### Rack Deck Perimeter Formula

I just derived this formula to calculate the total length of tubing needed for the perimeter of a rack deck...tell me if I'm right!

L = 2W + 2D - 8R + 2(pi)R

where

L = total length of tubing needed (single piece)

W = width of rack deck

D = depth of rack deck

R = radius of your tube bender

pi = ancient greek pie, 3.14...

or, simplified even further

L = 2W + 2D - 1.72R

If I'm right, this means that, starting with a 48-inch length of tubing and a bender with a 15/16-inch radius, the max depth you can bend a single piece of tubing into the perimeter of a 14-inch wide rack deck is about 10.8 inches (measured along the tubing's centerline).

Yes?

48 inches (aka 4 feet) is the magic number for tubing; I've been told that pieces longer than this trigger increased shipping charges.

UPDATE: There's more info on this in the comment thread at Alistair's photo.

L = 2W + 2D - 8R + 2(pi)R

where

L = total length of tubing needed (single piece)

W = width of rack deck

D = depth of rack deck

R = radius of your tube bender

pi = ancient greek pie, 3.14...

or, simplified even further

L = 2W + 2D - 1.72R

If I'm right, this means that, starting with a 48-inch length of tubing and a bender with a 15/16-inch radius, the max depth you can bend a single piece of tubing into the perimeter of a 14-inch wide rack deck is about 10.8 inches (measured along the tubing's centerline).

Yes?

48 inches (aka 4 feet) is the magic number for tubing; I've been told that pieces longer than this trigger increased shipping charges.

UPDATE: There's more info on this in the comment thread at Alistair's photo.

## 6 Comments:

I say yes!

It's the circumference of the circle--the four corners--plus the perimeter if it were a rectangle less the four right angle corners because they're really arcs.

Joe

Jim, I worked through my usual method using the bender gain factor, assuming a deck width of 14" and a depth of X. This calculation gives the points that I would mark the bend points on the tubing. Here's the link,

http://www.flickr.com/photos/duncancycles/4036778465/

I get just a hair over 11" for the depth. I have built such a rack a couple of times in the past and it did work.

I suspect the difference in our answers has something to to with how to take account of the tubing width.

Anyway, I hope this helps more than it confuses. Oh, and you should check my numbers!

It sounds about right.

You can get 6' or 8' lengths shipped cheaply from some sources. Just check with the supplier to see what the cost hit is.

It isn't hard to splice two pieces into one longer piece either. I did this to make my first cycle truck rack (18 x 20") out of 4' tubing.

I personally don't bother with the math and just do much simpler math that assumes perfect right angle corners. That gives 14x10 for a 48" piece of steel. 14x10 vs 14x10.8 isn't a large functional difference.

I agree with Alex. Splicing pieces together can be a very useful trick and really, when it comes to the size of the rectangle, exact final dimensions aren't too important.

I have my method, which works for me, but that doesn't mean that it's the best way. It's just one way to do it.

Alistair,

My value of 10.8 inches + 0.375 inches (dia of 3/8" tubing) = 11.175 inches, which matches your result.

So it may be that, as you said, the "bender gain factor" method takes into account the diameter of the tubing, and produces dimensions measured to the outside edges of the rack deck.

My derivation ignored tubing diameter entirely, and all measurements were based along the tubing's centerlines.

Hmmm.

Hello again Alistair,

Note that in the example in their manual, Swagelok does

notsubtract the gain factor from P1...(P1 = 3 inches)See Image Here

I worked through the rack-deck dimension problem, leaving off the gain factor from P1, and got 10.609375 inches as the value of "x". This, unfortunately, still doesn't match up with my previous result of 10.8 inches. Now I'm more confused!

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