williamshipman
Aug25-08, 06:54 AM
Hi guys.
I am trying to measure the moment of inertia of a remote controlled helicopter about its 3 principle axes at the centre of gravity. In all of the literature I have read relating to this project, everyone just glosses over this part. What I need to figure out is an experimental setup and method.
I have the following 3 equations that relate the moment about each axis and the 3 angular velocities to the angular accelerations. All of these equations are with respect a fixed axis system centred at the centre of gravity.
p_dot=M_x/I_xx -rq/I_xx (I_zz-I_yy )
q_dot=M_y/I_yy -rp/I_yy (I_xx-I_zz )
r_dot=M_z/I_zz -pq/I_zz (I_yy-I_xx )
p_dot, q_dot and r_dot are the angular accelerations. The angular velocities are p (roll), q (pitch) and r (yaw). The moments about each axis are M_x, M_y and M_z and the moments of inertia are I_xx, I_yy and I_zz.
So far, I have thought of putting the helicopter on a table and rotating it about one axis, then repeating the procedure for the other 2 axes. This has the small problem that, if the table rotates at a constant rate, the dot terms are zero. If the table is accelerating, then this could work but how would I know what the torque applied to the helicopter is?
I forgot to mention, the helicopter will be fitted with gyros to measure the orientation and accelerometers for the linear and angular accelerations. Thanks for your help.
I am trying to measure the moment of inertia of a remote controlled helicopter about its 3 principle axes at the centre of gravity. In all of the literature I have read relating to this project, everyone just glosses over this part. What I need to figure out is an experimental setup and method.
I have the following 3 equations that relate the moment about each axis and the 3 angular velocities to the angular accelerations. All of these equations are with respect a fixed axis system centred at the centre of gravity.
p_dot=M_x/I_xx -rq/I_xx (I_zz-I_yy )
q_dot=M_y/I_yy -rp/I_yy (I_xx-I_zz )
r_dot=M_z/I_zz -pq/I_zz (I_yy-I_xx )
p_dot, q_dot and r_dot are the angular accelerations. The angular velocities are p (roll), q (pitch) and r (yaw). The moments about each axis are M_x, M_y and M_z and the moments of inertia are I_xx, I_yy and I_zz.
So far, I have thought of putting the helicopter on a table and rotating it about one axis, then repeating the procedure for the other 2 axes. This has the small problem that, if the table rotates at a constant rate, the dot terms are zero. If the table is accelerating, then this could work but how would I know what the torque applied to the helicopter is?
I forgot to mention, the helicopter will be fitted with gyros to measure the orientation and accelerometers for the linear and angular accelerations. Thanks for your help.