# I Second moment of area of a quad copter arm?

1. Apr 2, 2016

2. Apr 2, 2016

### David Lewis

Do you mean the moment of inertia of the cross section of the arm about the neutral axis?

3. Apr 2, 2016

### minoroctave

yes, i think so. is that the same thing as the second moment of area? i am not sure

4. Apr 2, 2016

### David Lewis

Yes, in statics and strength of materials they're synonymous (although technically a misnomer). I assume you want to calculate stress or deflection in the arm due to bending load. If the arm is made out of styrofoam then I think the neutral axis* is offset from centroidal axis because tensile modulus is different than compressive modulus. *This is the reference axis from which you compute the second moment of area/moment of inertia.

5. Apr 2, 2016

### minoroctave

yes, I want to calculate the overall stiffness of the arm. from here https://www.engr.colostate.edu/~dga/mech325/figures/elastic.pdf , there is a equation for the stiffness of a loaded cantilever beam that involves knowing the second moment of area.but its for uniform cross section.
So do I assume the quad copter arm has a constant cross section or is that too much of an approximation?

6. Apr 2, 2016

### SteamKing

Staff Emeritus
In most cases for calculating bending stress of prismatic beams, the centroidal axis and the neutral axis are the same. If you have some really weird material, there may be a difference in the two, like there is for analyzing the bending of curved beams.

7. Apr 2, 2016

### SteamKing

Staff Emeritus
You can calculate the second moment of area of the foil section for the copter blade, but it would be really tedious to do if you don't know the offsets of the foil section:

Given that the individual blades are not prismatic, the difficulty in calculating the stiffness will not be confined to just evaluating the second moment of area.

It would probably be a more effective use of your time if you simply tested a blade by applying a known load to the tip and then measuring the deflection.

Ditto if you are talking about the arms which connect the drone body to the thrusters.

With curvy, swoopy bodies like this drone, beam stiffness is no longer a useful concept to apply, and not just because of the difficulty in calculation.

8. Apr 2, 2016

### minoroctave

thanks! also, after I obtain the stiffness values of the blade and the arm, how would they be combined into one representative stiffness value? for example, in the case of one arm with its two blades, how would the stiffness their values be combined?

9. Apr 2, 2016

### David Lewis

If you have CAD software, draw the 2D shape, convert it to a polyline or region, and invoke the property inquiries command. That should output values for "area, perimeter, centroid location, and 2nd moment."

On a cantilever beam, you can usually assume bending moment goes up as the square of distance from the tip, so you only need to investigate bending at the root end of the arm (where it attaches to the center pod).

Last edited: Apr 2, 2016