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本文从飞机的横-航向线性小扰动三自由度运动方程出发,导出了副翼操纵阶跃输入时,飞机三自由度滚转角速度、倾斜角的近似解析公式。同时,作为一种特例,直接从三自由度近似解析公式简化或单自由度的滚转角速度、倾斜角的计算公式。二者相比较,可得出荷兰滚模态、螺旋模态对飞机滚转性能影响的近似解析表达式。且用几架普通气动布局的大型喷气客机数据作为算例,进行了计算。计算是在H-89微型计算机上完成的。计算结果表明,荷兰滚模态Pss,Ф_t的影响较大,且主要取决于(ω_φ/ω_(nd))~2离开1的程度,螺旋模态对Pss,Ф_t(只限滚转60。)影响较小。可是,荷兰滚模态、螺旋模态的影响均是使Pss,Ф_t指标变坏的。此外,这二个模态对滚转模态时间常数T_R的影响必须计入。
In this paper, an approximate analytical formula of the three-degrees-of-freedom roll angular velocity and tilt angle of the aircraft is derived from the plane-to-heading three-DOF equations of motion. In the meantime, as a special case, the formula for calculating the roll angular velocity and tilt angle of the simplified or single-degree-of-freedom formula is directly approximated from three degrees of freedom. By comparison, the approximate analytic expression of the influence of roll mode and helical mode on the rolling performance of the aircraft can be obtained. The calculation is made by using the data of several large-scale jetliners with normal aerodynamic layout. The calculation is done on a H-89 microcomputer. The results show that the influence of roll mode Pss and Ф_t in Netherlands is large and mainly depends on the degree of (ω_φ / ω_ (nd)) ~ 2 away from 1. The spiral modalities Pss and Φ_t (only roll 60.) Less affected. However, the Dutch roll mode, the impact of spiral mode is to Pss, Ф_t index deterioration. In addition, the influence of these two modes on the roll mode time constant T_R must be taken into account.