Pressure, Density, Mass, Crushing Strength, Area Volume Tension, and

Wing Loading

Steve BelovarichEduardo Garcia

Adam MorgensternCraig Etienne

PressurePressure

Pressure is the force per unit area

Or, weight divided by area

P = W / APressure = 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

DensityDensity

Density is the weight per unit volume

Or, weight divided by volume

D = W / VDensity = Weight / Volume

A steel cube has a weight of 500 lbs

The cube is 1 cubic footSo, the density is : = 500 lbs per cubic foot

MassMass

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 StrengthCrushing 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 TensionArea 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 L2 and V α L3 (or L α V1/3)

so…A α V2/3

Area Volume TensionArea 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 LoadingWing 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 objectwhen 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…Wing Loading continued…

Ex: to scale up a plane by a factor of 5:it weighs 53 or 125 times as muchbut only has 52 or 25 times as much wing

areaTherefore, each square foot of wing must support 5 times as much weight.

The End