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Author Topic: Measuring the CG of a model airplane  (Read 362 times)
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NHFlier
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« on: October 04, 2019, 12:21:13 PM »

I recently found a method for measuring the center of gravity (CG) of a model airplane that I have not seen described before.  The method seems so easy and straightforward that I would be surprised if it has not been previously published somewhere.  However, I have been unable to find a description of it on the web, so I thought I would post it here.

Here's the idea: suspend the plane from two spring scales, one at the leading edge (LE) of the wing root chord and one at the trailing edge (TE).  Let F1 be the reading of the scale at the LE and F2 the reading of the scale at the TE.  Then, L, the location of the CG as a fraction of the root chord back from the LE, is given by:

L = F2 / (F1 + F2)

LP, the CG location as a percent of the root chord, is then 100 x L, and LD, the actual distance of the CG back from the LE of the root chord is L x R, where R is the length of the root chord:

   LP = 100 x L

   LD = L x R

Now, physics says that F1 + F2 is equal to W, the weight of the plane, so that L is also given by:

   L = F2 / W

If a separate balance is used for measuring W, only a single spring scale is needed at the TE, with the LE supported by a cord.  Because L is usually near 0.25, the capacity of the spring scale needed is about one quarter the weight of the plane.  I note that sets of spring scales covering a range of weights can be had very cheaply.

I have attached four photos, illustrating the application of the method to a variety of aircraft, as well as illustrating different setups that can be used.

The first photo shows the setup I used to determine the CG of an E-flite Edge 540QQ foamie.  The cords are heavy nylon threads.  One thread runs from the front scale, under the plane at the wing LE, and back to the front scale.  The other thread runs from the rear scale, under the plane at the wing TE, and back to the rear scale.  In the case shown in the photo, the front scale reads 195 g, (F1) and the rear scale 54.5 g (F2).  L is then calculated to be 0.218 or 21.8 percent of the root chord.  Since R in this case is 185 mm, the CG is calculated to be 40.4 mm back from the LE of the root chord.  The weight of the plane, calculated from F1 + F2, is 249.5 g, in good agreement with a direct determination of 248.5 g, as measured by a separate balance.

The second photo shows the method applied to a very light aircraft, an E-flite Champ.  Suspension was via fine black threads, and a single spring scale at the wing TE was used.  This scale reads 18.5 g.  The separately determined weight of the plane was 53.31 g, so the calculated CG is at 34.7 percent of the wing root chord.

The third photo shows application of the method to a much larger plane, a Flite Test Mustang.  It also shows an alternative method for routing the supporting cords.  Because of the size of the plane, the two spring scales used were suspended from a ceiling beam with stranded nylon strings attached to two hooks spaced a root chord's length (9 inches) apart.  The suspending strings were of equal length and had loops tied at each end.  One string was run under the left wing from LE to TE and the other string under the right wing in the same manner.  The loops on the two strings emerging from under the wing TE were attached to the rear spring, and the loops on the two strings from under the wing LE to the front spring.  In order too level the plane for measurement, the rear spring was attached to its ceiling hook by a string having a slipknot noose.  Sliding the slipknot up and down then leveled the plane.  In the configuration shown, the forward scale (F1) read 650 g and the rear scale (F2) read 175 g.  The CG was therefore calculated to be at 21.2% of the root chord, and the weight of the plane to be 825 g, in excellent agreement with an independent measurement of 824 g.  A repeat of the procedure using the single rear spring scale, the independently determined W of 824 g, and the same suspension system as for the Edge 540QQ, gave results of 21.8% for the CG, suggesting that the method has good reproducibility.

Are you a heli pilot?  The last photo shows the determination of the CG of a Blade mCX2 helicopter.  This micro coaxial heli was suspended from its lower blade at points equidistant from the drive shaft using fine threads.  The single rear spring scale reads F2 as 16.8 g.  An independent measurement of W gave 31.31 g, so that the CG is computed to be at 53.7 % of the distance between the two suspension points, or just slightly aft of the drive shaft.  What other method of measuring CG could be used to make this determination so easily?

I see no reason why this method could not be used to measure the CG of quite heavy model planes.  Replace the spring scales by digital luggage scales, and use block and tackle hoists or hand winches attached to a ceiling beam to raise the front and rear supports and to level the plane.  Digital luggage scales are quite cheap, and Harbor Freight has ratcheting winches and block and tackles for ridiculously low prices, so the whole setup could probably be bought for under $100.
 
Finally, a couple of comments on situations where this method has proved particularly useful: for the Edge 540QQ shown in the first photo, the vertical position of the CG apparently lies within the root wing chord.  As a result, no matter how the plane was balanced, whether upright or inverted, on fingers or sticks, or on a Great Planes CG device, the CG always lay above the point of suspension.  Consequently, it was very difficult to obtain the stable balance condition needed to make an accurate CG determination.

Another situation where this method proved especially useful was in setting up an electric powered plane at the CG recommended in its manual.  Once the plane was suspended from the scales, it was easy and fast to move the battery back and forth until the desired CG was obtained.  Marks were also placed at each trial battery position and the CG recorded for that position.  These markings then served to guide experimentation with the CG during actual flight trials.

