QPROP User Guide Version 1.21 Mark Drela 6 July 07 General Description =================== Motivation ---------- QPROP is an analysis program for predicting the performance of propeller-motor combinations. Its intent is to provide an alternative to the existing prop/motor simulation programs, which use relatively simple propeller models, and assume a brushed DC motor type. QPROP has a relatively sophisticated and accurate prop aerodynamic model, and a general motor model which can be implemented via a user-supplied subroutine if necessary. The companion program QMIL generates propeller geometries for the Minimum Induced Loss (MIL) condition. It can also generated windmill geometries for the MIL or Maximum Total Power (MTP) conditions. See the qmil_doc.txt document for more info. Propeller aero model -------------------- The propeller is modeled with an advanced blade-element/vortex method, which is essentially a considerably enhanced version of the analysis method of Larrabee. The enhancement is primarily in the correct accounting of the prop's self-induction, which makes QPROP accurate for very high disk loadings, all the way to the static-thrust case. The blade airfoil lift characteristic is assumed to be a simple linear CL(alpha) line with CLmax and CLmin stall limiting. The profile drag characteristic is a quadratic CD(CL) function, with an approximate stall drag increase, and a power-law scaling with Reynolds number. The model applies equally well to propellers and windmills. The theoretical formulation is described in far more detail in the document qprop_theory.ps Motor models ------------ Motor type 1 - - - - - - - The default motor type 1 corresponds to a brushed DC motor, and is modeled using the fairly standard approach with an rpm/Volt motor constant Kv, an electrical resistance R, and a constant rotational friction described by the zero-load current Io. The relations used are: voltage = V current = I torque = Q = (I-Io)/Kv rot.speed = w = (V-I*R)*Kv mech.power = P = w*Q = (V-I*R) * (I-Io) efficiency = P/(I*V) = (1-I*R/V) * (1-Io/I) The equations above assume Kv is in units of rad/s / Volt, although it is specified in the traditional units of rpm/Volt. Motor type 2 - - - - - - - Motor type 2 corresponds to a brushed DC motor, and is a more accurate extension of the type 1 model above. The extensions are improved models of the frictional torque, temperature-dependent resistance, and magnetic lags. See the motor_theory.pdf document for a complete description. Other motor types - - - - - - - - - Any other motor model can be coded in SUBROUTINE MOTORQ (in motor.f), as a Q(w,V) function. The derivatives dQ/dw and dQ/dV must also be returned. The subroutine source header fully describes the inputs and outputs. For non-electric motors, the "voltage" V passed to MOTORQ can represent any suitable power-control variable, e.g. throttle setting, fuel flow rate, etc. Input Files =========== Fluid constants file qcon.def (optional) -------------------- This optional file contains the fluid constants, in the following format: 1.225 ! rho (kg/m^3) density 1.78E-5 ! mu (kg/m-s) dynamic viscosity 340.0 ! a (m/s) speed of sound If this file is absent, QPROP will use the default constants defined in file src/QDEF.INC . The current defaults correspond to sea level air. Prop file --------- QPROP