CG for flat, pizza box wing...

[Robert Parisot]

Hi all,

"Building" a small pizza box style wing, (from a pizza box), and I'm hoping someone can tell me where to start with the CG. The plane is 12 3/4 inches wide, and 14 1/2 inches long, measured from the leading edge, to the trailing edge of the elevon.

Thanks!
Robert

Oh yeah, will if fly better if I put a vertical fin on it, in the center? And if so, what sort of dimensions, roughly?

[Ollie]

If you have spare pizza box material cut out a piece for the right or left half of the wing planform. Find the center of gravity of that wing half shape. An easy way is to use a plumb bob and string. Suspend the piece from an edge with a pin so thst it swings freely and the plumb bob from the same pin. Draw a line where the string falls along the surface. Switch the pin to another spot on the rim of the piece about 1/4 of the way around the circumference and draw another line along the string. Where the lines cross is the center of area (centroid) of the half wing planform. Draw a chord line through the point where the first two lines cross. That is the mean aerodynamic (effective) chord of the wing. Find the point 25% of the mean aerodynamic chord back from the leading edge. That is the aerodynamic center of the wing. This proceedure works because the pizza box material has uniform density across its area.

For pitch stability, the CG must be ahead of the aerodynamic center. How much depends on how much stability you want. I suggest that you start fllight testing with the CG at about 17 or 18% of the mean aerodynamic center back from the leading edge of the mean aerodynamic chord. This CG may result in a lot of reflex needed in the elevons to get pitch trim. As flight testing progresses, you can move the CG back in very small increments and reduce the reflex a little until it flies the way you want it to.

For planforms like rectangles, trapazoids, semi circles, semi ellipses, etc the effective or mean aerodynamic chord is the chord through the centroid of the area. The aerodynamic center of a wing is near 25% of the mean aerodynamic chord. The CG should be determined by its relation to the aerodynamic center for the desired stability. The distance that the CG is ahead of the aerodynamic center is the static margin and is expressed as a percent of the mean aerodynamic chord. The larger the static margin, the more the stability. Static margins from zero to about 7% of the mean aerodynamic chord may be used depending of the desires of the pilot, his flying skill, and the purpose of the aircraft. It is best to start with a generous static margin to allow for errors in aerodynamic center in relation to the 25% assumed location and, measurement errors. If the CG ends up much behind the aerodynamic center the plane will be uncontrollable.

Martin Simons shows a similar proceedure for tailed configurations in his book Model Aircraft Aerodynamics.

BTW, this proceedure works for any tailless wing shape. So, if you want to design fllying wings, save your old pizza boxes to make into analog computers of the mean aerodynamic chord.

[Robert Parisot]

Very much appreciate the detailed and lengthy reply, but I'm having a little trouble visualizing and or understanding your idea for finding the CG.

Any way to make it simpler?

Thanks!

Robert

[Ollie]

The basic principle is simple enough. The CG has to be ahead of the aerodynamic center of the object for stability. Take a plain stick and throw it. It won't be stable because the center of gravity is at the aerodynamic center (AC) of the object. Putting feathers on the stick moves the (AC) toward the feathers more than it moves the CG to the feathers. So, now the CG is ahead of the (AC). If you throw the arrow backwards, it will reverse itself end for end because it is stable with the CG ahead of the AC. If instead of converting the stick into an arrow you convert it into a javelin by adding weight to one end, you leave the AC at the middle of the stick but move the CG toward the weighted end. Again, no matter how you throw the javelin it will turn weighted end first because it is stable that way.

Now, apply the basic principle to your pizza box wing. First find the AC, then put the CG ahead of it. Well, the AC of a wing is very near 25 % of the mean aerodynamic chord (MAC). But where is the MAC? Well, the MAC is the chord goes through the centroid (center of mass) of the wing area. So all you have to do is find where the wing half balances along two different lines at right angles to each other and where the lines cross is the centroid of the wing half.

Still too much trouble? Well, there is always basket weaving or golf to pass the time.

If your head is spinning, forget the above proceedure and build a small, very accurate scale model of your design out of balsa wood or other light material. Put some modeling clay on the nose. Glide the balsa scale model and adjust the amount of clay untill the model glides in a straight line. Then measure the CG location of the balsa model and scale up the CG location for the pizza box design. If your scale model can't be made to glide straight because it veers to the side, it probably needs a vertical tail near the back to stabilize it laterally. This is a good test to find the CG position and the yaw stability for your design.

[Dereck]

Robert
All my tailless models (six or so models, around 4:1 aspect ration, very little taper) with symmetrical sections around 12% flew with the CG around 15%. Bill Evan's zillions of "Simitar" variants had a horrible looking section with a real forward high point and reflex, and flew at around 8% chord for the CG.

I'd start with your Pizza Box thing balanced at 8%, work it back later to 15%

yes, it needs a vertical fin. Stick it right at the back. As it ain't as far aft of the CG as it would be if there was a fuselage involved, I'd suggest 20% of the wing area, but you might get away with 15%. Square is probably as good a place to start at as any!

The 'flying scale model' isn't that bad an idea for about any model! Snag is, with your flat winged PB, your scale model won't be very stable as there's no-one controlling it. Indoor test gliding would be better, as there's much less turbulence in the lounge as opposed to outdoors!

Bearing in mind the size and cost of your PB, why not build the thing, fit the radio, ballast it to about 10% with just the radio fitted - no motor, battery etc. You could even use a small receiver pack as part of the ballast. Then take it outside and test glide it. If it stalls, move CG forward. If it spins in, or is hard to keep straight, stick more fin on. You'll even get a feel for how much control throw is needed and how much reflex up you'll need on the elevons - that goes hand in hand with the CG, within limits. Further aft CG = less reflex.

When it flips over and departs into flip-flops, you've got the CG too far aft!

Dicker with it until you feel happy, then fit the motor and stuff to keep the CG in place.


Good luck!

Regards

Dereck

[Robert Parisot]

Thanks Dereck (Ollie too). Lots of good info.

Now I just need to figure the AC I guess. (Either that, or just take up basket weaving.....)

;)