# Calibration of balances

Whichever balance is used, it is essential to carry out a prior calibration applying known forces in the various directions. The easiest way to apply the forces is to use weights and apply them in different directions using appropriate pulleys.

Imperfections in the alignments of the axes of the balance with the stream and interactions of different measured components may occur so that, for example, the application of a force of pure drag may slightly affect the reading of the lift and, generally, of all other components. The procedure to investigate and eliminate the interactions of a complex balance is impressive: the initial set-up of a six-component balance in a large wind tunnel can require months of work.

It is possible to measure the effect on each component of the application of forces along the other axes in turn, find empirical relationships and store them in a computer to use during testing to measure the actual components free from the interactions.

The procedure can be simplified if the interactions are so small that they can be considered linear and hence can be summed. A matrix of coefficients of influence, [C, y], for each applied force, {FA}, on the measured forces, {FM}, can be determined

{FM} = [Cj {Fa}

This matrix can then be inverted to determine, from the readings of the balances, the components of the applied force free from interactions:

{Fa} = [C,;]-1{Fm}