requires a fairly detailed description of the propeller geometry and blade airfoil characteristics. Although it would be nice to just specify the propeller's diameter and pitch, this is in general insufficient to accurately capture the propeller's performance. Crude input is sure to produce crude output. Hence, it is worthwhile to accurately measure the prop. See the accompanying document prop_measure.pdf for definitions and measurement techniques. Measurement of the blade angles can be done with a commercial pitch-measuring gauge. The blade angle beta at some radius r and pitch p is then computed using the following equation: beta = arctan[ p / (2 pi r) ] The prop file has the following format. Blank lines and lines beginning with "#" are ignored. Any text after a "!" is ignored, allowing convenient comments to be placed after the data. Graupner CAM 6x3 folder 2 3.05 ! Nblades [ R ] 0.50 5.8 ! CL0 CL_a -0.3 1.2 ! CLmin CLmax 0.028 0.050 0.020 0.5 ! CD0 CD2u CD2l CLCD0 70000 -0.7 ! REref REexp 0.0254 0.0254 1.0 ! Rfac Cfac Bfac 0. 0. 0. ! Radd Cadd Badd # r chord beta 0.75 0.66 27.5 ! root station 1.00 0.69 22.0 1.50 0.63 15.2 2.00 0.55 10.2 2.50 0.44 6.5 2.875 0.30 4.6 3.00 0.19 4.2 ! tip station, also gives R = r if R is omitted from Line 2 1) Line 1 is the propeller description name 2) Line 2 gives the number of blades, and optionally the reference radius R. If this R is omitted from line 2, then the tip station r value is used for R (R = 3.00 would be used in this example) 3,4) Lines 3 and 4 specify the linear CL(alpha) function for the blade airfoil: CL(alpha) = ( CL0 + CL_a*alpha ) / beta , clipped to CLmin..CLmax range where beta = sqrt(1 - M^2) is the local Prantdl-Meyer compressibility factor The CL0 intercept at alpha=0 is equivalent to the zero-lift angle: CL0 = -CL_a * alpha_ZL Because the CL(alpha) curve is often nonlinear, specifying CL0 is usually more reliable. 5) Lines 5 and 6 specify the 2-piece quadratic CD(CL,Re) function for the blade airfoil: CD(CL,Re) = [ CD0 + CD2*(CL-CLCD0)^2 ] * [Re/REref]^REexp where CD2 = CD2u if CL > CLCD0 CD2 = CD2l if CL < CLCD0 It's usually acceptable to crayon-fit a 2-piece parabola to the airfoil's drag polar from XFOIL or some other source, and read off the parameters. The Re-scaling factor crudely models Re variation effects on CD. REref is the Re value of the polar from which the CD0,CD2u,CD2l,CLCD0 parameters are obtained, and REexp adjusts the CD for other Re numbers. Picking REexp = -0.5 is reasonable for most low Re airfoils. For very large props with significant turbulent flow, REexp = -0.2 may be more realistic. An additional CD contribution is added to the quadratic CD(CL) if the CL is clipped at the stall limits: dCD_stall = 2 * [ sin(alpha-aCD0) ]^2 ; aCD0 = (CLCD0-CL0)/CL_a This gives the correct value CD = 2 for alpha ~ 90 degrees, and is reasonable for more moderate stalled angles. 