I don't mean to sound arrogant but machining is more of an art then a hard and fast set of rules. It's knowing the materials and how to attack them. It's knowing your machine and what works and what doesn't work with it. The only way you learn all of these things is experience. I've been machining for 35 years now.
So having said all of that the key is go slow. You notice that I worked from right to left removing the far out material first (material furthest from the chuck) constantly decreasing the hanging out mass first. Also, a properly formed and sharpend tool, set at the right height will make chattering none existent.
Now the most unbelievable statement... I never ever pick up a measuring device or a caliper when making my trek props, it's all done by eye. I know there are some reading this that are saying "bull shit" it is called years of experience machining.
Now the rant, when I make these item the first thing I always get is can you make me one? I am flattered by this but I really want my posts to inspire other to want to make one for themselves! A friend many years ago told me this little word of wit: If you want something bad enough you will find a way to do it, if you don't get it, then you didn't want it bad enough! I learned early on in life not to depend on others to do for me, when I want something you have to do it yourself. Don't be afraid to learn new things, get out of your comfort zone, that is the only way to learn! End of rant!