# How are the limits of the center of gravity chart established?

When one views a center of gravity limit chart, in this case a C-182T chart, one notices that the forward C.G. line has two small bends in it, one around 2250# mark and the other around the 2675# mark. Why the two bends in the forward C.G. limit line? What has happened at these two points? Image from: C-182T POH pg. 211

• Could you perhaps add an image or a link to the chart in question? – Thunderstrike May 29 '15 at 0:51
• I think it's likely that the limit actually curves but the engineers decided to make straight lines out of them in the manual so pilots could interpolate them better. – ratchet freak May 29 '15 at 8:20
• Correct me if I'm wrong but the area presented by a deflected control surface is the tangent of the angle of deflection (opposite side of "triangle"). The increase of area presented is linear to the angle of deflection. Coefficient of Lift is also linear with increased AOA, so yeah, they may be actually straight. – Robert DiGiovanni May 11 at 0:28

These "bends" (or sloped straight lines) are due to various structural constrains on the aircraft. In level flight, the sum of forces must be zero:

LiftWing - Weight - LiftTail = 0

The summation of moment should also be zero, otherwise the plane will pitch up or down.

The wing has a structural limitation, i.e. a maximum loading. Solving the above equations for constant LiftWing yields a slopped straight line. This is the "bend" portion you see in the graph.

Drawing these lines (shown as colored lines here) on top of a weight and balance graph yields: The resulted graph is the intersection of the various constraints.

In the C-182 graph, there are five constraints (five edges). Wing loading and tail loading is used as an example here, since I do not know what is the actual constraint used by the engineers. Another possibility is strength of the nose gear.

Main landing gear loading and aft tipping limit would have resulted in a downward slope, which does not correspond to the given graph.

• Interesting information, but it doesn't describe why there are two distinct kinks in the graph for the C182, which is what OP asked. – FreeMan May 29 '15 at 12:23
• @FreeMan I have edited the answer to relate to the OP's graph. It was already in the answer, but might not be very clear. – kevin May 29 '15 at 12:53
• Are you sure it's not about limiting stick forces??? If you post speculation, please spell out clearly that you are guessing. – Peter Kämpf May 29 '15 at 21:12
• @PeterKampf limiting stick force would be mathematically equivalent to limiting tail loading. – kevin May 30 '15 at 2:12
• @PeterKampf: I didn't say the graph is to scale, or did I? – kevin May 31 '15 at 14:33

There could be two reasons:

1. Performance: The more forward c.g. location demands more speed, so the wing can create enough lift to counteract the downforce from the tail. To keep the minimum speed below the 61 knots mandated by FAR part 23, the forward c.g. location at high gross weight needs to be restricted.
2. Stick forces: A more forward c.g. location translates into bigger elevator deflection angles for maneuvering. Again, the airworthiness requirements put lower and upper limits on them, and it could be that the upper limits are exceeded with the combination of high gross weight and forward c.g. location.