Determining the balance point BEFORE kit is assembled?

[frank mccune]

       Hello All:

       The above question says it all.  I am attempting to predict if a plane will be flyable when completed or will all of the effort be in vain.  I have seen finished airplanes so nose heavy or so tail heavy to make them useless.  They look great on the wall but...

         Suggestions/Comments

          Tia,

         

         

[Brett Buck]

       Hello All:

       The above question says it all.  I am attempting to predict if a plane will be flyable when completed or will all of the effort be in vain.  I have seen finished airplanes so nose heavy or so tail heavy to make them useless.  They look great on the wall but..
       

      Well, it's a lot less useless if you put on enough lead to balance it. I have seen people build an airplane, determine it is too tail-heavy, and hang it up without even trying to fly it. That makes no sense.

     But, yes, you can design it, estimate or weigh all the parts, and the, knowing where each part goes,  calculate the projected CG

    X_cg = sum of( X_part*M_part)/sum of(M_part)

    Where x = distance from some fixed reference for each part( use the CG of the individual part), and the ultimate distance of the CG from the same reference
             M = mass of each part . Note that the sum of the mass of each part is the total weight of the airplane

     Note that as much as I despise Excel, this is the sort of thing it was invented for (when it was VisiCalc) - bean-counter-like accounting tasks.

      Note that this tends to get subverted because it's hard to estimate the mass and mass distribution of the paint (which is approximately some areal density over the area of the surface). Paint mass is typically almost all behind the intended CG so more weight typically means more tail-heavy.

    Note also that once you have all this information, you can also *calculate the moments and products of inertia* since you have all the necessary information, I=sum of{mX²}, use parallel axis theorem to move it from your fixed position reference to the CG.

    Brett

[frank mccune]

     Hello Brett:

     I was sure that you would reply with a profound answer, thanks.

     The plane that got me thinking about this idea is a Brodak profile Spitfire that has a 48” wingspan.  With an OS .35S it is so nose heavy that it tips over to the front just sitting on the runway. Lol I guess that this plane will be adorned with a bit of lead under the stab.

     I have had other planes that were also very unbalanced in the past and if I had a way to predict the potential c/g, I could have incorporated heavier/stronger parts to avoid the problem.  Also, one could lengthen the body and/or the nose etc. without adding weight.:

      In any case, thanks for the informative reply!


       Be well,

       Frank

[Dan Berry]

On our Free Flight planes a tail-heavy condition happens a lot. We add weight to the nose to balance them.
Sometimes we find a nose-heavy situation. When we do find that we add weight to the tail.
I have been using this technique on control line planes with some success.

[Trostle]

On our Free Flight planes a tail-heavy condition happens a lot. We add weight to the nose to balance them.
Sometimes we find a nose-heavy situation. When we do find that we add weight to the tail.
I have been using this technique on control line planes with some success.

Brilliant!

Keith

[Dan Berry]

Brilliant!

Keith

We are always thinking......

[Ken Culbertson]

I am with Brett on this one.  You really never know what you have till you fly it and to not do that after all the work to finish a PA is just plain weird.  I am not sure that going to the trouble prior to building will get you where you want to be.   If it is a kit or proven design you are building then following the plans with proper wood selection is going to get you close.  If it is a new design entirely then you have to consider what you can change.  Bigger/smaller stab?  Different moments?  More/less side area?

Here is my solution, take it or leave it.  I fly electric and I build the ship as light as feasible to the point of being covered with enough dope on it to seal the polyspan.  Then I go out and fly it adjusting the tail weight till it is pretty close to what I want.  At the same time I check for any "ah sh**" conditions that I can fix before finishing.  That tail weight is my finish budget. (actually, because of how the weight is distributed, the budget is higher but tell me when anybody has ever put on a lighter finish than they expected!)

I think what you want to do will work and would probably lead to an overall lighter ship if you are able to distribute weight better during building but I still don't think it will get you where you want to go.   The optimal C/G is unique to every airplane and every flier so before you can test to see if it is right, you need to know where it needs to be.   

Ken

[Ken Culbertson]

On our Free Flight planes a tail-heavy condition happens a lot. We add weight to the nose to balance them.
Sometimes we find a nose-heavy situation. When we do find that we add weight to the tail.
I have been using this technique on control line planes with some success.

[Pat Chewning]

While building the kit, you could move the motor mounts as far rearward as possible -- perhaps in conjunction with choosing a short gas tank.  I would think that this would help especially if other builder's models have historically come out too nose heavy.

The kit designer SHOULD have worked it out so that the design and materials selected will get you pretty close.  Then adjust after building.