7,8) Lines 7 and 8 specify scaling factors and added constants to be applied to the following blade geometry data. SI units are required, so the factors of 0.0254 convert the radius and chord from inches to meters. The blade angle is input in degrees, and will be converted to radians. The factors are applied before the added constants. In summary: r_SI = r * Rfac + Radd (r_SI in meters ) c_SI = chord * Cfac + Cadd (c_SI in meters ) b_SI = (beta * Bfac + Badd) * pi/180 (b_SI in radians) The Rfac and Radd constants are also applied to the reference radius R, whether this is given in Line 2, or taken from the tip r value. R_SI = R * Rfac + Radd (R_SI in meters ) 9...) Lines 9 onward give the geometry for some number of radial locations, from root to tip. If R is given on line 2, the last station can be just short of the actual tip, with the remaining geometry obtained by extrapolation. If R is _not_ given on line 2, then the last station must be at the actual tip. The beta values are measured from the prop disk plane to the airfoil datum line from which alpha is defined for the CL(alpha) function. The chord and beta data are splined and interpolated to a much finer radial spacing, so only relatively few radial stations are required. However, overly coarse or irregular input might cause spline overshoots. The interpolated geometry is listed as output, and should be checked for smoothness. Advanced propeller file format - - - - - - - - - - - - - - - - The prop file format above assumes all radii have the same airfoil characteristics. As a more general alternative, each of the radial-station lines can optionally specify the local airfoil section properties. The more general format for the prop file is: Graupner CAM 6x3 folder 2 3.02 ! Nblades [ R ] 0.50 5.8 ! CL0 CL_a -0.3 1.2 ! CLmin CLmax 0.028 0.050 0.020 0.5 ! CD0 CD2u CD2l CLCD0 70000 -0.7 ! REref REexp 0.0254 0.0254 1.0 ! Rfac Cfac Bfac 0. 0. 0. ! Radd Cadd Badd # r chord beta [ CL0 CL_a CLmin CLmax CD0 CD2u CD2l CLCD0 REref REexp ] 0.75 0.66 27.5 0.80 6.1 -0.3 1.5 0.032 0.060 0.010 0.6 1.00 0.69 22.0 0.70 6.0 -0.3 1.4 0.030 0.056 0.014 0.55 1.50 0.63 15.2 0.60 5.9 -0.3 1.3 0.029 0.054 0.020 0.52 2.00 0.55 10.2 2.50 0.44 6.5 2.875 0.30 4.6 3.00 0.19 4.2 Only the three inner radii above have local airfoil properties specified. The remaining radii with the airfoil data absent will simply be assigned with the default data in lines 3-6. A partial airfoil data list can be given on any line. For example, the three inner radii do not have local REref and REexp numbers given. These will then assume the default values in line 6. Motor file - type 1 ------------------- The motor type 1 description file has the following format. Speed-400 3321 (6V) direct drive ! name 1 ! motor type (1 = permanent-magnet brushed or brushless DC motor) 0.31 ! motor parameter 1 , R (Ohms) for motor type 1 0.77 ! motor parameter 2 , Io (Amps) for motor type 1 2760.0 ! motor parameter 3 , Kv (rpm/Volt) for motor type 1 . . . 1) Line 1 is the motor/gearing description name 2) Line 2 is an integer specifying the motor model type. SUBROUTINE MOTORQ must implement the model of the specified type. 3...) Lines 3... contain motor model parameters which are simply passed to MOTORQ. The example shown is the default brushed DC motor model, which requires three parameters: Line 3 is the motor resistance. Line 4 is the no-load current, which is best measured at close to the expected operating rpm. Line 5 is the rpm/Volt constant. The specified voltage is defined at the motor terminals. If desired, the battery+wiring+ESC resistance R' can be added to the specified motor resistance: R -> R + R' In this case, the specified "Volt" will be the unloaded battery voltage. The computed "motor efficiency" will then seem unusually low, since