Supersonic speed

Shock waves from a Northrop T-38 Talon at Mach 1.1 at a height of just under 4 km

A United States Navy F / A-18E / F Super Hornet during transonic flight with a cloud disc effect in the rear area

Pressure curve when flowing out of a container with a Laval nozzle

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Video of a Grumman F-14 during transonic flight with a cloud disc effect

As a supersonic speed , short (the) supersonic , that is speed designated objects if it is greater than the speed of sound , d. H. when the objects move faster than the sound propagates in the same medium.

description

In air , the speed of sound under normal conditions (air at 15 ° C) is 343 m / s, which corresponds to 1230  km / h . The relative speed of an object to the speed of sound in air is also denoted by the dimensionless Mach number , so Mach 1 means movement at the speed of sound, Mach 2 that with twice the speed of sound, Mach 3 that with three times the speed of sound, etc.

The Mach number is not a unit of speed, but the ratio of the flow velocity to the speed of sound (temperature-dependent). Although the term supersonic speed in principle denotes all speeds with a Mach number> 1, the range of Mach numbers> 5 is also differentiated by the term hypersonic speed , since the aerodynamic properties change here.

Particularities at supersonic speed

Reaching and exceeding the speed of sound requires very high drive powers. When the speed of sound is exceeded, a cone-shaped shock wave forms around the moving object ( Mach cone , see also supersonic flight ). This shock wave can be perceived by a distant observer as a bang or clap of thunder.

The breaking of the sound barrier means overcoming the sharp rise on reaching the speed of sound air resistance, presented what aircraft designers long time before some problems. Another design challenge arises at flight speeds well above Mach 2: Due to the compression of the air, the missile heats up beyond the load limit of common building materials such as aluminum. This speed range is also known as the heat wall .

As a result of the adiabatic cooling of the air in the negative pressure zone at the rear of the aircraft, the water vapor condenses in the air and forms a cloud of water mist in a characteristic cone shape ( cloud disk effect ).

Gas dynamics

Neglecting the potential energy, the energy law for a compressible adiabatic flow for ideal gases can be expressed in the following form:

${\displaystyle h_{1}+{\frac {{c_{1}}^{2}}{2}}=h_{2}+{\frac {{c_{2}}^{2}}{2}}}$.

The enthalpy and the kinetic energy represent the total enthalpy, which in the case of adiabatic flow without energy supply or removal does not change for a stream filament.

The enthalpy of an ideal gas can be described by the specific heat capacity c _p or the isentropic exponent (specific gas constant ). ${\displaystyle h}$ ${\displaystyle \kappa }$ ${\displaystyle R_{\mathrm {s} }=R/M}$

${\displaystyle h=c_{\mathrm {p} }\cdot T={\frac {\kappa }{\kappa -1}}\cdot R_{\mathrm {s} }\cdot \ T}$

The following applies to the speed of sound a with an isentropic change of state (index "s"):

${\displaystyle a={\sqrt {\left({\frac {dp}{d\rho }}\right)_{\mathrm {s} }}}={\sqrt {\kappa \cdot R_{\mathrm {s} }\cdot T}}}$.

If a steady flow is assumed for state “1” , then enthalpy and total enthalpy are identical. If the critical speed of sound is reached in state “2”, then applies ${\displaystyle c_{1}=0}$

${\displaystyle a_{2}=c_{2}=a_{\mathrm {krit} }}$.

The Mach number indicates the ratio of the speed to the critical speed of sound. In the event that exactly the speed of sound is reached in a cross section, then also applies . ${\displaystyle c=a_{\mathrm {krit} }\rightarrow {\mathit {Ma}}=1}$

With the energy equation, the critical speed of sound can be determined from the data of the total state (= state of rest; index "t"):

${\displaystyle a_{\mathrm {krit} }={\sqrt {\frac {2}{\kappa +1}}}\cdot a_{\mathrm {t} }}$.

With the change in the state variables, the speed of sound also changes.

The continuity equation (law of conservation of mass) of a flow is expressed by:

${\displaystyle {\dot {m}}=\rho \cdot c\cdot A}$.

