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Touring Motor Gliders Association (TMGA)

Weight and balance


edwalker

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I’m in the process of preparing for my Commercial and CFIG checkrides, and I realized that I had to be able to explain the Phoenix weight and balance diagram to the DPE. The weighing form that Martin uses seemed unfamiliar, but I think I’ve figured out how to translate it into a presentation more commonly understood by pilots in the USA. Computing the weight is straightforward – what is unusual is the CG location format and how to compute it.

 

Most of us were taught the “weight x arm = moment” approach to balance, and so we are looking for a chart or table that expresses the various weights as occurring at stations, usually expressed as inches from a datum.  What is initially puzzling is that there is no indicated datum and no stations from which to calculate the moments.

 

Martin chose to use a system that appears to be more common in eastern Europe and in transport aircraft, expressing the CG location as % Mean Aerodynamic Chord (MAC). The MAC is the average chord for a wing. For a perfectly rectangular wing it is the same anywhere it is measured across the span, but for a tapered wing it has a particular, mathematically-defined location. For now, let’s skip that calculation since we don’t need more complexity. Just accept that it is a chord length that best represents the overall wing’s average chord.

 

As you probably suspect, % MAC as a CG location is a percentage of that length. The leading edge of the MAC (LEMAC) is used as a reference point. So a CG which is at 20% MAC is about a fifth of the way along the MAC behind the LEMAC. Now we can specify a CG range as a % MAC range. For the Phoenix the weight diagram says that the permissible range of the CG is 30% +/- 2%. That means our permissible CG range is from 28% to 32% MAC. If the computed CG lies within that range we are good to go.

 

So, to compute the % MAC for our aircraft we need to know the length of the MAC and where the LEMAC is with respect to the datum. Here’s where things get complicated. It is not initially clear what is the precise location of the datum, and I also found some of the abbreviations used in the weighing diagram to be unfamiliar, despite a detailed internet search. Nevertheless, I believe I have figured out what each one is. I will use my N42EW weighing diagram as an example- it might be helpful to get your aircraft weighing diagram and follow along (although there may be small differences).

 

Notice that the aircraft is positioned so that the longitudinal axis is parallel to the floor, situated on 3 scales with the wheel axles as the horizontal measurement reference points. Measurement “c” (540 mm or 21.26 in) is the vertical distance above the scale to the bottom of a properly inflated tailwheel tire.

 

Next look at “a” (69 mm or 2.72 inches). I believe that this is the distance from the datum to the wing root leading edge. The datum for the Phoenix appears to be the vertical plane orthogonal to the longitudinal axis which includes the two main wheel axles. If you look at the planform view of the phoenix earlier in the manual you’ll see that not only is the wing tapered, but it is initially swept forward and then back, so this root chord is not the location of the LEMAC (we’ll get to that in a minute). Finally, “b” is the distance from the leading edge of the root chord to the tailwheel axle, making a+b the arm for the tail weight.

 

So, now we can start doing some calculations. This is the formula from the FAA Weight and Balance Handbook:

 

     Eq 1                 CG % MAC = (distance aft of LEMAC / MAC ) * 100

 

Before we can use this formula, however, we must translate the non-standard abbreviations. As far as I can tell “bsat” is the abbreviation for MAC, “Xbsat” is the offset distance from datum to the LEMAC, and “xT” is the CG position.

 

First, let’s compute the CG position.

