Math for Calculating Area of Vertical Fin

To keep an airplane flying straight normally a vertical fin is needed, the position is usually above the horizontal stabilizer. For a sport rubber model 10% of the wing area is good proportion to try. What would be the area for the vertical fin using the 36 square inches of wing area?    [3.6 sq. in.]  After computing the square inches of the vertical fin, what function would you use on this area to get equal length sides?   [square root]   

Side View of Rubber Powered Model Airplane

You decide that for the shape of the vertical fin part of the area to the front will be a right triangle. You decide the rear part of the fin will now be a square with sides 1.5” long.  How much area will this be? [ 2.25 sq. in].  What do you think the next step will be?   Yes, [ 3.6” – 2.25” = 1.35 sq. in.] Now we need a right triangle of 1.35 sq. in. with the opposite side 1.5” long to match up with a side of the square with sides that are 1.5" long. How long will the adjacent side of this triangle be?

I started looking for a formula to compute the adjacent side given the area and the opposite side but did not find one. My reasoning was to create a rectangle by drawing in another triangle and doubling the area. This would make it easy to compute the adjacent side. 1.35 sq. in. x 2 = 2.7 sq. in for rectangle area.  Divide this by 1.5” which equals  1.8“ for the bottom side (adjacent side).    

Entire Vertical Fin

To check my method I divided the area of rectangle 1.5” x 1.8” /2 = 1.35 square inches. I could now put the triangle and square together to form a vertical fin with 3.6 square inches of area.  

If anyone has another solution to find the missing dimension of the triangle comment below.

Bill Kuhl

http://www.ideas-inspire.com

For an explanation of many aspects of simple aerodynamics with math problems check out my article Basic Aerodynamics With a Lesson

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Climb of an Airplane Maybe Not Intuitive

During the process of working on an article for the new website http://www.ideas-inspire.com on aerodynamics I ran across a couple of simple formulas regarding the climb of an airplane.

Lift = Weight x Cosine Angle of Climb

Thrust = Drag + (Weight x Sine of Angle of Climb)

I proceeded to test the lift formula with a hypothetical model airplane weighing 10 grams for climb angles of 30, 45, and 75 degrees. The results were rather shocking to me as I thought of the four forces of flight and how lift and weight are exactly equal in level flight. It would seem that lift would keep increasing more than weight as the airplane climbs. The cosine of the angle decreases as the angle increases however.  Here are my sample results:

30 degree climb      Lift = 10 grams x .866  = 8.66 grams     Cosine 30 = .866

45 degree climb      Lift = 10 grams x .707 = 7.07 grams    Cosine 45 = .707

75 degree climb      Lift = 10 grams x .259 = 2.59 grams     Cosine 75 = .259 

Sine of an angle increases with greater angles which means the thrust will be increasing as the airplane climbs steeper. That makes sense to me now and then when you think of the situation where the airplane is hovering the airplane will be completely supported by the thrust and there will be no lift from the wing. It also means that the thrust is pulling some of the weight upward, think of vectors.

To validate this I read further articles on the Internet and posed the question on a model airplane listserve.  It is true.

Embrace the Challenge of Learning 

Bill Kuhl

http://ideas-inspire.com

For an explanation of many aspects of simple aerodynamics with math problems check out my article Basic Aerodynamics With a Lesson

Using Online Calculator to Compute Lift

Most likely one of the first formulas one would see when studying aerodynamics is the formula for lift.  It can be seen re-written from various sources but it is the same formula.  I have been interested in applying the formula to model aviation but a couple of units of measure in the formula are not what you would normally work with in model aviation. The surface area units (square feet) is what would be easier to use with full-scale airplanes and velocity in feet per second is not what most of us think of.  To make this all easier I ran across lift calculator program on the Internet that makes it easy to work with whatever units your data is in.

Airplane in Level Flight Flies With Slight  Positive Angle of Attack 

Lift Formula

Lift = Coefficient of Lift x .5 x Density of Air x Velocity² x Surface Area

Additional Explanation:

The variables in the equation need further explanation.

Coefficient of Lift (cl)  is created to take several factors into account but the most dominant would be the angle of attack of the wing. Other factors would be the shape of the airfoil including the thickness. Coefficient is a word that has a different meaning in math but in physics it is a quantitative expression of some type of property; coefficient of friction is a very common coefficient.

Density of Air is mass per unit volume of Earth's atmosphere and can be found in tables. Factors to this variable are altitude, humidity, and temperature. This is why jet aircraft need to build up more speed to take off on hot days and from high altitude runways.

