Part 6: Air Drag and Cross Sections

This part of the series gives a good understanding (hopefully) of the effect area has on how efficient our quads move through the air.

Although the typical quadcopter cross section is relatively small, it is not negligible at the speeds they fly at. As we saw in Part 5, the force created from air drag is proportional to the surface area of the object – that is the area that is perpendicular to the direction of movement. A big problem with H frames and X frames is that they actually become more inefficient the faster we fly.

Another Quadcopter Design Issue:

Airline Example: Imagine you are on a passenger jet. The body is parallel to the ground as you are taking off. When viewing the body in the direction of movement, the cross section looks like a circle. Now imagine that as the plane gains speed, the body pitches forward more and more until it is nearly perpendicular to the direction of movement at top speed. When viewing the body in the direction of movement, it looks like a large cigar shaped building – the area is much bigger and not very efficient.

Why are quad frames designed like this? $1000 to anybody with a good answer. As a matter of fact, passenger jet air brakes pitch forward much like quads do – they create a larger cross sectional area and help slow the plane down.

H frame, X frame, and… Z frame?

Z frame
The “Z frame”… it’s a stretch, literally, but it’s the best I could come up with for now (Note: up to a 5s lipo fits inside the frame)

Update April 4, 2017: Double checking on other Z frames that are out there, I only came across one other which is the Moka Simplex. However, the layout and fundamental concept is completely different.

Assuming that we always are flying (relatively) parallel to the ground, we should always want the minimum amount of cross sectional area in this direction of movement. Most, if not all, quadcopters have their smallest cross section when their props are also parallel to the ground (since the props are parallel to the frame). However, we would not be moving forward at all since all the thrust would only give us upward movement. Below are front and side views of an H frame, an X frame, and a Z frame (projects C1/2, C3, C5) which has the frame offset from the props by 45°. I might be stretching it a bit calling it a Z frame (as viewed from the side). More like a smashed Z.

All 0

In order to move forward, the propellers must be pitched forward. This means (at least for the H and X frame examples above) that the cross sectional area (in the direction of movement) will increase; the faster we want to go, the more aerodynamic inefficiency is introduced.

H and X frames become more and more inefficient as the frame is pitched forward to go faster. On the other hand, as the Z frame is pitched forward to go faster, it becomes more efficient as seen below where all frames are at a 45° pitch:

All 45

Won’t the Battery Increase the Z frame Cross Section?

No. Up to a 5s lipo fits inside the frame.

Where to go from here

Now that we have gone through all the ways we can increase top speed and hopefully gained a better understanding, see what you can do with your quad. I can only hope this will help the hobby grow even more and help future frame designs become more efficient. Please share the results of your projects!

If you want to get a little more in depth on the (generalized) equations concerning the calculations of your quads top speed, you can take a look at Part 7: The Equations for Speed.