Zero Fuel Weight

Many airplanes, particularly light twins and heavier, have an operational limitation know as zero fuel weight. This limitation, while very familiar to the operators of heavier aircraft, is poorly understood and often ignored by operators of lighter aircraft. Zero fuel weight can be defined as the empty weight of the airplane, plus the weight of the unusable fuel, plus the maximum allowable payload (passengers, cargo, and crew). Expressed more clearly, any weight added to the airplane past the zero fuel weight must be in the form of fuel. Sounds like nothing to worry about, right?

Aircraft design is one of the most challenging engineering feats ever undertaken. Aircraft structure must be strong enough to be reliable (remain intact throughout the range of operational limitations), but be light enough to fly (provide the level of performance promised by the manufacturer and expected by the operator). The wing spar is the most critical component of the aircraft structure, and a prime example of this “just strong enough” design philosophy. Nowhere is this more critical than at the points where the wing spar is attached to the spar carry-through assembly. It is at these points where the stresses on the wing spar structure are particularly focused.

Note the illustration below:

In this illustration, the total gravitational effect has been divided into separate vectors for the fuselage and the wing assemblies. The fuselage weight vector represents the main force vector for the payload. The wing weight vectors resent the main force vectors of the weight of the fuel. The vectors of lift act from the centers of lift of the wings, and equal the combined vector amounts of weight in level flight. The rotational stress vectors represent the force of torque applied to the points where the wing spars are attached to the spar carry-through assembly.

The “just strong enough” design philosophy requires that the torque forces sustained by the wing-root attach points be pre-determined so that performance, structural integrity, and airframe life can be assured. The limitation of zero fuel weight is calculated so that an acceptable compromise between weight (performance) and strength can be reached. As long as zero fuel weight is not exceeded, the weight of the aircraft is distributed evenly enough along the lateral axis so that the rotational stress generated at the spar attach points is maintained within limits. Once zero fuel weight is exceeded, the wing produces torque around its center of gravity, increasing the rotational force vector at the spar attach point beyond the design limit. Note that these forces are magnified as the gust factor is increased (read: operated in severe weather conditions).

Let’s look at a realistic example: A Part 135 air cargo multiengine airplane is scheduled for a two-hour flight. The pilot loads the airplane to zero fuel weight, and then loads fuel to bring the aircraft weight up to maximum gross weight, exceeding minimum fuel requirements. Just before taxiing out, a cargo handler runs out to the airplane with a last-minute, time-critical, 60-pound package. The dispatcher has issued instructions to load the package and drain ten gallons to remain at maximum gross weight. Is this OK? NO!

As weight is reduced at the fuel tank stations, the center of gravity of the wing moves inboard. Since the center of lift is concentrated at a constant lateral station, its lever arm is increased. This longer lever arm increases the torque force around the wing CG and transfers that additional force to the inboard section of the spar. The rotational load on the spar at or near the attach points will exceed design limits once flight begins and lift is produced.

The FAA has issued and Airworthiness Directive against 400-series Cessnas in an attempt to address this issue, and an additional AD is impending at the time of this writing. To date, the goal of these actions is to enhance detection of overstress condition, rather than implementing a permanent fix.

Here are some web addresses where interested reading can be found:

http://a257.g.akamaitech.net/7/257/2422/14mar20010800/edocket.access.gpo.gov/2004/04-1658.htm

This a federal document that provides some background on the problem.

http://www.ntsb.gov/ntsb/brief2.asp?ev_id=20001205X00460&ntsbno=FTW99FA123&akey=1

This is a narrative of the NTSB accident investigation that prompted the original Airworthiness Directive against the 400-series Cessnas. Note that the blame is placed on a manufacturing defect, but that does not diminish the role that repetitive misloading may have played in the failure.

http://www.ntsb.gov/ntsb/brief2.asp?ev_id=20001212X21530&ntsbno=MIA00FA208&akey=1

This is narrative of an NTSB accident investigation of a Cessna 402 engaged in Part 135 cargo operations that crashed into the Caribbean Sea. Only parts of the aircraft and some cargo were recovered, and no probable cause is listed.

However, known circumstances outlined in this report point to wing spar failure, the report suggests that misloading played a factor. The radar tracking data indicates that the aircraft descended from 7000 feet to the last radar return at 1100 feet in 53 seconds (the last 5400 feet took 24 seconds). This descent rate is consistent with in-flight breakup. The report estimates the weight of the airplane at the time of the accident at 6800 pounds, 50 pounds below the maximum allowable takeoff weight of 6850. Of this 6800 pounds, 1517 pounds consisted of mail, as reported by the U.S. Post Office.