Here are my initial thoughts:
The republican plan is simple. Let the nationalist launch their initial attacks and have a mobile reserve ready to exploit any weakness that is exposed when the dust settles.
The defensive plan calls for holding the forces in southern Aragon to not be lured into the mountains, as that would prove to be costly I am sure. Around Madrid I will set up a tight defense with several brigades ready to help against any attack (i.e. local reserves). The northeastern front near Guadalajara is vital for the defense of Madrid, while the Sierra might be hard to hold against a tenacious attacker as it is well surrounded from all directions.
In the south my forces in southern Castilla-La Mancha will do an orderly retreat to the Siruela-Belalcazarline to have a shorter front behind the river. Meanwhile further south I will wait for the first round of nationalist attacks to settle before moving in to capture Granada, Malaga and eventually Cordoba. This will increase supply for all my forces and should allow for a defensible line between Malaga and Cordoba, whilst even threatening Sevilla and Cadiz. I will devote all the republican armored vehicles to this front.
In the north I will defend patiently with a large reserve of brigades to fill any gaps that might arise.
¡No pasaran!
