# Short summary

• ##### Conducted flow disturbance test with two cases; at the center (case 1) and at the largest velocity gradient (case 2)

– Overall, general trends of aeroforces and and disturbance torques are repeatable
– Effect of aerodynmic force was affecting majorly for z-direction
– Effect of torque disturbance was affecting for x and y direction
– The highest torque peak (x direction) was observed for case 1, and the highest aerodynamic force peak (z direction) was observed for case 2.
– Large offset force of x direction, noisy signal from the accelerometer must be addressed in future, and using a largequad instead may worth to try

# 1. Mean velocity profile

In order to see the jet profile from 1.5 m far, I measured flow velocity at 9 different locations using an industrial anemometer. Each point were repeatedly measured five times. And the result is below;

Fig 1. Jet flow profile

Although it is not 100% symmetric, in general the profile is what we are expected. As shown in the plot, the largest velocity gradient occurs from -0.2~-0.3 m. Therefore, I made a set point to be ~0.3 m  for case 2.

# 2. Thrust vs. flow velocity

Fig 2. Thrust force experiments

I thought it might be interesting to see the wind flow effect in terms of thrust force on the quadcopter. A result plot is given in Fig 3.

Fig 3. Thrust force vs. velocity magnitude.

If I turn on the fan only without running the quadcopter, order of magnitude of thrust force was ~0.01 N. However, there is noticeable increase of thrust forces, if the quadcopter is running and the fan is on in the same time.  That makes sense because incoming flow can result in more rotation on propellers. However, this effect seems to be taken into account, to achieve a better flow disturbance reduction on the vehicle.

# 2. Flow disturbance repeatability

In order to see whether we can obtain repeatable wind disturbance effect, I conducted the experiment five times for each cases;

Case 1: quadcopter located at the center (x = 0.0 m)

Case 2: quadcopter located at the largest velocity gradient (x = -0.3 m)

The results are shown in Fig 4-7.

Fig 4. Torque disturbance at the center

Fig 5. Torque disturbance at the largest velocity gradient

• Fig 6. Disturbance force at the center
• Fig 7. Disturbance force at the largest velocity gradient

Overall, general trends of disturbance forces and and disturbance torques seemed repeatable.

Specifically, aerodynmic force was acting majorly on z-direction, and  torque disturbance was dominant for x and y direction.
Although there was not a significant differences between case 1 and case 2, the highest torque peak of x direction was observed for case 1, the highest torque peak of y direction was observed for case 2. That physically makes sense, since in case 1, flow in x direction is uniform, and that equally pushes the quadcopter, which results in more roll rather than pitch.

I think the effect will be more dramatic for case 2 if we locate the quadcopter near the nozzle, since more drastic velocity gradient will be applied to the vehicle.

The highest disturbance force peak (z direction) was observed for case 2, which might be concluded that force disturbance is more dominant when the large velocity gradient change occurs.

However, there is a large offset error of the force in x direction, which makes the analysis unreliable. Also, noisy signal from the accelerometer must be addressed in future.

For the future experiments, I am suggesting followings;

1. I believe it might be worth to test with a largequad, since the largequad is more stable.
2. It could be also interesting to see the difference when the quadcopter is located near the nozzle.
3. I wish to make a vehicle produce some trajectory under flow disturbance, which mimics a realistic large wind shear scenario.

# Short summary of this week

• ##### Verifying our flow torque disturbance data is reasonable by utilizing simulation

– Modified PC app simulation code, which enables .csv reading
– Torque input capability in the code so that I could use experimental torque data as an input in the simulation
– Confirmed that simulation matches well with the experiment

• ##### Checking a reliability of our current hot wire data

– Highly assumed that our current hot wire is broken. Not sure whether it was initiated from the broken electronics.
– Cheap  anemometer (fan-type) is not accurate compared to the teaching anemometer (hot-wire type) values;
fan-type: min: 1.5 [m/s], max: 6 [m/s]
hotwire-type (more accurate): min: 2 [m/s], max: 10 [m/s]

• ##### Building a  new miniquad with Karan

– Building it a first time took around 7 hours
– Currently it is not working and re-soldering is required (currently solder is almost impossible to use; currently waiting for new soldering tips)
– Took a time-lapse video; might be helpful for beginners

# 1. Torque disturbance verification

We are in the process of verifying that whether our estimated flow disturbance $\hat{\tau}_{des}$ can be approximated to the true disturbance $\tau_{dist}$. Overall block diagram of given system is shown in Fig 1.