 

xT (aircraft CG) = Tail weight x (a+b)/m (aircraft empty weight)

xT (aircraft CG) = 22 kg x (69mm + 3894 mm)/326.9 kg

xT (aircraft CG) = 266.1 mm (10.48 in)

 

Next, we use the CG position (xT) to compute the % MAC using Eq 1. Before we can do that, however, we need to understand one more item. Because the wing is tapered and swept the LEMAC likely has an offset from the root chord. That arm is expressed at Xbsat. So the term “distance aft of LEMAC” is actually (xT- a – Xbsat). Note that the LEMAC is actually forward of the root (negative number):

 

CG % MAC = ((266.1 mm – 69mm – (-65mm)) /930 mm ) *100

CG % MAC = 28.2 % MAC

 

This might be easier to appreciate if converted to inches:

 

 CG % MAC = ((10.47 in – 2.72 in – (-2.56 in))/36.6 in) * 100

 CG % MAC = 28.2 % MAC

 

The permissible CG range is 30% +/- 2% ( i.e., 28 – 32 % MAC), so the plane is near the forward CG. One check on this is to use the W&B sheet for N42EW recomputed after the avionics installation. Plugging in the recomputed post-avionics CG (10.55 in) into the above, we can see that the aircraft remains within the CG limits:

 

 CG % MAC = ((10.55 – 2.71 – (-2.56))/36.6 * 10

CG % MAC = 28.4 % MAC

 

To bring this back to the more common way we do things, the permissible CG range in inches must then be from 28% MAC (10.39 inches) to 32% MAC (11.86 inches).

              

Note that the AOI does not have a traditional W&B calculation table or graph. I must assume that Martin has carefully considered the CG location, fuel burn and baggage with respect to the CG location so that all that must be measured is pilot and passenger weight. If pilot and passenger weight is above the minimum and below the maximum we’re good to go.

 

Another interesting thought is that it helps me understand why Jim once mentioned about how much better the plane feels with 30 lbs of baggage. This obviously shifts the CG aft closer to the center of the CG range, which takes some of the down-force work off the tail, improving wing efficiency.

 

Finally, it’s interesting to see how narrow the CG limits are (10.39 to 11.86). This is a tight design where we get a remarkable range of pilot, passenger and baggage weights controlled within a very narrow CG range.

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Ed,

Nice to see you prepping to the max for your commercial test.  Yes, the CG factors involved with the Phoenix are complicated, partly due to the differences in European Wt & Bal vs US style as you have pointed out,  and also airplane vs glider methods.

I have gone over your text and calculations which look good except for one thing.  The 30% +/_ 2% is for the empty CG of the plane, not the loaded CG.  Before the Phoenix can be shipped, the very controlled Wt and Bal is conducted by an outside engineering firm which certifies that it passes to the LAA of the Czech Republic.  I have been present during a couple of these inspections and understand the conditions and procedures.

We have weighed several planes in the US following delivery from Czech to verify the factory document.  Then the same planes have been weighed following the avionics installation in order to follow the same procedures used by the factory to verify that what we are changing is within the allowed parameters.  In all cases, the CG of the Phoenix is only slightly changed towards the rear with the addition of the avionics in the US, which is a good thing considering the forward CG of all of the planes.  We have also weighed two planes following damage repairs to verify that the CG was still within the +/_ 2% range, which they were.

You may notice if you puzzle it out, that the datum used by Seb Com for their revised Wt and Bal is the leading edge of the wing.

For airplanes, we are taught to go by the manufacturer's tables for CG calculations to insure that we are loaded within the range.  Airplanes have a huge capacity to be loaded outside the range due to rear seats, rear baggage compartments, multiple fuel tanks, etc.  A glider, not so much.  Front seat, rear seat, and some small baggage compartment are all that can be changed.  The most significant load factor is front seat vs rear seat, and especially a lightweight solo pilot who may require additional nose or seat weights to bring that person up to the (typical) 144 lb minimum load.  The same factor must be remembered for large people in a tandem seat glider; they must go in the rear!

Which brings us to maximum seat loads.  These are limited due to the load factor the seat is able to withstand when the plane is subjected to the max loading (+4G for the Phoenix).  Many glider operations will exceed the max load of the seat in order to give a glider ride by being careful that no aerobatic maneuvers are performed which may overload the seat and not flying in turbulence which could do the same.  After all, limiting paying customers in the US to less than 242 lbs can be difficult.  