now it also includes the battery, wiring, and ESC resistive losses. A gearbox with gear ratio G:1 reduces Kv by the factor 1/G: Kv -> Kv / G The power loss of the gearbox shows up as an increase in the zero-load current Io. An expected gearbox efficiency "etaG" can be modeled by increasing Io as follows: Io -> Io + I * (1-etaG) where I is the expected operating current. Motor file - type 2 ------------------- The motor type 2 description file has the following format. Speed-280 6328 (6V) direct drive 2 ! motor type (brushed DC, higher-order model) 0.70 ! R0 (Ohms) 0.160 ! Io0 (Amps) 3800.0 ! Kv (rpm/Volt) 3800.0 ! Kq (Amps/N-m)*30/pi 1.0E-5 ! tau (s) 5.7E-5 ! Io1 (Amp-s) 4.0E-8 ! Io2 (Amp-s^2) 0.012 ! R2 (Ohms/Amps^2) Line 3 is the motor resistance constant term. Line 4 is the no-load current constant term (independent of RPM) Line 5 is the rpm/Volt speed constant. Line 6 is the Amp/N-m torque constant. Theoretically this should be the same as Kv. Line 7 is the magnetic lag time. Line 8 is the no-load current linear term (proportional to RPM) Line 8 is the no-load current quadratic term (proportional to RPM^2) Line 9 is the motor resistance quadratic coefficient, modeling resistive heating effect. Program Execution ================= QPROP can be run in many different modes. Some possible execution commands are: % qprop propfile motorfile Vel Rpm [ Volt dBeta Thrust Torque Amps Pele ] (single-point) % qprop propfile motorfile Vel1,Vel2,dVel Rpm ["] (multi-point 1-parameter sweep over Vel, Rpm set) % qprop propfile motorfile Vel1,Vel2/nVel Rpm ["] (multi-point 1-parameter sweep over Vel, Rpm set) % qprop propfile motorfile Vel1,Vel2,dVel 0 Volt ["] (multi-point 1-parameter sweep over Vel, Volt set) % qprop propfile motorfile Vel1,Vel2,dVel Rpm1,Rpm2,dRpm ["] (multi-point 2-parameter sweep over Vel and Rpm) % qprop propfile motorfile runfile (multi-point, via file specification) The "propfile" and "motorfile" arguments are strings giving the filenames of the input files described above. The remaining arguments are numbers, as will be described below. Single-point run ---------------- The following Unix syntax is used for a single-point run: % qprop propfile motorfile Vel Rpm Volt dBeta Thrust Torque Amps Pele The parameters after and including "Volt" are optional. So a command could be as short as % qprop propfile motorfile Vel Rpm In either case, only the one point is computed, and a detailed radial output is generated. The arguments starting with "Vel" are used as follows: 1) "Vel" is always used as given. 2) The next nonzero argument in the list (except for "dBeta") is used as given. 3) "dBeta", which is the pitch-change angle in degrees, is always used as given, (assumed zero if omitted) For example, the command % qprop propfile motorfile 4.0 0 0 0.0 0 0.03 ( Vel Rpm Volt dBeta Thrust Torque Amps Pele ) specifies Vel = 4.0 m/s Rpm = unspecified Volt = unspecified dBeta = 0.0 deg Thrust = unspecified Torque = 0.03 N-m Amps = unspecified Pele = unspecified As another example, the command % qprop cam6x3 s400-6v-dd 0.0 0 8.0 which corresponds to one of the points in the multi-point case, specifies Vel = 0.0 m/s Rpm = unspecified Volt = 8.0 V dBeta = 0.0 deg and will produce the following output: # Graupner CAM 6x3 folder # # Speed-400 3321 (6V) direct drive # 0.31000 R (Ohm) # 0.77000 Io (Amp) # 