L-1011 Weight and Balance: Center of Gravity

L-1011 Center of Gravity

Looking at the operating envelope we can identify the limiting factors. Across the top we indicate the percent of the Mean Aerodynamic Cord. Across the bottom we indicate the index units. The chart also gives the in-flight and taxi forward and aft limits as well as the zero fuel weight forward and aft limits. 

L-1011 Weight and Balance: Maximum Useful Load

Maximum Payload (Weight Limited)

This is the difference between the maximum design zero fuel weight (MZFW) and operational empty weight (OEW). Payload consist of passengers, baggage and/or cargo.

Maximum Useful Load (Weight Limited)

This is the difference between the maximum design takeoff weight (MTOW) and operational empty weight (OEW). Useful loads consist of payload and usable fuel. 

L-1011 Weight and Balance: Weight Limitations

Maximum Design Taxi Weight (MTW) 225,900 KG 498,000 LBS

This is the maximum weight for ground maneuvers as limited by aircraft strength and airworthiness requirements. The weight of taxi and engine run-up fuel is included.

Maximum Design Takeoff Weight (MTOW) 225,000 KG 496,000 LBS

This weight must not be exceeded at the start of takeoff run. Any weight in excess of MTOW must be consumed during taxi and/or ground maneuvers.

Maximum Design Landing Weight (MLW) 116,900 KG 368,000 LBS

The maximum weight at which the aircraft may land without exceeding its structural limitations. Prior to landing, any weight in excess of MLW must be in the expendable fuel.

Maximum Design Zero Fuel Weight (MZFW) 153,300 KG 388,00 LBS

The maximum weight of the aircraft before expandable fuel is added. It is also the maximum sum of operational empty weight and payload.

L-1011 Weight and Balance: Arm Calculation

To facilitate calculation in the development of loading system the moment is reduced to a more workable magnitude by the following index equation:

Weight x (Arm - 1216.4)
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10,000 lb. in. or kg. in.

What we have done in this case is to change our frame of reference from the leading edge Mean Aerodynamic Cord (MAC) to the quarter cord, 25% of the Mean Aerodynamic Cord. All movement forward of the quarter cord will be negative numbers; all movement aft of the quarter cord will be positive numbers. The reason for using the quarter cord is that it is the approximate center of pressure on the wing. The aircraft will normally be operated at the center of gravity very close to the quarter cord.

Additionally, it is by convention, that is most if not all manuals are manufactured and indexed so that they refer to the quarter cord. By using the index system we simply add and subtract Index units, taking the and resolute and ensuring that it is within the operating envelope of the aircraft.

L-1011 Weight and Balance: Overview

Looking at the Lockheed L-1011 plan form view, we can see that the leading edge Mean Aerodynamic Cord is at the fuselage station 1143.0. The length of the cord, that is from the leading edge MAC tot he trailing MAC, is 293.5 inches long. For convenience of operation, then, we convert fuselage stations into percent of the Mean Aerodynamic Cord, 1,430, dividing that by the length of the Mean Aerodynamic Cord, 293.5. To convert the end result to a percent we will move the decimal point two places the left, and divide by 2,935. This will yield a percent of the Mean Aerodynamic Cord. If we wish to go the other way, that is find the arm; we would simply take the percent of the Mean Aerodynamic Cord and multiply it times 2,935 of the Leading Edge Mean Aerodynamic Cord of 1,143.0 and would have the original arm.

All this, of course, will lead to us being able to compute the center of gravity of the aircraft for any given arm.

L-1011 Weight and Balance: Mean Aerodynamic Cord

The Mean Aerodynamic Cord (MAC) by definition is the cord of an imaginary air foil which throughout the flight range has the same force vectors as the three dimensional wing. In the example above, we have a rectangular wing with a cord root of 100 inches and a tip root of 50 inches. In order to graphically locate the MAC, we simply add 50 inches to the lower half of the cord root and 100 inches to the upper half of the cord tip. The line connecting the two extremes will intersect a line drawn from the center of the root to the center of the tip. The point of intersection then represents the Mean Aerodynamic Cord, at the trailing edge we have the trailing edge MAC. At the leading edge we have the Leading Edge MAC. Note that the MAC is not the average cord, but is the cord to the centroid of area. Centroid is the center of mass. 

L-1011 Weight and Balance: Aircraft Dimensions

Thinking in terms of weight and balance, note the the main landing gear is some 1280 inches back from the forward portion of the aircraft. The leading Edge Mean Aerodynamic cord (LEMAC) is 1143 inches aft of the datum. The lateral balance is measured in inches and is referred to as buttline. There is a right buttline and a left buttline. Note that the landing gear is some 432 inches from center to center. The wingtips are 1864 inches from tip to tip. This is certainly a consideration in terms of lateral balance when dealing with fuel management and ground handling. 

L-1011 Weight and Balance: Overview

Over the next few blog posts we will take a look at the weight and balance limitations of the L-1011 and how to compute them. This is actually quite an interesting exercise in flight simulation since it also validates the physics model of the flight simulator. Load and Balance data is importation so that the flight crew and other personnel operate the aircraft within its operation envelope.

There are a few basic concepts that are used when calculating weight and balance of the Lockheed L-1011. To start with we will have a look at the profile of the aircraft (see above). Everyone is familiar with the basic size of the L-1011, but perhaps not how that can relate to weight and balance.

You might note form the diagram above that Station 0 is some 183 inches forward of the nose of the aircraft. This is designed that way so that if additional structure is added to the nose, the radome is changed or other things we will not end up with a negative number.

Additionally, you'll notice that the main floorboard of the aircraft is water line 200. The pavement on with the aircraft sits is water line 19. That means that water line 0 is some 19 inches below the surface of the earth! :) Again, this is done to avoid negative numbers. Working form forward to aft you might note that the landing gear is sitting at Station 540 when extended, and will retract to about Station 440 ... some 100 inches! This will have to be accounted for in the operational loading limits.

You might also note the relative position of the cargo compartments to the landing gear and wing arrangement.  In terms of weight and balance we can see how easy it is to have rather large moment changes on the L-1011. The overall length of the aircraft is some 164 feet, 2 inches which amount to 1970 inches !