T3

### Centrifugal compensation with only gyros and accelerometers

I used to think that either a GPS or a airspeed sensor was needed to perform centrifugal compensation for fixed wing applications. I noticed that several stabilization devices have become available on the commercial market, so I went back and revisited the math.

It turns out that centrifugal compensation can be performed with gyros and accelerometers only. This is useful for either applications in which it is desired to provide a fly-by-wire function without a GPS or airspeed sensor, or as a backup for when GPS fails.

The attached describes the math behind the technique.

Best regards,

Bill

CentrifugalCompensation.pdf

#### Replies

• I'm being picky ...

A quad has 4 rotors that always produce thrust perpendicular to the frame - that is why to can place a glass of water on it and make turns and the water does not creep up the sides of the glass as it would if a slip was actually occurring.

What I hear you saying is not something related to flight dynamics but personal copter flight behavior - you want your designated nose to always be going in the direction of travel.

I think a lot of people would like to fly that way, myself included, but I don't think the aircraft related terms "coordinated" and "slip" apply.

My 2 cents.

Joe

• T3

Joe,

The topic of skidding of multicopters and aerodynamic forces on them has come up from time to time on this forum. I cannot find them off hand, you might want to look around for them. Here are a few conclusions:

1. When a multicopter is tilted and flying in a straight line, you have to increase the thrust, to balance the force of gravity.

2. Unless you apply control commands properly, a tilted multicopter will slip toward the ground and lose altitude.

3. In addition to the perpendicular thrust of the rotors, there are other non-perpendicular aerodynamic forces as well that are created by airflow over all parts of the multicopter, including the rotors. In fact, the rotors themselves can generate lateral forces.

4. During a turn, if the turn is not coordinated, the water will spill.

There are also some interesting effects that depend on whether or not the multicopter is moving forward into "clean air", or sitting in its own downwash. And of course, there are some interesting effects of angular momentum.

The paper that Mark cited is a good source of more information on this subject:

Best regards,

Bill

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