Fig 1. Block diagram of given system (true dynamics)

Problem is $\tau_{dist}$ is unknown in the experiment. For this reason, I took disturbance estimate $\hat{\tau}_{des}$ as an input in the simulation, and compared to resulting disturbance $\hat{\tau}_{sim,des}$. Detailed procedure is shown in Fig 2.

Fig 2. Purpose of using simulation

As it is given in Fig 3. the simulation result is very close to the experimental data. Especially, if you see the third plot, the only difference is experimental data shows more noise, which is expected.

Fig 3. Simulation results and comparison to experimental data (Fan is on after ~25 [s])

# 2. Hot wire reliability

Fig 4. Teaching anemometer

As I reported in previous posts, our hot-wire and/or electronics are mal-functioning. Currently, voltage reading of hot-wire has stopped working, so we need to find an alternative.

Although we purchased a new fan-type anemometer, reliability of the anemometer is unclear. A better candidate can be a teaching anemometer, since it is more accurate, well calibrated, more compact than hot-wire+electronics set-up.

From the result, I figured out that current hot-wire is not accurate;

Hot wire data : max: 17 [m/s], min: 6 [m/s]
fan-type: min: 1.5 [m/s], max: 6 [m/s]
Teaching anemometer (most accurate): min: 2 [m/s], max: 10 [m/s]

Therefore, we can conclude our nozzle cannot produce the flow speed of what we expected, and we need to increase [rpm] in future experiments.

Problem now is I cannot borrow it for a long term, since it must be used for classes. I want to discuss this further in our future meeting.

# 3. Building a miniquad

I built a new miniquad with Karan, since it is our first time to build a quadcopter. I am planning to build one by purely myself, once we  build one successfully. Although we were able to build a miniquad, it is not working now. We have checked ESCs, and they looked fine. We believe that soldering can be the issue, and planning to continue once the new solder tip is ready.

Meanwhile, we took a time-lapse video of building a miniquad, since video is more intuitive for beginners. A sample link is attached.

## Update: Jason 2018-12-21

This week, I majorly focused on flow part of the research;

## 1. Checking the consistency of constant temperature anemometer (CTA)

• I have noticed that CTA does not show consistency, and I was trying to figure out which factor is causing this problem.
• The most significant phenomenon was that the measured voltage just drops down randomly, resulting in a significant change of velocity values.
• Currently, I am guessing that the electronics are malfunctioning since they are too old, but it is really difficult to figure out the source unless I can test this another CTA or electronics.
• By testing this many times, I realized that the circuit works properly for a couple of hours once it reaches proper level of voltage.

## 2. Time domain analysis for velocity near the nozzle

When the electronics was working properly, I tried to obtain the velocity w.r.t time, in order to analyze key flow parameters; $\bar{u}$ and $\left\langle u'^{2}\right\rangle$

Fig. 1. test specification

• Fan speed: 300 [rpm]
$\bar{u}=6.99\,[m/s]$, $\left\langle u'^{2}\right\rangle=0.33\,[m^2/s^2]$
the variance of fluctuation velocity is near to zero, which is desirable.

Fig. 2. velocity vs. time (fan speed: 300 [rpm])
• Fan speed: 600 [rpm]
$\bar{u}=13.84\,[m/s]$, $\left\langle u'^{2}\right\rangle=0.55\,[m^2/s^2]$
The average velocity was approx. two times of the previous case, which exactly matches with the doubling the fan speed. The variance was a bit higher than before.

