Calculating the Drag Force of a Drone Flying 190mph
In order to make important decisions about our drone, like the frame and motor size, we need to first analyze the last of the three forces that are preventing our drone from flying as fast as it likes (the others are gravity, and lift).
The drag force is perhaps the most complex of the forces we will be analyzing. It changes with regard to shape, medium, and many other factors. It is the reason that a TV does not fall at the same rate as an empty popcorn bag on earth. It is the reason a parachuter or parasail is able to stay in the air for a longer time than gravity would allow. Let's look at the equation for the drag force:
This may be a mouthful of baloney for some of you, so let's break it down. The symbol that looks like a "p" is density, and it represents the density of the medium the object is moving through. For water, this would be 997 kg/m^3, and for air, it would be about 1.22 kg/m^3. Because our object is moving through air, the latter value is relevant to us.
v^2 simply represents the velocity of the object squared. This also shows us that the drag force on the object is dependent on how fast our object is going, meaning that our drone will experience various drag forces while it is moving.
C(d) is perhaps the most complex variable in this equation. It represents the drag coefficient, which is a number that varies for any object's shape or size. The drag coefficient is not something easily calculated, and the biggest barrier in using just this equation to solve for our drag force. Although we can simply Google what the drag coefficient for a drone is and receive a close estimate, we are going to consult some advanced software to solve this variable for us.
A represents the area of the object. The only area calculated is the area of the surface that the medium will impact.
Like I mentioned earlier, we cannot solve this equation as we do not have all the variables defined, and using Google as an estimate is not precise enough when another method is available. SOLIDWORKS is a CAD (computer-aided design) platform that industry leaders in mechanical design and manufacturing use to model and machine components. SOLIDWORKS is very complex and useful as it has many plugins, including SOLIDWORKS Flow Simulation, which is a CFD (computational fluid dynamics) software platform. Using Flow Simulation, we can run tests to model what the drag force may be like on our drone.
I opened up SOLIDWORKS, modeled the drone, and after much pain of figuring out how to use Flow Simulation, finally set up a scenario that involved the object flowing through the medium of air at 85 m/s (190 mph) at an angle of around 10 degrees. I then ran the simulation tests and calculations, with the goal of analyzing the normal force on the drone frame. And voila, it worked! - but it wasn't exactly accurate.
Here is an image of over 10,000 air particles passing over the drone frame, and color-coded by their pressure. As you can see, the propellers in this scenario are just flat discs. This is because the angles propeller blades were throwings errors in Flow Simulation, so I switched over to flat discs.
The major problem with that is it distorts the value of drag force immensely. A propeller is an object that shapes airflow and produces lift by screwing through the air. It creates a low-pressure area in front of it and a high-pressure area behind it. That is not represented in the simulations I was running. Furthermore, if air were to rush toward a propeller, the propeller would spin - this is how a windmill works. Meaning, that the drag force in the direction of the movement of a propeller is not straight-forward at all.
My next step is to look into how I can determine the drag force of the propellers, which will allow me to choose what motors and frame size I must choose. I will then analyze how I can test the accuracy of my calculations in an affordable manner.