Terahertz radiation by optical rectification in single-walled highly aligned chiral carbon nanotubes (SWCNTs) irradiated by ultrashort laser pulses is comprehensively studied. We take into account the structural properties of SWCNTs, including the filling factor, alignment, and chirality, as well as the laser pulse parameters including the pulse duration and the wavelength. The second-order nonlinear susceptibility tensor and, consequently, polarization responsible for optical rectification in SWCNTs are derived based on symmetrical features.The effective dielectric constants of SWCNTs are also extracted using the effective medium approximation. Then, the propagation effects in terms of the group velocity dispersion and absorption at both pump and terahertz pulse frequency regions are investigated. By adjusting the laser and the structure effective parameters among those practically feasible, minimum velocity mismatch required for optimum optical rectification and coherent amplification at terahertz frequencies in SWCNTs are introduced. Comparing the electric field waveform and the spectrum of the generated terahertz pulses under various conditions reveals that SWCNTs with higher alignment and lower filling factor at chirality (6,4) irradiated by an ultrashort laser pulse with the wavelength of 1550 nm could provide the conditions for maximum terahertz radiation generation.