2760.0 Kv (rpm/Volt) # # rho = 1.2250 kg/m^3 # mu = 0.17800E-04 kg/m-s # a = 340.00 m/s # # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 # # V(m/s) rpm Dbeta T(N) Q(N-m) Pshaft(W) Volts Amps effmot effprop adv CT CP DV(m/s) eff Pelec Pprop cl_avg cd_avg # 0.000 0.1402E+05 0.000 3.377 0.2992E-01 43.94 8.000 9.4184 0.5831 0.0000 0.00000 0.1005E-07 0.2968E-10 0.4416 0.0000 75.35 0.000 0.7742 0.3801E-01 # # radius chord beta Cl Cd Re Mach effi effp Wa(m/s) Aswirl adv_wake 0.0202 0.0170 26.380 1.1945 0.15286 33356 0.084 0.0000 0.6657 7.843 15.97 0.1926E-02 0.0225 0.0173 24.311 1.1970 0.12900 38003 0.094 0.0000 0.6965 8.413 15.32 0.2053E-02 0.0248 0.0175 22.471 1.1985 0.11105 42391 0.103 0.0000 0.7210 8.922 14.69 0.2165E-02 0.0271 0.0175 20.856 1.1960 0.06964 46406 0.113 0.0000 0.7995 9.358 14.06 0.2258E-02 0.0293 0.0173 19.442 1.1445 0.06168 50050 0.123 0.0000 0.8025 9.551 13.16 0.2287E-02 0.0316 0.0171 18.191 1.1011 0.05578 53264 0.133 0.0000 0.8031 9.701 12.35 0.2308E-02 0.0339 0.0167 17.065 1.0632 0.05121 56095 0.143 0.0000 0.8021 9.815 11.61 0.2322E-02 0.0362 0.0163 16.026 1.0280 0.04748 58627 0.153 0.0000 0.7998 9.895 10.93 0.2330E-02 0.0385 0.0159 15.037 0.9927 0.04421 60982 0.164 0.0000 0.7967 9.942 10.30 0.2331E-02 0.0408 0.0156 14.071 0.9555 0.04119 63257 0.174 0.0000 0.7929 9.956 9.714 0.2326E-02 0.0431 0.0152 13.130 0.9171 0.03848 65428 0.184 0.0000 0.7882 9.939 9.163 0.2315E-02 0.0453 0.0149 12.219 0.8785 0.03609 67434 0.194 0.0000 0.7823 9.892 8.644 0.2298E-02 0.0476 0.0145 11.344 0.8406 0.03407 69203 0.204 0.0000 0.7750 9.817 8.153 0.2274E-02 0.0499 0.0141 10.511 0.8044 0.03242 70646 0.214 0.0000 0.7659 9.716 7.688 0.2246E-02 0.0522 0.0137 9.726 0.7705 0.03114 71668 0.224 0.0000 0.7549 9.590 7.246 0.2212E-02 0.0545 0.0132 8.988 0.7393 0.03019 72248 0.234 0.0000 0.7420 9.442 6.826 0.2174E-02 0.0568 0.0127 8.296 0.7103 0.02950 72435 0.244 0.0000 0.7273 9.276 6.430 0.2132E-02 0.0591 0.0122 7.647 0.6834 0.02902 72295 0.254 0.0000 0.7110 9.097 6.056 0.2088E-02 0.0613 0.0117 7.039 0.6582 0.02871 71907 0.264 0.0000 0.6931 8.911 5.706 0.2043E-02 0.0636 0.0111 6.469 0.6345 0.02852 71363 0.274 0.0000 0.6741 8.721 5.380 0.1997E-02 0.0659 0.0106 5.937 0.6125 0.02847 70566 0.284 0.0000 0.6537 8.526 5.074 0.1951E-02 0.0682 0.0100 5.449 0.5951 0.02883 68690 0.294 0.0000 0.6301 8.296 4.769 0.1896E-02 0.0705 0.0091 5.014 0.5857 0.02999 64640 0.303 0.0000 0.6002 7.988 4.440 0.1824E-02 0.0728 0.0078 4.638 0.5886 0.03271 57189 0.313 0.0000 0.5584 7.537 4.055 0.1720E-02 0.0751 0.0060 4.329 0.6110 0.03893 45098 0.324 0.0000 0.4919 6.824 3.557 0.1555E-02 This gives detailed aerodynamic characteristics of the blade along the radius. The first three columns are interpolated from the input geometry data in the prop file, and can be plotted and checked for smoothness. The remaining columns are computed via the propeller aerodynamic model. Cl = local blade airfoil lift coefficient. The inner radii are stalled at the CLmax limit Cd = local blade profile drag coefficient. Note the large Cd at the stalled stations. Re = local chord Reynolds number, which influences the Cd. Ma = local Mach number. This modifies the Cl and Cd functions. effi = local induced efficiency. This is by definition zero for a static case. effp = local profile efficiency. Wa = local axial propwash velocity. Aswirl = prowash angle from axial adv_wake = local wake advance ratio (somewhat arcane). If this output is dumped into a file, GnuPlot can be used to plot it. For example, % qprop cam6x3 s400-6v-dd 0.0 0. 