So the first week has been amazing. I got a lot done and so far my results are looking good. I spent the majority of the first week working out the math so that I could finalize my hypotheses.
On the left, you can see a basic thrust calculation that can be used for any aerodynamic body with a propellor. The calculation defines thrust as a function of thrust coefficients, air density, effective area, radius, and angular velocity of the propeller. Using this calculation, I was able to finalize my hypothesis that thrust, and therefore vertical acceleration, is proportional to the radius of a propellor.
After I had worked out my theory, I wanted to tests to confirm whether or not my hypotheses would hold true in what I call a "mini-experiment." Before dedicating 20 trials and hours of video analysis, I wanted to run 5 small trials and figure out whether the theories even made a significant difference in quadcopter performance. My setup was quite simple. I placed a 1meter mark on a door, and using frame by frame video analysis, I calculated the difference in time once the quadcopter's propellers began spinning to when the base of the drone had crossed the mark. Before I could test any modifications, I had to do a standard trial to have data to compare to. One trial video has been placed below so the setup can be displayed.
After all the videos were taken for the five trials, the 5 trials of data were compiled into a table and statistical analysis was done. Below is the data from the standard experiment. The final calculated value was determined to be 0.749s. This means that the unmodified drone took 749 milliseconds to reach 1 meter in height.
After the standard trial was complete, it was time to start modifications. First I wanted to test my radius hypotheses so I cut one centimeter of each side of each propeller. Then I ran the same experiment again. Below is one of the trials.
I ran the same analysis as in the standard trial as well as the same method of statistical analysis. The final result came out to be 0.785 seconds, which proved my hypothesis correct. Since the radius decreased, the drone produced less thrust and therefore accelerated slower.
I concluded the week by working on another hypothesis which is a bit more well known. Obviously, the mass of an aerodynamic body causes a decrease in acceleration. However, I wanted to prove it mathematically and in the real world. Thus, I set out to prove my theory mathematically first.
What the math proves is that while a body is hovering, the thrust produced must equal its weight. While this is obvious, it was quite tough to derive it. I found the thrust equations as a function of mass and power and solved for thrust in order to derive it. However, what this relationship proves it that acceleration is increased when thrust is larger than the weight (and drag, but that was ignored).
To prove this expirementally, I decided the easiest way to prove it would be to detach the hull. The hull is a frame that some quadcopter come with. Essentially, it acts as protection for the propellers in the case of a collision. Below is a trial without the hull.
The data from these 5 trials is below. As you can see, the quadcopter without the hull attachment is significantly faster than one with, by almost 0.1 seconds.
This week was quite successful. Next week, the plan is to transform these results in to more scientifically valid expirements.
