1. Quick weekly updates
- Finalized BOM for miniquad v2.0 and ordered the components.
- Completed the theoretical predictions of forces for proximity flight experiments using actuator disk model.
2. Detailed update of the theoretical predictions
- Actuator disk theory (a.k.a. momentum theory) has the following assumptions:
- Propellers are flat, bluff disks which accelerate the air flow. It doesn’t take into consideration the shape of the propellers or number of blades. It only uses the diameter of the propellers.
- The actuator disks are not accelerating, i.e. there is a constant (or zero) inlet flow velocity, and a constant exit flow velocity.
- By assuming that the inlet flow velocity is zero, we can predict the exit flow velocity (and also the velocity at the propellers).
- The thrust produced is assumed to be 1/4th of the weight of the quadcopter for which parameters are being calculated.
- Exit flow velocity (v0) is calculated using the formula v_0 = sqrt(2*T/(rho*A)), where T is the thrust, rho is the density of air, and A is the area of the propeller disk.
- Bottom quadcopter is assumed to be a bluff body with a drag coefficient (C_D) of 1.00. The affected area is the minimum of the projected area of the bottom quad, and the projected area of the flow field (4 * area of one disk / 2). The ‘/2’ comes from the fact that flow accelerates on exiting the propeller to twice the velocity (assuming the inlet velocity is 0).
Results of the calculations:
I predicted forces on the bottom quadcopter due to the airflow of the top quadcopter, which are as follows:
- LQ-MQ case: LQ experiences a force of 0.736 N. The force calculated experimentally came out to be in the range of 0.5-0.6 N which is pretty close (for vertical separations upto 2 m).
- MQ-LQ case: MQ experiences a force of 3.33 N. The experiments have not been performed for this yet. If the predicted value is close to the actual force, then the miniquad cannot hover below a large quad. This is because the weight of the miniquad itself is 1.5 N, and its theoretical maximum thrust capacity is 4.6 N (assuming maximum discharge from the battery).
Limitations of actuator disk theory:
- It does not give a dependence of the flow velocity on the distance from the disk.
- It is an ideal model which does not consider the shape of the propellers or the number of blades.
3. Planned work for next week:
- Conduct MQ-LQ experiments.
- Analyze the data of the above experiments and compare it with theoretical predictions.
- Look into ‘better’ models (theoretical or empirical) – something that can give a distance dependence.
4. Plans for next 30 days:
- Characterize torque disturbances on the bottom quadcopter.
- Analyze frequency content of disturbances (this might characterize noise rather than actual disturbances but still worth a try).
- Need to check out python packages for fft (fast fourier transform), or use MATLAB on bag files.
- Design a new rates controller to mitigate these disturbances.