Dynamics cheat sheet

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$my Latex and Tex4ht cheat sheet$

8 9 ( ) C mα = a (h − h nwb ) − a t ¯VH 1 − ∂ɛ ∂C ∂α + mp ∂α C mα = a wb (h − h nwb ) − a t V H ( 1 − ∂ɛ ∂α ) + ∂C mp ∂α C m0 = C macwb + C mop + a t ¯VH (ɛ 0 + i t ) [ 1 − at S t a S ¯C m0 = C macwb + ¯C mop + a t V H (ɛ 0 + i t ) ( )] 1 − ∂ɛ ∂α ∂C m ∂α Two versions of one for α wb and one one uses α C m0 is total pitching moment coef. at zero lift (does not depend on C.G. location) but ¯C m0 is total pitching moment coef. at α wb = 0 (not at zero lift). This depends on location of C.G. 10 ¯Cm0p = C m0p + (α − α wb ) ∂Cmp ∂α h n = h nwb + at ¯V ( ) a H 1 − ∂ɛ ∂α − 1 ∂C mp a ∂α 11 = h nwb + a t ( a wb [1+ a t S t a wb S 1− ∂ɛ ∂α )] ¯VH ( 1 − ∂ɛ ∂α ) − 1 a wb [1+ a t S t a wb S ( )] ∂Cmp 1− ∂ɛ ∂α ∂α Used to determine h n 19.3 definitions 1. Remember that for symmetric airfoil, when the chord is parallel to velocity vector, then the angle of attack is zero, and also the left coefficient is zero. But this is only for symmetric airfoil. For the common campbell airfoil shape, when the chord is parallel to the velocity vector, which means the angle of attack is zero, there will still be lift (small lift, but it is there). What this means, is that the chord line has to tilt down more to get zero lift. This extra tilting down makes the angle of attack negative. If we now draw a line from the right edge of the airfoil parallel to the velocity vector, this line is called the zero lift line (ZLL) see diagram below. Just remember, that angle of attack (which is always the angle between the chord and the velocity vector, the book below calls it the geometrical angle of attack) is negative for zero lift. This is when the airfoil is not symmetric. For symmetric airfoil, ZLL and the chord line are the same. This angle is small, −3 0 or so. Depending on shape. See Foundations of Aerodynamics, 5th ed, by Chow and Kuethe, here is the diagram. 98
2. stall from http://en.wikipedia.org/wiki/Stall_(flight) In fluid dynamics, a stall is a reduction in the lift coefficient generated by a foil as angle of attack increases.[1] This occurs when the critical angle of attack of the foil is exceeded. The critical angle of attack is typically about 15 degrees, but it may vary significantly depending on the fluid, foil, and Reynolds number. 3. Aerodynamics in road vehicle wiki page 4. some demos relating to airplane control http://demonstrations.wolfram.com/ControllingAirplaneFlight/ http://demonstrations.wolfram.com/ThePhysicsOfFlight/ 5. http://www.americanflyers.net/aviationlibrary/pilots_handbook/chapter_3.htm 6. Lectures Helicopter Aerodynamics and <strong>Dynamics</strong> by Prof. C. Venkatesan, Department of Aerospace Engineering, IIT Kanpur http://www.youtube.com/watch?v=DKWj2WzYXtQ&list=PLAE677E56C97A7C7D 7. http://avstop.com/ac/apgeneral/terminology.html has easy to understand definitions airplane geometry. ”The MAC is the mean average chord of the wing” 8. http://www.tdmsoftware.com/afd/afd.html airfoil design software 99
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Dynamics cheat sheet Nasser M. Abba
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18.7.2 Bi-Elliptic transfer orbit .
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are the natural frequencies of the
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Similarly, µ 2 is found ⎧ ⎫T
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Or in full form and ⎧ ⎫ ⎡ ⎨
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Hence The first eigen vector is Sim
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The transformation from modal coord
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Where F n = 2 T F 0 = 2 T ∫ T 0
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Let z = Re { Ze iωt} , z ′ = Re
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Now, u = Re { Ue iωt} , u ′ = Re
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Hence at t = 0 the phase of the res
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The following table gives the solut
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5.3 no loading (free) mu ′′ + c
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5.5 Impulse sin function Input is g
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Solution to single degree of freedo
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7 Some common formulas These defini
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8 Derivation of the solutions of th
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8.2.2 under-damped ζ < 1 The gener
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When ϖ ≈ ω but less than ω, le
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Hence the full solution is u p = p
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8.4 Response to impulsive loading 8
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where A = B = F 0 m 2ω √ ξ 2
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where ∆ is very small positive qu
Page 47 and 48: at t = t 1 ˙u (t 1 ) = −ξωe
Page 49 and 50: 8.5 references 1. Vibration analysi
Page 51 and 52: 11 Formulas sin 2 x 1cos2x 2 cos 2
Page 53 and 54: 12 Velocity and acceleration diagra
Page 55 and 56: 12.3 spring pendulum with block mov
Page 57 and 58: 13 Velocity and acceleration of rig
Page 59 and 60: 14.2 3D Not Using vehicle dynamics
Page 61 and 62: 14.2.2 Derivation for τ = Iω in 3
Page 63 and 64: 15 Wheel spinning precession x Mg
Page 65 and 66: 18 Astrodynamics 18.1 Ellipse main
Page 67 and 68: magnitude of ⃗r period T mean sat
Page 69 and 70: 18.3 Flight path angle for ellipse
Page 71 and 72: This diagram below from Orbital mec
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Page 75 and 76: 18.7.3 semi-tangential elliptical t
Page 77 and 78: 18.8.1 Rocket equation with plane c
Page 79 and 80: 18.10 interplanetary transfer orbit
Page 81 and 82: 2. Find speed of second planet V 2
Page 83 and 84: 1 mu = 324859; 2 alt = 1475.776; 3
Page 85 and 86: 18.11.3 Two satellite, separate orb
Page 87 and 88: 1 TOF:=hohmann_rendezvous_2(theta=0
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Page 91 and 92: 18.14 Orbit changing by low contiuo
Page 93 and 94: C r below is the core chord of the
Page 95 and 96: 1 C L = ∂C L ∂α α = C Lα α
Page 97: 1 2 3 C Lwb = ∂C L wb ∂α wb α
Page 101 and 102: http://en.wikipedia.org/wiki/Flight
Page 103 and 104: http://www.grc.nasa.gov/WWW/k-12/UE
Page 105 and 106: http://en.wikipedia.org/wiki/Lift_c
Page 107 and 108: http://adamone.rchomepage.com/cg_ca
Page 109 and 110: From http://www.solar-city.net/2010
Page 111 and 112: Page 184, flight dynamics principle
Page 113 and 114: Image from http://www.americanflyer
Page 115 and 116: From FAA pilot’s handbook I do no
Page 117 and 118: zero-lift angle The angle of attack
Page 119: Image from http://www.aerospaceweb.
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Dynamics cheat sheet

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