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Old 09-05-2011, 07:45 PM
Les Les is offline
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Default calculating circles

Does anyone know of equations for determining fitting circles around the circumferance of another circle? Basically, to calculate size and number of tube fins that will fit where the fin will be a different size than the main tube?

Thanks
Les
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Old 09-05-2011, 08:35 PM
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The way I do it pretty archaic--but effective: I measure the circumference with a dressmaker's tape, then divide the measurement by the number of fins.
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Old 09-05-2011, 08:39 PM
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I'm confused - the circumference of the main tube?

I am just in the design phase. I'm trying to figure out what size main tube to what size tube fins X quantity I'll be able to fit so I ks to ordernow what part
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Old 09-05-2011, 08:40 PM
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Quote:
Originally Posted by Les
Does anyone know of equations for determining fitting circles around the circumferance of another circle? Basically, to calculate size and number of tube fins that will fit where the fin will be a different size than the main tube?




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Old 09-05-2011, 09:00 PM
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Quote:
Originally Posted by Les
I'm confused - the circumference of the main tube?

I am just in the design phase. I'm trying to figure out what size main tube to what size tube fins X quantity I'll be able to fit so I ks to ordernow what part

Oops. Never mind. I misunderstood.
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Old 09-05-2011, 09:07 PM
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You can try this:

Add the outside diameter of the airframe tube to the outside diameter of the desired fin tube. Multiply by pi. Divide this total by the outside diameter of the tube fins you wish to use. This result will be the number of fin tubes you can get around the airframe tube.

Example: 4" outside diameter airframe tube and 2" outside diameter fin tubes
4+2=6 6*3.1416=18.85" circumference
divided by the diameter of the fin tubes (2")
18.85/2=9.425 tubes
subtract the fraction (0.425) means nine tubes
to find the spacing between the fin tubes multiply the dropped fraction (0.425) by the circumference (18.85)
0.425*18.85=8.01 (8)
divide this number by the number of fin tubes (9)
8/9= 0.89" gap between tube fins after they have been mounted

To find the spacing between the mounting (glue point) marks on the 4" diameter tube multiply outside diameter of airframe tube by pi then divide by the number of fin tubes
4*3.1416=12.566
12.566/9=1.396" or (about) 1 3/8"
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Last edited by RandyT0001 : 09-05-2011 at 09:13 PM. Reason: Not sayin' :P
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Old 09-05-2011, 09:30 PM
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Quote:
Originally Posted by Les
Does anyone know of equations for determining fitting circles around the circumferance of another circle? Basically, to calculate size and number of tube fins that will fit where the fin will be a different size than the main tube?

Thanks
Les


The number of circles that can be formed around an inner circle (assuming we're not talking about politics) can be found from the following:

n = INT{180/arcsin[M2/(M1+M2)]}, where M1 is the inner circle diameter and M2 is the diameter of the outer circle.

n is an integer, and is the nearest whole number to the value computed from the above; depending on the geometry, n is either rounded up or down.

For example, if M1 is greater than M2 then the maximum number of M2s that can be fitted around the outside of M1 will be the rounded down value from the relation above.

If, however, M1 is less than M2, then n must be rounded up from the value calculated from the relation above (and in this case, one will find that the maximum diameter that can fit between those larger outside tubes will in fact be bigger than the value initially selected for M1).

Magic happens when M1 = M2; then n is precisely 6. We see this, for example, in the Custom Rockets Razor, the Squirrel Works Tuber, or any other rocket that uses tube fins of the same diameter as the airframe.

Let's do a couple of examples:

Say M1 = 0.976" (BT-50) and M2 is 0.543" (BT-5). The relation above returns a value of 8.6; this means eight BT-5s will fit around a BT-50, but with a little space in between. There's not enough room for nine BT-5s to sit tangent to the BT-50 and to each other.

Let's say M1 is 0.543" (BT-5), and M2 is 3.1" (LOC 3" tube). The value returned from the equation is 3.087, which means you need four LOC 3 " tubes to make a space for that BT-5, and it of course will fit in there quite comfortably. With three LOC 3" tubes there won't be quite enough space for the BT-5 to just slide in, although if you're lucky with the particular tube diameters you have on hand you might be just able to make it fit (!) when it's so close.

I hope this is of help to you, and best of luck with your project.
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Old 09-05-2011, 09:36 PM
Les Les is offline
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GREAT! Thanks guys
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Old 09-05-2011, 10:06 PM
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I thought I'd add a footnote concerning the method that Randy has posted. Those of you who may have your calculators out may have noticed that Randy's method and my equation return slightly different values, especially so in the case where the diameter of the fin tube is the same as the diameter of the airframe.

The difference comes into play when the outer circumference that Randy calculates is divided by the diameter of the fin tube. What's actually being divided is arc length, not the straight line distance (chords, in fact) between the centers of the fin tubes. Since the arc travels a longer distance between the same two points, Randy's method will return a slightly bigger space.

In virtually every practical example Randy's method works just fine and gives a quick answer. Just remember that when the fin tubes and the airframe are the same diameter that precisely six will fit.
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