**4.3 Measurements protocole**

The supersonic nozzles of the wind tunnel are curved nozzles which will produce isentropic flows by adjusting the generating pressure *Po* and the static pressure *P*<sup>1</sup> measured in the test section. The latter will be adjusted by adjusting the opening of the motorized butterfly valve which separates the test chamber from the pumping unit.

The test model is positioned in the isentropic zone, where the flow conditions are stabilized as showed on **Figure 9**. Outside this zone, the Mach number and pressure change and no longer correspond to the isentropic values for each nozzle. The total force measured by the balance corresponds to the force exerted by the flow as well as that created by the suction of the pumping unit. In order to keep only the force created by the flow, a measurement of the residual pumping force is made by isolating the model/balance assembly from the flow. To do this, a plate mounted on a rotating piston is inserted into the flow in front of the model, so that the model is no longer subject to the aerodynamic forces generated by the flow. The force of interest is the difference between the total force and the residual force.

The aerodynamic force measurements are done in two steps: first, the values of the drag and lift modules corresponding to the waverider exposed in the flow are recorded, then in a second step, the plate is placed between the waverider and the flow to record the offsets of both modules. For both steps, the acquisition time is 10 seconds with an acquisition frequency of 1000 kHz. This operation is repeated 5 times for each position of the wave rider in the flow, in order to have an average value which is representative of the aerodynamic forces. Since the isentropic flow is homogeneous in a given volume which depends on the nozzle used, special attention has been paid to the placement of the waverider in the flow whatever the angle of incidence. For this purpose, the position of the waverider is corrected using motorized translations, so as to reposition the waverider to its initial position without angle of incidence as illustrated on **Figure 10**. The reference point is the center

**Figure 9.** *Assembly of the sting balance/model in the test chamber.*

**Figure 10.** *Coordinates correction of the model location in (x-y) plane.*

of the waverider. The determination of the drag and lift forces is a function of the measured values of the respective modules and the angle of attack of the waverider. The correction is given by changing the Cartesian coordinates into cylindrical coordinates following these equations:

$$\text{Drag}\_{real} = \text{Drag}\_{measured} \* \cos\left(\Theta\right) + \text{Lift}\_{measured} \* \sin\left(\Theta\right) \tag{1}$$

$$\text{Lift}\_{real} = \text{Lift}\_{measured} \* \cos\left(\Theta\right) - Drag\_{measured} \* \sin\left(\Theta\right) \tag{2}$$
