In this paper, we study the average packet error probability (APEP) and effective throughput (ET) of the control link in unmanned-aerial-vehicle (UAV) communications, where the ground central station (GCS) sends control signals to the UAV that requires ultra-reliable and low-latency communications (URLLC). To ensure the low latency, short packets are adopted for the control signal. As a result, the Shannon capacity theorem cannot be adopted here due to its assumption of infinite channel blocklength. We consider both free space (FS) and 3-Dimensional (3D) channel models by assuming that the locations of the UAV are randomly distributed within a restricted space. We first characterize the statistical characteristics of the signal-to-noise ratio (SNR) for both FS and 3D models. Then, the closed-form analytical expressions of APEP and ET are derived by using Gaussian-Chebyshev quadrature. Also, the lower bounds are derived to obtain more insights. Finally, we obtain the optimal value of packet length with the objective of maximizing the ET by applying one-dimensional search. Our analytical results are verified by the Monte-Carlo simulations. Keywords – UAV, URLLC, packet error probability, effective throughput, short packet transmission.