What are those 2 compartments on the side of the chariot, above the wheel. The ones that cross over each other making an 'x'. I've tried researching but have unfortunately not found much about what purpose they serve.
Steve is correct in his comment. The rear-facing case was a quiver for arrows, and the forward-facing one was a case designed to hold a bow. Very few chariots survive from ancient Egypt and until recently what these cases were made from, and how they were constructed was largely a matter for conjecture. We now know that they would have been made from leather.
The leather trappings and harness for an ancient Egyptian chariot were identified in an archive at the Cairo museum back in 2011. The collection includes the quiver and bow-case. They featured in a 2013 NOVA/PBS documentary Building Pharaoh's Chariot.
Details from the examination of the leather trappings and harness have actually provided key insights into ancient Egyptian chariot building, and will be the focus of a new publication Chariots of Ancient Egypt, expected later this year. (Although, having seen the price tag, I'll be reading it at the library rather than buying a copy for myself!)