Weight and balance graph scale

8 Answers

1. 
   

   
   

   Andy Neumann on Aug 02, 2011

   To your first question: Are there diagonal moment lines on the chart too?  The only reason I can think of off the top of my head is that to make the diagonal moment lines be straight, they have to expand the scale of the x-axis at the top.  Why the engineers can’t live with curving moment lines–I have no idea. To your second question: good question.  I would think the line would be bent too.  The reality is that when you burn fuel, the line connecting the two points (takeoff and landing) will not be perfectly linear.  The shape of the line would depend on the shape of the fuel tank, the angle of attack in level flight, etc.  So your straight line from takeoff to landing is at best a guess anyway.  I think the engineers just put enough safety factor in there to satisfy the certification requirements and let the pilots use a straight line.  This is definitely a question for John Collins! 

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2. 
   

   
   

   Etienne74 on Aug 02, 2011

   The graph looks identical to the one on the last page (page9) of this pdf:
   http://www.fliegen.ch/cms/pdf/afm/Archer_3/ArcherIIISection6.pdf
   So the edges are the envelop, no other diagonal lines as momentum.
    

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3. 
   

   
   

   Andy Neumann on Aug 03, 2011

   Ok, I think I might know why, but this is only a guess and I’m putting it out there so that some other insightful person can elighten us both. 
   Imagine two scenarios.  One airplane is lightly loaded and its take-off weight and C.G. is 1500 lbs and 85 in.  The second airplane is more heavily loaded and it’s take-off weight is 2400 lbs and 92 in.  Now if we were to add one more 150 lb passenger to each of these airplanes, in the aft seat, you would see a change in the weight and C.G.  Without calculating it out yet, I ask you if you can imagine which airplane’s C.G. will change more?  Will the 1500 lb airplane’s C.G. be more affected by the addition of 150 more lbs or will the 2400 lb airplane be more affected?  Since the C.G. location is determined by a “weighted average” of all the different weights that make up the airplane and its load, the more an individual item weighs as a percentage of the total, the more it will affect the C.G.  So, the 1500 lb airplane’s C.G. should change more when we add the passenger than when we add the same to the 2400 lb airplane.
   If you do the calculation, you see that C.G. moves aft about twice as far (2.88 inches more) in the case of the 1500 lb airplane (vs. 1.45 inches for the 2400 lb airplane). 
   Now what does this look like on the chart?  Go ahead and plot the two example airplanes both before and after you add the passenger.  (You should have four points, with lines connecting the two close ones for each airplane.)  What you will find is that even though the C.G. is moving different amounts in each case, the angle and length of the line connecting the two points is the same for both cases.  Pretty neat huh? 
   And here’s why that’s useful.  You can now use that same angle and length of line anytime you add a 150 lb passenger in the aft seat, no matter what the load or C.G. is already on the airplane.  There are companies that make little weight and balance “stencils” that have all the different angles and lengths already on them.  When you want to calculate your weight and balance, you just lay the stencil on the chart and trace lines for each item, starting at the basic empty weight and C.G.  You never have to run a single calculation!  This would not work if the envelope had regular x and y axes for weight and C.G. 
   Thanks for making me think!  I hope someone can explain this better than I did. 

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4. 
   

   
   

   John D. Collins on Aug 03, 2011

   Etienne,

    

   It appears from the referenced W&B diagram that you referenced in your second post, that the layout of the diagram is based on a X axis of moment, but then labeled with CG. The vertical Y axis is weight.  It could have been drawn with the X axis as CG in inches, then the curves would not be present.  Normally when a CG diagram is laid out with the X axis as moment, one can do the W&B calculations for the individual moments and add all of them together to plot the total moment verses the weight.  In the example you referenced, there is no moment shown on the X axis, so one needs to first calculate the total moment, then calculate the CG location for that weight by dividing the total moment by the total weight.  This sort of defeats some of the purpose of the layout of the diagram.

   I am not sure of the specific type that you are referring to with the type P28T, but the closest I could find in the TCDS (Type Certificate Data Sheet) is the PA28-201T Dakota.  The TCDS contains the FAA approved data for each model of aircraft including the CG envelope.  The CG envelope for the PA28-201T is as follows: at 2900 pounds, the aft and forward CG limits are 90 and 86 inches. At 2240 pounds and lower, the aft and forward CG limits are 90 and 78 inches.  In between these values, the forward CG changes and is a straight line between the two weights.  If you plot them on a moment scale, the forward CG limit will result in a curved line.  However, if the moment at full fuel is plotted at full fuel, fuel at destination, and fuel at exhaustion, they will form a straight line if the diagram X axis is also in moment, regardless if it is labeled as such or not. If the X axis was the CG  in a linear fashion, then the fuel at the three points plotted as a CG would form a curved line.  So the layout of the diagram has the advantage of being able to use a straight line to connect the various fuel weights.

