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 Subject: Mathematical calculation Category: Science > Math Asked by: edburton-ga List Price: \$30.00 Posted: 17 Nov 2006 12:33 PST Expires: 17 Dec 2006 12:33 PST Question ID: 783626
 ```Hello, Please provide the radius necessary to form an arc over 600mm long so that one end of the arc is: 2 millimetres 5 millimetres 8 millimetres behind the other end of the arc Then do the same for a lenght of 768 mm i.e. the arc length is 768mm long. and one end has to be behind the other 5 mm 8mm 10 mm What I am trying to do is to bend an aluminium tube evenly so that one end of the tube is these small distances behind the start of the arc. What I actually want to do is bend my mast on my model sailing boat these small amounts (say 5mm) backwards from a where a straight piece of aluminium would be. If you have the equation on a spreadsheet that would be even better. Thank you VERY much!``` Request for Question Clarification by livioflores-ga on 17 Nov 2006 19:20 PST ```Hi!! Your question is not clear to me, is there a chance that you can upload an image or diagram of what do you need? A good place to post image files is Rapidshare: http://www.rapidshare.de```
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 Subject: Re: Mathematical calculation From: myoarin-ga on 18 Nov 2006 04:44 PST
 ```HI, After the third reading of your question, I believe I understand. You have two masts for your model boat(s), 600mm and 768mm long/high. You want the mastheads to be 8mm and 10mm, respectively, to the aft of the straight line of the way the masts are stepped (not necessarily vertical). Don't we need to know how far from the deck the intermediate measurements from the straight line are? From pictures, it appears that some marconi masts are not a simple arc but curve more at the top. Can't you just plot those points on 1:1 scale and with a French curve find the line that is required?```
 Subject: Re: Mathematical calculation From: redbelly98-ga on 18 Nov 2006 12:16 PST
 ```Okay, here's a spreadsheet solution using Excel. You'll have to be a little patient to follow along on this procedure. The idea here is that the answer approaches the "exact" value, without actually getting there. But for your purposes it is more than close enough. In cell A1 of the spreadsheet, put 600 (or whatever mast length you want) In cell A2, put 2 (or whatever displacement you want) Next come the formulas In cell A3, put a starting guess for the radius. I used: =10*A1 (That's 10 times whatever the mast length is) In cell A4, we use this guess to get closer to the correct value. Here is the formula to put in A4: =\$A\$1/ACOS(1-A\$2/A3) Now COPY the formula from A4 down to the cells in the next 20 or so rows, i.e. cells A5 through A25. You'll see the number approach a nearly constant value. To see how close the answer is, we can use a formula to see the actual displacement for the different values of radius. Starting in cell B3, put this formula: =A3*(1-COS(\$A\$1/A3)) Then copy the formula in B3 down to cells B4 through B25. At some point the number will become VERY CLOSE to the desired displacement entered in cell A2. For example, here are is the result for a 600 mm mast length and 2 mm displacement: 600 2 6000 29.97500833 23237.25455 7.745751517 45730.98413 3.936005782 64154.17813 2.805720426 75985.82783 2.36885048 82696.39959 2.17662693 86270.7712 2.08644564 88115.48903 2.042765767 89052.59128 2.021269864 89524.87484 2.010606846 89761.95595 2.00529643 89880.73228 2.002646474 89940.17959 2.001322804 89969.9181 2.000661295 89984.7911 2.000330622 89992.22855 2.000165305 89995.94752 2.000082651 89997.80706 2.000041325 89998.73686 2.000020663 89999.20176 2.000010331 89999.43421 2.000005166 89999.55044 2.000002583 89999.60855 2.000001291 The starting guess of 6000 mm radius would give an actual displacement of 29.97...mm, which is not at all close to the 2mm we want. BUT: once the radius gets to be 89940.1..., the actual displacement is already 2.0013..., more than close enough to the required 2 mm. I hope this is clear enough to follow. FYI, for your other numbers I get 600 mm mast length: 90,000 mm (or 90 m) radius for 2 mm displacement 36 m radius for 5 mm displacement 22.5 m radius for 8 mm displacement 768 mm mast length: 59 m radius for 5 mm displacement 36.9 m radius for 8 mm displacement 29.5 m radius for 10 mm displacement Regards, Mark```