Using a loadcell, data will be recorded in Newtons and Newton-Metres. These are measured in the aircraft body axis, as the loadcell is attached to, and moves with the model. The forces measured by the loadcell are: axial (x), sideforce (y) and normal (z), with the moments being: roll (l), pitch (m) and yaw (n).

To determine the longitudinal static derivatives, a full AoA sweep needs to be conducted through a sensible range. For a generic tube and wing aircraft, this is normally between -5 and ~18 degrees, depending on where the stall angle occurs for the wing being tested. It is important to go past the stall point by a couple of degrees to see how sharp the stall behaviour is. This needs to be conducted for each elevator setting you wish to test.

To determine the lateral-directional static derivatives, a full AoS sweep needs to be conducted through a range of AoAs. The maximum sideslip angle can be selected based on the expected maximum crosswind the vehicle will encounter. If this is unknown, a range of -10 to 10 degrees will suffice. Given the -5 and ~18 degrees range specified for the longitudinal studies, sideslip sweeps should be completed at intervals of 3 degrees AoA. This needs to be conducted for each aileron and rudder setting you wish to test.

!!! It is critical that when you install your model in the wind tunnel that you ensure the model does not touch any of the surrounding tunnel infrastructure. This will give faulty readings as part of the forces and moments are being transferred to the object being touched !!!

The first step is to convert the raw forces and moments into non-dimensional coefficients. For forces, this is done by taking the test dynamic pressure and wing reference area into account, for example,

C_x = x/(Dynamic Pressure x Wing Reference Area)

C_y = y/(Dynamic Pressure x Wing Reference Area)

C_z = z/(Dynamic Pressure x Wing Reference Area)

For moments the reference length is added. For lateral-directional cases, this is the wingspan, whereas for longitudinal cases this is the mean aerodynamic chord.

C_l = l/C_x = X/(Dynamic Pressure x Wing Reference Area x MAC)

C_m = m/C_x = X/(Dynamic Pressure x Wing Reference Area x MAC)

C_n = n/C_x = X/(Dynamic Pressure x Wing Reference Area x Span)

As lift and drag are forces in the wind axis, i.e. perpendicular and parallel to the airstream, they are a combination of both the axial and normal forces with the AoA considered. When considering the normal force acting at the mounting point and going through the top of the vehicle, and the axial force acting to the rear of the vehicle, the lift and drag are calculated using the following relationships.

L = -Z cos(AoA) +Xsin(AoA)

D = -Z sin(AoA) - Xcos(AoA)

The aerodynamic derivatives are gradients of data denoted by the output variable on the Y-axis, with the input variable on the X-axis. For example, the derivative C_L_alpha is the gradient of the output (C_L) against the input (alpha, or AoA). Note that these derivatives are calculated based on radians, not degrees. For systems with non-linear behaviour, it is not practical to present a gradient fit of the complete dataset as it will not be indicative of the derivative about any point. In this case, local derivatives can be calculated using the central difference method, where the datapoints either side of the angle of interest are used to calculate a local gradient.

The gradients of the rolling and yawing moment coefficients against AoS as well as the pitching moment versus AoA determine the aircraft stability. The criteria for stability are given below.

C_l_beta < 0

C_m_alpha < 0

C_n_beta > 0

C_y_beta < 0

Finally, measurements in the wind tunnel are taken at the reference location of the loadcell. This means your data is recorded for a single reference point, which should correspond with a Centre of Gravity (CoG) of the vehicle. Ideally, you would mount the model at the estimated CoG to prevent the need for more data post-processing. However, if you wish to analyse the stability/trim conditions over multiple CoGs this can be easily completed using moment shifting correlations. For a more comprehensive outline of these please consult "Low Speed Wind Tunnel Testing" by Pope et. al.