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# Coil Dimensions

- To: <femm@yahoogroups.com>
- Subject: Coil Dimensions
- From: "Samuel Ace Winchenbach" <swinchen@eece.maine.edu>
- Date: Sun, 18 Nov 2001 10:46:45 -0500
- Importance: Normal

    Hello, all

    A friend and I are currently building a high current coil gun for our
    senior design project at the University of Maine. Recently we have been
    trying to optimize the coil design, and I believe we are relatively
    close. Here is what we have so far:

    We know that amp-turns (NI ? a.k.a. Magneto-Motive Force) is the most
    important factor when designing the coil.
    Our power supply is a bank of large electrolytic capacitors (47 mF)
    charged to 340 volts. We are also setting a current limit of 100 Amps,
    even though the HVIGBT we have is rated to 400 amps continuous. Based on
    these numbers our coil resistance has to be 3.4 Ohms. So basically what
    we have found so far is to get the highest NI do the following steps:
    1) Select the largest wire you can afford
    2) Wind as many layers onto the barrel as needed to make the
    necessary resistance.

    What we are not taking into account is the length of the barrel, and the
    thickness of the coil winding. Right now we have a barrel (and
    projectile) fixed at 1 foot long. And the coil windings have no limit.
    At a certain point the distance from the center of the coil has to start
    making a big difference correct? How do you determine the best length
    and coil windings? By shrinking the length of the barrel you create
    more force on the projectile, but that force is over a shorter distance.
    Also how do you calculate inductance with J.A? I have looked at several
    examples and it does not make sense to me. Included is the femm model of
    our coil, and the matlab script I wrote to help us determine the optimal
    number of layers. Thanks in advance for your help,

    Samuel Ace Winchenbach
    University of Maine Electrical Engineering
    swinchen@eece.maine.edu

    /==== snip ====/

    Our barrel is 5/16? in diameter, a foot long piece of garolite. It has
    an inside diameter of ¼?. We are currently using 18 AWG magnet wire,
    with 0 series resistance.

    EDU>> help CoilOpt

    function CoilOpt(
    BarrelDiam (in),
    CoilLength (ft),
    WireDiam (mm),
    ResPerkm (Ohms/km),
    SeriesRes (Ohms),
    Voltage (Volts),
    CurrentLimit (A)
    )

    EDU>> CoilOpt((5/16),1,1.0668,20.9,0,340,100)

    ----- Non-Optimized Coil Packing -----
    |
    | NI (Amps*Turns): 2.783180754224393e+005
    | NI/L (Amps*Turns/CoilLength): 9.131170453492102e+005
    | J (Amps/Meter^2): 8.559402374851990e+007
    | CoilWidth (Meters): 0.010668000000000
    |
    | Resistance (Ohms): 3.481627984561275
    | Current (Amps): 97.655465060504994
    |
    | WireUsed (ft): 546.538946954199220
    | Number of Layers: 10
    | Turns Per Layer: 285
    | N (Total Turns): 2850
    |
    --------------------------------------

    ----- Optimized Coil Packing -----
    |
    | NI (Amps*Turns): 2.838475142859972e+005
    | NI/L (Amps*Turns/CoilLength): 9.312582489698071e+005
    | J (Amps/Meter^2): 9.036465157159652e+007
    | CoilWidth (Meters): 0.010305559007572
    |
    | Resistance (Ohms): 3.755185253889620
    | Current (Amps): 90.541471861562101
    |
    | WireUsed (ft): 589.481415986892440
    | Number of Layers: 11
    | Turns Per Layer: 285
    | N (Total Turns): 3135
    |
    ----------------------------------

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    <div class=Section1>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>Hello, all<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>A friend and I are currently building a high current coil
    gun for our senior design project at the </span></font><st1:place><st1:PlaceType><font
    size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>University</span></font></st1:PlaceType><font
    size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'> of </span></font><st1:PlaceName><font
    size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>Maine</span></font></st1:PlaceName></st1:place><font
    size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>. <span
    style='mso-spacerun:yes'> </span>Recently we have been trying to optimize the
    coil design, and I believe we are relatively close.<span
    style='mso-spacerun:yes'>  </span>Here is what we have so far:<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>We know that amp-turns (NI &#8211; a.k.a. Magneto-Motive
    Force) <span class=GramE>is</span> the most important factor when designing the
    coil.<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>Our power supply is a bank of large electrolytic capacitors
    (47 mF) charged to 340 volts. <span style='mso-spacerun:yes'> </span>Weare
    also setting a current limit of 100 Amps, even though the HVIGBT we have is
    rated to 400 amps continuous. Based on these numbers our coil resistance has to
    be 3.4 Ohms.<span style='mso-spacerun:yes'>  </span>So basically what we have
    found so far is to get the highest NI do the following steps:<o:p></o:p></span></font></p>

    <p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo1;
    tab-stops:list .5in'><![if !supportLists]><font size=2 face=Arial><span
    style='font-size:10.0pt;font-family:Arial;mso-fareast-font-family:Arial'><span
    style='mso-list:Ignore'>1)<font size=1 face="Times New Roman"><span
    style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></font></span></span></font><![endif]><font
    size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>Select the
    largest wire you can afford<o:p></o:p></span></font></p>

