Cantilever wing spar design

[David Lewis]

If you're going to design/modify/relocate wing spars, my advice in any case is to carry the spars all the way through the center section. If they don't continue all the way to the tip, that might be OK in some situations, but if any spar stops before it gets to the center, the wing could fail.

Bending moment is unevenly distributed in a cantilever wing. The drawing illustrates a lift distribution diagram (blue curve) and a moment diagram (red curve). To plot the moment diagram:
Start at the wing tip (point A). Bending moment is zero.
As you move from point A to point B, bending moment increases EXPONENTIALLY.
From point B to point C, moment increases LINEARLY.
At point C, moment reaches its maximum value.

FUN FACTS
1. Area under the load diagram = weight of the airplane x load factor. Load factor indicates how many g's the airplane is pulling. The horizontal axis of the load diagram is length or distance, and the vertical axis is force divided by span.
2. The aerodynamic load on the wing from B to D is zero. That's why moment increases (or decreases) linearly in this region.
3. Lift from B to D is generated by the fuselage due to endplate effect. That's why the fuselage portion needs to be included in wing area calculations.

[davidchoate]

David, How do I figure out by fomula the stall speed, or the airspeed needed to fly?

[David Lewis]

Stall speed = [2 * wing loading/(air density * max lift coefficient)]^0.5
You can assume max lift coefficient to be about 1.3.
[wing loading] = N/m^2
air density = 1.225 kg/m^3
Here is an online calculator: http://adamone.rchomepage.com/calc_stallspeed.htm
-------------------
Example: Messerschmitt Bf-109 kit #401:
weight = 5 oz (= 1.39 N)
load factor = 3.5 (i.e. airplane pulling out of a dive or in a 73 degree banked turn)

Lift (= 1.39 N * 3.5) = 4.86 N
Wing area = 97 sq in (= .0627 m^2)

Speed = [2 * wing loading/(air density * lift coefficient)]^0.5
= [(2 * 4.86 N / .0627 m^2) / (1.225 kg/m^3 * 1.3)]^0.5
= 9.88 m/s (= 22.1 mph)

[Coloradoken]

Moment diagram and engineering analysis is most impressive, especially for a musician.

[NcGunny]

Dave doesnt the formula change with birds like the SR-71 and F-117 where the actual cabin is considered a major portion of the wing? I akways considered them to be frisbees powered by jet engines.

[David Lewis]

Indeed it does. An airplane actually has 3 lift coefficients:
1. CL of the airfoil (a.k.a. section CL), obtained from wind tunnel data.
2. CL of the wing, which is always less than than section CL due to 3D effects such as tip loss.
3. CL of the airplane (a.k.a. total CL), which takes into account lift from fuse and stab.

Ideally you'd like to plug total CL into the formula, but wing CL (barring unusual configurations) is close enough for model airplane purposes.

[David Lewis]

Example: Messerschmitt Bf-109 kit #401:
span = 24.38 in (= .620 m)
weight = 5 oz (= 1.39 N)
load factor = 3.5

Lift (= 1.39 N * 3.5) = 4.86 N

Max lift concentration (at centerline)
= 4 * lift / pi * span
= 4 * 4.86 N / pi * .620 m
= 10.0 N/m

We are interested in the aerodynamic load supported by the wing
(blue shaded area in the load diagram)
Replace the distributed load by a single resultant force.
Max bending moment (at centerline)
= 2.00 N * 0.155 m = 0.310 N-m

[woundedbear]

Dear Mr. Lewis This is the woundedbear I am a diagnosed dyslexic. I was tested over the course of two days by people who do that for a living, so there is no doubt about it. The Doctor who order the testing was quite impressed, and confused by the fact that my reading comprehension tested out to be on the second year college level. So I guess that explains a lot about me, and the long rambling e-mails and comments that I put on this forum. Being dyslexic just means that I have to try twice as hard to learn half as much. You are a very intelligent man, and if you would be so kind. Tell me how I can learn about aeronautics ? What books I should read and what web sites I need to study to understand just what makes an airplane fly. I have a real thirst to learn everything I can about heavier than air flight. This is something that will be very hard for me to do. Because of my mathematical skills are so poor, I can do basic math "OK", if you put a $ sign in front and a decimal with only two digits to the right, I can add, subtract, multiply, or divide it. However when you start putting letters in the mix I am hopelessly lost. I remember my teachers telling me how important math was going to be in life, but I was too lazy, and didn't even try. Well here's my e mail address davewoundedbear@gmail.com , and I look forward to hearing from you.