8.0 > out.dat % gnuplot gnuplot> plot "out.dat" u 1:2 w linesp gnuplot> plot "out.dat" u 1:3 w linesp gnuplot> plot "out.dat" u 1:4 w linesp gnuplot> plot "out.dat" u 1:10 w linesp will plot the interpolated chord and blade angle distributions, and also the local cl and propwash velocity. Multi-point runs ---------------- For multi-point runs, one or more of the four numerical arguments is replaced by the following constructs: Vel replaced by Vel1,Vel2,dVel Rpm replaced by Rpm1,Rpm2,dRpm Volt replaced by Volt1,Volt2,dVolt Dbeta replaced by Dbeta1,Dbeta2,dDbeta . . Vel replaced by Vel1,Vel2/NVel Rpm replaced by Rpm1,Rpm2/NRpm Volt replaced by Volt1,Volt2/NVolt Dbeta replaced by Dbeta1,Dbeta2/NDbeta . . etc. The constructs indicate a range of individual parameter values. For example, 5.0,10.0,1.0 -> 5.0 6.0 7.0 8.0 9.0 10.0 0.0,1.0/10 -> 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Note that the step size can be given directly, as ",1.0" above, or indirectly via the number of intervals, as "/10" above. The output will now consist of the operating parameters for all combinations of the specified parameters thus specified. For the files used as examples above, % qprop cam6x3 s400-6v-dd 0.0,12.0/6 0.0 7.0 0.0 the following output is produced: # QPROP Version 1.20 # # Graupner CAM 6x3 folder # # Speed-400 3321 (6V) direct drive # 0.31000 R (Ohm) # 0.77000 Io (Amp) # 2760.0 Kv (rpm/Volt) # # rho = 1.2250 kg/m^3 # mu = 0.17800E-04 kg/m-s # a = 340.00 m/s # # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 # # V(m/s) rpm Dbeta T(N) Q(N-m) Pshaft(W) Volts Amps effmot effprop adv CT CP DV(m/s) eff Pelec Pprop cl_avg cd_avg 0.000 0.1259E+05 0.000 2.712 0.2454E-01 32.36 7.000 7.8635 0.5879 0.0000 0.00000 0.1001E-07 0.3019E-10 0.3957 0.0000 55.04 0.000 0.7713 0.4079E-01 2.400 0.1263E+05 0.000 2.480 0.2440E-01 32.26 7.000 7.8210 0.5893 0.1845 0.00060 0.9099E-08 0.2983E-10 0.0297 0.1087 54.75 5.953 0.6983 0.3701E-01 4.800 0.1271E+05 0.000 2.220 0.2405E-01 32.02 7.000 7.7203 0.5925 0.3328 0.00120 0.8035E-08 0.2901E-10 0.0133 0.1972 54.04 10.66 0.6135 0.3432E-01 7.200 0.1286E+05 0.000 1.939 0.2347E-01 31.60 7.000 7.5534 0.5977 0.4417 0.00178 0.6861E-08 0.2769E-10 0.0078 0.2640 52.87 13.96 0.5213 0.3272E-01 9.600 0.1307E+05 0.000 1.640 0.2260E-01 30.94 7.000 7.3013 0.6053 0.5088 0.00234 0.5613E-08 0.2579E-10 0.0049 0.3080 51.11 15.74 0.4248 0.3213E-01 12.000 0.1338E+05 0.000 1.326 0.2137E-01 29.94 7.000 6.9476 0.6156 0.5314 0.00286 0.4336E-08 0.2330E-10 0.0032 0.3271 48.63 15.91 0.3276 0.3256E-01 where... V = airspeed rpm = prop rpm Dbeta = pitch change in degrees T = propeller thrust Q = propeller torque Pshaft = shaft power = Q*w , w = rpm*pi/30 Volts = motor voltage Amps = motor current effmot = motor efficiency = Pshaft/(Volts*Amps) effprop= prop efficiency = TV/Pshaft adv = advance ratio = V/(w*R) CT = thrust coefficient = T / (0.5 rho (wR)^2 pi R^2) CP = torque coefficient = Q / (0.5 rho (wR)^2 pi R^3) DV = slipstream velocity increment eff = overall drive efficiency = effmot*effprop Pelec = electrical power = Amps*Volts Pprop = prop power = V*T cl_avg = power-weighted average of local cl(r) cd_avg = power-weighted