RE: Center of Gravity "CG" Computations

RE: Center of Gravity "CG" Computations
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RE: Center of Gravity "CG" Computations - 12/24/2007 9:14:04 PM

feihu

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Jim:

The exactness of the CG setting is really of no consequence so long as it is within the flyable limits of the CG range; that's why the fingertip method works fine.
The pilot of a General Aviation airplane or a Jet Transport (and some RC pilots too) could care less who or how many people get aboard (which causes a change in the exact location of the CG) so long as you're within the flyable CG range.
I use math in the design phase to eliminate the need for unwanted ballast.

feihu

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Post #: 26

RE: Center of Gravity "CG" Computations - 12/24/2007 10:58:20 PM

RC Specialties

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You are absolutely right. There is always a most forward and most aft cg limit (cg range). Loading can vary to keep the cg within that range. However, in RC airplanes the real only variable is fuel loading. The empty weight cg can be an exact one. It can be adjusted to get the best flight/performance for the full fuel to empty range.

Jim

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RE: Center of Gravity "CG" Computations - 12/25/2007 2:03:38 AM

buzzard bait

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Most formulas assume you know what CG you want, and that the problem is compensating for sweepback or taper or whatever. But those things are usually common sense and easy to deal with. The real issue is where the CG should be. To find that I've been using the following formula for about 25 years and I still surprised at how well it works on a wide range of designs:

tail area/wing area x tail arm/wing avg chord = TV (tail volume)

The 'tail arm' can be estimated as the distance from the leading edge of the wing to the leading edge of the stab, taking into account taper, sweepback, etc.

then CG = 16 + 36(TV)

That gives the CG as a percent of the chord. It's all based on "tail volume", which tells you how much power the stabilizer has to keep the center of pressure in the right place. If you think about the formula, you can see that a wide wing chord requires a more forward CG, all else equal, and a long tail arm allows a more rearward CG, for example.

The first time I used it was on a glider that seemed unstable in pitch. I stuck two quarters in the nose and it flew fine. The puzzle was that it had been balanced according to the plans. But the formula showed that the CG on the plans was wrong, and the quarters moved it to the right place by the formula -- and by how it flew. I've used it on every one of my airplanes since.

I've never found another set of plans with the CG too far rearward, but I have found that many have very conservative CGs. For example, the CG on the Balsa USA Stick 40+ was a full inch farther forward than the formula predicted was necessary. By that time I had so much confidence in the formula that I made the very first flight with the CG well aft of the position on the plans -- it flew fine that way.

Many times people complain that a certain design needs nose weight to balance, but in fact, none is necessary if you know that the CG can be farther back. You can adjust later, but it is much easier to know during the building process.

Jim

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RE: Center of Gravity "CG" Computations - 12/25/2007 3:01:52 AM

Mitsu1

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quote:

ORIGINAL: joseph185

The CG has to be measured on the Mean Cord and where this point is depends on the shape of the wing. You cant just measure 1/3 back from the leading edge Model Aircraft News done an article on this exact thing in the April 2007 issue you will find this helpful the article is " Balancing Act" it shows how to balance with the different chord wings they are not all the same.

I'll have to look up that April issue of MAN. I probably don't have it, because I don't remember seeing that article and I subscribe to FLY RC magazine instead of MAN. I too like knowing exactly where the actual "0" balance point is, because when I go thru the tedious placement of all components, I want to know that I won't be having to start all over again to get it right.

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RE: Center of Gravity "CG" Computations - 12/25/2007 3:11:58 AM

RC Specialties

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Jim,

Very interesting. Do you measure from the nose or the end of the prop shaft for a glow plane? I guess it really wouldn't matter as long as you use a constant. I will have to ponder this a while. Great concept, I will have to try it.

Jim

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RE: Center of Gravity "CG" Computations - 12/25/2007 2:53:08 PM

buzzard bait

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Sorry, Jim, it's hard to explain without a diagram. Conceptually, the tail arm is the average distance between the wing and the stab. The simple way is to measure from the leading edge of the wing to the leading edge of the stab.

For a straight, constant chord wing, of course, it is easy. But the stab is almost always swept back some -- just take about the average point, but a little closer to the fuse. The concept is to measure at the point on the leading edge where half the area is on one side and half is on the other (the 'MAC'). You can calculate it, but I always eyeball it. Same with the wing, if it has taper or sweepback.

This formula is in many books. Gordon Whitehead, in his book on scale models, has a different version that is algebraically the same.

