《空气动力学英文(Chapter_5)》课件.ppt

中英文日报导航站 中英文日报导航站 中英文日报导航站 中英文日报导航站 Where Where The lift distribution which yields minimum induced drag is the elliptical lift distribution 中英文日报导航站 5.3.3 General Lift distribution Effects of aspect ratio and on the induced drag 中英文日报导航站 The induced drag is inversely proportional to AR, but how to verify it with experimental results? Prandtl’s verification ※ total drag of a finite wing 中英文日报导航站 中英文日报导航站 ※ drag coefficients of two wings with different aspect ratio, assuming that the wings are at the same if the shape of the airfoil is the same for these two wings, then the profile drag coefficients will be the same. Moreover, the variation of e between thee wings is only a few percent and can be ignored. 中英文日报导航站 中英文日报导航站 中英文日报导航站 中英文日报导航站 中英文日报导航站 中英文日报导航站 中英文日报导航站 中英文日报导航站 谢谢使用！ 中英文日报导航站 Induced angle of attack at the arbitrary spanwise station For general cases, w is much smaller than , then 中英文日报导航站 Induced angle of attack in terms of the circulation distribution along the lifting line. It is an important result in our process for the derivation of the finite wing theory. We have to review back to remember based on what tools and approximations this result is achieved. 中英文日报导航站 Relation between the effective angle of attack and the lift coefficient Lift slope of arbitrary airfoil shape 中英文日报导航站 中英文日报导航站 Fundamental equation of Prandtl’s lifting line theory It simply states that the geometric angle of attack is equal to the sum of the effective angle plus the induced angle of attack. It is an integro-differential equation. Why it is called as lifting line theory? What are the known and what is the unknown inside this equation for general cases? 中英文日报导航站 After the solution is obtained from the fundamental equation of the lifting line theory, three aerodynamic characteristics can be achieved 1. Lift distribution 2. Total lift 中英文日报导航站 Lift coefficient 3. Induced drag and induced drag coefficient