Using the empty Wt and Bal, one then refers to the placards in the glider and in the AOI or POH to insure compliance.  Isn't this what everyone does on their glider checkrides?  You point out the various placards to the DPE and explain how you are in compliance with the CG.  I have never had a DPE question an applicant beyond what was shown to them on the placards.  Or ask to see the Wt and Bal in the POH during the preflight, because the POH is usually not in the plane, nor is it required to be in the plane.  I have had DPEs take the applicant to task for pulling out a Wt and Bal chart and not being able to fully explain it however.  If this happens to you, Ed, you can be sure that your well thought out CG process will keep you out of any trouble.

The exception to the use of placards only in gliders is using tables when water ballast is used in the wings and tail, which is super critical, to say the least.  Normally this is covered during the oral exam because usually the glider used for a checkride is not capable of water ballast.

DPE oral exam trick question:  "If we have to be careful not to exceed aft cg, why on earth do some gliders come with tail ballast tanks that can be loaded up with water?"

The Phoenix is not your usual glider, it really is more similar to an airplane.  And the CG becomes a bit more complicated.  But it is certified as a  glider, and as such, following the CG route of other gliders (placards) works for the DPE, and in the real world.  Run this by your CFIG, whose job it is to know what your DPE expects and tests for.

So, taking your Phoenix as an example Ed, we see that the empty weight is 748 lbs, and the MTOW is 1320 lbs.  As long as you do not exceed the MTOW, adhere to the max and min seat weights, don't load the baggage compartments with more than 110lbs, you will be within the proper CG range for the Phoenix.  Which is exactly what you said in your summary.

cheers,

Jim

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Hi, Jim -

Thanks for taking the time to review this and making some editorial comments. I wish you could write a column every month, slowly dispensing your accumulated wisdom on all things Phoenix. I tend to remember things better when I have to teach them, so writing this out was an important part of my learning, and I figured it might as well benefit the rest of the group.

Blue skies *, 

Ed

 

* with appropriately placed CU

 

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Just one more thing.... Jim's comments about the difference between an empty weight CG and an operating CG are important. I couldn't find any information about the operating CG range in the AOI, but I remembered this evening that there is a section in the maintenance manual that lists the operating CG range as 20-35% MAC. So the practical flying CG range is much larger than I originally thought.

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  • Registered

I'm pleased to see this discussion, because I had no idea how to determine the CG. I got interested in doing it when Dynon added the capability to Skyview, and because I notice a definite difference in the thermalling trim setting with full tanks and a beefy passenger, compared to just me and 8 gallons in the plane.

What's the optimum CG for soaring? Can you tell when you have the optimum CG tell by how much you have to pull back the trim lever from, say, 60 knot cruise to 48 knot thermalling?

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Let me add some quick and dirty observations from aeronautical engineering that might help explain some things:

Aero engineers do all of their computations related to CG as % MAC.  It's easy to understand as one is trying to represent the lift of the wing as a single vector and there are some computations to get to this representation.  In the US the flight manuals are converted to make it easy to add components as weight-arms from an arbitrary datum from which measurements are easy.  So I think it is kind of cool that the designer expresses them based on the real limits.  That information is shielded in our flight manuals.

Generally, weight and balance limits have dozens of things that impact them and engineers need to do calculations for each condition to find out which one is the constraint.  I will summarize typical constraints:

aft limit:  static stability limit, stall/spin recovery, nose tipping

fwd limit:  nose gear unstick, nose tipping, control authority limits

max gross weight: maximum load computations, Va computations, landing gear or seat crush limits for hard landings, minimum climb rates, stall speed limits, ...

When the CG moves aft the performance can be improved (less trim drag), but that is hard to sense.  Actually, the flying qualities (perceived harmony of the controls) tend to improve to a certain point and then start to degrade, depending upon some dynamical characteristics like the phugoid and short period mode longitudinally.  CG limits don't impact the lateral/directional flying qualities that much.

