822,336. Grounded aircraft trainers. LINK AVIATION Inc. Dec. 22, 1955 [Dec. 27, 1954], No. 36861/55. Class 4. Grounded aircraft trainer apparatus comprises a computer deriving at least one signal representing a simulated ground velocity of the aircraft simulated, means deriving at least one signal representing a simulated wind velocity, and means combining said signals vectorially to derive a further signal representing a simulated velocity relative to the air. The general layout is shown in block form in Fig. 1, and comprises an axial force and acceleration computer 1, a velocity computer 2, a wind control apparatus 3, a vectorial adding computer 4, a dynamic pressure computer 5, a side slip and angle of attack computer 6, and a moment computer 7, some of the interconnections being shown. In addition there is a computer for simulating ground effects, e.g. braking and steering. Dummy controls provide inputs, and the outputs are used for operating flight instruments with or without an external visual display. The computers comprise positional servos for each flight parameter, of the type in which the position of the output shaft is determined by inputs to a summing amplifier and a time derivative or other functional e.g. tangent, feedback. Each servo operates potentiometers sliders for multiplication, and may have a variable feedback resistance for division. Amplifiers (not all shown) are used for polarity reversal when necessary in the equations below and elsewhere. Axial forces and accelerations computer (Fig. 2).- The axial force along the X-axis is computed as WAx = T cos a cos # + W sin y + Ds cos # + Ys sin # where W is the aircraft weight, Ax the X-axis acceleration (the X-axis being along the flight path), T the thrust, α the angle of attack, # the side slip angle, y the angle of elevation, Ds the drag coefficient, and Ys the lateral force. Ds is computed as q SCD, where CD = CDO + CDLG# LG + CDWF #WF +KCL<SP>2</SP> where q is the dynamic pressure, S a nominal wing area, CD the drag coefficient, CDO the basic drag, #LG the landing gear displacement and CDLG its drag coefficient, #WF the wing flap displacement and CDWF its drag coefficient, and KCL<SP>2</SP> is the induced drag CL being the lift coefficient. A thrust potential is fed to a cosine potentiometer R-201 adjusted by the side slip angle servo M-500, and the output fed to a cosine potentiometer R202 adjusted by the angle of attack servo M501. The resultant T cos α cos # signal is fed to summing amplifier U-203. A constant voltage at terminal 200 energizes a potentiometer R-203 adjusted by the aircraft weight servo M-299, the output being fed to a sine potentiometer R-204 adjusted by the flight path elevation angle servo M-301 to derive a signal W sin γ fed to amplifier U-203. Terminals 207, 208, 205 and 206, are fed with potentials derived from suitably contoured potentiometers driven by by Mach number servo, to represent the coefficients of the drag equation as functions of Mach number. The CDLG and CDWF potentials at terminals 207 and 208 are modified by landing gear and wing flap potentiometers R-214 and R-215, summed in amplifier U-207, and multiplied by q by potentiometer R-216 adjusted by the dynamic pressure servo M-401. The result is fed to amplifier U-202. The K of the drag equation fed to terminal 206 is multiplied twice by the lift coefficient by potentiometers R-212 and R-213 adjusted by the CL servo M-505. The output is fed to amplifier U-206, together with the CDO potential from terminal 205. The sum is multiplied by the dynamic pressure q by potentiometer R-217 and fed to amplifier U-202. A ground forces drag from amplifier U-208, Fig. 7, is also added. The resultant total X-axis drag is multiplied by cos # by potentiometer R-211, and fed to amplifier U-203. The lateral force Ys is derived from a potential at terminal 202 which is a function of Mach number, multiplied by q by potentiometer R-205 and modified by the side slip angle # by potentiometer R-206, and from a second Mach number function potential at terminal 203 which is modified by the rudder displacement by potentiometer R-207, and multiplied by q by potentiometer R-208, the two signals being summed in amplifier U-201. This force is then resolved along the line of flight, being multiplied by sin #. by potentiometer R-209, and fed to amplifier U-203. The feedback potentiometer R-218 of this amplifier is adjusted by the aircraft weight servo M-299, whereby the sum of the inputs is divided by the weight, so that its output is the X-axis acceleration Ax. The lateral acceleration Ay is computed in amplifier U-204 as where ° is the angle of bank. The T cos α sin # term is derived from potentiometers R-230 and R-231, the W cos y sin ° term from potentiometers R-203 ,R-232 and R-233, the latter being adjusted by the angle of bank servo M-601, the Ds sin # term from amplifier U-202 and potentiometer R-234, and the Ys