Fig. 3. velocity vs. time (fan speed: 600 [rpm])
• Fan speed: 900 [rpm]
$\bar{u}=21.81\,[m/s]$, $\left\langle u'^{2}\right\rangle=1.43\,[m^2/s^2]$
The average velocity was approx. three times of 300 rpm case, which exactly matches with the tripling the fan speed. The variance was higher than before, since higher velocity resulted in more noise.

Fig. 4. velocity vs. time (fan speed: 900 [rpm])

## 3. Mean velocity profile

I measured several velocity points along the horizontal (x-axis) direction, in order to obtain mean velocity profile. The result is given in Fig. 6.

Fig. 5. Measuring velocity for horizontal (x-axis) direction

Fig. 6. Mean velocity profile with respect to x-axis

Although it is not 100% accurate measurement (since we do not have a linear stage), one can observe that the velocity profile is a slight notch shape, which can be found for a regular fan without flow straightener (honeycomb). Therefore, we can conclude that the current honeycomb does not ensure 100% uniform velocity profile, although it definitely helps to make the profile uniform.

From Jan 2, I am planning to

• See the flow profile with a certain distance (50cm, 100cm, 150cm), and try to quantify the flow properties. Also I will compare the result with the theoretical values.
• Double check the order of magnitude of the velocity with a portable velocity sensor
• Finish the simulation of torque disturbance
• Talk to potential undergrad researcher about the project

In a month, I will finish the flow characterization on drone so that I can aim the results to upcoming conferences.

## Update: Jason 2018-12-09

This week, I focused on three different things

• Analyzing experimental torque disturbance data and its comparison to simulation
• Preparation and presentation for a meeting with a potential sponsor
• Preliminary velocity data analysis using CTA (constant temperature anemometer)

## 1. Torque disturbance data analysis

I started analysis on torque disturbance data. I had fixed a bug in my python script, which caused a huge order of magnitude for the disturbance torque. Although the order of magnitude became more plausible, still we have an issue with the result.

Fig. 1. 1. X-direction torque 2. Y-direction torque 3. Z-direction torque (with fan on)

Problem is that there is a very small lag between the disturbance torque and the motor torque. Since the command torque is proportional to the error of angular velocity ($\underline{n_{B}}=-\frac{\underline{J_{B}^{B}}}{\tau_{\omega}}\left(\underline{\hat{\omega}}-\underline{\omega_{cmd}}\right)$), we would expect some lags. However, the level of lag is very small, as it is shown in the graph. I looked at Karan’s data, and similar level of small lag was observed.

In order to figure out the reason, I ran a simulation with a torque input (10 [mNm], x-direction only) from 27-31 [s], and results are shown.

Fig 2. Simulation results with a torque input (Position, velocity, angular velocity, and motor forces)

Fig 3. Torque results, x-direction (enlarged)

Fig 4. Torque results, overall

However, as one can see from the position plot, I was adding too much torque input, which resulted in very high magnitude of the torque.

I will try to make a similar simulation of our experiment, to properly compare the results with our experimental data next week.

## 2. CTA preliminary test

I also started collecting velocity data of the jet utilizing CTA. As an initial stage, I manually hold the sensor and measured center-line velocity.

Fig 5. Flow velocity measurement description

Results are as follows;

Fig 6. Jet velocity w.r.t time.

• While I will need further analysis of the experimental data, $\left\langle u'^{2}\right\rangle$ for example, I have noticed that the voltage of hot-wire circuit is not consistent. I will need to conduct further experiment to figure out the consistency of our sensor.
• Also, I will compare the experimental jet velocity with theoretical values, and see whether there is a self-similarity as well.

This week, I have learned that

• Thorough, logical way of analyzing/reasoning the given data
• Utilizing/connecting the knowledge that I have learned from the class

Next week (Specifically, before the general progress meeting Dec/19, considering my hectic schedule on finals/project) I am planning to finish the tasks that I stated Section 1 and 2.

In a month, I will finish the flow characterization on drone so that I can aim the results to upcoming conferences.

## Update: Jason 2018-11-30

I wish to identify flow disturbance effect on quadcopters, so that we can do better position tracking, and predictions under large flow disturbances (wind gusts, large shear flow).

