I've written a few questions about this topic, but this part I never asked.
How do supersonic or transonic speeds affect lift distribution over the whole wing? How does the root's changing pressure distribution compare to that at the tip?
In other words, why do supersonic or transonic speeds affect the wing differently over span?
(This might seem like a duplicate of my other question, but it's asking something different)
In pure subsonic flow the pressure distribution is the combination of the flow around a body, where air has to speed up locally to make way for that body, and the flow around an inclined flat plate. Things will become more complicated if the rear end of the body is blunt and causes the flow to separate locally.
If you raise the Mach number, density changes will become greater and will require larger speed changes to let air flow around the body. Please remember the tube explanation from this answer to explain what happens in detail.
Things become really different once the local flow speed becomes supersonic. When before a contraction in the body would cause the flow to slow down, it will now accelerate further. This will lead to a local drop in pressure when before, at subsonic speed, pressure would increase. Eventually, this supersonic pocket will collapse in a shock, so speed drops to subsonic while pressure rises immediately. Below I copied an example of typical speed distributions from US patent 3,952,971 by Richard Whitcomb.
Speed and pressure distributions are very similar, only that pressure changes with the square of speed.
This extension of the low pressure area on the wing will shift the center of pressure backwards. If you increase flight speed further, the supersonic area will increase until at Mach 1 it will extend over the whole length of the airfoil.
On a straight wing this will happen the same way over wingspan. Only on swept wings will sweep effects make root and tip pressure distribution look different. But what happens can all be explained by the same basic principles:
