B Form 2a: Fill & Download for Free

In addition to the proofs given in the other answers, here is a proof I discovered while helping my kid with her homework.Consider the standard quadratic equation:[math]ax^2 [/math][math][/math][math]+ bx [/math][math][/math][math]+ c = 0[/math]We can rewrite this as:[math]ax^2 +bx = -c[/math] , then, assuming [math]a \ne 0[/math], we can divide by [math]a[/math] :[math]x^2 [/math][math][/math][math]+ \frac{b}{a}x = -\frac{c}{a}[/math]After factoring, we get:[math]x(x +\frac{b}{a}) = -\frac{c}{a}[/math]Now comes the interesting part: the left hand side is a product between a number and the same number plus some quantity. How about if we express this product in terms of the midpoint between these two numbers?Let’s define a new variable [math]y = x [/math][math][/math][math]+ \frac{b}{2a}[/math] and rewrite the equation as:[math]\left(y - \frac{b}{2a}\right)\left(y [/math][math][/math][math]+ \frac{b}{2a}\right) = -\frac{c}{a}[/math]which is nothing but:[math]y^2 - \left(\frac{b}{2a}\right)^2 = -\frac{c}{a}[/math]or:[math]y^2 = \left(\frac{b}{2a}\right)^2 -\frac{c}{a}[/math]Now it’s easy to solve for [math]y[/math]:[math]y = \pm\sqrt{\frac{b^2}{4a^2} - \frac{c}{a}}[/math]or:[math]y = \pm\frac{\sqrt{b^2 - 4ac}}{2a}[/math]Going back to the original variable [math]x[/math]:[math]x = -\frac{b}{2a} \pm\frac{\sqrt{b^2 - 4ac}}{2a}[/math]which becomes the familiar:[math]x =\frac{-b \pm\sqrt{b^2 - 4ac}}{2a}[/math]

When I first started to do research on the B-2A Spirit, I thought the same thing. At speed and altitude, there is not much of a problem as the pilot can use the split ailerons for ‘Yaw’ control. The only place that this would be a problem would be at very slow speeds during the initial takeoff run and during landing.The B-2A lands and takes off at about 127 kts. During takeoffs, the reinforced main landing gear doors act a twin vertical stabs. There were several launches I saw where the landing gear was fully retracted while the gear doors are fully extended.So, in the slimmest terms, the B-2A does have vertical stabs, but they point down and retract after a certain knots indicated is reached, the ‘Flight Control Computers’ will do the rest.

First, it is Northrop….. I corrected it for you, and Jack Northrop’s family breathes a sigh of relief. Remember that most aerospace companies trace themselves to one person, and Jack did get to visit the B-2A when I was on the development team.Those are Not tails. Those are trailing edges of a Single wing that contain control surfaces.Indeed, the development stopped for about “six months” when we had to design those control surfaces into the aircraft. Originally, the B-2A was supposed to be a High Flyer. Cruise above 40,000 feet, stealthy and slip in and do its thing and then slide away.Except in the HEAVILY defended areas in then Western Soviet Union that was a death sentence. Therefore the B-2A was expected to drop down to “tree top height” above the ground and do its thing. With the high speed flight and turbulence, the plane would be uncontrollable with only that center “beaver tail”. One needs Moment Arm from the center of gravity to control rotations, and the B-2A is very short. Therefore, we went from a single Beaver Tail and added the two saw-teeth, one on each side, to get some more surface area for control surfaces and to get some more Moment arm.The B-2A looked a Lot like the B-21 at the start. Added the two saw teeth during the development.Let us sit back and wait to see what actually rolls out onto the Palmdale runway for first flight…. Shall we?