducer
• Current (I) Kmtr -gt Force (f)
• Voltage (V) lt- Velocity (dx/dt) Kmtr
• I V electrical power
• f dx/dt mechanical power
• Assuming 100 efficient transduction
• I V f dx/dt

15
In a coil gun,How does Kmtr vary with x?
x

• F Kmtr I
• Assume I (equivalent magnet surface current) 1
• Force is proportional to radial field
• Kmtr is proportional to radial field

16
Last Semester

• Electromagnetic Transducer
• Current (I) Kmtr -gt Force (f)
• Voltage (V) lt- Velocity (dx/dt) Kmtr
• I V electrical power
• f dx/dt mechanical power
• Assuming 100 efficient transduction
• I V f dx/dt

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What we should expect

• Drop a magnet through a series of coils
• Measure voltage V(t) dx/dt Kmtr(x)

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Do we Know dx/dt?

• V(t) dx/dt Kmtr(x(t))
• dx/dt g t
• x(t) ½ g t2
• We can experimentally determine V(t)
• We can predict dx/dt, x(t)
• We can experimentally determine Kmtr(x)!!!

19
Last Semester

• Electromagnetic Transducer
• Current (I) Kmtr(x) -gt Force (f)
• Voltage (V) lt- Velocity (dx/dt) Kmtr
• I V electrical power
• f dx/dt mechanical power
• Assuming 100 efficient transduction
• I V f dx/dt

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Next Week (after Spring Break)Do DESIGN for

• Contest
• Longest Distance
• Highest Muzzle dx/dt
• Different Categories for 1, 2, 3, N stages
• Best Energy Efficiency
• Different Categories for 1, 2 3, N stages

• YOU must decide
• of stages
• of turns of wire/stage
• Geometry of each coil
• Timing of switches
• YOU can use
• Hand Analysis
• FEMLAB
• YOU must show
• Your approach to Quantitative, Analytic Design

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This Weeks Lab

• Is an EMPIRICAL way to determine Kmtr(x) for
  various coil geometries
• You can use it in the coming weeks
• You MUST corroborate its findings with
• Hand analysis, or
• FEMLAB
• Why?
• Because you will learn to PREDICT how design
  changes will QUANTITATIVELY affect performance

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What Have we NOT modeled?

• Electrical Resistance of coils
• Current Turn-on time of coils
• Friction of Barrel
• Air Resistance
• Inaccuracy (tolerance) of magnet
• Inaccuracy (tolerance) of initial placement
• Inaccuracy (tolerance) of construction