cos # term from amplifier U-201 and potentiometer R-210. A lateral ground forces potential is applied by terminal 711, Fig. 7, and the sum divided by aircraft weight by potentiometer R-219 to produce an output from amplifier U-204 of Ay, the lateral acceleration. The vertical acceleration Az is computed in amplifier U-205 as WAz = T sin α + W cos y cos Ï + qSCL The T sin α term is derived by potentiometer R-235, the W cos y cos ° term from potentiometers R-203, R-236, and R-237, and the q SCL term from a fixed potential at terminal 213, and potentiometers R-221 and R-222. A vertical ground forces potential is applied at terminal 701, Fig. 7. The sum in amplifier U-205 is divided by the aircraft weight by potentiometer R-220 as before, giving an output of Az, which may be used to feed a vertical accelerometer indicator Iz. Axial velocity pitch, height, azimuth, elevation, and ball bank angle computers, Fig 3.-The X-axis acceleration Ax derived in Fig. 2 is fed to an integrator I-301 having an output Vx, the X-axis velocity. The vertical component of this is derived by sine potentiometer, R-302 adjusted by the pitch servo M-301 and applied to a rate of climb indicator I-RC, the capacitor C-301 introducing a simulated lag. The rate of climb is integrated by integrator I-302, and applied to the height servo M-302. A cosine potentiometer R-301 derives V h , the horizontal component of V x , which is fed to a ground-speed servo M-303. The velocity Vx is resolved into northerly and easterly-components by cosine and sine potentiometers R-305 and R-306 positioned by the azimuth servo M-300. The horizontal components of these two components are then derived by cosine potentiometers R-303 and R-304, the resultant northerly and easterly ground speeds being then integrated by integrators I-303 and 1-304 and the simulated course is then plotted on a map R.M. by a pen. The azimuth angle # p is found from # p = (Ay cos Ï - A z sin Ï) /V x cos y An Ay potential is applied to terminal 211, multiplied by cos ° by a cosine potentiometer R-307 adjusted by the bank angle servo M-601, and fed to amplifier U-301. An Az potential is fed to terminal 212, multiplied by sin ° by a sine potentiometer R-308, and fed to amplifier U-301. The sum is fed to amplifier U-302, the feedback resistance R-309 of which is a cosine potentiometer adjusted by the pitch servo to effect division. The output is fed to amplifier U-303 the feedback resistance R-310 of which is adjusted by the Vx servo M-306. The output of this, # p is fed to an integrator I-305 feeding the azimuth servo M-300. The angle of elevation is computed from where g is the acceleration due to gravity. The A z cos ° term is derived by terminal 212 and cosine potentiometer R-312, and fed to amplifier U-304. The Ay sin Ï term is derived from terminal 211 and sine potentiometer R-313 and fed to amplifier U-304. A constant potential is applied to terminal 399 and multiplied by cos γ by cosine potentiometer R-314, the result being fed to amplifier U-304. The output of this is fed to amplifier U-305, the feed back resistance R-315 of which is adjusted by the Vx servo. The resulting output is fed to integrator I-306 and positions the elevation angle servo M-301. Fig. 3 also shows two forms of ball bank angle computer. In one, the Ay potential forms the input of a conventional servo M-307, the A z potential energizing the follow-up feed back potentiometer. The servo shaft is coupled to a linear to arc tangent converter L.A.T. which positions the simulated indicator I-BB. Alternatively, as in dashed lines, the follow up is derived from a tangent wound potentiometer R-316 itself energized by by the Az potential. In this case the indicator I-BB is directly coupled to the servo M-307. Airspeed, dynamic pressure, and Mach number computers, Fig. 4.-The airspeed Vp is computed as where # pw is the difference in azimuth between the wind direction and flight path. The ground speed signal V h from Fig. 3 is applied to a potentiometer R-401 adjusted by the V h servo M-303. The resultant signal V h 2 is fed to amplifier U-401. A constant potential is applied to terminal 499, so that the potentiometers R-403 and R-404 adjusted by the instructor's wind speed (Vw) control D-401 derive a signal V w 2 fed to amplifier U-401. A potentiometer R-402 adjusted by the instructor's control D-401 is energised by a V h potential, to derive a signal 2 V h Vw, energizing a potentiometer R-405. This is cosine wound and adjusted by the output of a differential 405 having as inputs the azimuth # p and the setting of the instructor's wind direction control D-402. The resulting signal 2 V h V w cos # PW is fed to amplifier U-401 which thus has an output Vp<SP>2</SP>, fed to an airspeed servo M-400 having follow up potentiometers R-406 and R-407 giving a square law characteristic. The Vp<SP>2</SP> signal also energizes a potentiometer R-408 adjusted by the height serv