Put into HTML Format and edited in minor ways June 17, 2007
Ptuh! There, I said it. When I open up a book on a subject like this I feel like a person who just awakened in the middle of a minefield, and though the words are somewhat familiar they all have slightly twisted meanings. Assumptions I am not aware of lie in wait, ready to explode confusion through my poor brain. Luckily I have an uncle who is an engineer and is patient with me, spending hours translating my poorly aimed questions into knowledge. You may think I lie, seeing the computer program attached to this article. Well, I use my Radio Shack Color Computer because I was never successful in mastering the slide rule, even though I bought a number of them. I always forget the steps of any complicated problem, and the computer does not. Once I figure out how to do something I stuff it into the computer real fast and makes lots of notes (REM statements) so that next time I look at the program I can figure out what I did. I solve complicated problems by chaining together little problems I have previously solved.
This program is the result of a desire I had to optimize the design of model airplane wing spars. It is limited to the box type of spar because that is the design I prefer to use, although it should be accurate for I-beam spars, and for solid spars if you input a value for the spar cap equal to half the total spar height.
The first assumption made was about the strength of wood. Wood varies considerably in strength depending on species, moisture content, grain defects, and density. For model purposes kiln dried defect free wood is all you would ever consider using. Moisture content decreases strength. Grain should not cut across the spar at less than a slope of one inch in fifteen and the finer you get the grain, the better. Strength of all wood varies directly with density because the increased weight is due to thicker cell wall material in the wood sample.
The force applied to a section of wood is called stress and is measured in pounds per square inch. By doing a little research in wood construction texts I found 9000 PSI to be the Modulus of Rupture, or point at which spruce or Douglas Fir will fracture. The value for balsa is lower as is indicated in the program notes. Change the 9000 in statement 450 to a value between 2500 and 4000 if you are using balsa spars. 9000 is a maximum value for spruce but my experience shows that for good quality spruce it works for a spars subjected to bending loads only, which is the way spars are loaded in flight when a wing is designed with the required torsional stiffness. I have tested spruce to failure, but not balsa. I leave that up to you.
The loads on the wing spar are equal to the lift the wing is producing. In level flight this is the same as the weight of the airplane, but in turns, pull-ups, or any maneuver other than straight flight at constant airspeed (non-rectilinear translational movement, to you engineering students) an additional load is imposed. The term load factor is used to talk about these maneuvering loads and it is a multiplier of the airplane's weight in straight and level flight. Full size light planes like the Cessna 172 are designed for an ultimate load factor of 5.7 positive and 2.3 negative. The pilot will find another load factor, the limit load factor, in his FAA approved flight manual. The limit load factor is 2/3 of the ultimate load factor for US Certification. An aerobatic aircraft will have an ultimate load factor of 9, usually positive and negative. I designed my 1/6 scale Cub for a load factor of 6 without the struts. A high speed aerobatic model should probably be designed to a load factor of 12 for really wild flying without maximum speed restrictions. A maneuver bringing the load factor up to twelve would require the wing of a 6 pound model to support 72 pounds.
Of course, a wing does not consist of just the main spar. There are leading and trailing edges, the rear spar, and the covering or sheeting materials that all contribute to the wing's strength. In designing the wing of the model I think it is best to design the spar to support the entire load to keep the problem simple and solvable, or determinate, as an engineer would say.