Gordon points out a nice use for the formula. Say you want to build a WWI model that is notorious for flipping on its nose when it lands. Using the formula, you can calculate how much to enlarge the stab in order to move the CG back, say, a half inch. It is much less noticeable than angling the gear forward.

If the wing and/or stab are elliptical, what then? I take a piece of cardboard, measure it, and weigh it. Then I trace around the wing or stab outline, cut off the rest and weigh again. The area is proportional to the weight.

Jim

< Message edited by buzzard bait -- 12/25/2007 3:09:51 PM >

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RE: Center of Gravity "CG" Computations - 12/28/2007 3:40:51 PM

RC Specialties

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Jim,

That clears it up a little. When establishing the cg, do you compensate for the fuel loading range. This will always move it forward on RC aircraft unless the tank is mounted on the cg. I have been guilty of adding a larger than specified tank and not considering that when full the most forward cg limit will be exceeded.

Jim

< Message edited by RC Specialties -- 12/28/2007 3:45:26 PM >

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RE: Center of Gravity "CG" Computations - 12/28/2007 10:25:45 PM

buzzard bait

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Jim, I have not compensated for fuel, so my planes take off more nose heavy than what I calculated and measured. But a little extra weight up front is safe -- the goal is to make sure the plane is still balanced OK when it has run out the tank. Jim

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RE: Center of Gravity "CG" Computations - 12/28/2007 10:35:35 PM

RC Specialties

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I agree. I always set up my warbirds a little nose heavy. Thanks for the info.

Jim

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RE: Center of Gravity "CG" Computations - 12/28/2007 10:57:44 PM

rcairflr

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quote:

ORIGINAL: RC Specialties

I have not found a thread that specifically talks about balancing and CG computations

I thought I would start this thread to discuss easy ways to compute changes to a CG without it being a trial and error method. It can easily be done using mathmatics with perfect results.

You can compute exactly the weigh to add to a desired location and the CG will be exactly where it should.

Do you want to move your servos to the tail. You can compute what effect it would have and how to compensate before actually making the change.

Calculate where to place servos batteries, etc. to limit the amount of ballast weight needed.

Let's talk about those CG problems!

D x Wa/ Wt= Distance CG will move

D=Distance from CG weight was added
Wa=Weight added
Wt=total weight of airplane

So if I add 8 ounces 10 inches aft of CG on a 25 pound airplane. 10 x .5 pounds/25.5=.196 inch change in CG

Try the above formula, it's what I use and works great. The information came from a copy of 3D flyer magazine. Hope this helps

I only use this to see how much my CG will change when and if I have done a modification to the weight of the airplane. For me I will continually make small changes in the CG of my airplane over numberous flights until it fits my flying style. At that point I don't care where the CG is, just how the airplane flies.

< Message edited by rcairflr -- 12/28/2007 11:02:30 PM >

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RE: Center of Gravity "CG" Computations - 12/29/2007 12:12:29 AM

RC Specialties

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rcairflr,

You are correct, a change to the cg can be calculated if you have a known cg. In this case let's say 18.0 inches aft of the datum line. Let's say the datum is the end of the prop shaft. If you add .5 lbs at 28.0 inches the following would be the result. I converted to ounces for the example.

Weight x arm = moment

Moment Arm WT
7200 18.0" 400 OZ. (current CG)
+224 28.0 + 8 oz.
____________________________________________________

7424 18.19" 408 oz.

Adding 8 oz. at 28.0" aft of the datum moves the cg .19 inches aft. The important thing is to have a fixed datum to do you calculations from.

Jim

< Message edited by RC Specialties -- 12/29/2007 12:14:09 AM >

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RE: Center of Gravity "CG" Computations - 12/29/2007 11:26:57 PM

timothy thompson

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it is simple physics! and it is important info to know. this is a result of the arf age, 30 yrs ago we all knew these tables now its balance to the manual. ive found many manuals wrong

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RE: Center of Gravity "CG" Computations - 12/30/2007 1:17:53 AM

rcairflr

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Ignore this post. Made a mistake. See next post

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< Message edited by rcairflr -- 12/30/2007 4:27:06 AM >

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RE: Center of Gravity "CG" Computations - 12/30/2007 4:28:37 AM

rcairflr

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CG is usually measured as a % of MAC ( Mean Aerodynamic Cord), the MAC of a wing can be figured out by squaring the wing as depicted in enclosed drawing. Once you have your MAC it is just a matter of deciding what % is desired for CG. On a aerobatic mono-wing airplane 28-30% is a good place to start.

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