Why is the top left corner (Forward CG) usually cut off on a weight and balance chart?

11 Answers

1. Best Answer
   
   

   
   

   Kent Shook on Nov 23, 2010

   I can’t say for sure that this is the definitive answer – And I believe you mean the top left corner (the corner representing forward CG and heavy weight – that should be less ambiguous!). But, here goes…

   As described in some recent posts, the tail must provide a downward force to keep the airplane flying straight and level. The slanted line where the corner is cut off represents the maximum allowable down force that the tail can provide and still have enough authority left to raise the nose in the landing flare.

   Basically, at a light weight the tail is able to keep the plane in balance even with a CG that is very far forward – Think of this as a pitch-down moment provided by the CG of the aircraft being in front of the CP, and a pitch-up moment provided by the tail. If you were to keep the CG in the same place but make the airplane heavier and heavier, that pitch-down moment would increase to the point where the tail could not balance it out. Thus, as the plane is heavier, the CG needs to be closer to the CP, providing a lower pitch-down moment despite the increased weight. (Actually, the pitch-down moment would be equal all along the slanted line.)

   Using the kid on the seesaw example again – Let’s say the kid is 100 pounds, and 10 feet from the fulcrum, providing a 1000 foot-pound moment. (The kid represents the down force provided by the tail in this example.) Let’s say an alligator suddenly appears beneath Dad on the other side of the seesaw, so we need to keep Dad in the air so he doesn’t get eaten. Dad is going to be the aircraft’s CG and the fulcrum is the CP.

   If Dad is light – Say, 150 pounds – He can be farther away from the fulcrum (6 2/3 feet) and Junior will still be able to keep him up in the air. But, if Dad gets heavier (or our airplane gets heavier) – Let’s say 200 pounds – Junior (the tail) will only be able to keep him in the air if he’s 5 feet or less from the fulcrum (CG). If Dad is 250 pounds, he’ll have to be 4 feet or less from the CG, etc.

   Note that in this example, we’re talking about moments around the aircraft’s CP, not its datum plane. However, it would be possible to determine the location of the CP by using the two non-90º corners of the W&B envelope, or really any point on the slanted line, because they should all have the same moment around the CP. Geek alert! I’ve gotta go try this now. 🙂

   Hope this makes sense.

   +1 Votes 2 Votes  1 Votes

2. 
   

   
   

   Brian on Nov 25, 2010

   Definitely a geek alert for that last paragraph Kent. 🙂 Your assumption is correct though: The forward center of gravity limit is typically due to a limitation with the tail forces in exactly the way you described. However, keep in mind that it is not the only limiting factor:
    

   § 23.23   Load distribution limits.
    top
   (a) Ranges of weights and centers of gravity within which the airplane may be safely operated must be established. If a weight and center of gravity combination is allowable only within certain lateral load distribution limits that could be inadvertently exceeded, these limits must be established for the corresponding weight and center of gravity combinations.
   (b) The load distribution limits may not exceed any of the following:
   (1) The selected limits;
   (2) The limits at which the structure is proven; or
   (3) The limits at which compliance with each applicable flight requirement of this subpart is shown.
   [Doc. No. 26269, 58 FR 42156, Aug. 6, 1993]
    
   If you’re interested, I keep all of the regulations quickly accessible on my sites resources section. Go ahead to my profile and follow the link to the site and visit the resources section.
    
   Part 23 is one section few people seem to read, but it has some interesting information in my opinion. Heck, it is far more fun to read than 91 and 61!

   0 Votes 1 Votes  1 Votes

3. 
   

   
   

   The Red Baron on Nov 25, 2010

   Interesting point and answer!
   I always considered the datum as the fulcrum…or the “center of balance”…from which the CG was measured.  The CG is not necessarily the center of balance.
   Center of Pressure…that’s interesting, too!  Would that be the center of balance…or more the datum?  (By center of balance, I mean “fulcrum”)

   0 Votes 0 Votes  0 Votes

4. 
   

   
   

   Wesley Beard on Nov 25, 2010

   Qt:  The Red Baron
   Some interesting definitions:
   Datum:  The reference point where all references are measured from.  On the Cherokees it is the front of the propeller hub and on the Cessnas it is the firewall.  The actual point is irrelevant but we need to have a common reference point.
    