I have found this method of CG determination to give precise results and to be reasonably simple to do, and I hope this might be the case for other modelers.
Attached files Thumbnail(s):
Measuring the CG of a model airplane
Measuring the CG of a model airplane
Measuring the CG of a model airplane
Measuring the CG of a model airplane
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OZPAF
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« Reply #1 on: October 05, 2019, 12:13:09 AM »

Interesting method NH. It would seem that it is really only necessary to use one scale and a supporting string at the other end of the root - as you did for your loop.
I'm a little suspicious of spring balances as far as accuracy is concerned though - digital scales could be used(similar to the luggage ones you mention).
Good point re those aircraft where the vertical position of the CG is within the wing causing problems with the stability of the model on a pivoting type system.
Thanks for submitting.
John
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VictorY
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« Reply #2 on: October 05, 2019, 09:54:16 AM »

You don't need scales at all with a Vanessa CG rig.  Wink
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NHFlier
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« Reply #3 on: October 05, 2019, 12:26:00 PM »

I'm a little suspicious of spring balances as far as accuracy is concerned though - digital scales could be used(similar to the luggage ones you mention).

John

Good point, John.  In my experience, spring scales are accurate enough for model work.  I do a couple of things with a spring scale to ensure accuracy:

First, make sure the scale reads zero with nothing attached.  Many spring scales have a method of zeroing the pointer, but if none is available, just correct the observed weight by the observed zero.

Second, calibrate the scale using an accurately known weight that is at or near the maximum range of the scale.  A proportional correction can then be applied to any other observed weight.  (Actually, any balance, digital or analog, should be checked for accuracy against a known weight).

In my opinion, the worst problem with spring scales is not accuracy, but reading the darn things to any sort of precision!  For example, the marks on my 250 g spring scale are at 5 g intervals.  You can read this to maybe +/- 1 or 2 g, which is usually accurate enough, as long as you are not using it to weigh a 10 g object!  This, by the way, brings up another point.  When using a spring scale, use one with the smallest possible capacity.  I own spring scales with capacities of 30 g, 100 g, 250 g, 500 g, 1 kg, 2 kg, and 5 kg.  This pretty much covers the range of model planes I currently own.

I love digital scales, having used them for many years in my profession (retired organic chemist).  However, I cannot find any digital hanging scale suitable for measuring the relatively small weights of models like the Champ or even the Edge.  For example, the scale I bought for calibrating my torque wrenches can only be read to +/- 0.01 lb (+/- 5 g), which seems typical for this type of scale.

Tom
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NHFlier
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« Reply #4 on: October 05, 2019, 12:43:30 PM »

You don't need scales at all with a Vanessa CG rig.  Wink

The Vanessa CG Machine (creswellrcflyers.org/Text/Vanessa_CG_Machine.pdf) is simple, cleaver, and I wish I had invented  it!

However, I am sort of a numbers type guy, which is what I like about my method.  Of course, wrong numbers are worse than no numbers at all!

Tom
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lincoln
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« Reply #5 on: October 05, 2019, 06:55:36 PM »

I think that if you used light foam blocks to support the model, and accounted for the weight, a regular scale would do a fine job.
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NHFlier
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« Reply #6 on: October 05, 2019, 09:00:14 PM »

I think that if you used light foam blocks to support the model, and accounted for the weight, a regular scale would do a fine job.

Good idea, and should definitely work.  As a matter of fact, I came up with my method while wondering how an expensive commercial digital CG machine that supports the plane from underneath works.  I figured that the machine must use two cradles spaced a known distance apart, measures the force at each using load cells, and computes the CG from there.

A bit of a postscript on digital versus spring scales:

Out of curiosity I used my digital scale (sold as a fish scale!) to make a measurement of F2 and W on the Mustang, as John suggested.  The attached photo shows the setup.  I got F2 = 0.18 kg and W = 0.82 kg (this scale can only be read to +/- 0.01 kg, not +/- 0.01 lb, as I originally stated).  These numbers agree quite well with those measured previously using the two spring scales.  The calculated position of the CG using the digital scale is then at 22.0 % of the root chord, in not bad agreement with the values of 21.2 % and 21.8 % obtained with my spring scales.  A bit of statistical analysis (done by assuming standard deviations of 0.01 kg for both F2 and W) gave 95% confidence limits of 19.5% to 24.5% for the digital scale measurement.  Thus, the agreement between the measurements using the two types of scales is actually quite good.

If anyone can come up with a digital hanging scale that can be read to better than +/- 0.01 kg, please let me know.  I've looked all over the web and have yet to find one.

Tom
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Re: Measuring the CG of a model airplane
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OZPAF
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« Reply #7 on: October 07, 2019, 08:06:41 PM »

Thanks for that extra feedback NH.

That's not a bad idea Lincoln. Actually if separate digital scales were used - you could duplicate full size weighing methods but I think NH's approach is a good compromise.

John
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