[FLOYD CARTER]

I'm not going to offer advice.

I'm puzzled why an experienced modeler would even think to ask such a question.

Anyway, the responses so far have been adequate... and also logical.

[john e. holliday]

If I remember right my second Rat Race model had you move the forward or back to balance it close enough for finish.  It was the Midwest Rat Race.  My first Rat Racer was the Guillows kit that I learned to fly 35 size planes with.   Mr Brooks put the first flight on it and then helped me on the second flight and I been fairly successful since.

[Brett Buck]

  I was sure that you would reply with a profound answer, thanks.

  BTW, I think Paul Walker actually does what I suggested to calculate it ahead of time. That's more-or-less exactly what they do for full-scale airplanes, and satellites, too. In the case of a satellite, it is tens of thousands of lines of mass, position and inertia of every single nut/bolt/screw. We test it, and it is routinely accurate to 1/16" and a few ounces for a 10,000 lb satellite that is 15x25x10 feet with all the components stowed .

     It seems daunting to start with, but, depending on how you do it, it might be as little as maybe 50 components for a simple  airplane and a few hundred for a built-up full stunt plane.

       Brett

[Brett Buck]

I'm not going to offer advice.

I'm puzzled why an experienced modeler would even think to ask such a question.

    Unfortunately, people can sometimes be so obsessed with the Almighty Ounce, that they give up before they even try. I wasn't kidding, people just hang the airplane up rather than even try to fly it with the extra weight.

      An example case - a local guy build a Barnstormer, and though a series of misadventures with paint, it wound up *severely tailheavy*. To the point that to get to a decent CG, it required *6 ounces*  in the nose. Grant you, that's a lot, but because it was so heavy, he chose to fly it without. Of course, it was a disaster and uncontrollable. He managed to get it back on the ground in one piece and was going to hang it up. I convinced him to balance it correctly and fly, he did it, it flew pretty well, and even with the 6 ounces, it wasn't ridiculously heavy. But - he took out all the weight and hung it on his wall, because "it was too heavy". I saw it fly, it was perfectly fine and flew better than a lot of OTS airplanes, but no, the scale said something else, so that was it.

     It definitely happens, despite all of these "too heavy" planes winning contest after contest.

     A variant on this is trying to fix a CG problem (usually tail-heavy) with trim adjustments. There is no trim adjustment that will fix a CG problem aside from fixing the CG, you can narrow the handle spacing or something like that, but then your airplane is both unstable and insensitive.

    Brett

[Dave Hull]

Sometimes we will have a new plane show up at the field that is "too heavy." Often, these are really beautiful. As you can imagine, perhaps there was more attention to firmer wood to make it more durable. More paint to make it look great. More trim to further improve the looks. I generally tell them, after they fly it and can't seem to accept it at that weight, that there is usually enough room in my truck that I could take it home and eliminate their on-going angst. While they may be somewhat disappointed in the weight, I have yet to take one of those beauties home---and they seem to keep flying them, often with some dohickies installed to help handle the higher wing loading....

If you want some better insight into air vehicle and satellite mass properties analysis, check out the Society of Allied Weight Engineers (SAWE) website. If you want to read about aircraft that have had really interesting mass props issues, take a look at:  A-12 (cancelled), V-22 (battles between contractor(s) and NAVAIR over weight, but ultimately successful), A-4 (very, very successful weight management), F-111, Mig-25 (successful).  I have yet to find a good source on the Vigilante, but I strongly suspect a very interesting mass props history there.

The Divot

[Brett Buck]

If you want some better insight into air vehicle and satellite mass properties analysis, check out the Society of Allied Weight Engineers (SAWE) website. If you want to read about aircraft that have had really interesting mass props issues, take a look at:  A-12 (cancelled), V-22 (battles between contractor(s) and NAVAIR over weight, but ultimately successful), A-4 (very, very successful weight management), F-111, Mig-25 (successful).  I have yet to find a good source on the Vigilante, but I strongly suspect a very interesting mass props history there.

   My limited interactions with the Weight and Power Control board have resulted in +70 lbs in one case, and something like +300 in another. I was also present, but not responsible for, the day our item went from a projected 5000 lbs to 8500 lbs in one afternoon - a development that resulted in an entirely new program to be spun up to lift it!

    Brett

[RC Storick]

But, yes, you can design it, estimate or weigh all the parts, and the, knowing where each part goes,  calculate the projected CG

    Xcg = sum of( Xpart*Mpart)/sum of(Mpart)

In my limited experience with math of this caliber I see no spot for the cord of the wing and the amount of paint added to it.

[Brett Buck]

In my limited experience with math of this caliber I see no spot for the cord of the wing and the amount of paint added to it.