   For a fun exercise describe your location in the room you are sitting in?  I am currently 2ft from the south wall and 3ft from the west wall.  In this example, the SW corner becomes my reference point (datum).  I am also 6ft from the north wall and 6ft from the east wall (NE corner is reference point).  Both pinpoint my location in the room using different reference points.  The datum is just a reference point the manufacturer picked to make their calcations.  Nothing more.
    
   Center of Gravity:  The point where the moment-pounds on both sides are equal.  This means the CG is the point where both sides will balance if on a fulcrum at that point.
    
   Center of Pressure:  The point where all of the lift vectors act.  If you were to tie a string to the top of an airplane at the center of pressure.  The airplane would nose over.  It should never be center of balance as that would make the airplane display neutral static stability

   +1 Votes 1 Votes  0 Votes

5. 
   

   
   

   Brian on Nov 25, 2010

   We have been using fulcrum interchangeably with CG when that isn’t accurate, myself included. For that I am sorry.
    
   The fulcrum is merely a point of rotation, it need not be the center point or the center of balance. The CG is the center of balance, as you put it. The datum is merely a reference point, it has no value other than being used as a reference.
    
   For instance, on a Robinson R-22 helicopter, the datum isn’t even inside the aircraft. So we know it isn’t the center of balance. 🙂

   0 Votes 0 Votes  0 Votes

6. 
   

   
   

   Brian on Nov 25, 2010

   …Qt: Wesley Beard… It should never be center of balance as that would make the airplane display neutral static stability…
    
   Only for longitudinal stability; directional and lateral aren’t effected by this relationship. I think you knew that, I am adding it for the rest of the readers. 🙂

   0 Votes 0 Votes  0 Votes

7. 
   

   
   

   The Red Baron on Nov 26, 2010

   “The CG is the center of blanace, the point where both sides will balance if on a fulcrum at that point.”
   However, this does NOT mean the AIRCRAFT is in balance.  If my CG falls outside of the CG limits envelope box, my aircraft will be out of balance.  (too aft or too far forward CG)
   While I understand the concept, that’s why referring to the CG as the Center of Balance was always a bit confusing to me. 

   0 Votes 0 Votes  0 Votes

8. 
   

   
   

   Brian on Nov 28, 2010

   …Qt: The Red Baron…”If my CG falls outside of the CG limits envelope box, my aircraft will be out of balance.”…
    
   Why would you assume this? Where ever the CG is is where the center of balance is. CG, by definition, is the center of balance. In other words, if we had a really big pencil and a really strong fella he could jab that pencil point under the CG/center of balance, hoist the bird into the air, and she would sit on the tip of the pencil perfectly in balance.
    
   When you calculate your CG you have your center of balance. You are calculating the point where if the plane were hoisted up on the tip of a pencil at that point it would sit balanced. All the chart does is say if that calculated center of balance is safely within aircraft limits or not.
    

   0 Votes 0 Votes  0 Votes

9. 
   

   
   

   John Doe on Jan 27, 2011

   Interesting!  Never considered these points before.
   However if this is the case, it would seem that the line at the upper right corner of the w&b charts would be cut off diagonally as well…instead of the farthest most aft acceptable CG limits remaining at max weight (continously).
   An aft CG means we will operate at a lower AOA.  If too much weight is aft, it would seem as if the the amount of elevator (or trim) required to operate at this lower AOA would put too much stress on the tail.
   Therefore, I’m suprised that the farthest most aft CG line isn’t cut off (diagonally) as well.

   0 Votes 0 Votes  0 Votes

10. 
    

    
    

    Wesley Beard on Jan 28, 2011

    John Doe, Your’re reasoning is sound for the farthest forward CG and not the farthest aft CG.  Remember, there is a tail down force that is provided by the elevator.  Effectively, the wings have to lift the weight of the airplane plus the tail down force.  At the farthest aft point, the tail down force will be minimum (meaning a lower AoA).  It also means the center of pressure (lift) and center of gravity are closer together.  Just like in a teeter totter, the closer those are together the less extra force is needed to counteract the pitching moment.
     
    The top left corner is cut off because as the airplane slows down, the elevator becomes less effective and doesn’t have the force needed to keep the nose of the airplane up in a landing flare.  

    0 Votes 0 Votes  0 Votes

11. 
    

    
    

    dbabka on Apr 06, 2011

    Any idea how to determine the cut off points on the CG envelop.  I am currently designing an aircraft and I am having trouble finding a good way to deterime the max take off weight at the most forward CG location and the most forward CG location for the absolute max take off weight

    0 Votes 0 Votes  0 Votes