Pressure, Density, Mass, Crushing Strength, Area Volume Tension, and Wing Loading Steve Belovarich Eduardo Garcia Adam Morgenstern Craig Etienne

Pressure  Pressure is the force per unit area  Or, weight divided by area  P = W / A  Pressure = Weight / Area  A cubic foot of steel weights about 500 lbs  The bottom face of this cube has an area of 1 square foot  So, the pressure exerted on this bottom face is : = 500 lbs/square foot

Density  Density is the weight per unit volume  Or, weight divided by volume  D = W / V  Density = Weight / Volume  A steel cube has a weight of 500 lbs  The cube is 1 cubic foot  So, the density is : = 500 lbs per cubic foot

Mass  Mass is the aspect of matter that is affected by forces, according to physical laws.  We perceive the mass of an object when we try to move it  When we try to lift an object, we perceive its mass as weight, due to the gravitational force that the earth exerts on it.  Your mass is how much you weigh  The mass of the steel cube is 500 lbs.  The mass of a 10 lb weight is 10 lbs!!

Crushing Strength  The ability to withstand pressure exerted on the object by gravity and the object’s mass.  Example: Could there be a King Kong?  NO!  A King Kong would weigh 8000 times as much at it’s bones could support  It’s own weight would crush its bones into splinters!!!

Area Volume Tension  Area-Volume Tension is a result of the fact that when an object is scaled up, the volume of this object increases faster than the surface area and faster than areas of cross sections.  The reason for this is that as an object is scaled up, it’s volume goes up with the cube of the linear scaling factor, whereas the surface area of the object only goes up with the square of the linear scaling factor.  A α L 2 and V α L 3 (or L α V 1/3 ) so…A α V 2/3

Area Volume Tension  A cat can jump out a 2 story window and be unharmed, whereas a human would probably break a few bones. If we think of a human of a scaled up version of a cat, this makes sense. The kinetic energy gained by a falling object is proportional to its weight, and therefore is proportional to it’s volume. On impact, most of this energy is absorbed over the surface area of the object. Since volume scales faster than area, the energy gained scales faster than the surface area to absorb the energy. Therefore, the human has more potential for injury.

Wing Loading  The weight being supported divided by the area of the wings  Usually measured in pounds / square feet  Proportional to the power necessary for sustained flight  Proportional to the length of the flying object when scaling up or down, weight changes with the cube of the length of the object. Wing area changes with the square of the length.

Wing Loading continued…  Ex: to scale up a plane by a factor of 5: it weighs 5 3 or 125 times as much but only has 5 2 or 25 times as much wing area Therefore, each square foot of wing must support 5 times as much weight.

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