As part of the Mars Surface Exploration Program, NASA intends to land a series o
ID: 2078049 • Letter: A
Question
As part of the Mars Surface Exploration Program, NASA intends to land a series of 200 kg instrument packages on the surface of Mars to study surface chemistry, meteorology, etc. The instrument packages will be soft-landed on the surface with parachutes. In parachute design it is more convenient to define A to be the total surface area of the parachute, A = pi d^2/4, rather than its cross-sectional area when inflated. With this definition the drag coefficient is experimentally seen to be on the order of 0.55. Earth's atmospheric mass density is about 1.22 kg/m^3. Assume that the Martian atmospheric mass density is about 1% that of the Earth's and determine the diameter of the parachute that will be needed if the maximum acceptable impact velocity is 25 m/s. The acceleration of gravity at the surface of Mars is 3.72 m/s^2.Explanation / Answer
g=3.72 m/s2
v=25 m/s
drag coefficient=0.55
density=0.01*1.22 kg/m3
m=200kg
In this case, drag force must be balanced by weight for smooth landing
W=(1/2)*coefficient*density*Area*Velocity^2
Thus A=(200*9.8*2)/(0.55*0.01*1.22*25^2)=934.7243 m2
Since Parachute inflated area =(1/2)*4*pi*r^2 =934.7243 m2
thus r=sqrt(934.724/2)=21 m radius
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