   

      I would note, if it is not clear, that each "part" can be defined the way it makes sense. You *could* do it with large assemblies like the wing, the tail, the fuselage, but, figure you have 40 wing ribs, that's 40 entries, each with a weight and a position (in 3 dimensions), you have 4 engine screws, that's 4 more, you have 4 blind nuts, that's 4 more, etc. Large parts would be subdivided into a bunch of sections, etc. That's how your summation gets hundreds of elements.
   
     You break it down into as many pieces as necessary to get the accuracy you want.  For instance, for the finish, you more-or-less know how many ounces the finish will be, say, 10 ounces when you consider everything from the tissue on out, whatever you think it is. You can pretty easily calculate the surface area. Divide it out, and you have the areal density in ounces/square inch. Then break the surface up into as many pieces as you want, say, 4 square inches, use the areal density to calculate the weight, determine the distance from the reference position to the center of the area , and you have the mass and position of each piece. Do that for each piece, and you have all the elements of the summation.

   Example with made up, but reasonable, numbers. Say the total paint area is about 1800 square inches (600 for the top of the wing, 600 for the bottom, 150 for the top of the stab, 150 for the bottom, etc). Figure that including the tissue or carbon, it's about 10 ounces total. That means it weighs about 0.0056 ounces/square inch. Divide the entire surface into 5 square inch chunks, that's .0278 ounces for each chunk, and there are 360 of them, each with a center position from some reference. Thats 360 separate entries, and 360 elements of X*m in your summation.

  Same thing for any large component, the fuselage sides might be 48" long and 6 " high, I might take that in 8 6"x6" long pieces. Figure 5 lbs/cu ft, 6"x6"x1/8" is 0.0026 cubic feet, so each section weighs ~.21 ounces, there are 8 of them, so each fuse side weighs 1.6ish ounces. Each peice weighs about the same but has a different position, sum them all up, get the CG.

      Depending on how you do it, there may be 100 total items, or 1000, but the basic idea is the same.   The sum of all the masses it the total mass, that's the denominator, the mass*position products all added together is the numerator, divide one by the other and the result is a distance from the "reference" position to the CG.

    For purposes of computing the inertia, you can probably reasonably ignore the inertia about the center of each "chunk" and assume that each part is a point mass.

   Brett

   

[Ken Culbertson]

Now you have me thinking about how to put this easily into a formula that a computer could use.  I am not what you could call a "programmer" in today's sense but I have done some rather complicated work with route and production scheduling integrated with purchasing and labor that required me to develop and use programs.  This was in the late 70's when computers were not on everybody's wrist and there were no utilities/apps you could go out and buy.  With any popular language (I prefer the "Basics" simply because you can read the code like an algebraic expression instead of some geek jumbo.

You could subdivide the top view into a grid like already suggested and assign 2 values to each grid cell: weight and distance to the "x" axis.   For the sake of this exercise we are looking for the place on the "Y" axis where the sum of the effective weight of the cells above and below the "X" axis net to zero. All of this is well within the capabilities of Excel VBA or VB or a host of others that can "talk" to Excel and do simple calculus.

Keep in mind that the "X" axis is not the C/G and also keep in mind that we are not trying to find the center of gravity for the ship, only the balance point along the fuselage with the wings level.  That keeps the math simple and parallels how it is done in practice.  Issues like mounting bolts and blind nuts are one unit (bolt & Nut) x 2 for the aft and same for the forward. Hinges, 1 unit x # hinges.

It might be possible to do the same thing with a grid based graphics program like "Paint" and use pixel colors for weight.  Probably too much but there might be some graphics programmer out there that would be able to pull that one off.

I am totally guessing here but I would suspect that a grid cell size over 1/2" will not be any better that a sophisticated guess, I would suggest 1/8".  You need to be able to have one cell be a rib and the nest one over be thin air.

As a side note, I would express the weight value as a thickness of a material type.
That way you could set up a reference table and manipulate the weight and thickness of the wood and the coats of paint.

I suspect that writing a system like this would take a lot of time.  The core calculations once the grid is built are simple and could be done overnight.  Even the POC that is sitting in your closet that got replaced by the soon to be POC on your desk can manipulate a 10,000 x 10,000 cell grid in seconds, *but* making entering the data it needs to be any better than a SWAG is another issue.

Maybe next year after the house is finished and I have my classic, PA and profile on the wall I will give this a shot.

However, I still contend that 4@ 15 second trim flights are an easier route.

