How big of a parachute would it take to “float” a Boeing 747 down safely to earth?
Considering that the aircraft weighs 870,000 lbs and the cruising altitude is 32,900 feet?
Just a question I was wondering about.
Is there some kind of formula for weight – parachute size?
the equation for drag is: fd = -0.5*C*p*A*v*v
where fd is the force of drag, C is the drag coefficient, p is the density if air, v is the velocity.
equating it to the force of gravity on the 747 fg = m*g, we can solve for the area of the parachute.
Assuming that an acceptable and survivable crash speed is 10 meters per second (a little over 20mph) and that the drag coefficient for a parachute is about 1, and the the density of air is 1.2 kg/m^2. Converting the 870,000lb aircraft to 400,000 kg and using g = 10 m/s^2 we get the following equation:
400,000*10 = 0.5*1*1.2*A*10*10
solving for A gives 666,000 m^2. Which equates to a circle with a radius of 145 meters (about 475 feet)
Oops. Karpenisi pointed out that I have an error. I believe my answer of 666,000 m^2 is probably OK, but I converted it incorrectly (I hit the wrong button on the calculator). 666,000 m^2 is a circle with a radius 1500ft. which equates to 7 million square feet.
KLM Boeing 747-400 cruising over the Himalaya