During flight testing they usually test across the CG and weight envelope and verify that all flying qualities and performance parameters are achieved.  It is not uncommon to make adjustments in the configuration or the limits to resolve problems that were hard to compute in advance.  One of my professors took us to the airfield and we walked around and saw all of the fixes that were added to configurations probably in flight test.

In most airplanes, you must do the calculation for forward and aft limits as the fuel is burned.  Most CG software will show the CH position at the initial fuel loading and then at zero fuel loading.  I'd have to see what is written, but I doubt that the CG limits presented automatically take into account margins for fuel burn.  However, it is not uncommon to place the fuel tanks in such a position so that fuel burn minimally impacts the movement of the CG.

As JIm wrote, gliders will often have Weight/CG limits expressed as weight limits in the seats since there are so few other variables.  However, that doesn't help much when equipment is changed and things like water ballast or fuel are added back in.

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For me, 180 lb pilot, 7 gallons of fuel (or less) and 30 pounds of baggage in the far aft baggage compartment is best.  This results in a nice aft cg, but easily within the range.  Probably more important are gap seals on the elevator which prevents the air spoilage from stalling the elevator as slow speed.  Both of these combined allow a 40kt thermal speed.

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  • 10 months later...

I’m going with these excellent suggestions, 30 lbs in aft baggage compartment immediately.  Losing 30 lbs to get to Jim’s 180 will take some time.....

I’m working on a spreadsheet now for the w&b calcs.

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  • 4 years later...

Hi Ed.

We are just about to go through the weight and balance on my aircraft and I was also trying to understand the calculations, so thanks for your very detailed analysis.

You might be interested to know that the factory (Pure Flight) have a spreadsheet for calculating the CoG. It is not my place to disctrubute this but I imagine you can get it from the factory.

Just to be sure, can you please confirm my understanding of the following 3 points:

- Xbsat, which is fixed at -65mm is the distance from the aerodynamic, average leading edge to the actual leading edge at the root?

- You said the datum is the wheel axles, but the diagram shows all measurements from the leading edge. I would say the drawing datum is the leqaading edge. When you say the datum is the axle plane, are you referring to the datum for the moment arm calculations? i.e. is the drawing datum different to the calculation datum?

- There is no talk about the different wing tips and which one to measure. Does it matter? Should we measure both? It is easier to use the short tips in the hangar when measuring, but I always fly with the longs. I wonder if the MAC moves when the tips are changed?

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Hi, Barry -

Apologies for the delay - I just saw this today. 

The day-to-day W&B of a Phoenix is pretty easy and doesn’t require much in the way of computation, so this diagram was always a mystery I reserved for my A&P colleagues. Prior to my CFIG exam I remember looking at it, realizing that the examiner was likely going to ask me about it, and I was finally required to figure out what it meant. Looking back, I think I eventually satisfied myself that I had the basic idea of the %MAC concept, and I shared that info to give others the general idea. I wrote it out mostly to convince myself I could understand it by explaining it. One of the problems, however, was the absence of specific definitions of the variables. Despite the fact that %MAC is widely used outside general aviation, I had never seen these labels, and repeated efforts with Mr. Google didn't help.

Over the years I've learned that there are two types of precision in aviation: 1) good enough knowledge to explain to a flight examiner that you have a general idea of what's going on, and 2) getting to the only right answer because your life depends on it. I was clearly in category 1 when I did this, but, since you are doing an initial weight and balance for your “new” phoenix you're in category 2. Thankfully the factory has the resources to help you out here. I tried to figure this out again to help you, but as I re-acquired the same throbbing headache I had when I first wrote this, I thought it was best to leave it to the experts.  :)

Glad to see that you're far enough along with the repair that you need this info. That factory spreadsheet will be a real help, and if you get a copy it would be good to share. Hope things continue to go well!

 

Ed U15/05

 

 


 

 

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