MEE30003 Machine Design Tut 1: Modelling exercises Task 1 Consider the fictional character Iron Man. Assume the repulser technology that allows him to fly works by pushing air away from his feet. Determine the repulser diameter air velocity combinations that will allow him to hover. 1
MEE30003 Machine Design Listing all the knowns and unknowns, this will help you to think of equations to use. Unknown: m ; Vi, air ; Vf, air ; D Knowns: g Find: Determine repulse diameter (D) / air velocity (v) combinations to allow Iron Man to hover (stay stationary in the mid- air). Schematic Diagram / FBD: Fgravity, body T Equations to consider: N2L: dp d mv 1 F = ma = dt wherep = linear momentum = mv Mass flow rate equation: m = pvA where m = mass flow rate; p = density of flow; A = cross-sectional area Note: FYI, continuity equation: dt Fair, repulser P2, V2, A2 D?, V1, A1 flow direction P101A1 = P202A2 = constant Assumptions: g = 9.81 m/s; n= no. of repulsers; Vi = 0 (initial velocity when Iron Man is on the ground); Vf (velocity when Iron Man stays mid-air). 2
MEE30003 Machine Design Solutions: By N3L, the air also exertsequal and opposite force (Fair, repulser) on one of the repulsers (n1). & by N2L, Fair, repulser n1 4| mv = d(mv dt At Assume that the velocity increases linearly with time. Since vi = 0 (Mr. Iron Man is at rest on the ground), Fair, repulser n1 At Amv = mfuf-miVi tf - ti _mgof = At At mf Vf = mvf (1) Making use of the mass flow rate equation, m = pvA = pvo' TED2 4 Subst. (2) into (1), Fair, repulser n1 = mv =(pro ) vo = (pVo 2 TD2) Hovering in the mid-air -> in =m (equilibrium): ( ): ¿ Fy = 0 n X Fair, repulser n1 - Fgravity, body = 0 TID2 n (pv, 2 TD2) = mirong 3 Assuming Robert Downey weighs 85 kg, Iron Man suit = 65 kg, miron = 150 kg; g= 9.81 m/s2; p = 1.2 kg/m3; n = 2 (since the question mentions only Mr. Iron Man's feet) From (3), n pv 2 TD2 -) 4 = mirong (2) 2(1.2) v02 Th) = (150) (9.81) VoDo = 27.940 (ANS 3