9.loading-graphs. Loading Graphs
A loading graph is a weight and balance computation tool published in Section 6 of the Pilot's Operating Handbook (POH) or Aircraft Flight Manual (AFM) that allows the pilot to determine the moment for each loaded item without performing arithmetic with awkward arm values. Instead of multiplying weight by arm and dividing by a reduction factor, the pilot reads the moment directly off a graph. Loading graphs are most common on Cessna single-engine aircraft and are used in conjunction with a center of gravity (CG) moment envelope to verify that the loaded airplane will remain within both weight and balance limits for the entire flight.
Anatomy of a Loading Graph
A typical loading graph plots:
- Vertical axis (Y): Load Weight, in pounds, from 0 up to the maximum allowable for that station (for example, 0–400 lb).
- Horizontal axis (X): Load Moment, expressed in pound-inches divided by 1,000 (lb-in/1000). The reduction factor of 1,000 keeps the numbers manageable.
- Diagonal lines: One sloped line for each loading station — pilot and front passenger, rear passengers, fuel, baggage area 1, baggage area 2, and sometimes oil. The slope of each line equals the arm (distance from the datum) for that station.
The steeper the line, the farther aft the station; the shallower the line, the farther forward. Fuel lines often account for usable fuel only and may be labeled in gallons as well as pounds (avgas at 6 lb/gal).
Procedure for Use
- Begin with the basic empty weight and basic empty weight moment from the airplane's individual weight and balance record. These are unique to the specific tail number — never use generic POH sample numbers for an actual flight.
- For each loaded item (front seats, rear seats, fuel, baggage), enter the loading graph on the vertical axis at the item's weight, move horizontally to the appropriate station line, then drop straight down to read the moment in lb-in/1000.
- Record each weight and its corresponding moment on a loading worksheet.
- Sum the weights to obtain total ramp weight, then subtract taxi/runup fuel burn to get takeoff weight.
- Sum the moments (in lb-in/1000) to obtain total moment.
- Verify total weight does not exceed maximum gross takeoff weight.
- Plot the total weight versus total moment on the CG Moment Envelope (a separate chart). If the plotted point falls inside the envelope, the airplane is within CG limits. If it falls outside, items must be rearranged, removed, or fuel adjusted.
Example
Assume a Cessna 172 with the following loading:
- Basic empty weight: 1,500 lb, moment 56.0 (lb-in/1000)
- Front seats (pilot + passenger): 340 lb → from graph, moment ≈ 12.6
- Rear seats: 170 lb → moment ≈ 12.4
- Fuel (40 gal × 6 lb/gal = 240 lb): moment ≈ 11.5
- Baggage area 1: 50 lb → moment ≈ 4.7
Totals: Weight = 2,300 lb, Moment = 97.2 (lb-in/1000). The pilot then plots 2,300 lb against a moment of 97.2 on the CG envelope. If the point lies inside the normal category envelope, the loading is legal for normal-category operations (which permit limited acrobatic maneuvers and a load factor of +3.8/–1.52 g).
Critical Considerations
- Fuel burn shifts CG. Always check both takeoff and landing (zero-fuel or minimum-fuel) configurations. In many singles, fuel arm is near the CG so the shift is small, but in aircraft with fuselage tanks the CG can move significantly as fuel burns.
- Reduction factors must match. A loading graph using lb-in/1000 cannot be combined directly with a moment table using lb-in/100. Mismatched factors are a common student error.
- Read each station's line — do not use one line for all stations. The most frequent error is reading the fuel weight against the rear-passenger line or vice versa.
- Maximum baggage placards still apply even if the graph extends higher; structural floor loading limits (e.g., 120 lb in area 1, 50 lb in area 2 on a 172) cannot be exceeded.
- Forward CG increases stall speed, increases stability, and lengthens takeoff roll. Aft CG reduces stability, can make recovery from stalls or spins difficult or impossible, and is generally the more hazardous limit to violate.
The loading graph is fast, graphical, and well-suited to training airplanes, but the pilot remains responsible for verifying that the airplane is within all weight, CG, and category limits before every flight, in compliance with 14 CFR 91.9 (operate per the AFM/POH) and 91.103 (preflight action).