Re: Vx versus Vy
If you make a graph of rate of climb vs. airspeed (with airspeed as the independant variable on the x-axis and rate of climb as the dependant variable on the y-axis), you will get an inverted "U" shape. If you draw a line from the origin of the axes (0,0) so that it will just touch the curve at ONE point, that is Vx. This way of showing it using basic geometry shows that Vx is of course this speed because it is the speed where the ratio of vertical speed to horizontal speed is the greatest. By the nature of the shape of that graph (an inverted "U"), Vx is then less than Vy (which would be the maximum point of the "arch".
The main point:
The difference is that at Vx, you are getting the most feet of altitude for each foot over the ground. At Vy you are getting the most feet of altitude for each minute flown. It can be confusing thinking about the multiple variables in the problem. The reason you don't want to climb at Vy if you need to clear an obstacle is because sure you will get higher sooner, but you will also have covered much more distance because you are going faster. At Vx, the rate of climb is less than Vy (which can be confusing because then why do you use that speed to clear an obstacle?), but you are moving more slowly forward, so at a given point (like the end of the runway), you will be at a higher altitude than if you climbed at Vy and were at that same point.
The reason that the graph of Rate of climb vs. airspeed is the shape it is has to do with lots of variables such as the difference between the drag curve (aka power required) and the power curve (aka power available).
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