17. [12 pt] Taking MEEN 3700 has made you slightly crazy and you have therefore,

Question

17. [12 pt] Taking MEEN 3700 has made you slightly crazy and you have therefore, decided to enter the Redbull Flugtag competition this summer in Louisville. The goal is to develop a human powered flying machine capable of the longest flight possible from a tower into a river (see figure). Besides planning to use a prodigious amount of duct tape, you have also decided to put your fluid dynamics knowledge to good use and develop a basic dynami model. The machine's mass M is set by the imum wing span D. Using your chosen materials (duct tape and cardboard) you estimate a maximum wing chord length of C and thickness (. Based on the foot speed of your most athletic friend, you estimate an initial horizontal velocity U competition rules as is the max- V. Part A) Derive an equation for the time t it will take your flying machine to fall into the river with style assuming it is at terminal vertical velocity V when it is released from the platform at height H. Use the density of air ? the assumption that the appropriate planform area equals the wing area

Explanation / Answer

Using lift coefficient and planform area lift on the wing is

Fl=Cl*0.5PV2*C*D P=Density of air (for lift frontal area across flow will be considerd)

V=velocity of plane vertical

Net force=M*a=M*g-Fl=M*dv/dt=M*V*dV/dh

solving the eqn

final velocity at bottom will be vertical

Vb=(M*g/Y)0.5*(1-e-2YH/M) Y=0.5*Cl*P*C*D

solving the time differential equation

eYt/M=((Mg/Y)0.5+Vb)/((Mg/Y)*0.5-Vb)

this equation gives time.

For part b)))

initial velocity=U

Fd=Cd*0.5*P*V2*D*L (frontal area for drag is D*L)

in x direction

lets call A=Cd*0.5*P*D*L

than in x direction

M*ax=Fd=AV2=-MVdv/dx=-Mdv/dt v=instantaneous speed in x direction

solving in time

Vf=MU/(AtU+M) Vf=final speed in x direction

solving for L in x differential equation (limits for velovity in integration are Vf and U)

L=(M/A)ln(U/Vf)

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