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,


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Hi Bill,

It would be nice to support a minimal setup without GPS or airspeed sensors.

Do you plan to implement this in MatrixPilot?


Hi Mark,

This feature is already partially implemented in the MatrixPilot_wjp_HelicalTurns branch and the helical turns tag. If you define CENTRIFUGAL_WITHOUT_GPS to be one, centrifugal compensation will be computed without GPS or airspeed sensors, but that is as far as I went with it. There would be a modest amount of work to create an entirely GPS-less option, including the elimination of all other GPS dependent code and features.

I had asked the MatrixPilot community if there was any interest in a minimal setup without GPS. There was not much response, so I put this feature aside for now. If there is sufficient interest, and if someone is willing to modify the rest of the code, a minimal setup would be fine with me. Keep in mind that there are already numerous GPS-less products on the market, including the Guardian, and SAFE technology, for example.

Best regards,


Thanks Bill,

I was wondering whether this feature would be beneficial for multicopters flying without GPS or under trees. I'll have to do some testing to see whether it helps me in my backyard.

Thanks for mentioning the Eagletree Guardian, I wasn't aware of it yet. It's $200 cheaper than the Vector autopilot.

73, Mark


The math for the method described in this discussion was developed for fixed wing, I doubt that it will work very well for multicopters. It assumes that there is a centrifugal acceleration equal to the cross product of the rotation rate vector and the airspeed vector. I do not think that is the case for multicopters. Perhaps there is another GPS-less method that would work for them.

Best regards,


Oh, it seems like there's no good estimate for airspeed in that case.

I do try to fly coordinated turns with multicopters though to avoid skidding.

73, Mark


I use to fly A6's for the Marines during Viet Nam so I understand coordinated turns and skidding.

I am new to multicopters so your statement "coordinated turns with multicopters" does not make sense to me.

In a plane there is a fuselage, wings, rudder, and a defined direction of flight (thru air - not ground) with respect to the fuselage.

In a plane, coordinated turns are important to make sure nose tracks during the turn so that the angle of attack of the wind to each wing does not change.

In a multicopter, there are no wings and there is no nose.  The user may assign a line on the copter and say -- that's forward but it has no flight concerns as I can see.

In fact, you can place a multicopter in a turn and perform 360 yaw spins with no adverse effects.

Please explain if I'm incorrect so I may gain insight into copter flight.

Thanks. Please don't take my comment as being aggressive -- I just want to check my understanding.

Thanks in advance for your reply.


Hi Joe,

You definitely have more full-scale experience than I, all of my solo time was in a Cessna 150 :)

But I'm not sure what you mean by "you can place a multicopter in a turn and perform 360 yaw spins with no adverse effects".

Certainly a multicopter can fly sideways, but it must be tilted in the direction of flight to maintain non-zero airspeed. And many multicopters have non-symmetric bodies, which I would refer to as a fuselage. And by "coordinated turn" I mean the net acceleration vector is perpendicular to the body frame Y axis i.e. there is no lateral acceleration.

One might also think of rotor disks as "wings", and there is something called "translational lift" for helicopters, which probably applies to multirotors as well.

Since I flew helicopters before I flew multirotors, perhaps my technique is different from that of pilots who started out with multis, but I do try to keep the "nose" pointed in the direction of flight, especially when flying FPV.

73, Mark

Bill, I thought you might be interested in this paper which I turned up while refreshing my memory on coordinated turns: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19810013509.pdf

73, Mark

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.

Thanks for you reply.



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,


Hi Bill, 

I finally got around to playing with this concept in multicopters, and it's looking very encouraging for estimating airspeed. Here's a plot from a quadcopter flight log where I flew circles in a "coordinated" way, and also with constant heading. The inertial airspeed estimate looks sane and in reasonable agreement with my (poor quality) GPS data:


Thank you so much for your time and effort in testing this concept in multicopters. It performed better than I expected. It is my conjecture that the combination of your expert piloting skills and the performance of the feedback controls (I assume you were flying your system?) that provided conditions that satisfied the assumptions that my math was based on.

Best regards,


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