    

    

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5. 
   

   
   

   Wes Beard on Aug 03, 2011

   Andy, you are absolutely correct!  I didn’t make the connection till I read your post but know that it is correct.  Some transport category aircraft in the corporate world have Weight and Balance plotters that have different slopes for the different moments (weight at different parts of the airplane) that can be placed on the aircraft.  I found them difficult at first but after using them just a little bit really liked them.
   Each weight and balance plotter is designed specifically for each aircraft serial number and the plotter has to be updated every time the aircraft get a new weight and balance.
   http://www.flyincg.com/vector.html
    

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6. 
   

   
   

   John D. Collins on Aug 04, 2011

   I don’t know if I can explain it better than Andy, but I will offer a different view on the same subject.  As explained in my earlier post, the graph’s X axis is the moment.  Moment is a weight times a distance from the datum. Restating the earlier observation from Etienne, the Y axis is the weight.  When you draw the envelope of the CG limits, which are a moment arm distance, on a moment scale (weight times distance), anytime the moment arm distance remains constant, the line will be a straight line and directly proportional to the weight of the item.  That works for the rear CG limit and the forward CG limit below a specified weight.  It also is a straight line at the constant maximum gross weight.  The only portion of the CG limit that won’t be a straight line is where the CG limit changes with weight, which is the case on the forward portion of the CG limit between the maximum gross weight and the point where the forward CG remains constant.
    
   So anytime the distance of the moment arm is a constant, as it is for the front seat passengers and pilot, rear seat passengers, the baggage, the oil and the fuel, then any changes in the moment values are directly proportional to the weight of the item since the moment arm remains constant.  This is the theory that is used by the plotters that help the pilot quickly do a weight and balance, since all the plotted items are a straight line and at the same CG location and therefore the same slope.
    
   With movable seats, the moment arm for the pilot and passengers will not strictly be a constant, but the difference will often not materially affect the result, since the distance between the CG and the seat locations is often relatively small, with the result that this difference is often ignored.

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7. 
   

   
   

   Andy Neumann on Aug 05, 2011

   Oh, I just realized something about your “bent line” question.  And I want to retract what I said in my initial post.  The line connecting your 3 points should NOT be bent.  What is linear is the change in total moment, but the C.G. does not change linearly as you burn fuel.  As I talked about in my second post, the C.G. changes less when the airplane is heavy and more when the airplane is light.  Again, the change in C.G. is NOT linear…it changes slowly at first and then faster as you burn fuel. 

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8. 
   

   
   

   Etienne74 on Sep 04, 2011

   Apologies for the late reply, it kept me busy though.
   The P28T I was referring to is in this case a Piper Arrow IV.
   I have read/studied your elaborate answers (highly appreciated), discussed it as well with my instructor. This came up as an answer:
   “Moment= W*A where W is Weight in pounds and A is arm in inches aft datum.
   Also, aircraft CG location equals the sum of all moments divided by the all up weight.
    
   A certain load change, e.g. adding a passenger, or using fuel, causes a CG change. So, one can say the delta CG caused by the load change is (CG2-CG1)=(M2-M1)/W .
    
   So, the delta CG caused by a certain delta moment is also a function of W. In order to plot moment changes (see POH Figure 6-13) as straight lines in the CG Range and Weight graph (POH Figure 6-15) the graph must therefore expand with increasing weight. The distance between the CG lines at 1400 lbs is approximately half the distance between the CG lines at 2750 lbs.
     
   This enables the use of a special weight and balance plotter, which basically draws straight lines with a certain slope for each specific load (passenger, bagage, fuel).
     
   Note: unfortunately the scales of Figure 6-13 and 6-15 differ from each other.”
    
   I saw the Vector demo (youtube) movie and that looks really neat and very easy to use.

   However, when I put in the three points in my graph (6-15, see my earlier link to the PDF), I really can’t get a straight line from that. Maybe when I put in more dots, I get straight segments in the line. But as I only change the fuel weight, only one factor influences the CG datum. Though when burning fuel, I guess the change in CG is becoming larger as the fuel burned as a % of total weight increases (e.g. first your burn 10gallons on 2400lbs total weight and later on 10gallons on 2200lbs as you fly).
    
   I will draw in more dots on the 6-15 graph and see the effects.

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