What does "Mach" mean? How many kilometers did you fly at Mach 15 for an hour?

We often hear that the speed of the plane has reached Mach number, and the fastest plane in the world has reached Mach number.

At present, the most famous NASA X-43 and Blackbird fighters, including the space shuttle, can reach Mach number.

Is Mach a speed unit?

Strictly speaking, Mach number is not a speed unit, but in a compressible fluid, the performance of the fluid is affected by compressibility at a given Mach number and has nothing to do with other variables.

This compressible fluid can be a liquid or a gas.

Since Mach number is defined as the ratio of two speeds, it is a dimensionless number.

How did you get the Mach number? How to understand the dimensionless Mach number? If you fly at Mach 15 for one hour, how many kilometers do you fly?

Next, this paper will explain the invention of Mach number and the comparison between them in detail, and answer the questions mentioned in this paper.

The appearance of Mach number must mention one person, and he is ernst mach.

He lived in the Austrian Empire and was an Austrian physicist and philosopher.

His most outstanding contribution to physics is taking a series of photos. Don't underestimate these photos, they reveal the motion performance of objects at high speed.

For example, the photos of spark shock wave and ballistic shock wave reveal how the object produces compressed air in front of the bullet or shell when it moves at supersonic speed.

Mach recorded all this with schlieren photography, and then he published a related paper in 1887.

In this paper, it is pointed out that when an object moves in the air, the spherical disturbance wave propagates at the speed of sound c, and when the object velocity v is greater than c, a conical envelope surface with the object as the vertex will be formed in front of the waveform.

The relationship between the angle formed by the generatrix of the cone and the direction of motion of the object was later named "Mach angle" by Planter.

However, Mach number was not named by Mach himself, but Jacob Acret, a Swiss aviation engineering expert, found in his later physical research that if the ratio of air velocity v to ground sound velocity a is specified as a characteristic number, the definition of similar properties in viscous compressible flow can be greatly simplified.

This discovery makes people pay attention to the ratio relationship between Mach numbers and the importance of the ratio coefficient between different fluids.

So how did you get this proportional relationship?

Considering that Mach is mainly used in space flight, gas is emphasized as the fluid for analysis and explanation, so the concept of sound speed must be mentioned.

In gas or liquid, sound consists of compressed waves, while in solid, waves propagate in two different types, longitudinal waves and shear waves.

P wave is confined to one plane, which is the only sound wave propagating in gas and liquid.

Shear waves, also known as shear waves, only appear in solids because only solids can support elastic deformation. Generally speaking, shear waves appear in the form of a pair of orthogonal polarizations.

Due to the propagation of sound waves in different media, the speed of sound is variable, which depends on the material characteristics of wave propagation.

In fluid, only compressibility and density of medium are important factors, because fluid does not transfer shear stress.

Another thing to know is that the medium in which sound waves propagate is not always adiabatic, so the speed of sound will change with frequency.

The earliest experiment on this kind of research was calculated by the famous physicist isaac newton in the19th century, but in later experiments, people changed the data calculated by Newton in that year.

Back to the propagation of sound velocity we mentioned earlier, what we can know so far about the utilization of sound velocity in air is that the most important factor affecting sound velocity in air is temperature.

The speed is proportional to the square root of absolute temperature, which is about 0.6m/s per degree Celsius.

At the same time, the speed of sound also increases due to humidity. The difference between 0%~ 100% humidity is about 1.5m/s, and the magnitude of this humidity effect increases significantly with the change of temperature.

As far as Mach number is concerned, the academic definition is: if Mach number is less than 1, the flow rate is less than the sound speed; If the Mach number is greater than 1, it means that the macroscopic motion speed of the object is faster than the speed of sound. For objects flying in the air, when the object flies forward, it will bring continuous disturbance to the air, and the gas in front will be "scattered" through an energy transfer.

If the object moves faster, the gas will be compressed, and the fluidity will be different from that of incompressible flow.

Generally speaking, the compressibility of gas must be considered for objects with Mach number over 0.3.

The most direct manifestation of this change is that the air resistance will increase significantly and a shock wave will appear, which is what we call "sonic boom".

After understanding these basic principles, we can make simple calculations. If you fly at Mach 15 for one hour, what is the flight distance?

At present, academic circles divide flight into six categories: subsonic speed and Mach number.

Through the relationship between the sound speed and Mach number, plus the speed of the object, let's simply calculate it now.

According to the formula M=u/c, where m stands for Mach number, u stands for speed and c stands for sound speed, here we assume that the object is flying at an altitude of 10,000 meters, not near the ground, because the air temperature at high altitude will affect the sound speed, and the value of c is 295 m/s.

According to the calculation, if you fly at Mach 15 for one hour, the flying distance is 15930 km. If you fly at this speed, you can circle the earth for more than an hour.

If the height changes, the corresponding temperature and humidity will also change. As we said before, the speed of sound will change because of these physical factors, so the speed of sound is different in different States.

To some extent, the speed of sound represents a temperature change, which is why some indicators of aircraft use pressure difference to represent the real airspeed during flight.

Finally, we need to know that Mach is not the speed in the ordinary sense and cannot be directly used to express the speed movement.

For speed itself, Mach number is a function of temperature and real airspeed.

As far as this speed is concerned, it has surpassed all flying aircraft on earth. Even the X-43 made by NASA and the US military has a speed of only Mach 9.6.

This has entered the category of hypersonic. As one of the fastest manned aircraft at present, you must have strong physical fitness and superb flying skills to fly this kind of aircraft.

Generally speaking, the speed range of most fighters is only at supersonic speed. In terms of design, development and cost, once it exceeds this range, many factors must be considered.

No matter the material or the overall design, the resistance caused by shock wave, high temperature friction and kinetic energy accumulation should be minimized.

If the entry speed is basically the same as that of a meteorite falling or a spaceship landing, the air will be ionized due to the strong compression of the air.

Due to ionization, electromagnetic signals cannot reach the inside of the flight cabin, so astronauts will lose contact during this period.

In daily life, there is also this phenomenon of high-speed movement, such as whipping.

In the process of waving the whip, the grandfather in the park will move at a high speed, and the sudden change of the whip tip will form a supersonic shock wave at the front end or part of the whip.

It is this energy that crackles in the air.

Racing cars, airplanes, rockets, and human beings' pursuit of speed seems endless. How fast can it be?

Presumably, even the speed of Mach 15 can't satisfy this wish.