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<DIV><FONT face=Arial size=2>Hi Terry,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>OK, here's a more user-friendly method =
for you that
will give you the correct position of the rib anywhere along its =
length.
(You can also use this method to plot out points on a template. =
Compute
numerous points and connect the dots. :-)</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Clamp any part of the rib against a =
flat surface,
concave side up (soundboard side down). With this arrangement,
let:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>h = the height of the rib above the =
flat
surface</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2>r = radius of the rib</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>d = the distance =
along the rib
you are measuring, with respect to the clamp point. For instance, =
if you
clamp in at the middle of a 4 ft rib and measure at the end, d =
would be
2. Of course this is approximate. More accurately, d =
would be
the distance from the clamp point to the position <STRONG>on the flat =
surface,
directly underlying the measurement point</STRONG>. (Think right
triangles.)</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Then:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>h = r - Sqrt ( r^2 - =
d^2) </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>So for a rib of 60 ft radius (720 in =
radius), these
would be some of the elevations, h, as a function of distance, d, from =
the clamp
point:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>
<TABLE cellSpacing=0 cellPadding=2 width=134 border=0>
<TBODY>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>d (in)</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>h (in)</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16>
<P></P></TD>
<TD width="50%" height=16>
<P></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.001</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.003</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>3</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.006</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>4</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.011</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>5</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.017</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>6</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.025</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>7</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.034</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>8</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.044</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>9</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.056</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>10</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.069</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>11</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.084</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>12</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.100</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>13</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.117</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>14</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.136</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>15</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.156</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>16</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.178</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>17</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.201</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>18</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.225</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>19</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.251</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>20</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.278</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>21</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.306</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>22</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.336</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>23</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.367</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>24</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.400</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>25</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.434</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>26</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.470</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>27</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.506</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>28</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.545</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>29</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.584</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>30</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.625</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>31</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.668</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>32</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.711</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>33</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.757</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>34</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.803</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>35</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.851</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>36</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.901</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>37</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>0.951</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>38</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.003</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>39</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.057</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>40</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.112</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>41</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.168</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>42</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.226</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>43</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.285</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>44</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.346</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>45</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.408</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>46</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.471</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>47</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.536</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>48</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.602</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>49</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.669</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>50</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.738</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>51</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.809</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>52</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.880</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>53</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>1.953</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>54</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.028</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>55</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.104</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>56</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.181</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>57</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.260</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>58</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.340</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>59</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.421</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>60</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.504</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>61</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.589</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>62</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.674</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>63</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.762</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>64</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.850</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>65</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>2.940</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>66</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>3.031</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>67</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>3.124</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>68</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>3.218</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>69</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>3.314</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>70</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>3.411</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>71</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>3.509</FONT></P></TD></TR>
<TR>
<TD width="50%" height=16><FONT face=Arial size=2>
<P align=center>72</FONT></P></TD>
<TD width="50%" height=16><FONT face=Arial size=2>
<P =
align=center>3.609</FONT></P></TD></TR></TBODY></TABLE></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Hope that helps!</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Peace,</FONT></DIV>
<DIV><FONT face=Arial size=2>Sarah</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>
<A title=mfarrel2@tampabay.rr.com
href="mailto:mfarrel2@tampabay.rr.com">Farrell</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A =
title=pianotech@ptg.org
href="mailto:pianotech@ptg.org">Pianotech</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, December 11, =
2003 7:00
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: Rib =
dimensions</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial>Lots of good methods for calculating the =
radius of an
arc have been provided. But there is also the question of whether the =
curve is
a true arc or some other shape (this assumes you have a specific shape =
as a
target). Most of the provided methods do not address that concern - in =
fact
you could have an obtuse angle with two straight sides rather than an =
arc.
That's why I suggested making a number of measurements along the curve =
-
offsets from a straight line.</FONT></DIV>
<DIV><FONT face=Arial></FONT> </DIV>
<DIV><FONT face=Arial>Terry Farrell</FONT></DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>
<A title=absolutepiano@comcast.net
href="mailto:absolutepiano@comcast.net">Absolute Piano</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A =
title=pianotech@ptg.org
href="mailto:pianotech@ptg.org">pianotech@ptg.org</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, December 10, =
2003 4:40
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Rib dimensions</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2><FONT face="Times New Roman"
size=3>Hello,<BR><BR>I'm trying to apply some science to my =
soundboard rib
making and I am<BR>looking for "tables of static values for =
the
Resisting Moment (W) and the<BR>Moment of Inertia (I) for all the =
possible
cross sections of sugarpine and<BR>spruce (DIN 1052 Class I will
suffice).<BR><BR>What is the formula for converting pounds/inch =
squared to
kg/cm squared?<BR><BR>Given a right angle connected to the outside =
of an arc
of a circle, how do<BR>you prove the circle is 60'? (I made a jig =
for
crowning ribs that is<BR>adjustable and I want to calibrate
it.<BR><BR>Thanks,<BR><BR>Jude Reveley,
RPT</FONT><BR></FONT></DIV></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>