Cooperative Adaptive Cruise Control (CACC) is a technology that allows groups of vehicles to form in automated, tightly-coupled platoons. CACC schemes exploit Vehicle-to-Vehicle (V2V) wireless communications to exchange information between vehicles. However, the use of communication networks brings security concerns as it exposes network access points that the adversary can exploit to disrupt the vehicles' operation and even cause crashes. In this manuscript, we present a sensitivity analysis of CACC schemes against a class of resource-limited attacks. We present a modelling framework that allows us to systematically compute outer ellipsoidal approximations of reachable sets induced by attacks. We use the size of these sets as a security metric to quantify the potential damage of attacks affecting different signals in a CACC-controlled vehicle and study how two key system parameters change this metric. We carry out a sensitivity analysis for two different controller implementations (as given the available sensors there is an infinite number of realizations of the same controller) and show how different controller realizations can significantly affect the impact of attacks. We present extensive simulation experiments to illustrate the results.