Solving the Supersonic Speed Problem in Physics

[Schalchlin05]

I really have no idea what category this type of question goes in. I'm actually a senior in high school but I think this may be a college level question because I'm in the highest level physics class my school offers and the teacher doesn't know how to do it. I saw it on a UIL test for science. It said that this bird could somehow fly at mach 3.8..what angle does the supersonic wave (i think that's what it called it) come off at? If anyone knows how to explain the solution to this problem please do. Thank you.

 

[brewnog]

The sine of the Mach angle is equal to the reciprocal of the Mach number...

Was the 'bird' made by Lockheed perchance?

 

[Schalchlin05]

thanx a lot...and I'm not sure if it was or not

 

[Astronuc]

For notes on Oblique shock waves, see -

http://www.grc.nasa.gov/WWW/K-12/airplane/oblique.html

for more details, see NACA 1135.

http://www.grc.nasa.gov/WWW/K-12/airplane/Images/naca1135.pdf

Mach 3.8 maybe too high for the SR-71 Blackbird, which reportedly had a maximum speed of 3.3+ under the right conditions.

 

[Nenad]

Thats a quick freaking bird.

 

[Clausius2]

I really have no idea what category this type of question goes in. I'm actually a senior in high school but I think this may be a college level question because I'm in the highest level physics class my school offers and the teacher doesn't know how to do it. I saw it on a UIL test for science. It said that this bird could somehow fly at mach 3.8..what angle does the supersonic wave (i think that's what it called it) come off at? If anyone knows how to explain the solution to this problem please do. Thank you.

The angle to what Nenad has referred as $$sin\theta=M^{-1}$$ is what you are looking for. To add something, that angle is the angle formed by a weak shock wave far away from the body (at the order of ten times the characteristic length of the body). This wave is the so-called Mach Wave. It is named as a Weak Wave because behind it the flow remains supersonic. At very short distances of the body nose, the proper form of the surface enhances a Bow Shock, which has a variable $$\theta$$ because the Mach Number varies behind it from subsonic to supersonic at larger distances.

 

[Sled Head]

I would say that the angle is more like a radius, but at the front of the aircraft it is a flat perpendicular at which it forms the radius. This is called the doppler effect and shock wave.
Like a point on the inside surface of a ball.
See this link- http://www.physicsclassroom.com/class/sound/u11l3b.cfm

As far as the speed limit of the SR-71 Blackbird. The aircraft has no speed limit.
People say, how can this be? But can you understand how the SR-71 can get better fuel mileage the faster it goes?

The SR-71's "speed limit" is actually limited by temperature. Which is 427 degrees "C" at the propulsion systems Inlets.

These are called-
Axisymmetric Supersonic Variable Geometry Inlets

The conical tip in front of the engines are called the "spike". The spike moves forward and aft within the nacelle opening.
Some people think, that as the spike moves aft the opening gets larger. This is not exactly true.

A simplistic explanation-
What happens is, the very front of the opening gets bigger but the area inside actually gets smaller. The position of the spike controls the position of the super sonic shock wave of air pressure entering the nacelle. "SHOCK TRAP Bleed". The forward by-pass doors help stabilize and maintain the sub-sonic air pressure entering the front of the engine.

The jet engine itself P&W J58 is a turbo by pass whereas unneeded air is by-passed around the engine through the nacelle and back to the ejectors afterburner.

What this does is give higher volumes of air at altitudes where little air exist.
The reason why the SR gets better fuel mileage the faster it goes, is because at those altitudes the air is so thin that there is less drag on the aircraft and the inlets create air pressures at better than sea level.

The SR's speed is limited not by power but by temperature. As speed increases so does the temperature and when these alloys heat up bad things start to happen. They start to expand, warp, and buckle. their characteristics start to change and weaken. The SR crews were not to let inlet temperatures exceed 427 degrees C.

The aircraft's temperature during high MACH at altitude are dynamic due to external air temperatures and density. Although it may be very cold, like -70 the little air that does exist heats up the airframe to over 1000 degrees.

Official speed records were set by the SR-71 on a few different occasions. An official top speed was achieved at 2190 mph. These are tightly controlled closed course records where the the aircraft had to slow way down in order to refuel.

UN-official speeds were reported at MACH 3.5 during evasive maneuvers from missile attacks. It was also reported that the faster it flew the smoother the ride and the pilot felt like it could go much faster. It has been said "theoretically" the aircraft could go MACH 6 in a dash.