Poor Man's Carton Short Radius Curve

Introduction: Poor Man's Carton Short Radius Curve

About: I’m Fernando Zigunov, a refrigeration engineer R&D specialist, interested on a myriad of scientific subjects. I graduated as a Mechanical Engineer at UNISINOS unversity and now am aspiring to join for a PhD p…
Hello workshop partners!

For some temporary experiment I was doing, I needed to connect a blower onto a tank pipe that was at an angle of ninety-degrees in relation to it. But since it was only a experiment, I didn't want to buy piping (a small radius bend in this case) just to know if it would work.

Because of this, I decided to make a DIY piping bend, quickly. All you need is:
  • Scrap cardboard (here using a 12-milk pack carton)
  • Scissors
  • Ruler
  • Set-square (Optional)
  • Duct tape!
  • Computer with CAD software
I know, the result is not even near good, but sometimes we don't want to buy finished products just to do know if something works!

Step 1: Draw What You Wanna Make

I could spend a lot of time sketching and tracing lines with ruler and compass to know the exact locations of the points and to cut with the exact radius that I want to cut, but here we want to be fast! So, grab your CAD software and draw the knee that you wanna make. (In my case I wanted to build a 150-mm-diameter bend with inner radius of 50mm)

Step 2: Decide How Many Sections to Make It

Well, now you have to decide how many sections your bend will have. Obviously, the bend will be something polygonal, approximate, and you want to make the least amount of sections if you wanna save work. But the lesser sections, the rougher your bend will be. Find a balance.

Here, I made it with three sections for a 90-degree bend.

The angle of each middle-section is determined by dividing the bend total angle (90 degrees in this case) by the number of bends minus one. In this case, the angle of the central section is 45 degrees. The angle of the tip sections is half the middle-section angle. Therefore, it will be 22,5 degrees.

Remember, when you do this, your sections will end up with elliptical cross-section after rolled. This is because when you cut a cylinder on a plane whose normal makes an angle with its axis, the geometry of the section will always be an ellipse.

What I did here, by making the tip angle half the mid-section angle, is reducing the effect of this ellipse-circle mismatch, when you connect it with an uncut tube.

Step 3: Sketch the Flat Pattern (Part 1)

To sketch the flat pattern of the bend sections, we must divide the circular cross-section of the bend by an integer number. I chose eight parts, because it was pretty sufficient. This method doesn't allow you to do many divisions, because the work increases a lot. 

Create projection lines of the divisions onto the bend. Then, create concentric circles on the points that were sketched. Sketch polygonal lines of the intersection of the circles with the section lines that we created before.

Calculate the unrolled length of the pipe by multiplying the diameter by PI. In this example, 150*3,14159=471,2385. Create a line that represents this planform. We will work on it to build the flat pattern. 

Divide this line in eight identic parts. Each CAD software has a specific command that does that. Here I named the sections to ease the explanation for the next step.

Step 4: Sketch the Flat Pattern (Part 2)

Now you have to copy the length of the lines that we sketched on the left-side view of the bend to the planform. The first photo shows how I did it: I created a blue circle whose radius comes from the center of the first section to the center of the second section. This is the length that I want to copy. This circle was moved to the corresponding points, in this case 01 and 05. Since there are two points named 01, there are three circles for this case.

Copy the other lengths the same way and you will finish with a fish-like structure made of circles. See the figures to understand better.

Now you have to join the upper nodes of these nine circumferences to create the right profile of the flat pattern. When you roll it, you will have the first bend section!

In order to save your scrap cardboard, you want to offset the next bend pattern 180 degrees. This way, each cut will generate two profiles (the same sine profile). Clearly, since this is a rough approximation, there will be errors that will propagate if you make too many sections, but for most cases I think it will be sufficient.

To offset 180 degrees, I changed the position of the copied circles four slots to the left. This way, 01 goes on 05, 02 goes on 06 and so on. The picture is easier to understand!

Continue on copying the circles until you finish all the bends. 

Step 5: Now to the Cardboard Cutting

You can choose to print your drawing or copy the measurements and resketch it on your cardboard. In my case, since I'm not very handy, I copied the sketch with ruler and pen.

After sketching, cut the flat patterns.

Step 6: Make Hoops

Now you need to "roll" your cardboard. Since rolling is very hard without appropriate tools, I just bent the cardboard on the eight divisions that I made previously.

After bending, make hoops and close them with duct tape.

Step 7: Join the Hoops

I used duct tape to join the hoops. Cut little pieces of tape and glue the hoops together to ensure the position is acceptable.

After that, use a lot of duct tape to seal it.

Step 8: Enjoy!

This is it, your bends are finished! With this technique you can make all connections, even piping!

This same procedure can be used to make aluminum tinkering to insulate air conditioning pipes and so on! 

Hope you found it useful! Thanks for reading!

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