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02 Aug 27 - Standard Atmosphere

02 Aug 27 - Standard Atmosphere - AOE 2104Intro to...

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Virginia Tech Lecture 2 AOE 2104—Intro to Aerospace Engineering Fall 2009 27 August 2009 AOE 2104 Introduction to Aerospace Engineering Lecture 2 Standard Atmosphere

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Virginia Tech Lecture 2 AOE 2104—Intro to Aerospace Engineering Fall 2009 27 August 2009 Review of the Syllabus - Questions? Force add students – see me after class!
Virginia Tech Lecture 2 AOE 2104—Intro to Aerospace Engineering Fall 2009 27 August 2009 Standard Atmosphere – Why and How? Designing an aircraft requires knowledge of the four basic aerodynamic quantities. What are they? P, ρ , T, and V What else do we need to know? Aircraft operating conditions vary with altitude. We can relate p and V. –p, ρ , and T are related through the Equation of State. Need to obtain a relation for p, ρ , or T as a function of altitude in order to compare experimental (wind tunnel) and actual flying conditions. Standard Atmosphere Model provides? the variations of these 3 properties with altitude.

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Virginia Tech Lecture 2 AOE 2104—Intro to Aerospace Engineering Fall 2009 27 August 2009
Virginia Tech Lecture 2 AOE 2104—Intro to Aerospace Engineering Fall 2009 27 August 2009 Before describing the variations of p, ρ , and T with altitude, one needs to define what altitude is to be used. 3 Types of Altitudes: Geometric (aircraft) h G = altitude measured from sea level. Absolute (usually used for space applications) h a = altitude measured from the center of the Earth. └►h a = h G + r where r is the radius of the Earth. e.g. Newton’s Law of Gravitation Geopotential (“fictitious” altitude) h = fictitious altitude used to compute the Standard Atmosphere Model. Altitudes - Definitions

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Virginia Tech Lecture 2 AOE 2104—Intro to Aerospace Engineering Fall 2009 27 August 2009 Hydrostatic Equation First step to calculate the variations of p, ρ , and T with altitude consists in finding the relation between pressure, density and altitude. Consider an element of fluid at rest with dimensions (1,1,h G ): p Increasing altitude 0 ( ) 0 (1 1) (1 1 ) ( ) (1 1) 0 G Vertical F pS mg p dp S p dh g p dp ρ = ⇒ - + + + = ⇒ - × × + × × × + + × × = G dp = -ρgdh Hydrostatic Equation Note : p, ρ , and g are functions of h G Top and bottom surface area Volume of the fluid element
Virginia Tech Lecture 2 AOE 2104—Intro to Aerospace Engineering Fall 2009 27 August 2009 First, let assume that gravity does not vary with altitude, so that g = g 0 the value of gravity at the surface of the Earth. Replacing in the H.E we get Note that h G has been replaced by h so the equation numerically matches the H.E.

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02 Aug 27 - Standard Atmosphere - AOE 2104Intro to...

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