Aircraft fuel tanks are generally within the wings. They are approximately rectangular but have detailed internal structure. A key aspect of aircraft safety is the ability to have accurate measurement of the amount of fuel in the tank. To determine this, the height of the fuel at certain points within the tank is measured and then the fuel volume calculated. However the relationship between height and volume depends crucially on the pitch angle, α, and roll angle, β, of the tank. (This is clear to all of us when we drive a car and see that the indicated fuel level in the tank depends on whether we are going up or down hill at the time.) At present Airbus uses lookup tables to link height to volume for a set of pitch and roll angles. As the fuel tanks become more and more intricate, the huge amount of data required becomes an issue. The problem posed to the Study Group was whether the lookup tables can be replaced by suitable functions.

To solve this problem we require a combination of numerical analysis and geometry. Numerical methods are needed to determine suitable approximations to the relationship between height and volume. However, generating such approximations turns out to be very subtle, because of the way that the fuel interacts with the tank geometry. The height-volume curves are nonsmooth and have to be approximated very carefully. An understanding of the way that this nonsmoothness arises and how the resulting curves can be approximated forms the basis of this study.

Problem presented by
Chris Slack, Airbus

Study Group contributors
Chris Budd (University of Bath)
Jens Gravesen (DTU, Lyngby)
Andrew Hill (University of Bath)
Jan Van lent (University of Bath)
Eddie Wilson (University of Bristol)