    <p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo1;
    tab-stops:list .5in'><![if !supportLists]><font size=2 face=Arial><span
    style='font-size:10.0pt;font-family:Arial;mso-fareast-font-family:Arial'><span
    style='mso-list:Ignore'>2)<font size=1 face="Times New Roman"><span
    style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></font></span></span></font><![endif]><font
    size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>Wind as many
    layers onto the barrel as needed to make the necessary resistance.<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>What we are not taking into account is the length of the
    barrel, and the thickness of the coil winding.<span style='mso-spacerun:yes'>
    </span>Right now we have a barrel (and projectile) fixed at 1 foot long. <span
    style='mso-spacerun:yes'> </span>And the coil windings have no limit.<span
    style='mso-spacerun:yes'>  </span>At a certain point the distance from the
    center of the coil has to start making a big difference correct?<span
    style='mso-spacerun:yes'>  </span>How do you determine the best length and coil
    windings?<span style='mso-spacerun:yes'>  </span>By shrinking the length of the
    barrel you create more force on the projectile, but that force is over a
    shorter distance.<span style='mso-spacerun:yes'>  </span>Also how do you
    calculate inductance with J.A?<span style='mso-spacerun:yes'>  </span>Ihave
    looked at several examples and it does not make sense to me. Included is the <span
    class=SpellE>femm</span> model of our coil, and the <span class=SpellE>matlab</span>
    script I wrote to help us determine the optimal number of layers.<span
    style='mso-spacerun:yes'>  </span>Thanks in advance for your help,<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>Samuel Ace <span class=SpellE>Winchenbach</span><o:p></o:p></span></font></p>

    <p class=MsoNormal><st1:place><st1:PlaceType><font size=2 face=Arial><span
    style='font-size:10.0pt;font-family:Arial'>University</span></font></st1:PlaceType><font
    size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'> of </span></font><st1:PlaceName><font
    size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>Maine</span></font></st1:PlaceName></st1:place><font
    size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'> Electrical
    Engineering<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><a href="mailto:swinchen@eece.maine.edu";>swinchen@eece.maine.edu</a><o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>/==== snip ====/<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>Our barrel is 5/16&#8221; in diameter, a foot long pieceof <span
    class=SpellE>garolite</span>.<span style='mso-spacerun:yes'>  </span>It has an
    inside diameter of ¼&#8221;.<span style='mso-spacerun:yes'>  </span>We are
    currently using 18 AWG magnet wire, with 0 series resistance. <span
    style='mso-spacerun:yes'> </span><o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>EDU&gt;&gt; help <span class=SpellE>CoilOpt</span><o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'> </span><span class=GramE>function</span>
    <span class=SpellE>CoilOpt</span>(<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'>    </span><span
    class=SpellE>BarrelDiam</span> (in),<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'>    </span><span
    class=SpellE>CoilLength</span> (ft),<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'>    </span><span
    class=SpellE>WireDiam</span> (mm),<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'>    </span><span
    class=SpellE>ResPerkm</span> (Ohms/km),<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'>    </span><span
    class=SpellE>SeriesRes</span> (Ohms),<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'>    </span>Voltage (Volts),<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'>    </span><span
    class=SpellE>CurrentLimit</span> (A)<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'> </span>)<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>EDU&gt;&gt; <span class=SpellE><span class=GramE>CoilOpt</span></span><span
    class=GramE>(</span>(5/16),1,1.0668,20.9,0,340,100)<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'> </span>----- Non-Optimized
    Coil Packing -----<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>|<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| NI (Amps*Turns): 2.783180754224393e+005<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| NI/L (Amps*Turns/<span class=SpellE>CoilLength</span>):
    9.131170453492102e+005<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| J (Amps/Meter^2): 8.559402374851990e+007<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| <span class=SpellE>CoilWidth</span> (Meters): 0.010668000000000<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>|<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| Resistance (Ohms): 3.481627984561275<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| Current (Amps): 97.655465060504994<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>|<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| <span class=SpellE>WireUsed</span> (ft):
    546.538946954199220<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| Number of Layers: 10<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| Turns <span class=GramE>Per</span> Layer: 285<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| N (Total Turns): 2850<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>|<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span
    style='mso-spacerun:yes'> </span>--------------------------------------<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span style='mso-spacerun:yes'> </span>----- Optimized Coil
    Packing -----<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>|<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| NI (Amps*Turns): 2.838475142859972e+005<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| NI/L (Amps*Turns/<span class=SpellE>CoilLength</span>):
    9.312582489698071e+005<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| J (Amps/Meter^2): 9.036465157159652e+007<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| <span class=SpellE>CoilWidth</span> (Meters):
    0.010305559007572<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>|<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| Resistance (Ohms): 3.755185253889620<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| Current (Amps): 90.541471861562101<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>|<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| <span class=SpellE>WireUsed</span> (ft):
    589.481415986892440<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| Number of Layers: 11<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| Turns <span class=GramE>Per</span> Layer: 285<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>| N (Total Turns): 3135<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'>|<o:p></o:p></span></font></p>

    <p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
    font-family:Arial'><span
    style='mso-spacerun:yes'> </span>----------------------------------<o:p></o:p></span></font></p>

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