Since hemi-head has an excellent surface-to-volume ratio, minimal heat loss to the cylinder head, and room for two large valves. Besides, its spark plug locates at or near the center of the chamber to promote a strong flame front. Theologically, these allow squeezing more power from the same chamber volume comparing to regular design.
Its major drawback is that it can not apply more than two valves. However, most radial design can only have two valves too. So, it looks reasonable to apply hemi-head on radial engine design.
If an engine like R-1820 were updated with hemi-head, is it possible to squeeze 100 hp more while using 87 octane gas?