Ken
 

[Brett Buck]

Now you have me thinking about how to put this easily into a formula that a computer could use.  I am not what you could call a "programmer" in today's sense but I have done some rather complicated work with route and production scheduling integrated with purchasing and labor that required me to develop and use programs.  This was in the late 70's when computers were not on everybody's wrist and there were no utilities/apps you could go out and buy.  With any popular language (I prefer the "Basics" simply because you can read the code like an algebraic expression instead of some geek jumbo.

You could subdivide the top view into a grid like already suggested and assign 2 values to each grid cell: weight and distance to the "x" axis.   For the sake of this exercise we are looking for the place on the "Y" axis where the sum of the effective weight of the cells above and below the "X" axis net to zero. All of this is well within the capabilities of Excel VBA or VB or a host of others that can "talk" to Excel and do simple calculus.

   This is exactly the sort of thing Excel was made for, it hardly takes any real knowledge of programming. That's a severe defect for most uses, but in this case (doing operations on long columns of numbers) it is ideally suited.  Afterward it is merely data entry, manual or automatic.

   The *point* of doing it, of course, is to be able to change the design or the arrangement of the parts (like engines and batteries) to make sure you can get the CG in the desired location, or at least in the right range, before you build the whole airplane and find you have to add weight somewhere.

     Of course, lighter is not always better, but if you are way off on the CG, you are compelled to add weight whether it helps or not.

    Brett

[RC Storick]

This formula gives a linear balance but I always thought that the balance point was determined by the cord of the wing. 27-30% etc.. Also one extra coat of paint moves the balance point back.

[Perry Rose]

It's been my experience building any kit ever put on the market that the balance point is marked on the plans. After building and finishing and just before first flight balance the model at the spot located on the plans. End of problem.

[Brett Buck]

It's been my experience building any kit ever put on the market that the balance point is marked on the plans. After building and finishing and just before first flight balance the model at the spot located on the plans. End of problem.

 Frank's initial question was how to you figure it out where it will balance before it is built (presumably to change something to make it come out right with no extra weight), and there is really one way to do that, some variant on the mass and distance calculation.   

   Where it *should* be balanced is another (interesting) question. Might beware of some of the "recommended" CGs, some of them (like the Flite Streak) are radically too far aft for stunt.

     Brett

[Dave Hull]

Having done this for real money while working on a fighter jet.....

1. There are standalone programs already out there you could look at either using, or reviewing to see how they do it. These are for proposal estimating and initial design studies. I think Ken would be surprised at how close an estimate can be achieved by someone who is familiar with the type of product being studied (ie. a PA stunter) who used even a coarse estimating method, as long as it was complete. I agree that Excel is an excellent way to do this. Typically this is merged with the parts list.

2. The industry standard is to do the precise calculations using solid modeling (CAD) which has the mass props calculations embedded in it.

3. You need both methods or your mass properties management plan (required by government contracts) will fail. That's because you have to start with weight estimates, allocations, even educated guesses and mature those while the CAD details are created. These might not meet in the middle until pretty late in the project. Constant updates and model reconciliation are required so that mitigation can be applied (ie. spend money to get the weight down, or to move the CG back to the design point, or....)

4. Part of the confusion here appears to be because people aren't getting the overall process. The aero guys will refine the aerobody shapes and using CFD will come up with stability numbers, etc. That helps them define where they want the CG. (They do this also for inertias, etc.)  The designer and mass props guys keep working hard to make the aerostructure plus the systems come out with the CG in the desired place. So there are two sets of calcs happening simultaneously:  A design goal (from aero), and a current estimate (from the mechanical designers and components people). These have to converge by the flight test.

5. Just use centroids and point masses. The first estimate might only treat a wing panel as one item--but it takes skill and prior experience for this to be close. That's why SAWE guys compare notes. And certainly guys in big aerospace companies do. That first estimate gets everyone thinking about what the real issues are going to be

6. Paint is no problem at all. You can skin a CAD model and get it, but that's more work than you need. The CAD will give you the centroid of any specificed surface along with the area. Then get your moment arm from datum. Pick your primer thickness (already specified on government contracts), topcoat thickness (ditto), and with a bit of testing you can ensure you have the correct densities. What is actually harder is that the more complex the shape (ie. not just a big flat panel) the heavier the paint goes on around the complex features. Of course, that rule certainly applies to models as well.

7. It is common design practice to put the origin of the coordinate system way out in front of the plane. This is to ensure that the nose of the plane never grows past that resulting in some negative signs in the calcs which have a tendency to screw up some people's math. Lesson learned, just don't go there. After the design is done and fielded, the company may relate all maintenance to a firewall or radar bulkhead datum as appropriate to make it practical for the maintainers. Same deal with a satellite bus. There are known easy ways to do things--and then ways that are invented by guys who got stuck on the project and never did any mass props in their life. Oops. The weight estimate is off by 30% and we just found out after two years of design work....?