average of local cd(r) The parameter table format above can be dumped into a file and plotted in GnuPlot. For example, % qprop cam6x3 s400-6v-dd 0.0,12.0/6 0.0 7.0 0.0 > out.dat % gnuplot gnuplot> plot "out.dat" u 1:4 w linesp will generate lines of Thrust vs Airspeed for the fixed voltage of 7V. Alternatively, the file can also be imported into a spreadsheet for plotting. More than one argument can be given a range construct. With the command % qprop cam6x3 s400-6v-dd 0.0,12.0/7 0.0 5.0,9.0,1.0 0.0 the following output is produced: # QPROP Version 1.20 # # Graupner CAM 6x3 folder # # Speed-400 3321 (6V) direct drive # 0.31000 R (Ohm) # 0.77000 Io (Amp) # 2760.0 Kv (rpm/Volt) # # rho = 1.2250 kg/m^3 # mu = 0.17800E-04 kg/m-s # a = 340.00 m/s # # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 # # V(m/s) rpm Dbeta T(N) Q(N-m) Pshaft(W) Volts Amps effmot effprop adv CT CP DV(m/s) eff Pelec Pprop cl_avg cd_avg 0.000 9497. 0.000 1.531 0.1474E-01 14.66 5.000 5.0289 0.5828 0.0000 0.00000 0.9928E-08 0.3186E-10 0.2973 0.0000 25.14 0.000 0.7663 0.4920E-01 2.000 9529. 0.000 1.384 0.1461E-01 14.58 5.000 4.9917 0.5840 0.1900 0.00067 0.8920E-08 0.3137E-10 0.0199 0.1109 24.96 2.769 0.6855 0.4460E-01 4.000 9598. 0.000 1.217 0.1433E-01 14.40 5.000 4.9107 0.5865 0.3379 0.00133 0.7726E-08 0.3033E-10 0.0088 0.1982 24.55 4.866 0.5906 0.4131E-01 6.000 9710. 0.000 1.031 0.1387E-01 14.11 5.000 4.7800 0.5903 0.4386 0.00197 0.6398E-08 0.2870E-10 0.0050 0.2589 23.90 6.187 0.4868 0.3961E-01 8.000 9878. 0.000 0.8302 0.1320E-01 13.65 5.000 4.5839 0.5956 0.4865 0.00258 0.4978E-08 0.2637E-10 0.0030 0.2898 22.92 6.641 0.3778 0.3950E-01 10.000 0.1011E+05 0.000 0.6148 0.1224E-01 12.97 5.000 4.3087 0.6019 0.4741 0.00315 0.3517E-08 0.2334E-10 0.0018 0.2854 21.54 6.148 0.2680 0.4098E-01 12.000 0.1043E+05 0.000 0.3863 0.1098E-01 11.99 5.000 3.9440 0.6080 0.3866 0.00366 0.2079E-08 0.1970E-10 0.0009 0.2350 19.72 4.635 0.1623 0.4370E-01 0.000 0.1109E+05 0.000 2.094 0.1947E-01 22.60 6.000 6.3961 0.5889 0.0000 0.00000 0.9967E-08 0.3088E-10 0.3478 0.0000 38.38 0.000 0.7687 0.4437E-01 2.000 0.1112E+05 0.000 1.925 0.1935E-01 22.52 6.000 6.3615 0.5901 0.1710 0.00057 0.9115E-08 0.3053E-10 0.0276 0.1009 38.17 3.851 0.7002 0.4055E-01 4.000 0.1118E+05 0.000 1.735 0.1908E-01 22.35 6.000 6.2858 0.5925 0.3106 0.00114 0.8119E-08 0.2977E-10 0.0125 0.1840 37.72 6.940 0.6208 0.3775E-01 6.000 0.1129E+05 0.000 1.528 0.1866E-01 22.06 6.000 6.1645 0.5964 0.4157 0.00169 0.7020E-08 0.2858E-10 0.0073 0.2479 36.99 9.169 0.5344 0.3600E-01 8.000 0.1144E+05 0.000 1.307 0.1804E-01 21.61 6.000 5.9848 0.6019 0.4838 0.00223 0.5844E-08 0.2689E-10 0.0047 0.2912 35.91 10.46 0.4432 0.3524E-01 10.000 0.1165E+05 0.000 1.073 0.1718E-01 20.96 6.000 5.7350 0.6092 0.5120 0.00273 0.4625E-08 0.2467E-10 0.0031 0.3119 34.41 10.73 0.3502 0.3551E-01 12.000 0.1194E+05 0.000 0.8280 0.1604E-01 20.04 6.000 5.4051 0.6181 0.4957 0.00320 0.3401E-08 0.2196E-10 0.0020 0.3064 32.43 9.936 0.2584 0.3673E-01 0.000 0.1259E+05 0.000 2.712 0.2454E-01 32.36 7.000 7.8635 0.5879 0.0000 0.00000 0.1001E-07 0.3019E-10 0.3957 0.0000 55.04 0.000 0.7713 0.4079E-01 2.000 0.1262E+05 0.000 2.520 0.2444E-01 32.29 7.000 7.8349 0.5888 0.1561 0.00050 0.9262E-08 0.2995E-10 0.0361 0.0919 54.84 5.040 0.7114 0.3781E-01 4.000 0.1268E+05 0.000 2.310 0.2419E-01 32.12 7.000 7.7601 0.5912 0.2877 0.00100 