My first post here. My apologies if I'm breaking any rules, but I thought I might be able to help.

At the time of the Norman conquest, Knights (not necessarily nobles, but rather defined as someone who fights from horseback) used kite shields (long and pointed at the bottom, rounded at the top). This type was strapped to the arm and body and gave great protection to the legs and shoulder. As it wasn't common at this time to have armoured legs, the protection was crucial. Horses were small, but large enough to bring your legs at an ideal height to be easily injured.

There then appears a transition shield in the early 12th century , which in illustrations seems to be flat topped and shorter overall. Less protection, but much more maneuverable. Having used both to fight with, I can vouch that the flat topped is much, much easier to use.

In the late 12th century, the shape evolved again, giving the shape you have posted. This is known as a 'heater' shape sheild. For this name, we have the victorians to thank. They named it after heater irons(used for flattening clothes) , as they shared the same shape.

The sheild is typically much shorter than the flat topped kite, and lighter too. Knights at this time were now wearing leg armour, so the length wasn't needed. Barrel helms are being used, so it didn't need to be as high. I fight with one weekly, and an opponent skilled in its use is incredibly difficult to beat.

Sorry, probably went off topic a bit there. I hope I helped though.