# Free fall detect of rotating object

Navid T
Hello
I have a projectile project. we throw an object with variable speed but about 80 mps and about 90 degrees from Earth level. our goal is to find maximum height that is usually between 250 to 350 meters by means of 3 axis accelerometer and 3axis gyro ( MEMS technology ). In fact we use start of free falling of object to detect maximum height of throw. when object rotation is very low our detection is good, we find place that 3 axis of accelerometer give zero g to detect free fall and start of free fall is our maximum height. our problem is when object has more rotation speed, z axis of accelerometer gives another values instead of zero g because of centrifugal force of rotation. we tried to correct these values by means of gyro angular speed but that was not so good too. now I'm looking for some formulaor relation between accelerometer and gyro values to find maximum height or free fall of rotating object without using throwing initial speed.
In simple form I'm looking for some way or formula to find maximum height of throwing object that rotates around random axis with angular speed more than 100 rpm, and i have just 3 axis accelerometer and 3 axis gyroscope data not initial velocity.
I have some graph of sensor outputs if it can help
Regards

we find place that 3 axis of accelerometer give zero g to detect free fall and start of free fall is our maximum height.
So at other time points the air resistance is high enough to be detected by the accelerometer?

If the accelerometer sensor is not on the axis of rotation, it will detect the centripetal acceleration towards the axis. To separate the air resistance acceleration from this, you could try to decompose the accelerometer signal into directional frequencies (how fast the direction relative to the object changes). The angular velocity from the gyro will tell you the directional frequency of the air resistance acceleration, so you have to find the temporal minimum of that frequency component in the accelerometer signal.

Navid T
Navid T
I'm not sure what you mean by air resistance acceleration! our object is rotating around itself and most of accelerations are around z axis from centrifugal force, but i don't know what you mean! do you mean air resistance that cause object to slow down speed? or rotation?!
+: is there any idea to find maximum height or free fall of this objects without accmeter? more simple way?
Regards

Last edited:
Well, without air resistance, the object would be in free fall as soon as it leaves the launcher.
Is the air resistance significant?

Navid T
I think in this case air resistance isn't matter, object is 5 kilograms and start to go toward sky by 80 meters per second speed and is rotating, maximum height is about 300 meters too, unfortunately i don't understand how air resistant cause acceleration to an object with 80 ms speed and 300 rpm! can you tell me more about air resistance effect on accelerometer?!
+ I'm still looking for any other way to detect maximum height of abject without accmeter! maybe some more simple way?!

Altimeters are often based on pressure measurements. GPS is a possibility.

Navid T
You say air resistance doesn't matter, but 80mps is pretty fast for a 5 kg object. Even with a ball shape, there has to be some air resistance.

Navid T
thanks khashishi, yes we have air resistance and it's not small too but what's it to rotational accelerometer and gravity? i use difference between +1,-1G and 0G to detect start of free falling if there was no rotation and it works in all situations without rotating, our problem started just after rotation not air resistance! i mean if our object doesn't rotate it works properly and air resistatnce doesn't make problem, but when object rotates it doesn't work and we see centrifugal force effect on our logs not something relative to air!