Math and Pilots

  As most of you know, I teach in the Bush of Alaska.  That means, out where I am, you cannot drive on a road anywhere.  The only way to get to and from most other places is via airplane.  Small 6 to 9 seats per plane which haul freight, mail, and people.

Is amazing how much math a pilot actually uses even with the technology we have today.  On the way back to the village, the person in front of me showed this huge book full of charts, graphs, and information on how long a landing strip is needed based on speed and temperatures.  Head winds can cause a plane to use more fuel because it is is being slowed down or a tail wind can make the trip quicker using less fuel.

Most pilots use headings which are in degrees with a speed or a use of vectors, even if you don't think of it as a vector.  You have to control speed, angle of approach or take-off, air speed, wind speed, ground speed, etc.  So many things to think about.

So what are some of the math used by pilots when operating an airplane?  There is true airspeed, minimum landing distance, etc

 You can calculate your  true airspeed by any of the following:
1. taking half your altitude, adding it to your indicated airspeed
2. divide your airspeed by 1000 and multiply the result by 5.  Add this to your indicated airspeed.  
3. increase indicated airspeed by 2% per thousand feet of altitude.

The minimum runway length is the length of the actual landing distance/ 60 percent which results in a longer length.  Calculating the minimum runway length required for a wet landing strip is the same but you have to multiply the actual landing distance by 115% before dividing by 60%. 

If you want more detailed information on runway lengths check out this pdf as it has some very technical information, complete with the mathematics.

Temperature affects how much lift is needed to get a plane off the ground. It turns out the higher the temperature, the air density decreases so a plane needs more runway, a faster approach with a poor climb rate. 

With just a bit of looking, one can find all sorts of information on these topics and more.  It is also possible to find the same information in graphic form so students can learn to read graphs for a real world situation.

I just looked at three factors in detail and you can see the math involved in it.  This is cool.  I will look at more factors in future columns. 

As always, let me know what you think.