Airfield Models Formulas use with Flying Model Aircraft

Trigonometry for Model Airplane Builders

May 05, 2015



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Airfield Models (http://www.airfieldmodels.com/)Trigonometry for Model Aircraft Builders

Trigonometry is the tool of choice when working with angles.  A baffling problem can often be simplified by illustrating it with a triangle.

Use Trigonometry to convert an angle to a measurement.

Building Surface

For example, wing dihedral is easily represented by a triangle.  The building surface is one side of the triangle, the wing panel is the second side and the amount the panel is propped up at the tip is the third and final side of the triangle.

 
 

About Triangles

A triangle has six parts three angles and three sides.  The three angles always add up to 180.  If you know two of the angles, add them together and subtract that total from 180 to find the third angle.

If you are a builder you will sometimes find that you are provided with a useless piece of information, such as the dihedral angle.  All that you really need to know is how far to prop up the wing tip when you glue the wing halves together.

This is where trigonometry comes to the rescue.  If you design your own models you will find that you use trigonometry even more frequently.  Again, it is not difficult.  It is just a matter of understanding how to use it.  You don't have to know why it works, but if you care to you can read the proofs in a high school geometry book.

By the time I was in high school I had already designed many models and I would say the two most useful classes I took in regards to model-building are Geometry and Algebra.

You probably remember sitting in class asking yourself, "What will I ever use this for???"

I was fortunate enough to already have the answer to that question by the time I got there so I found the classes interesting and very useful.  I have used the knowledge I gained ever since.

Geometry is extremely useful at the drafting table.  Almost everything you learn is practical when it comes to drawing.  If you want to design your own planes, then you'll be doing a lot of trial and error work in your shop if you don't know how to do the math.

Algebra is excellent for finding the missing answer.  For example, if you scale a plane with a wingspan of 60" and a chord of 9-3/8" to have a span of 72" then Algebra is the most efficient way to find the new chord.

 
 

Terminology

  • Theta () represents the unknown angle you are solving for.  If you know the angle and are solving for sides of the triangle, then write the angle on your diagram rather than the symbol.

  • A Right Triangle is a triangle having one 90 angle.  This is the best triangle to use to represent various problems we encounter.  The other two angles can be anything that add up to 90, such as 45 and 45 or 60 and 30.  Note that no triangle can have two 90 angles which would be a straight line and not a triangle at all.

  • Hypotenuse is the name of the longest side of a right triangle.

 
 

The Three Primary Trigonometric Functions

Tip: Windows 95 and later come with a Calculator applet that can do everything we need.  The calculator is normally found in the Programs -> Accessories folder of the Start Menu.

  • After starting the Calculator applet, select Scientific from the View menu to make the trigonometry functions available.

Everything that follows assumes that we will be working with Right Triangles.

There are three primary trig functions, Sine, Cosine and Tangent (SIN, COS and TAN on most calculators).  These terms were created to scare school children back in the day when educators thought that fear was an effective teaching tool.  If you are still reading, then you're about to find out how simple these functions are.

The above three functions each do essentially the same thing divide the length of one side of a triangle by the length of another side.  That's all there is to it.

A triangles sides are referenced from the corner.  The hypotenuse is always the longest side.

Your average right triangle.

Sine = the length of the opposite side of the triangle divided by the length of the hypotenuse.

Sine = Opposite Hypotenuse

Tangent = the length of the opposite side of the triangle divided by the length of the adjacent side.

Tangent = Opposite Adjacent

Cosine = the length of the adjacent side of the triangle divided by the length of the hypotenuse.

Cosine = Adjacent Hypotenuse

Confused?  All you need is a calculator that has trigonometry functions and it is one key press.  Enter the angle, press the appropriate function and out pops the number.

How to Remember
Trigonometric Functions

Thanks to Graham P. for providing the following method to help remember the three primary trigonometric functions:

Some Sine =
Old Opposite
Horse Hypotenuse
Caught Cosine =
Another Adjacent
Horse Hypotenuse
Trotting Tangent =
On Opposite
Asphalt Adjacent

For example, if you want to know the Sine of 5 then enter 5 into the calculator and press the SIN key.  Your calculator should display 0.0871557 give or take some decimal places.  Basic algebra solves the rest (one equation, one unknown).

The above works only when you know the angle.  If you know the lengths of sides of the triangle but not the angle itself then you can use the Arc functions to find it.

Arc functions turn the number from the trigonometric function (Sine, Cosine or Tangent) back into the angle.  These functions are Arcsin, Arctan and Arccos (noted as SIN-1, TAN-1 or COS-1 on most calculators).

For example, lets say you are given the measurement to prop up the wing tips for the correct dihedral.

You know the wing span and the amount the tips are propped up which are two sides of the triangle.  Divide the height the wing tip is propped up by half the wing span, and that is the Sine of the dihedral angle.  Now put that number in your calculator, press Arcsin (SIN-1) and the calculator will display the angle.

 
 

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Copyright 2003 Paul K. Johnson