09 Sept 28 - Dimensional Analysis, Lift Drag and Moments

09 Sept 28 - Dimensional Analysis, Lift Drag and Moments -...

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Click to edit Master subtitle style AOE 2104--Aerospace and Ocean Engineering Fall 2009 Virginia Tech 29 September 2009 Lecture 5 AOE 2104 Introduction to Aerospace Engineering Lecture 5 Dimensional Analysis Lift, Drag and Moments
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Click to edit Master subtitle style Virginia Tech Please make sure that your essay is passed to the front of the class. This essay will be out of 10 points (each problem worth 2 points) and I should have them back to you by next class AOE 2104--Aerospace and Ocean Engineering Fall 2009 29 September 2009 Lecture 5
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Click to edit Master subtitle style Virginia Tech Basic Aerodynamics Any questions ? What’s a stream tube? What are the 2 types of aerodynamic forces and what are their respective sources? What is Euler’s Equation? Assumptions? What’s a streamline? What are the physical principle and the assumptions used to derive the Continuity Equation? What is the Continuity Equation? What is Bernoulli’s Equation? How is it derived? Assumptions? AOE 2104--Aerospace and Ocean Engineering Fall 2009 29 September 2009 Lecture 5
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Click to edit Master subtitle style Virginia Tech Dimensional Analysis We have talked about airspeed and altitude. We know both of these combine to create lift and drag, but how? We know the properties of air (p, ρ ,T) vary with altitude. We also know that we only need 2 of these properties since we have the Equation of State. We can use Bernoulli to find the velocity at any point along a streamline. We know that the compressibility effects can’t be neglected as you approach the speed of sound. What other properties of the airplane or its environment might be related to the creation of lift and drag? Size of the airplane? Its Height, Width, Frontal Area, Volume? What about the viscosity of air that could cause drag? AOE 2104--Aerospace and Ocean Engineering Fall 2009 29 September 2009 Lecture 5
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Click to edit Master subtitle style Virginia Tech Dimensional Analysis So let the forces on the airplane be a function of a bunch of variables, let say F = F( ρ ,p,L,g,V,a, μ ) where μ the viscosity of air and L is a given dimension. But at this point we don’t know if we need to look at the wing span (L), or the wing area (L2) or even the volume of the aircraft (L3). And the same is true for all the other parameters. To find out, we go through a process called Dimensional Analysis. AOE 2104--Aerospace and Ocean Engineering Fall 2009 29 September 2009 Lecture 5
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Click to edit Master subtitle style Virginia Tech Dimensional Analysis Let be completely general and say that F = F( ρΑ , VB, LC, μ D, gE, pG, aH) Now to obtain an idea of how these parameters combine to produce the forces acting on the airplane, we need to look at the units , in other words find A, B, C, D, E, G, and H . From Newton’s 2nd Law we know that:
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09 Sept 28 - Dimensional Analysis, Lift Drag and Moments -...

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