An autonomous airborne network (AN) consists of multiple unmanned aerial vehicles (UAVs), which can self-configure to provide seamless, low-cost and secure connectivity. AN is preferred for applications in civilian and military sectors because it can improve the network reliability and fault tolerance, reduce mission completion time through collaboration, and adapt to dynamic mission requirements. However, facilitating seamless communication in such ANs is a challenging task due to their fast node mobility, which results in frequent link disruptions. Many existing AN-specific mobility-aware schemes restrictively assume that UAVs fly in straight lines, to reduce the high uncertainty in the mobility pattern and simplify the calculation of link lifetime (LLT). Here, LLT represents the duration after which the link between a node pair terminates. However, the application of such schemes is severely limited, which makes them unsuitable for practical autonomous ANs. In this report, a mathematical framework is described to accurately compute the \textit{LLT} value for a UAV node pair, where each node flies independently in a randomly selected smooth trajectory. In addition, the impact of random trajectory changes on LLT accuracy is also discussed.