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Why does a shockwave move further towards the trailing edge with increasing camber?

Also, is the shockwave the thing above the aerofoil or behind it?

enter image description here

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    $\begingroup$ I think there's no better explanation out there than this one. Let us know if it helps in answering your question. The shock waves is where the red zone ends toward the trailing edge. The blue zones are where speed is low, possibly detached boundary layer. $\endgroup$
    – sophit
    Mar 28, 2023 at 20:38
  • $\begingroup$ Anyway it would be nice to know the source of those two pictures: is the different airfoil the only difference among the two? Or also speed or AoA is different? Without this information is not possible to correctly answer this question. $\endgroup$
    – sophit
    Mar 30, 2023 at 8:03

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The increased curvature of the higher camber at the end of the airfoil will keep the speed on the upper side high. As a consequence, there is little deceleration which would force a shock.

Remember that a shock in transsonic flow is the forceful ending of a supersonic pocket of air. It will be delayed until the rising pressure of the decelerating surrounding and still subsonic air makes it inevitable. Within the shock the flow accelerates in order to fill the space vacated by the thinning airfoil contour (see here for a more complete explanation) and outside of it it decelerates. That cannot last forever, but adding camber will stabilize the supersonic pocket by adding a suction area over the highly curved contour which keeps the air from decelerating as early as it does for the uncambered version.

The same, btw, happens with a downward deflected flap, because the kink in the contour at the hinge point also creates a local suction peak.

is the shockwave the thing above the aerofoil or behind it?

The shock lies in the thin line separating the dark red and green areas on the upper side of the airfoil. Its strength is proportional to the inclination of that line, i.e. it is strongest near the surface. It is, however, spread out into a triangle from the interaction between the boundary layer and the shock which makes it look like the greek letter $\lambda$, hence the name Lambda shock. This is typical for transsonic flow.

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  • $\begingroup$ I don’t think Peter is correct here- For the flow velocity to still have increase there would have to be a favourable pressure gradient but, after point of max thickness there isn’t. Therefore even with the curvature, it wouldn’t help $\endgroup$
    – RobertA
    Mar 29, 2023 at 21:19
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    $\begingroup$ After point of max thickness flow is already supersonic (dark red colour) and therefore speed does increase. If it were subsonic then you'd be right. $\endgroup$
    – sophit
    Mar 29, 2023 at 21:26
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Sorry if one of the new writers is acting up a bit, but the question does bring some interesting aspects of airfoil design into play.

Firstly, the use of a slightly lowered trailing edge can be used to improve airflow over the upper wing by creating lower pressure behind the wing. This will increase the lift coefficient with slightly more drag$^2$. Nothing new there. 172 operators know it as "Flaps 10".

Why it is so important to understand this in the trans sonic realm has much more to do with controlling pitch tendencies, as the center of pressure changes, due to Mach effects.

Supercritical wings are designed to minimize, not increase, wing camber due to a phenomena known as "tuck", which can lead to an unrecoverable dive. Tops of these wings are "flattened" to minimize shockwave formation.

The lift generation comes more from the bottom front, with undercamber in the back to balance the center of pressure. These wings literally "surf" along on bottom pressure, not unlike their sea side counterparts$^1$.

So, from a practical point of view, that is why undercamber is seen in supercritical wings.

$^1$this is why slats and flaps are so valuable when big airliners slow down to lower Mach speeds. Supercritical wings more closely resemble an inverted classic airfoil. Not surprisingly, these also make for a fairly good hypersonic lifting body design.

$^2$ this is why flaps can be retracted for better climbing performance - climbing is done with excess thrust. (thrust available - drag)

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  • $\begingroup$ What you call undercamber is called rear loading in the literature. Its reason is fairly simple: If you need to limit overspeeds, you can only add lift when the overspeeds from thickness are low, i.e. where the airfoil is thin. $\endgroup$ Mar 30, 2023 at 15:30

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