All About Alitutde


Altitude is something that we are trained to care about from our very first beginnings as students.  Why? Simply put, if we don’t care about altitude we will most likely end up dead.

Galileo leaning tower experiment

“Galileo’s Experiment at the Leaning Tower of Pisa” from the Wolfram Demonstrations Project

So, altitude is important.  How does it go by so quickly?

We’ve all heard that 120 mph (or 53 m/s) is terminal velocity for a human being.  And we tend to accept that fact and not think about it too much.

Until now…

Let’s start at the beginning.  If we drop an object from a sufficiently high enough platform, we notice that the object will accelerate (due to gravity) until it reaches a terminal velocity.  Newton’s second law tells us that all objects will fall with the same rate of acceleration regardless of their mass.  Galileo’s Leaning Tower of Pisa experiment showed that two objects dropped from the top will hit the ground at around the same time…not at radically different times like people (at the time) believed.  You can play around with mass on this site if you wish.

Terminal velocity is achieved when the frictional forces of air are equal to the force of gravity.  The frictional force of the air is going to depend on a few variables: density of the air, the shape that is falling through the air, etc.

Let’s talk about air density:

I think most people have no problem understanding that higher air density means higher friction….and lower density results in less friction. What affects air density?  This deserves its own post, but we will summarize and say that increased altitude, increased temperature, and increased humidity all result in a decrease in air density.  For every 520 feet of increased density altitude, terminal velocity will increase by about 1%.

What about the shape falling through the air:

Different shapes will have different drag coefficients.  That’s why if you are in a normal belly-to-earth body position your terminal velocity will be one speed while if you ball up your terminal velocity will increase. By changing your drag coefficient while not changing your mass, you can increase your terminal velocity….an inadvertently end our skydive quicker.

cross sectional area

from NASA https://www.grc.nasa.gov/www/k-12/rocket/shaped.html

What if we have about the same body shape, but there is a difference in mass:

Jump long enough and you will jump with all different body shapes and masses.  Let’s say that we have two skydivers that are the same height, have the same torso length, and their arms and leg length are identical. These two jumpers will essentially have the same cross-sectional area.  Now, we will make one weigh 150 pounds while the other will weigh 190 pounds.  Which falls faster?  The one with greater mass.

Intuitively we all seem to understand the points about how our cross-sectional area/drag coefficient  and mass relate to terminal velocity. We have experienced the thrill of increasing our fall rate while performing acrobatic maneuvers (front loops, diving, etc). and have probably overheard people muttering about which jumpsuit they should wear so that they will have a similar fall rate to whomever they are jumping with.  If you want to play around with this there is a basic interactive on the Physics Classroom website.

calculating terminal velocity

from http://www.wikihow.com/Calculate-Terminal-Velocity

Although we say that terminal velocity for the human form is 120 mph, there is actually a range and the 120 figure is its average.

So, how long does it take to get to terminal velocity?

Well, physics refuses to answer that question for us.  The physicist will tell you that you can only approach terminal velocity (due to the mathematics involved), but we can look to see how long it would take to reach 99% of terminal which is good enough for us.  The figure below shows us how much time it takes to reach terminal velocity (time is on the left y-axis and elapsed distance is on the right y-axis with the x-axis showing speed in mph), but this is assuming that we are standing still when we jump…great for all of you base jumpers.

When leaving from a fixed object it takes roughly 1500 feet to reach terminal velocity, whereas when leaving from an airplane USPA (United States Parachute Association) tells us that it takes approximately 1000 feet.

acceleration from time 0

from Green Harbor Publications: http://www.greenharbor.com/fffolder/speedtime.pdf

Hope you enjoyed thinking a little about terminal velocity and how we get there.

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