Engineering of Distributed Systems

1
Engineering of Distributed Systems

• Coil Gun Lecture 1

2
EDS in Three Acts

• Part 1 Diffusion
• Example (EDS) Spread of heat
• Example (EDS) Heat Sinks
• Part 2 Fields (Quasi-Statics for impressing
  your friends)
• Example (Physics) Electric Magnetic Fields
  and Forces
• Example (EDS) Magnetic Fields and Forces
• Example (Math) Vector Calculus
• Part 3 Waves
• Example (EDS) Sound
• Example (Physics) Radio, Optics
• Example (EDS) Tsunamis
• Example (EDS) The Cochlea (inner ear)
• Example (EDS) Whips, Dinosaur Tails

3
How are we going to learn about fields in MCEDS ?

• How about building a permanent magnet coil gun?
• Available Parts
• 1½ ft.3/8 i.d. plastic pipe
• Length of Wire
• Very Strong (Neodymium Iron Boron) ¼ o.d.. 1
  long magnet
• Big Power Supply

4
Basic Idea

• We know (from grade school) that N-N or S-S
  Magnetic Poles Repel Each Other
• Lets use this to propel the magnet
• Why do magnetic poles repel each other?
• A You may know this from physics
• Well review it anyway
• Can we use a coil instead of one of the magnets?
• Sure!

5
Can we run one of these backwards?
6
How we might do it

• Load Magnet in Front of a Coil of wire
• e.g. inside of a tube with coil wrapped around
  slightly behind magnet
• Run an electrical current through wire to create
  an electromagnet.
• Magnet is repelled by electromagnet, shooting it
  down the tube

7
What is the magnetic field of a solenoid coil. vs
a magnet ?
8
What is really going on in permanent magnets?
9
Why do like magnetic poles repel one another?
10
Lorentz Force on a Wire
http//hyperphysics.phy-astr.gsu.edu
11
How do we calculate the force?Part 1How fast
does the field drop off?

• Coulombs law for monopoles Says 1/(r2)
• What does Gausss law say this forces this to be
  true?
• What about dipoles? (e.g. magnetic fields)
• They drop off as

12
Last Weeks Lab
x

• Result
• Far away field dies off as
• Nearby somewhat different

13
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

14
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

15
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.

16
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

17
Hydraulic Analogy of Gausss Law

• Garden Hose Outlet in Bag

18
What if we enclose a volume with no (or balance
/-) flux sources?

• Divergence Free Field
• What goes in must come out

19
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

20
Force on magnet is due togradient of coils
axial field coils radial field
x

• If axial field dies off with 1/(x3) (far away),
  and radial field gradient of axial field, then
  radial field falls off as
• 1/(x4) (far away, differently close in)

21
Is there another way to approach this problem?

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

22
This weeks lab

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

23
Review Why does Faradays Law of Induction Work?

• Sliding Bar thought experiment

Result Voltage generated is proportional to
CHANGE in flux through surface
24
This weeks lab

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

25
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

26
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
• Kmtr drops off with 1/(x4) (far away, differently
  close in)

27
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

28
What we should expect

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

29
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)!!!

30
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

31
Next WeekDo DESIGN for

• Contest (after Spring Break)
• 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

32
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

33
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