external small tubes around larger tubes

[shockwaveriderz]

I am looking for a means to determine in advance how many outer smaller body tubes will go around the circumference of a larger inner body tube. This of course is right the opposite of how many small tubes will fit inside a larger tube.

I assume that somebody here in TRF knows the mathematics to this solve this problem.

As an example how many bt-20 will surround a bt-60 ? But more importnatly, will they mesh side by side so that no space is left between any of the bt-20.

It would be great if a solution could be devised such that I could enter the larger inner tube outside diamter, and it would simply tell me the number of and the body tube size that I could use.

For example, I might want to use bt-5 around a bt-60... or heaven forbid! I might want to surround a bt-60 with 1/8" dimeter tubes.

I think you get the idea of what I am looking for.

anybody that can help it would be greatly appreciated.


terry dean

 

[bigone5500]

On a BT60 tube, rocksim says 10, BT20 and 12, BT5. If you want 1/8" tubes with a wall thickness of .013", then 45 will fit around BT60.

I know I cheated, but I'm lazy that way...

 

[FROB]

Just a guess, but since:
- exactly 6 tubes will fit around the circumference of another tube of equal OD;
- the circumference is proportional to diameter;
so...
N= 6x ODcenter/ODouter ?

 

[jbuscaglia]

John Brohm has a report on Engine Cluster Geometry over at YORS in the "Building Tips" section. While I don't think it specifically addresses your question, the equation that he derives for calculating the size of the central void of an n-sided polygon cluster should be able to be rearranged to give you the answer you need.

 

[rocketguy101]

According to Mark's Handbook for Mechanical Engineers,

the relation is r = R x sin(180 deg / n)

where r = radius of the small tube (say d/2)

R = radius of the large tube + radius of small tube (say D/2 + r )

n = number of small tubes

rearranging for n

n = 180 / (arcsin( r/R ))

on a calculator, make sure you are working in degrees when you do the arcsin (sin^-1) function.

on excel you need to convert from radians so the excel formula will look like

=180/(ASIN(B4/B6)*180/PI())

r is in cell B4
R is in cell B6

with this equation, and setting D= 1.637 and d= .736, I get 9.962 tubes pretty close to 10 BT-20 around a BT-60.

changing d to .514 I get 13.01 BT-5 around the BT-60

setting d = D gives me 6

 

[shockwaveriderz]

David:

thanks for that but I don't understand how to make the spreadsheet . I've attached what I thought you said but its not coming out correct. there'e a 14kb excel spreadsheet inside the .zip

anybody want to help here?

thanks

terry dean

View attachment inneroutertubes.zip

 

[afterburner]

There is an online calculator for you on EMRR:

https://www.rocketreviews.com/cgi-bin/myemrr/tubefinbox.cgi

 

[rocketguy101]

David:

thanks for that but I don't understand how to make the spreadsheet . I've attached what I thought you said but its not coming out correct. there'e a 14kb excel spreadsheet inside the .zip

anybody want to help here?

thanks

terry dean

in your cell B6, you have =B2/2 + B1 (which would be D/2 + d)

you should have =B2/2 + B4 (which is D/2 + r)

when I made the change, it comes out correctly.

 

[shockwaveriderz]

thanks to all that helped !

terry dean

 

[Chrisn]

you dont need maths to do this, you can either do it with a compass and 60 degree square, or buy the tubes and line em up

 

[sandman]

you dont need maths to do this, you can either do it with a compass and 60 degree square, or buy the tubes and line em up

I just do it in CAD.

The tubes don't fall down that way.

 

[Handeman]

Guess I'm way behind on this thread. I'm kind of a paper and pencil type of guy. For just one quick calculation, I would add the diameters of the BT and external tubes, multiply by pi and divide by the diameter of the external tube. I would probably do this right on the wood top of my work bench. Sand paper makes a great eraser.