To experimentally produce the flow disturbance, I have set-up experiments to produce an open jet utilizing a square nozzle. This set-up will help us to produce repeatable, characterized flow disturbances so that we can conduct quantitative analysis for the flow acting on the quadcopter.

This week I have done some preliminary flow disturbance tests using the nozzle set-up, and tried to analyze the flow.

Video link;

https://drive.google.com/open?id=1K2hiHg-gTH4IrCoQ6709HcCuJIcwcjDr

After today’s meeting, we obtained the conclusion that the order of magnitude for disturbance torque is too high (~0.1 Nm)

$\left[\underline{n_{D}}\right]^{B}=\left[\underline{J_{B}^{B}}\right]^{B}\left[\underline{D^{B}\gamma}\right]^{B}-\left[\underline{n_{B}}\right]^{B}$

After the meeting, I have thought about that and I re-plotted disturbance torque using the estimated angular velocity.

I think using estimated angular velocity is more desirable  for two reasons

1. The estimator utilizes mocap data, which reduces the error between the rate gyro data and the real angular velocity on the body.
2. The filter is applied to the estimator, so smoother signal results in less noisy results after differentiation (e.g. forward Euler).
Resulting equation is,

$\left[\underline{n_{D}}\right]^{B}=\left[\underline{J_{B}^{B}}\right]^{B}\left[\underline{D^{B}\omega^{BE}}\right]^{B}-\left[\underline{n_{B}}\right]^{B}$,

where $\left[\underline{n_{D}}\right]^{B}$ is disturbance torque, and $\left[\underline{n_{B}}\right]^{B}$ is motor torque on body frame.

Fig. 1. Disturbance torque, $\left[\underline{n_{D}}\right]^{B}$ 2. Motor torque, $\left[\underline{n_{B}}\right]^{B}$   3. Inertia multiplied by angular acceleration, $\left[\underline{J_{B}^{B}}\right]^{B}\left[\underline{D^{B}\omega^{BE}}\right]^{B}$ 4. Disturbance force

I have obtained Disturbance torque by subtracting ‘2. Motor torque’ from ‘3. Inertia multiplied by angular acceleration’.

For the angular acceleration term, I have used first order forward Euler method to calculate the derivatives of the estimated angular velocity. The order of magnitude is ~0.04 Nm at max., which is more reasonable than the result using derivatives of rate gyro data (~0.1 Nm). However, still the value of torque disturbance is higher compared to the torque produced by motors (~0.006 Nm at max.)

Although I am not sure whether the order of magnitude 0.04 Nm is reasonable, qualitatively, it makes sense to have higher value of z-torque, since flow is acting on the vehicle by x-axis.

This week, I have leaned that

• How to write a python script for analyzing/plotting pickle data
• A way to calculate force and torque due to disturbance
• How to reason about the given plots
• Better way of presentation slides/methods of my research for a potential sponsor

Next week, I will focus more on flow part of the nozzle. Specifically,

• I will locate the hot-wire where the miniquad was located during the preliminary test, and see the velocity values. I am also planning to compare the result with theoretical velocity, which only holds for laminar flow, and see whether the result matches
• I will also re-do the test near to the nozzle, and see if that makes a much difference to the disturbance effect
• I will make a full preparation of sponsor presentation on next Thursday based on the  comments that I got from yesterday’s mock-up presentation.
• I will read the paper named “External Wrench Estimation, Collision Detection, and Reflex Reaction for Flying Robots” https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8059847,
which is about detecting other environmental effects to avoid collision. That would help me to provide some intuition of analyzing flow disturbance effects of our case
• I forgot to ask Prof. Makiharju that whether we can utilize Particle Image Velocimetry (PIV) of his lab. and doing some flow analysis of quadcopters such as the figures of the paper “Wind Characterization Using Onboard IMU of sUAS” https://arc.aiaa.org/doi/abs/10.2514/6.2018-2986. It might be worth to discuss this with him.

Fig. Flow effect of rotors utilizing PIV technique (ref. from the paper)
• In a month, I am aiming to finish the static drone test (make it hover in one position with fan on) with jet flow characterization utilizing hot wire sensor.