I saw a project on Hackaday featuring a model rocket with moveable fins to stabilize the rocket's trajectory: Hackaday. The goal was to arc the rocket to a horizontal trajectory and keep it there.

In the comments section, one of the project members proudly states that the rocket used accelerometers only to determine the rocket's attitude: Comment 174820. Other comments on the article opine that without gyroscopes the project goal should have been impossible.

Take the following thought experiment:

If we consider the rocket to begin accelerating along some straight flight path, the accelerometer will measure the acceleration vector to point through the nose of the rocket. Suppose that as the rocket reaches speeds where aerodynamic forces become non-negligible, unbalanced construction or aerodynamic forces cause the rocket to rotate some small angle to a new flight path that balances the forces. There will be some fluttering of the acceleration vector as the rocket experiences aero forces and transitions to the new path, but when it reaches steady state the acceleration vector will again point through the nose of the rocket. No angular difference will be measured. Does this mean that an accelerometer cannot be used to determine orientation of a rocket under power?

  • $\begingroup$ For a model rocket the measured acceleration will be the acceleration of the rocket minus 1g pointing down. One can use the latter for coarse pointing. Would I do it? No. A couple of $50 MEMS gyroscopes will do a much better job and get us probably within 0.01 degree/s of offset. For a 100s flight (really... for a hobby rocket?) that's a 1 degree error. $\endgroup$
    – CuriousOne
    Apr 30 '16 at 0:43
  • $\begingroup$ You can determine orientation with a set of three orthogonal accelerometers by calculation. $\endgroup$ Apr 30 '16 at 11:23
  • $\begingroup$ "measured acceleration will be the acceleration of the rocket minus 1g" How would the accelerometer measure the 1g? Since an accelerometer can be thought of as a ball suspended inside a box by springs, and since gravity will accelerate all components of the accelerometer equally, how will it ever detect the acceleration due to gravity? $\endgroup$ May 2 '16 at 17:13

It turns out you cannot use an accelerometer to determine the attitude of a rocket at any time other than when it is experiencing the normal force from the earth.

This is explained in some detail in this article: Thinking About Accelerometers and Gravity. The key point from the article is this line: "An accelerometer never senses gravitational acceleration . . . An accelerometer is a device that senses deviation from freefall."

That this isn't intuitively obvious to people is apparently an age-old problem. Goddard committed the same fallacy when he tried to stabilize his early liquid rockets by placing the engine at the top (source), and the hackaday project commits the same fallacy in a new form. Reading further into the hackaday project I also discovered a complete lack of understanding about the effect of CG and CP on rocket stability.

There's also a similar discussion at the Space stackexchange: Accelerometer in space, although it isn't exactly the same scenario.


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