For the skeptics out there, it is expected that a serious mass props team can keep tabs on things down to a percentage point or so. I suspect that any launch customer for a new airliner gets a garenteed weight--if the structure/systems are too heavy his payload has to go down. So why would he buy it?  So mass props are watched very, very carefully. In Brett's example, a certain booster system only has some much go. If your payload is too heavy, you won't make the design orbit. Tough to get a tow up there....

Also remember that if the machined fittings all go to the high side, the error from that could exceed a percent. But this is also a statistical analysis, so you can apply Gaussian functions or skew functions as your judgment and prior experience guides you. You use error bars. You watch as the data converges as the thing comes together. Same deal with stunt. You weighed your stab after the glue dried?

You want to design a plane? Go collect all--not some, but all--the hardware and weigh it to the nearest gram. Sketch your outline. Put point masses of your components where they belong. Run the numbers. Keep moving, fixing and updating. A lot of work? Sure, but that is actual design, not draw-n-hope. For a hobby, draw-n-hope is fine; the designs are mostly similar anyway. For a 10 year project that is costing us all taxpayer dollars? Dude, do the work and get it right!

Dave

[Kim Doherty]

Frank,

If you are designing something where you are going "off the board for a thousand" then follow Brett's advice. If you are just wondering how to ensure your next standard stunter will trim out then do the following:

Build all of the major components, do not do the cowl but include the block in the list below. Cover them and dope them (at least the initial clear coats) or if using money cote prepare the mating surfaces so you can still glue everything together. Build the nose of the model but do not carve to shape or finish it in any way. Do not install the firewall at this point. (you will add the firewall and any engine mounting hardware to the list below.) If an IC model make the motor mounts go all the way from behind the leading edge out to the end of the nose.

Mark the position of the leading and trailing edge of the wing and stab but do not cut out. You may wish to modify them. Do not close off the rear or front of the fuselage, you may wish to modify them. Do not install hard mounts for anything as you may wish to modify them. We are only trying to assess the effect of the position of the various masses on the desired CofG. Note that properly laid out, you should be able to achieve the complete usable CofG range by just moving a battery no more than 1/2 of an inch. not so easy with a fuel tank but doable) To do this of course requires that the model balance on the design CofG. If you use up the ability to reposition "components" just to achieve balance AFTER you have finished the model you will not be able to easily fine tune the balance for best trim. You will have run out of things to move.

Gather ALL (and I do mean ALL of you hardware, motor/engine wiring fuel tubing, etc. Leave NOTHING OUT !!

Assemble the basic structure with tape and pins. The wing only needs to have the designed CofG aligned with the same spot on the fuselage. I.E. you do not have to slide the wing into place, just tape or rubber band the wing or stab/elevator flat to the fuselage side. Tape each piece of hardware, battery, wheels, engine, tank, canopy, in its respective place. Move whatever you need to move to make the model balance just a touch nose heavy. (the model will just slowly lower the nose when held at the CofG on you fingers.) Two reasons we want to be nose heavy: The finish will move the CofG rearward, and you have at least a two to one ratio of needed weight to balance over having a tail heavy model. Don't forget the firewall.

Make sure you have room to install each component with room to access it and install/remove it (battery?). When you are happy, mark everything and make measurements so you can recreate the layout. Take it all apart and finish the model. At WORST you should be within half an ounce of being spot on the designed CofG.

Do not be afraid to move the wing cut out forward a bit or move the battery into the leading edge space etc. THE MODEL MUST BALANCE!!!

I do this with every model I make. I have never needed the full half ounce in the tail.

With apologies for adding to this a couple of times.

Kim.

[Mark Mc]

This is what I’ve done on profiles.  I build the wing and cover it ready to install.  Cut and build the tail surfaces, covering them (since I use only Monokote, can’t use dope/paint in my household) ready to fly.  Build the fuselage up and cover, ready to fly.  I make sure to bring the engine bearers further back in case I need to move the engine back for balance.  Then I put a large rod on the workbench and set the fuselage across it.  Then I tape the tail surfaces flat on the rear of the fuselage where they would be glued in place when assembled.  Then set the wing across the fuselage where it would be when glued in.  Stack on any additional parts you expect to put on the plane.  Set the fuel tank and engine in place.  Then roll the rod back and forth until I find where the whole mess balances on the rod.  That is approximately where my balance point will come out when assembled.  If necessary, I can cut back the engine well to balance.  I have yet to have a nose heavy plane above 1/2A size.

Mark