I have decided to build a quad-copter for no particular reason, outside of: It’s awesome and I’m bored. But let’s be honest, many things start that way.
So how do you build a quad-copter exactly? Well, I have no idea, so I suppose I better find out. As luck would have it, I know just the person to talk to. Google.
After doing a bit of research, I determined the best place to start is the math. I want this thing to fly, of course, so I need to be able to generate enough thrust to get off the ground. Thrust is generated by spinning propellers. the larger a propeller is, the more air it moves and the more thrust is generates. Similarly, the faster you spin the propeller the most thrust you will get. Is high RPM or large props going to be more effective though? Presumably, there is a trade-off somewhere, which means there must be an optimal ratio of speed to size for a given chassis. Unfortunately, the math for calculating thrust is ugly and depends on a large number of outside factors (air temperature, altitude, etc…), things that are outside our control. There are a number of calculators available on-line that take a number of parameters in, then output the theoretical thrust. The one I used is found on personal.osi.hu.
The numbers we get from this are very rough estimates. After playing with it for a bit I decided on either 9×4.7 or 10×4.5 props. They would give me around 4-4.5kg of thrust at an achievable RPM according to the calculator, assuming 4 identical props. I am going to aim to have my ‘copter around 2kg to allow for plenty of headroom. Let me explain the measurements for the props. A 9×4.7 prop means that the prop is 9″ in diameter and has a 4.7″ pitch. The pitch is the distance the propeller would travel forward through a solid medium with one complete revolution.
With that done, I need to be able to turn the propellers at a good speed. I’d like to be able to do at least 10000RPM to achieve the thrust I calculated previously. How much power is required to turn a 10×4.5 propeller at 10000RPM? I found the following equation relating power to speed and size. Again, this is an approximation but that is good enough for my purposes:
Where Kp is a propeller constant, D is the diameter of the propeller in feet, P is the pitch in feet, and RPM is the speed in thousands of rotations per minute. From this equation we can see that while the propeller constant and the pitch do have some effect on the power, those terms are dwarfed by the quartic diameter and cubic RPM terms. So, by and large, power is a factor of the diameter of the prop and the speed you want to spin it at. For example, with the 9×4.7 props, the power required to generate that quoted 4kg of thrust is approximately:
The constant of 1.31 is just a number I pulled from a table of different propeller manufacturers for a relatively well known propeller manufacturer. So I need motors capable of 163W of output power and 9×4.7 props in order to get the performance I am looking for. Probably…