Velocity is the speed that the air is moving over the wing horizontally from the front of the airfoil. It is labeled velocity because it is a vector quantity, the air is moving from a specified direction. In the formula this is specified in feet per second but miles per hour is what most people in the US think of. Note velocity is squared, this means it is the dominant variable in the equation and the reason that the amount of lift increases substantially as velocity increases.  

Surface Area is given in the formula in square feet which is great for full-scale aircraft but square inches or square centimeters would be easier to relate to with model aircraft.

My Hand Launch Glider Converted to Catapult Launch

Online Calculator Website:  http://www.ajdesigner.com/phpwinglift/wing_lift_equation_force.php

With the calculator website I wanted to give it a try but I did not have any data currently but thought of an article on the AMA Glider website Kurt Krempetz entitled, “Catapult Glide Time Prediction Theories.” This isn’t exactly what I wanted because unless a glider is in lift, the amount of lift is slightly less than the weight of the glider because it is going down the glide slope.  From the article I was able to retrieve weight of the glider, wing surface area, velocity, density of air, and CL (coefficient of lift).

Coefficient of Lift  - .34

Weight of Glider – 5.5 grams

Wing Surface Area – 28 square inches

Velocity – 12.86 feet per second

Density of Air - .071 pounds per cubic foot

Data Plugged into Online Calculator

Plugging all of this into the calculator gives 5.47 grams of force which is slightly less than the 5.5 grams weight of the glider which seems completely reasonable. By the way, 12.86 feet per second is about 8.77 miles per hour.

I really need to think more about how I might use this tool, to me it is fascinating to see how math works out with real world applications.

Bill Kuhl
http://www.ideas-inspire.com

For an explanation of many aspects of simple aerodynamics with math problems check out my article Basic Aerodynamics With a Lesson

Handling a Delicate Situation in Model Building

When I show many people the delicate balsa and tissue model airplanes I build, the response I often get is that they could never build something so delicate that requires so much patience. With experience you learn how much pressure you can use when handling delicate structures and then you still break the balsa wood at times. In one of my current projects a Guillow’s PC-6 Porter rubber powered model airplane I thought I had done everything in advance correctly before gluing a certain piece but still managed to break several balsa pieces. 

Broken Structure Caused by Mistake While Building

Side Keel Before Placing in Slots

The significance of this situation goes way beyond model airplane building as I see it. These are some of the general ideas that I see that are important:

*  Learn the properties of what you were working with and get a good understanding of the risks when performing a delicate operation.

*  Perform small subtasks and test as much as possible before attempting the major operation.

*  If there is a failure in what you are trying to do, know how to remedy the situation.

Grain of the Wood Appears in Direction of Dark Lines

Balsa Breaks Easily Along the Grain

Back to the model building, I needed to glue a side keel into many bulkhead slots, the grain on the bulkheads was running in a direction that would make it very easy to break the balsa along the grain. For my first subtask I took a balsa strip the same thickness as the side keel and made sure it would fit into each slot in the bulkheads. Next I did a test fit of the entire side keel in the slots just like it would be placed for gluing, the fit was good.

Broken Parts Repaired

After pulling the side keel out, I applied glue into all the slots and again put the side keel in place.  This time the keel did not slide into place as easily and I applied too much pressure. In an instant I heard that awful sound of balsa snapping and pieces were displacing in several directions. One of the bulkheads had broken along the grain and then the side keel broke in that same region of the airplane. With plenty of experience fixing broken airplanes, the repair was easy.

Kit Box for PC-6 Porter

What will I do next time in a situation like this?  Maybe I could grip each bulkhead closer to the slot as I press the side keel in. A CYA (super glue) could be used and the glue would wick into the joints after the pieces were fitted.  Ideas to think about and this is what keeps me interested.

Bill Kuhl
http://www.ideas.inspire.com

Related

Guillow's PC-6 Porter Review

Pitching Your Idea Before Shark Tank

Lately I have been a big fan of the popular television program Shark Tank where entrepreneurs pitch their ideas to wealthy business people in hopes of them investing their company.  My father made his pitches to business people also but never borrowed ANY money his entire life.  He was looking for other companies to produce his products which through his persistence did happen. His idea that got him started was a clevis for a tractor that was easy to use and did not wear out as quick as other designs. One businessman he showed it to said, "kid I look at so many ideas everyday, I just do not have time to look at another one". My father quickly responded he would be willing to pay the guy to look at it. The guy agreed to look at it for no payment and this was the start of several business deals.

Father's Design Produced by Farm-eze

Produced by His Company

My father went to the effort to get patents on his ideas and made contracts where he would receive royalty payments for units other companies would produce while still being able to produce in his own small manufacturing business.  At one meeting the sales people were talking about how many of a large farm item they could sell, my father said, "I can't even paint that many"!

