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The Florida Technological University four-component strain-gage balance is an internally mounted, half-inch diameter balance capable of measuring four components of load: front and rear normal force, axial force, and rolling moment. Measurement of these components is accomplished by means of sixteen strain gages that are mounted on the balance and wired into four full bridge circuits. When the balance is subjected to a load, the strain gages, through a small resistance change, indicated the strain a balance element is undergoing. This report presents a description of the balance and its support equipment, and outlines specific calibration procedures necessary to their successful implementation. These calibration procedures take two forms: that of calibrating the readout equipment, and that of calibrating the balance itself. Also contained in this report is a method of reducing calibration data into a set of parameters applicable to the balance. To aid in the calibration of the balance, a calibration assembly was designed and built. Two calibration models were designed to facilitate the incremental loading of the balance and the interpretation of the readout data.

The terminal stage of a minimum-time mission of a high- performance aircraft is studied using both a reduced-order "energy" model formulation and a point-mass model formulation of the aircraft. The mission is confined to vertical plane maneuvers, and is defined as consisting of three stages; a climb to the dash point,a steady-state dash at the high velocity point, and finally, a terminal transient from the dash point to the final state. This terminal maneuver evolves outside of the flight envelope, rapidly decreasing altitude while increasing the velocity to values greater than the dash velocity. The velocity then decreases from this maximum value as required in order to meet the final state specification. Some of the trajectories that are generated during this terminal transient maneuver experience dynamic pressures that will exceed the dynamic pressure limit unless a constraint is placed on the state variables. Because of the need for enforcing this state constraint, a direct adjoining method for handling state constraints in the optimal control problem is studied. A numerical example is given to demonstrate the application of this method of handling state constraints for the case of the dynamic pressure limit. Finally, trajectories are generated that lead from the dash point to a final state having lower altitude and energy values than those of the dash point, and observations are made concerning the characteristics of these maneuvers. / Master of Science

A new gage which can measure skin friction and heat flux simultaneously was designed, constructed, and tested. This gage is the combination of a non-nulling type skin friction balance and a heat flux microsensor. By mounting the heat flux microsensor directly on the surface of the floating element of the skin friction balance, it was possible to perform simultaneous measurements of the skin friction and the heat flux. The total thickness of the heat flux microsensor is less than 2 μm, so the presence of this microsensor creates negligible disruption on the thermal and the mechanical characteristics of the air flow. Tests were conducted in the Virginia Tech supersonic wind tunnel. The nominal Mach number was 2.4, and Reynolds number per meter was 4.87 x 10⁷ with total pressure of 5.2 atm and total temperature of 300 °K. Results of the tests showed that this new gage was quite reliable and could be used repeatably in the supersonic flow. This gage also has an active heating system inside of the cantilever beam of the skin friction balance so that the surface temperature of the floating element can be controlled as desired. With these features, the effects of a temperature mismatch between the gage surface and the surrounding wall on the measurements of the skin friction and the heat flux were investigated. An infrared radiometer was used to measure the surface temperature distributions. Without the active heating, the amount of temperature mismatch generated by the gage itself was from 2.5 °K to 4.5 °K. The active heating produced the temperature mismatch of 18.7 °K. The largest temperature mismatch corresponds to the levels typically found in high heat flux cases when it is expressed in dimensionless terms. This temperature mismatch made sizable effects — a 24 % increase in the skin friction measurement and a 580 % increase in the heat flux measurements. These experimental results were compared with the computational results using the Computational Fluid Dynamics code GASP. The input flow conditions were obtained from the boundary layer measurements. The temperature mismatch was input by specifying the density and the pressure at each grid point on the wall. The Baldwin-Lomax algebraic turbulence model was used with the thin layer approximations. The comparison showed that the difference in the skin friction and heat flux was less than 10 % of the measured data when the temperature mismatch was less than 8.5 °K, but the difference was increased as the amount of the temperature mismatch increased. It is presumed that the disagreement between the measurements and the calculations was caused mainly by deficiencies in the turbulence model for this complex, developing viscous flow, because the Baldwin-Lomax model cannot account for the multiple length scale in this flow. / Ph. D.

The design, development, construction, and instrumentation features of a supersonic shock tunnel that produced high temperature supersonic flow for a short duration, on the order of 2 msec, are presented. The shock tunnel was equipped with a Mach 3 supersonic 2-D nozzle. Test runs were conducted using air and helium drivers at driving pressures varying from 200-450 psig (1.4-3.1 MPa gage), with the driven gas in all the cases being ambient air. Pressure and temperature measurements were made to document the operating conditions of the tunnel. Total pressure measurements were made in the settling chamber of the nozzle where the flow Mach number is 0.14 (weakly subsonic). Static pressure measurements were made at the exit of the nozzle to establish the unsteady starting process of the nozzle. Total temperature measurements using thermocouples were made in the settling chamber of the nozzle to identify the maximum temperature attained in the flow. Surface heat flux measurements were made at the exit of the nozzle and compared with previous skin friction measurements. The measured pressures and temperatures compared well with the predicted values for the air driver. In the case of the test runs with the helium driver the nozzle started, but the flow was unsteady. Consequently, there were difficulties in making measurements and interpreting them. The surface heat flux and skin friction followed the Reynold's analogy within 50% during the steady run time of the shock tunnel. / M.S.