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Unformatted text preview: Rocket with gravity & Drag Consider a small rocket launched by the Longhorn Rocket Association v e = 200 m/s 5 sec b t = 1 f m kg = 9.81 / o g N kg = .25 r m kg = 7700 m α = .1 p m kg = 3 1.204 / 20 o kg m at C ρ = .1 D C A = t ∆ = .05 Assignment: 1. Write a MATLAB Function, Rocket, that will calculate the velocity and the height for a rocket considering both drag and gravity. Assume you are launching near the earth’s surface. You will be given a ∆ t and a final time. a. Input will be the Rocket parameters: v e , m f , m r , m p , t b, ∆ t, β = m f / t b , C D A and g o . b. Use 3 additional functions to calculate the components of the velocity due to thrust, gravity and drag at each time step. c. The function Rocket will put time, height, velocity and the 3 velocity components due to thrust, gravity and drag into vectors to be returned to the calling program. There will be no printing in this function. d. The MATLAB code which calls Rocket will do the printing and plotting. 2. Create a table of time, height, velocity, velocity components from thrust, gravity & drag for 3 cases: a. Ignoring gravity and drag (g o = 0 & C D A = 0). Call velocity and height v & h. b. Gravity is included and drag is ignored (g o = 9.81 & C D A = 0) vel & height: vg & hg c. Include both gravity and drag (g o = 9.81 & C D A = given ) vel & height: vgd & hgd 3. Plot the three values of velocity, v, vg and vgd, as a function of time on one plot. 4. Plot the three values of height, h, hg and hgd, as a function of time on one plot. Discussion: 1. Discuss the results without gravity and drag ( v & h), including only gravity (vg & hg) and with both gravity and drag (vgd & hgd). How do they compare? WHY? 2 . Gravity does depend on height. Does your rocket go high enough so that this is a factor that should be considered? Why/Why Not?? Rocket Equations A. Flight in Free Space: ( 29 ( ) (0) ( ) ( ) ln( ( )) | 1 ( ) r p f e e t r p f r p f m m m dM t M t dv t v v t v M t M t M t m m m t m m m t β β β + + = - = = = + + +- + +- ( ) ln(1 ) e r p f t v t v m m m t β β = + + +- ln(1 ) f R e r p m v v m m = + + B. Flight considering Gravity: Near the earth ( ) ln(1 ) e r p f t v t v gt m m m t β β = +- + +-...
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- Fall '07