Clevis Drawing for Patent

It would appear eventually larger companies would copy his ideas anyway but patents only run so many years. He once noticed a component from a John Deere product looked almost exactly like the same part in his design, I think he was flattered. His business was a huge part of his life and he worked in his shop until he just couldn't any longer.  Recently I found a video segment of him demonstrating several of the metal working machines he used.


Bill Kuhl

http://www.ideas-inspire.com

History of Champall Manufacturing Video

Mousetrap Car Progression of Ideas

If there was only one project that I had to pick out as the best for learning basic principles of physics it would have to be the mousetrap car. No doubt in a large part because of the efforts of one man, Alden Balmer aka Doc Fizzix.  I purchased at least a couple of his kits and his book on mousetrap cars before trying to build any type of mousetrap car of my own design.

This project might appear so simple but I see many students struggle with it, using improper materials or sloppy workmanship will not give good results.  Recording data on motion I believe is much easier with a model that moves slowly in two-dimensional space compared to flying projects like model rockets or airplanes.

The Spring from the Mousetrap Powers the Car

My Mousetrap Car Design has been Built Around the World

In my progression of designing and teaching with mousetrap cars I have tried several ideas and materials but the objective has been to simplify the design while fixing any problem areas. My first couple of mousetrap cars were built from bamboo skewers which worked well but I felt this was too much structure for the students to build. The next mousetrap cars were built from balsa structure which worked well but I thought a foam chassis would be cheaper and a little less work. It seems that when projects have too many pieces the difference between the students that are faster in the construction and the slower builders gets greater.

For my next class with the mousetrap cars I plan to introduce the connection with Newton's Laws of Motion and the mousetrap cars. It would also be a good opportunity to introduce simple machines and the concept of mechanical advantage.


Bill Kuhl

http://www.ideas-inspire.com

The Evolution of My Mousetrap Car Design

PS
Thank you to all those that have viewed my blog, no doubt by the end of the day it will be 30,000 views in less than a year. This inspires me to keep on writing.

Fly Forever Paper Plane - Exercise in Critical Thinking

What would seem impossible can be possible but when it comes to visual media it seems we are being tricked everyday. At least I do not believe everything I see in advertising. There have been a couple of videos on YouTube lately related to flying a paper plane that are getting a huge number of views under the premise that the planes could fly forever. The source of the energy is by artificial  means but the basic science for the lift is well known science; thermal air currents and dynamic lift.

In this first video a paper plane is kept aloft by the heat coming from the heat rising from an electric range, my range has different size burners so I can not accurately repeat the experiment. Many people believe this video is real and many think this has been faked.  I am leaning to that it has been faked but not completely positive and I will give some of the points I have considered.

Consider:

* What do we know?   There are a lot of very popular videos in the Internet that were faked. Many get a huge number of views and it is a marketing technique.

* The videos can be based on sound actual principles of science.

* There are people that are so sure that what is presented is real they blast people that question that it is real with very nasty comments.

* Personally I have been so sure something to be true and was proven wrong, that is not a great feeling so I try to listen to others with an open mind.

*There is a very popular television show based on proving what is real and what is not Mythbusters.

* The observations of the people stating that it is a fake are not always accurate either, this reduces their credibility.

* There are many demonstrations that can be done that would appear to be impossible or look like magic.

*Some demonstrations require very accurate execution and might not be easily repeatable.

Example Glider Circling stove:

* Now this is based on a thermal which is rising air that airplanes and birds can maintain or rise in with no propulsion other than gravity pulling down the glide slope while the air pushing up maintains or increases the altitude.

*Model free flight gliders can circle in thermals outdoors without any control.

Free Flight Model Glider Could Circle in Thermal Lift 

Radio Control Glider can Stay Aloft in Thermal Lift

This Tiny Foam Glider Stays Aloft by the Air Over the Cardboard Being Pushed
Many People Think This is Impossible but I Have Done it Many Times
Darcy Whyte Photo

* It would appear in the video that flaps on the paper glider which is a flying wing so the surfaces are known as elevons are directed to turn to the outside of the circle.  Maybe the glider has a tendency to slide to the center of the circle and a turn outwards is needed to balance this.

* The flight looks so smooth within such a close proximity, whenever an airplane flies the air is disturbed behind the aircraft. It would seem flying in such a small circle the plane would be rocking in its’ own wake.

Additional Info:

Dynamic Soaring Paper Airplane Video

Walkalong Gliders by Phil Rossoni in picture above

Darcy Whyte Walkalong Glider Info

ScienceToymaker Air Surfing

Bill Kuhl