Tube Fin size formula

blackwing94 said:

I want to try a (big) 7 tube fin project. Am I doing this right?

I'm trying to figure out the formula for sizing tube fins. If I want 7 tube fins, what will their radius be, given a main body tube size?

I think I'm running into the problem of:
A math person can get two 1 foot boards from the 2 foot board. A carpenter can only get one 1 foot board because the saw blade took away space from the remainder of the board... real life meets math.

Forgive the graphics. I used powerpoint. Not very exact. But you get the idea. And I had to muck with the font to get π to show up.

The total length of the diameter of all the tube fins added up (left) should be
equal the arc length around the center of all the tube fins around the body tube (right).
View attachment 341923View attachment 341924

t = Body Tube radius
r = tube fin radius (what we're solving for)
n = number of tube fins

2π(t+r) = 2 r n (solve for r)
2πt+2πr = 2rn
2πt = 2rn-2πr
2πt = r(2n-2&#960
r = 2&#960;t/(2n-2&#960 <-- the magic formula

My test case is 6 tube fins. I think, if you have 6 tube fins, they should be the same size as the body tube. But I get a slightly different answer.

For a 4 inch diameter body tube the radius would be t = 2 inches (radius is half the diameter) I kind of expect a radius of the tube fin to be 2 inches as well.
For 6 tube fins.
r = 2&#960;2/(2*6-2&#960
r = 4&#960;/(12-2&#960 = 2.198 (close, but not 2. Is it close enough?)

Am I doing this right? Thanks for any help.

Click to expand...

What you're calculating is the arc length between the two tubes, which has a bit of curve to it, so it's slightly longer.

I had to calculate this a while ago when I was building a Saturn 1B. You can do it, but you need some trig:

Imagine a right triangle between the center, the contact point of two tubefins, and the center of a tubefin. This triangle has sides r+t, r, and something else, and its center angle is 360/(2n).

So:
sin(360/2n) = r/(r+t)

Solve for t:
(r+t) sin (360/2n) = r

r sin (360/2n) + t sin (360/2n) = r

t sin (360/2n) = r - r sin (360/2n)

t = r / sin(360-2n) - r

That -should- work.

I don't have the Sport Rocketry articles at my fingertips, but I'm almost certain Larry reiterates the correct formula at least once in his *pod series:

https://www.rocketreviews.com/larry-brand-page.html

https://www.rocketreviews.com/by-airframe-diameter.html

Try this.

Larry Brand the TubeFin Dude suggests using the next standard tubing size smaller for a 7 fin tuber and using an appropriately sized shim to mount the 7th tube to the body tube. It isn&#8217;t perfect but it works quite well.

For example, if your body tube is a 3&#8221; diameter tube, use 2.6&#8221; diameter fins.

Larry used short 7 fin tubes as a means of reducing drag. His recommendation was to use tube fins that were shorter in length than in diameter...high aspect ratio rather than low. A low aspect ratio would be a tube fin that is longer than it is in diamter.

That being said, I&#8217;ve always built my tube fin rockets with &#8220;square&#8221; fins, that is fin length and diameter being the same. They fly like they&#8217;re on rails even in a breeze.

Six and seven tubers seem to be a sweet spot for drag with 7 fins having the edge.

LithosphereRocketry said:

What you're calculating is the arc length between the two tubes, which has a bit of curve to it, so it's slightly longer.

I had to calculate this a while ago when I was building a Saturn 1B. You can do it, but you need some trig:

Imagine a right triangle between the center, the contact point of two tubefins, and the center of a tubefin. This triangle has sides r+t, r, and something else, and its center angle is 360/(2n).

So:
sin(360/2n) = r/(r+t)

Solve for t:
(r+t) sin (360/2n) = r

r sin (360/2n) + t sin (360/2n) = r

t sin (360/2n) = r - r sin (360/2n)

t = r / sin(360-2n) - r

That -should- work.

Click to expand...

I see what you mean about my original plan including some extra curvy space. Thanks. Hmmmm, I could not get your formula to work against the values from the "tube fin calculator" posted above, but you got me thinking. I used your idea and applied some of my own trig and came up with:


t = radius of tube fin
r = radius of body tube
n = number of tube fins
For 6 tube fins, 360/2*6 = 30 degrees.
sin(30) = t/r+t (opp/hyp) (I see now that's almost what you started with)

Replace the test case of 30 degrees with 360/2n
Solve for t:
ø = 360/2n
t = (sin(ø) * r) / ( 1 - sin(ø))

That seems to work.

