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The Steak Drop article from the What If? book says:

The steak spends a minute and a half over Mach 2, and the outer surface will likely be singed, but the heat is too quickly replaced by the icy stratospheric blast for it to actually be cooked.

At supersonic and hypersonic speeds, a shockwave forms around the steak which helps protect it from the faster and faster winds. The exact characteristics of this shock front—and thus the mechanical stress on the steak—depend on how an uncooked 8 oz. filet tumbles at hypersonic speeds

How does this happen? I have read the Wikipedia page of Shock wave in supersonic flows, but it doesn't say anything on the protection of the wave from the impact of the medium.

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  • $\begingroup$ I think he might be referring to a bow shock, but I'm not sure that it would "protect" the body behind the shock. $\endgroup$
    – Kyle Kanos
    Nov 24, 2016 at 16:38
  • $\begingroup$ I agree with Kyle, though a bow shock can standoff in front of the moving object (sometimes called a piston), the "shocked" gas behind the shock will be greatly heated. In the case of hypersonic flight, there can even be spalation and ionization due to the extreme conditions so I doubt the shock will protect the steak from heat. Perhaps they are referring to the ram pressure experienced by the steak? The "spread-out" shock wave would act like a larger surface area that could reduce the local ram pressure on the steak, but that's a reach... $\endgroup$ Nov 25, 2016 at 13:57

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I am not really sure what is exactly meant by "protecting" the steak. For instance, here are some schlieren images from some NASA wind tunnel tests. Hypersonic schlieren testing with blunt and sharp nozed bodies.

Notice, for a blunt nosed body you will always observe a bow shock with a certain standoff distance from the body. However, for a sharp nosed body you will mostly always observe attached oblique shocks emanating from the nose of the body. As the Mach number is increased to larger values, the bow shock will "wrap" closer to the surface of the body, but will never actually touch the body. Similarly, for a sharp nosed body, the oblique shocks will approach the body's surface forming a very thin layer called the shock layer. The physical nature of this layer is very complex with sharp entropy and vorticity gradients and the formation of viscous boundary layer effects.

Physical effects characteristic of hypersonic flow

It is true that in the blunt nosed body case, the flow just behind the leading edge of the bow shock is subsonic. In which case, the flow will expand supersonic around the body even though the body is technically moving with a hypersonic Mach number. I suppose maybe this is what was meant by the shock "protects" the steak from faster wind speeds. However, in no way would this physically "protect" the steak. With high enough velocities, the gas behind the shock waves in both cases will be completely dissociated and ionized. Oddly enough, this generally happens within the boundary layer. For instance, here is a typical temperature profile for a hypersonic boundary layer.

Hypersonic boundary layer temperature profile

The heat transfer by thermal conduction into the steak would be governed by Fourier's law,

$$ q = -k\nabla T $$

In this case, we would be focused on the temperature gradient normal to the steak, $\partial T/ \partial y$. In most cases this is a very large gradient as indicated in the image. Moreover, because the maximum temperature usually happens at an intermediate distance between the surface and the edge of the boundary layer, you can easily observe heat transfer in the form of radiation from a radiating plasma just above the surface when the speeds are high enough. Regarding this bit of physics, the steak would be mostly disintegrated and not protected.

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  • $\begingroup$ What are $T_e$ and $T_W$? I think I have missed the important bit when asking the question. The air the author referred to is the icy stratospheric blast that makes the steak frozen before cooked all the way through. Maybe the sound barrier protects it from frozen? $\endgroup$
    – Ooker
    Nov 24, 2016 at 18:16
  • $\begingroup$ $T_e$ is the temperature of the freestream flow just above the boundary layer. $T_w$ is the wall or surface temperature. For this particular problem, the freestream temperature above the body is shock heated and could be calculated assuming either a calorically perfect, thermally perfect, or equilibrium gas flow. $\endgroup$
    – TRF
    Nov 24, 2016 at 19:16
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I am not sure exactly what the phrase "protect [it] from the faster and faster winds" is referring to either, but it may be the fact that the Mach number behind the (normal) shockwave drops to the inverse of the Mach number outside of the bow wave,

$$M_2=\frac{1}{M_1}$$

and the airspeed in the space between the shockwave and the object causing it is correspondingly reduced also. Of course, the temperature of the air in this area has increased as well, so I am not sure what "protection" we are talking about here. Certainly the shear stresses on the surface will be much lower than they would be if there was no shockwave.

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Given that the noses and leading edges of supersonic aircraft melted in early years before more advanced technology prevailed (and is still a possibility when exceeding design speeds) ...I think that given time a reality -impaired supersonic steak would eventually cook if not evenly.

Assuming a bow shock formed... The bow shock would prevent the "icy stratospheric (wind) blast" from ever nearing the steak, Thus no heat would be transferred away from the steak by convection to the normal temperatures of stratospheric atmosphere. As previously stated objects forming a bow shock are trapped inside the bow shock thermal environment and subject to all the temperature created by compressing air at the surface of the bow shock...albeit at a distance. Yes, the exact temperature created at the surface of the bow shock is affected by interaction with the surrounding atmosphere - but mainly only on the leading outside surface. As result the cooling convection effect is not dominate in the area of direct forward compression but only as the bow shock begins bleeding off around the sides and later increases as turbulence begins mixing the bow shock air with normal speed air. Thus a hypersonic steak would nicely wrapped in an oven of sorts with only the trailing edges in relatively cool air...all assuming that reality did not disintegrate the steak.

A bow shock would never form around a steak even if it was frozen. Steaks lack both mechanical strength and aerodynamic stability and streamlining. Such a steak would break apart like early airplanes reaching their maximum subsonic speed as headwind forces exceeded mechanical strength. That assumes that the steak is stable in "flight". More realistically a steak would tumble and spin due to aerodynamic instability then fragment due to centrifugal force exceeding mechanical tension strength long before headwind/bowwave forces became an issue.

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