The equation is differentiated according to x :

${\displaystyle {\frac {A(x)\cdot (\rho \cdot c(x))}{dx}}=0}$.

Using the product rule one obtains:

${\displaystyle {\frac {dA}{A}}=-{\frac {d\rho }{\rho }}-{\frac {dc}{c}}}$.

With the differential form of the energy law

${\displaystyle {\frac {d\rho }{\rho }}=-{\frac {cdc}{a^{2}}}}$.

can be transformed under the condition of an isentropic flow:

${\displaystyle {\frac {dA}{A}}={\frac {cdc}{a^{2}}}-{\frac {dc}{c}}}$.

The Mach number is defined by the ratio of speed to the speed of sound ${\displaystyle {\mathit {Ma}}}$

${\displaystyle {\mathit {Ma}}={\frac {c}{a}}}$.

This gives Hugoniot's equation:

${\displaystyle {\frac {dA}{A}}=({\mathit {Ma}}^{2}-1)\cdot {\frac {dc}{c}}}$.

From the equation can be seen:

• In the case of a subsonic flow with Ma <1, a further acceleration (d c > 0) occurs when the cross-section is reduced (d A <0); this is the case with a nozzle with a convex design.

• The speed of sound ( Ma = 1) can be reached when d A = 0. This case is achieved with the narrowest cross section of a Laval nozzle, which has a convex inlet and, after the narrowest cross section, merges into a diffuser which has a convergent design. Another prerequisite for reaching the speed of sound in the narrowest cross-section is that the critical pressure ratio is exceeded.

• From Hugoniot's equation it can be seen that when the speed of sound is reached and d c > 0, a further increase in speed is possible if d A > 0 and the cross section is designed as a diffuser.

Technically, a supersonic speed is produced in a Laval nozzle . In the narrowing inlet cross-section, the flow is accelerated up to the speed of sound, as long as the critical pressure ratio p0 / pa is reached. A further acceleration of the flow takes place in the diffuser part. At the outlet of the diffuser to the environment, a shock wave occurs that is not isentropic.

Objects at supersonic speeds

The following list enumerates various objects that reach supersonic speed:

• the tip of the whip when the whip cracks (relevant for example for Goaßlschnalzen )
• many explosives produce a supersonic shock wave
• Rifle and cannon balls: since the late 19th century, projectiles with high muzzle velocities have been aerodynamically optimized for supersonic flight ( ogival shape)
• Turbine parts of jet engines can reach supersonic speeds, but efforts are made to avoid this with propellers, turbofans and helicopter rotors.
• Meteoroids usually enter the earth's atmosphere at a speed of 12 to 72 km / s, which corresponds to about 35 to 215 times the speed of sound. Due to the high level of warming, they usually burn up in the higher layers of the atmosphere.
• Return and debris from spacecraft and launch vehicles. They burn up or wear heat shields or elements. The re-entry speed is around Mach 25.

The last two examples already reach hypersonic speed , as did the V2 as the first rocket in 1942 .

The first supersonic aircraft was the Bell X-1 (actually a rocket aircraft ), which first reached supersonic speed in 1947.

In addition to aircraft and rockets, rocket sleds (i.e., rail - guided rocket-propelled sleds) were built for testing purposes, and they first reached supersonic speeds in the 1950s.

For record drives, some cars powered by rockets or jet engines were also designed, which were designed to reach supersonic speeds:

• Spirit of America (to no avail)
• Budweiser Rocket (December 17, 1979 - not officially recognized)
• ThrustSSC (October 15, 1997 - the first recognized supersonic land vehicle ( S uper s onic C ar))

Cars with supersonic speeds have the problem that there is no negative pressure between the underside of the vehicle and the ground when the speed of sound is approached, and even overpressure occurs, so that the cars threaten to float on it.

Web links

Wiktionary: supersonic speed  - explanations of meanings, word origins, synonyms, translations

• The sonic boom
• Breaking the Sound Barrier LiveScience Image Gallery