AlphaSheeppig

The presentation went surprisingly well. The two presentations before me were really bad, so any nervousness I had been feeling vanished. The questions were tricky, but I was prepared for them... They were the generic sort though - along the line of asking me to elaborate on how I validated my simulations, the guy that kept asking obvious questions (to test whether I understood what I was saying, I guess), and then the one who asked me to speculate on where results from some other unrelated case would fit into my data - ironically, it was the exact same thing my advisor asked me when I first started getting results. Thanks to everyone who gave advice. All of it helped. To anyone who stumbles across this at a later time looking for advice, the best advice I can possibly give after having been through it once is to have in depth knowledge what you are talking about.

Lol... You mean everything then? It's a LOT of work, but a good place to start is to go to a local college and university and ask what textbooks they prescribe first years in whichever fields you're looking at learning, and then work through those books. In my personal experience, math is the hardest to understand, so I'd guess it's easier to start with, say, physics, and then as you require this or that mathematical technique, go learn that technique. I find that math is often easier to learn when you see it's applications right from the start so you don't get overwhelmed by the abstractedness (if that's even a word) of it all.

Yes, it can be done practically... Get yourself a cheap R/C plane from a hobby store, get a wireless security camera with decent picture quality and a good range that can transmit to your laptop, and then use duct tape to tape it onto the plane, and then be prepared for a lot of crashes until you get the hang of flying it. To control it with your iPhone is a different story, since as far as I know, the iPhone isn't capable of transmitting radio waves you need to control a typical R/C aircraft (usually 27 MHz or 2.4 GHz, depending on what type of plane you use). There's a video tutorial on how to make one here.

The F-117 is really in a class of it's own. They say bats fly into it at night because their echolocation can't pick them up... It's not really any curved surface that is a problem, but rather concave surfaces, since these tend to reflect the radar waves straight back. In general, with modern stealth aircraft (now I'm talking along the lines of the F-35 and F-22), the approach is more to eliminate the concave surfaces (such as where the wings meet the fuselage) by blending these with a flat surface, or by making it a sharp corner. These have the disadvantage that at some critical angle they reflect the radar waves straight back, but if the angle is even slightly off, then the radar is deflected enough to be invisible, if it is detected, it would be pretty small, and would maybe be mistaken for a flock of birds or something. I guess it could possibly be the same with the rotor blades... If the rotor blades were made of a composite material such as carbon fibre (which is very likely) then they are semi-transparent to radar to start with...

In terms of radar invisibility, the blades need not be the classic airfoil shape. They can be angular or diamond shaped, which ruins their aerodynamics, but deflects the radar. You just put on a bigger rotor and more powerful engine, and it makes up for the reduced lift from the rotors. Look at the F-117, which is shaped such that it reflects radar, no matter which direction it comes from. There is no reason why you couldn't apply the same principles to a helicopter. The pics I've seen seem to show some sort of sharp corner on a surface of what seems to be a rotor blade. A big no-no in subsonic aerodynamics, because it reduces the lift and increases the drag drastically, but it would greatly reduce the radar cross section of the rotor blades. The tail rotor, which is much more clearly shown in pics, seems to be masked, and has stumpy blades with a very short chord - basically taking a minimalist approach. The helicopter must be a real bitch to control, but I guess that wasn't really one of the designers' priorities...

For the silence, have you considered the ridiculously loud whoosh whoosh whoosh of the blades spinning through the air at close to the speed of sound (for any decent thrust), and then maybe some humming from some transformers to power the magnets and then the engine or generator used to make the electricity - batteries are out of the question for any reasonably sized craft because they just weigh far too much. Apart from the magnets, the propulsion system you are proposing is known as a ducted fan. They are indeed more efficient than open rotors, and produce more thrust, and produce less noise... The main reason helicopters rotor blades are open is because ducted fans are just far too heavy. The number one rule when designing anything that can fly is to keep it as light as possible.

Yup, the answer is 8. How far did you get with trying to work it out? Consider that the left hand side, being made up of sin and cos, will oscillate between some maximum and minimum values...