To achieve a goal, we need to have a detailed understanding of the factors that determine the outcome of that goal. What factors are important? Of these factors, which is the most important? What factors can be easily changed?
However, our force (in the form of thrust), is constantly changing. As we saw in Part 2 of the Speed Optimization series, Our thrust will be at a maximum at zero velocity and will decrease linearly with speed until max speed is reached. So in other words, our force is dependent on the very thing we are trying to find (velocity).
To throw another egg in this mess, our thrust (or more specifically, our net thrust) will be further reduced due to air drag. Of course, air drag is also dependent on velocity.
This problem of finding our velocity is an egg heads dream; this is a perfect problem to solve using calculus and differential equations. Luckily, for those of us that see this as a nightmare, we can use a program called excel and something called Numerical Methods to solve differential euqations.
If you are using a tablet or phone to view this, I apologize for the image sizes! If you click on the equations, a larger picture will open up which is much easier to read.
Update April 22, 2017: I updated the spreadsheet due to an error (I will admit when I screw up!). Also, I have added a 0-60mph time which is to be used for comparison purposes only since this spreadsheet is assuming instantaneous impulse.
Here is a link to the spreadsheet I made using the above formulas. This has been a good general guideline (so far) in determining top speed. Also of note is that I am assuming the center of gravity and center of thrust are aligned.
Although these calculations get us in the ballpark, there is a recurring theme: to calculate speed accurately would be nearly impossible due to the multitude of factors that could only be determined experimentally in this case.
Most of all, I have found this spreadsheet to be a great tool for determining what factors affect speed the most and to what degree.
Take note of the top speed and the voltage at top speed of each run and average them.
Input the average voltage into the spreadsheet.
See what the spreadsheet calculates as your max speed.
If your actual top speed was faster than what the spreadsheet says, lower the Cd value; if slower, raise the Cd value.
Keep adjusting the Cd value until the spreadsheet is roughly calculating the same speed your quad obtained.
From here, you can see how changing different parts of your build (reducing area, motor kv, prop pitch, weight, etc.) will affect your top speed with a fair amount of accuracy.
Good luck and I am always open to questions, ideas, and criticism.