[woundedbear]

Dear Mr. Lewis This is the woundedbear I am a diagnosed dyslexic. I was tested over the course of two days by people who do that for a living, so there is no doubt about it. The Doctor who order the testing was quite impressed, and confused by the fact that my reading comprehension tested out to be on the second year college level. So I guess that explains a lot about me, and the long rambling e-mails and comments that I put on this forum. Being dyslexic just means that I have to try twice as hard to learn half as much. You are a very intelligent man, and if you would be so kind. Tell me how I can learn about aeronautics ? What books I should read and what web sites I need to study to understand just what makes an airplane fly. I have a real thirst to learn everything I can about heavier than air flight. This is something that will be very hard for me to do. Because of my mathematical skills are so poor, I can do basic math "OK", if you put a $ sign in front and a decimal with only two digits to the right, I can add, subtract, multiply, or divide it. However when you start putting letters in the mix I am hopelessly lost. I remember my teachers telling me how important math was going to be in life, but I was too lazy, and didn't even try. Well here's my e mail address davewoundedbear@gmail.com , and I look forward to hearing from you.

[David Lewis]

Dave, Thank you for your kind comments and encouragement. I don't want to clutter the forum with things members don't care about but if enough are interested it would be an awful lot of fun to start a thread on model aero-engineering here so that we can all benefit from the discussion. I like the Q&A format to keep me going in the right direction. Sometimes my explanations are obscure or incomplete. More knowledgable members can help us out on the questions I can't answer. What do you think?

[Coloradoken]

Mr. Lewis
As an avid modeler, registered professional engineer, former pilot and college professor I would also be interested in your proposed discussion idea. Sounds like a fun as well as educational activity.

[woundedbear]

Hi Mr. Lewis, In your reply you asked what I thought about starting a thread about model aeronautics. Well I think that would be the greatest thing that has ever been posted on this forum. I would support that, and if it were put a vote everyone here on the forum would vote a resounding YES ! Such a thing would help all on us, who want to know more about aeronautic as it applies to building better flying model airplanes. It would help in converting to RC, or modifying Guillow's planes to fly higher and farther, and that's what it's all about here on this forum don't you think ? I am of the old school of "if it looks right it'll fly right", but given the chance I think everybody would like to know exactly why an airplane does what it does "fly". Learning the stuff that you have learned yourself would also be a great help in trimming a plane once built, and in knowing why an airplane suddenly crashes. YES if put to a vote I'll be the first to vote YES !

[davidchoate]

Hi David. I read a very good article in Model Aviation magazine from AMA. It dealt with converting control line kits to RC, but it was a very easy to understand lesson on the basic aerodynamics for flight. I am beginning to understand now how tail moment, nose moment, wing area vs. tail area, and decolage affect flight. I finally made a RC conversion that works ! Thanks to You, Bill Gaylord, and Mitch. I have not been on in a while because I had to build some larger RC kits to learn to Fly at My RC Club. These smaller planes are not very good in the wind. Well anyway, I just wanted to say thanks.

[davidchoate]

Do You think the stabilizer is too small?

[David Lewis]

Stab might be a little small for me, a low time pilot. Try it and see how it goes. If you move CG forward, it makes it easier to live with, especially under gusty conditions. When it comes to small airplane stability, there may be no simple formula or rule of thumb -- too many unpredictable variables at very low Reynolds number -- so you revert to trial and error.