Numerical and Analytical Takeoff Field Length Calculations for Jet Aircraft

Purpose - The greater of two distances (Balanced Field Length or Takeoff Distance +15%) results in the Takeoff Field Length (TOFL). The TOFL is a takeoff distance with safety margins according to Certification Standards for Large Aeroplanes by EASA (CS-25) and FAA (FAR Part 25). Simple analytical approximations for the TOFL are checked against more demanding numerical simulations to determine the validity of the simple solutions and to implement adjustments for them as necessary. --- Methodology - The differential equation of the aircraft's acceleration is solved in MATLAB together with varying engine failure speeds. Analytical calculations of the Balanced Field Length by Torenbeek, Kundu, and Loftin are investigated. This includes the evaluation of statistical data. --- Findings - Analytical approximations deviate by 0.1% to 28.2% from the numerical solution. The most accurate analytical approximation is the simple method proposed by Loftin based on statistics. It shows deviations of less than 5.4%. The results confirm that the TOFL for jets with four engines is determined by the Takeoff Distance +15%, while for jets with two engines, the Balanced Field Length is decisive for TOFL. --- Research limitations - Simplifying assumptions had to be made e.g. regarding rotation time and speed, flap geometry, and asymmetric drag. While ground distances were solved numerically from acceleration and deceleration, air distance and rotation distance had to be determined analytically. --- Practical implications - A reliable and tested analytical procedure is useful for quick aircraft performance estimates and to include an inverse TOFL method into aircraft preliminary sizing. --- Originality - This seems to be the first report to provide a systematic check of available analytical approximations for the TOFL in comparison with a numerical solution.

研究目的：两种距离（平衡场长(Balanced Field Length)或起飞距离加15%）中的较大值即为起飞场长(TOFL)。起飞场长是符合欧洲航空安全局(EASA)《大型飞机认证标准第25部(CS-25)》与美国联邦航空管理局(FAA)《联邦航空条例第25部(FAR Part 25)》规定的带有安全裕度的起飞距离。本研究通过高精度数值模拟对起飞场长的简易解析近似方法进行验证，以评估简易解法的有效性，并在必要时对其进行修正。---研究方法：在MATLAB中求解飞机加速度微分方程，并结合可变发动机失效速度开展分析。研究了Torenbeek、Kundu与Loftin提出的平衡场长解析计算方法，其中包含对统计数据的评估。---研究结果：解析近似方法与数值解的偏差范围为0.1%至28.2%。其中精度最高的解析近似方法为Loftin基于统计数据提出的简易方法，其偏差小于5.4%。研究结果证实，四发动机喷气式飞机的起飞场长由起飞距离加15%决定，而双发动机喷气式飞机的起飞场长则以平衡场长为决定性因素。---研究局限：本研究不得不作出若干简化假设，例如关于抬轮时间与速度、襟翼几何构型以及非对称阻力的假设。尽管地面滑跑距离可通过加减速过程进行数值求解，但空中飞行距离与抬轮距离仍需通过解析方法确定。---实际应用价值：一套经过验证的可靠解析流程，可用于快速估算飞机性能，还可将起飞场长反演方法纳入飞机初步尺寸设计环节。---研究创新性：本研究似乎是首份将现有起飞场长解析近似方法与数值解进行系统性对比验证的学术报告。