# Deformation balances

7.3.3.1Resolution of forces

The bending moment produced in a sting by the aerodynamic force is proportional to the difference of the readings of two strain gages, assumed to be identical, compressed on one side and elongated on the other side of the sting. The sting is made with a series of hollow sections properly oriented to offer different flexibility depending on the direction of the

Sting with three-component strain gage balance

components to be measured. In the scheme of Figure 7.25, strain gages are arranged in pairs on the horizontal plates of the frame at the measuring lift and pitching moment. The force and the moment can be calculated from the bending moments, M1 and M2, as computed by the deformation detected by two pairs of strain gages placed at two points at a distance x1 and x2 from the origin of the axes. The force normal to the line joining the two points is given by:

P M – M2 F =-

x1 – x2

and the moment is determined by the equation:

M = M2x1 – M1x2 x1 – x2

In Figure 7.26, strain gages are arranged on the vertical sides in order to measure drag (axial force) but also normal force contributes to deformations.

The rolling moment can be measured by one or more pairs of strain gages placed at ±45° with respect to the axis of the sting: the torque is

Interaction of normal force on axial force

proportional to the differences between strains in these two main directions. Alternatively, the rolling moment can be measured in terms of tension and compression on either side of the central axis of the sting. In the usual procedure the rear of the sting is connected to the tunnel through a buffer that allows the freedom to roll through a braking element to which are attached strain gages.

The strain balances rarely have six components as they are usually designed ad hoc for a particular model. The arrangement of strain gages can be quite complicated even considering the need to compensate for the temperature sensitivity. Since strain gages cannot be considered perfectly equal to each other, an accurate calibration is needed, which can be very challenging with six components.