Help me with mah physics
So if I had an Aircraft A and an Aircraft B, and Aircraft A was flying twice as fast as Aircraft B (both over Mach 1 at all times), how are the Mach Angles of the planes related?
Formula:
Mach Angle = Sin^-1(speed of sound / speed of aircraft)
December 17, 2012
10 Comments • Newest first
Unfortunately, it's not the ratio. Angle[A]/Angle[B] leads to some weird function that converges to 0.5 from below but ends up with an error once it dips below (1/3).
It's... odd.
[B] = [A]/2
I think the answer would be the ratio.
There is no relationship since they are not dependent on each other obviously.
Or rather, when I hear relationship, I think of directly/inversely or a ratio of the two.
I think the ratio then would just be 0.5:1...Wrong but I'm sure it's a ratio.
[quote=HolyDragon]Did you try relating them to the sound of speed and making a formula for that by subing v for Plane A and 2v for plane B?[/quote]
Yeah, I did something of the sort. So v[A] = 2v[B], or v[B] = v[A]/2.
I ended up with:
Airplane A:
Angle[A] = sin^-1(a/v[A])
or
Angle[A] = sin^-1(1/M[A])
Airplane B:
Angle[B] = sin^-1(2a/v[A])
or
Angle[B] = sin^-1(2/M[A])
(I know I messed up the notations, but you can't really do subscripts here, so that'll have to do. XD)
But yeah. I have the formulas for each one, but I don't know how they're related to each other. Tried graphing and everything, but didn't see much of a pattern.
EDIT:
@above: Ooh, you gave me an idea.
So I tried graphing y = Angle[A]/Angle[B], and I got a function that gradually converged towards 0.5 as the Mach Number (x-value, with the equations I used) increased.
Not sure what this means, though. XD
Here's my crappy guess xD
Let v be = Aircraft B's speed, and by doing a quick google search, we find that the speed of sound = 742 mph
[sin^-1 (742 mph / 2v)] / [sin^-1 (742 mph / v)]
I'm bored and felt like doing this horribly wrong.
Did you try relating them to the sound of speed and making a formula for that by subing v for Plane A and 2v for plane B?
[quote=Satoshi1234]Come on, my dear math people who prowl Basil at night. Where y'all at...[/quote]
did you not* hear me F=MA
Come on, my dear math people who prowl Basil at night. Where y'all at...
pi/6 A = B
That's a total guess btw.
inertia