Tubing Calculator 1.2 2018-09-25

Use this tool to compare the relative strength and weight of round and square tubing. Select the size, shape, and material of two different pieces of tubing for a side by side comparison:

Wall = Wall thickness is shown in the same unit used for input.
Area = Cross section area in mm2, inches are converted to millimeters.
Mass = Mass of cross section area x length. This is ONLY an estimate based on material density. The actual weight of carbon fiber products will vary due to the concentration of resin used in each one.

I = Second Moment of Inertia, Ixx = Iyy for round and square tubing.
J = Torsional constant for a thin-walled closed section. formula updated in v1.2.
D = Deflection, with one end of the tube fixed and a 2 pound weight (0.9kg) placed on the other end.

As you may have noticed, the images update in real time as the dimensions are adjusted. They should be an accurate representation of the wall thickness and the scale between A and B.

Default Example

The default values represent two of the most common tubing sizes for medium-sized drones. On the left is 15mm square tubing and on the right is 16mm round tubing. Both are carbon fiber and both have a 1mm wall. Its easy to see the round tubing wins here because it is almost as strong while being 15% lighter. But this is only part of the picture if you're trying to build a drone that is lighter overall. For example, consider the difference in weight when you add motor mounts to fit the round tubing while many motors can be attached to square tubing with minimal added materials or no motor mounts at all.

Stronger?

When looking at the results, one side may say it is "stronger" than the other. This is a relative figure, assuming both tubes have the same construction. Different types of carbon fiber construction have different strengths. For example, tubes made with unidirectional fibers will not be as strong as tubes made with the fibers woven at different angles. Most of the carbon fiber tubing used for drones is made with layers of fabric running in different directions for optimal strength.

Relative strength is calculated from the formula for resisting torsional (twisting) force in a thin walled tube section. To achieve optimal flight characteristice, a drone needs stiff arms that resist the twisting forces from the motors. There is often a tradeoff between the amount of stiffness desired and weight. Many commercial drones use tubing that provides plenty of stiffness but makes the drone heavy and reduces flight time.

Deflection values are rough estimates because they assume the same modulus of elasticity for all carbon fiber tubing, which is not the case in reality. I included it to show how length and diameter will affect deflection, all other things being equal. I tested several pieces of tubing by clamping them to a table at 12 inches and 24 inches, then measured the actual deflection when I hung a 2 pound weight from the end. The results were fairly accurate.

Square vs Round

As I posted on my Ardupilot blog, there's a lot of confusion surrounding square versus round tubing and its application for drones. I made the following graphic to show the difference in simple terms:



Before I built this calculator, I was using this one but you can only check one size at a time and the square tubing calculator is on a different page. Since then, I've added the formulas for deflection and torsional stress in a thin-walled tube.

Recommendations

Use this tool to compare different sizes and shapes of tubing. Try to find the best balance between strength and weight. Depending on the size of your motors and props, you may be able to use a lighter tubing that isn't as strong. Any time you can reduce weight, you will increase your flight time and also the life of some parts. It might seem that round tubing is the best choice but this is not always the case. It is more difficult to attach and align motors to round tubes and you might find that motor mounts can weigh as much as the tubes themselves. Using 15mm square tubing with the motors attached directly to the tubing will definitely be lighter than 16mm round tubes plus motor mounts.

If you find any bugs or if you have suggestions for improvements, please contact me!

Enjoy