Lecture+2-Standard+Atmosphere

# Lecture+2-Standard+Atmosphere - AOE 2104Intro to Aerospace...

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Click to edit Master subtitle style Virginia Tech Lecture 2 AOE 2104 Introduction to Aerospace Engineering Lecture 2 Standard Atmosphere AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010

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Click to edit Master subtitle style Virginia Tech Lecture 2 Review of the Syllabus- Questions? AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010
Click to edit Master subtitle style Virginia Tech Lecture 2 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. AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010

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Click to edit Master subtitle style Virginia Tech Lecture 2 AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010
Click to edit Master subtitle style Virginia Tech Lecture 2 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) hG = altitude measured from sea level. Absolute (usually used for space applications) ha = altitude measured from the center of the Earth. └►ha = hG + 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 AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010

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Click to edit Master subtitle style Virginia Tech Lecture 2 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,hG): 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 hG Top and bottom surface area Volume of the fluid element AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010
Click to edit Master subtitle style Virginia Tech Lecture 2 First, let assume that gravity does not vary with altitude, so that g = g0 the value of gravity at the surface of the Earth. Replacing in the H.E we get Note that hG has been replaced by h so the equation numerically matches the H.E.

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Lecture+2-Standard+Atmosphere - AOE 2104Intro to Aerospace...

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