Again, if you see a problem, let me know.

I don't need no stink'n tube fin calculator! :neener:

blackwing94 said:

I see what you mean about my original plan including some extra curvy space. Thanks. Hmmmm, I could not get your formula to work against the values from the "tube fin calculator" posted above, but you got me thinking. I used your idea and applied some of my own trig and came up with:
View attachment 341956

t = radius of tube fin
r = radius of body tube
n = number of tube fins
For 6 tube fins, 360/2*6 = 30 degrees.
sin(30) = t/r+t (opp/hyp) (I see now that's almost what you started with)

Replace the test case of 30 degrees with 360/2n
Solve for t:
ø = 360/2n
t = (sin(ø) * r) / ( 1 - sin(ø))

That seems to work.

Again, if you see a problem, let me know.

I don't need no stink'n tube fin calculator! :neener:

Click to expand...

On mine I accidentally typed 360-2n instead of 360/2n in the last equation. Is that the problem?

I'll fix it next time I'm at a real computer.

Sent from my LGL44VL using Rocketry Forum mobile app

Maybe you solved for t (body tube) and should have solved for r (tube fin)?

Note: I revered the variables (opps) on my second post.
r = radius of body tube
t = radius of tube fin.

I have it as


...where d3 and c4 are the radii of the body and fins. You'll note that it gives 6 if body and fins are the same, just spits out the ratio e.g. 6:1, 7:1 etc.

I set it up this way so I can just put all my tubes in a spreadsheet to tell me what combos are workable.

I plan on making custom mandrels and rolling fiberglass body and tube fins. Like I said, I'm shooting for something a little... bigger. :smile:

Just out of curiosity, is there some reason it is critical to go with 7 tubes instead of 6?

Reason I'm asking is because 6 is a no-brainer. Just use same tube size as the core body tube and you're golden. From Aerodynamic standpoint, I think the larger radius 6 tubes will be more effective than the smaller 7 tubes.

so 6 tubes will work as well as 7 and be a whole lot easier.

In fact, you can just lay them out in pairs on a flat surface to mate each pair, then they should self-level themselves when you stick them on the body.

A guy named Larry Brand, back in 2008 and 2010 did a study of tube fin rockets and wrote that for a 6 tube fin rocket, the fin can appears to act as a "dimensionless drag plate". But with a 7 tube fin rocket, the fin can acts more like the fin can on a normal 3FNC rocket. The six tube fin rocket, for whatever reason, produces allot more drag than a 7 tube fin rocket.

See:
Larry Brand, &#8220;Tube Fin Rocket Aerodynamics Revisited&#8221;, Sport Rocketry, January-February 2008
Larry Brand, &#8220;Tube Fin Rocket Aerodynamics Revisited Part 2&#8221;, Sport Rocketry, March-April 2008
Larry Brand, &#8220;Tube Fin Rockets &#8211; Seven Beats Six Part 3&#8221;, Sport Rocketry, March-April 2010

6 tubes stick out farther into the airstream than 7 tubes.

blackwing94 said:

A guy named Larry Brand, back in 2008 and 2010 did a study of tube fin rockets and wrote that for a 6 tube fin rocket, the fin can appears to act as a "dimensionless drag plate". But with a 7 tube fin rocket, the fin can acts more like the fin can on a normal 3FNC rocket. The six tube fin rocket, for whatever reason, produces allot more drag than a 7 tube fin rocket.

See:
Larry Brand, &#8220;Tube Fin Rocket Aerodynamics Revisited&#8221;, Sport Rocketry, January-February 2008
Larry Brand, &#8220;Tube Fin Rocket Aerodynamics Revisited Part 2&#8221;, Sport Rocketry, March-April 2008
Larry Brand, &#8220;Tube Fin Rockets &#8211; Seven Beats Six Part 3&#8221;, Sport Rocketry, March-April 2010

Click to expand...

I stand corrected. Thanks. Not sure I understand it, but interesting.

here is a rocketreview by the master himself on a 7 fin model

https://www.rocketreviews.com/scratch-golden-acorn-by-larry-brand.html