0.8404E-08 0.2933E-10 0.0166 0.1701 54.32 9.238 0.6428 0.3505E-01 6.000 0.1278E+05 0.000 2.082 0.2379E-01 31.83 7.000 7.6464 0.5948 0.3923 0.00149 0.7459E-08 0.2842E-10 0.0100 0.2333 53.52 12.49 0.5682 0.3340E-01 8.000 0.1292E+05 0.000 1.841 0.2321E-01 31.41 7.000 7.4797 0.5999 0.4688 0.00197 0.6451E-08 0.2712E-10 0.0066 0.2813 52.36 14.73 0.4895 0.3241E-01 10.000 0.1312E+05 0.000 1.588 0.2242E-01 30.80 7.000 7.2498 0.6068 0.5158 0.00243 0.5401E-08 0.2541E-10 0.0046 0.3130 50.75 15.88 0.4086 0.3213E-01 12.000 0.1338E+05 0.000 1.326 0.2137E-01 29.94 7.000 6.9476 0.6156 0.5314 0.00286 0.4336E-08 0.2330E-10 0.0032 0.3271 48.63 15.91 0.3276 0.3256E-01 0.000 0.1402E+05 0.000 3.377 0.2992E-01 43.94 8.000 9.4184 0.5831 0.0000 0.00000 0.1005E-07 0.2968E-10 0.4416 0.0000 75.35 0.000 0.7742 0.3801E-01 2.000 0.1404E+05 0.000 3.163 0.2983E-01 43.87 8.000 9.3913 0.5839 0.1442 0.00045 0.9382E-08 0.2949E-10 0.0452 0.0842 75.13 6.326 0.7205 0.3539E-01 4.000 0.1411E+05 0.000 2.933 0.2958E-01 43.70 8.000 9.3208 0.5860 0.2685 0.00090 0.8625E-08 0.2900E-10 0.0211 0.1573 74.57 11.73 0.6599 0.3291E-01 6.000 0.1420E+05 0.000 2.684 0.2921E-01 43.43 8.000 9.2132 0.5893 0.3708 0.00135 0.7792E-08 0.2826E-10 0.0129 0.2185 73.71 16.11 0.5938 0.3139E-01 8.000 0.1433E+05 0.000 2.424 0.2867E-01 43.03 8.000 9.0570 0.5939 0.4507 0.00178 0.6905E-08 0.2723E-10 0.0087 0.2676 72.46 19.39 0.5243 0.3033E-01 10.000 0.1451E+05 0.000 2.153 0.2793E-01 42.45 8.000 8.8431 0.6001 0.5072 0.00219 0.5980E-08 0.2586E-10 0.0062 0.3043 70.75 21.53 0.4525 0.2979E-01 12.000 0.1475E+05 0.000 1.873 0.2696E-01 41.66 8.000 8.5633 0.6081 0.5395 0.00259 0.5035E-08 0.2416E-10 0.0045 0.3281 68.51 22.48 0.3800 0.2978E-01 0.000 0.1539E+05 0.000 4.083 0.3557E-01 57.31 9.000 11.0507 0.5762 0.0000 0.00000 0.1009E-07 0.2931E-10 0.4856 0.0000 99.46 0.000 0.7772 0.3578E-01 2.000 0.1541E+05 0.000 3.849 0.3548E-01 57.25 9.000 11.0248 0.5769 0.1345 0.00041 0.9486E-08 0.2915E-10 0.0548 0.0776 99.22 7.698 0.7284 0.3343E-01 4.000 0.1546E+05 0.000 3.599 0.3525E-01 57.08 9.000 10.9579 0.5788 0.2522 0.00082 0.8805E-08 0.2874E-10 0.0259 0.1460 98.62 14.40 0.6738 0.3116E-01 6.000 0.1555E+05 0.000 3.330 0.3489E-01 56.83 9.000 10.8554 0.5817 0.3516 0.00123 0.8056E-08 0.2814E-10 0.0160 0.2045 97.70 19.98 0.6143 0.2976E-01 8.000 0.1568E+05 0.000 3.051 0.3438E-01 56.45 9.000 10.7079 0.5858 0.4323 0.00162 0.7261E-08 0.2728E-10 0.0110 0.2533 96.37 24.41 0.5517 0.2871E-01 10.000 0.1585E+05 0.000 2.762 0.3369E-01 55.92 9.000 10.5071 0.5913 0.4939 0.00201 0.6432E-08 0.2615E-10 0.0080 0.2920 94.56 27.62 0.4870 0.2804E-01 12.000 0.1607E+05 0.000 2.464 0.3278E-01 55.18 9.000 10.2456 0.5985 0.5359 0.00238 0.5580E-08 0.2475E-10 0.0059 0.3207 92.21 29.57 0.4213 0.2779E-01 Again, the two-parameter table format above can be dumped into a file and plotted in GnuPlot. For example, % qprop cam6x3 s400-6v-dd 0.0,12.0/7 0.0 5.0,9.0,1.0 0.0 > out.dat % gnuplot gnuplot> plot "out.dat" u 1:4 w linesp will generate lines of Thrust vs Airspeed for the five voltages 5-9V. Alternatively, the file can also be imported into a spreadsheet for plotting. Operating-parameter run file ---------------------------- This optional file specifies the airspeeds and voltages to be imposed on the prop/motor combination. The file format is 0.0 12.0 7 ! Vel1 Vel2 Nvel (m/s) 10000 16000 0 ! Rpm1 Rpm2 Nrpm 5.0 9.0 5 ! Volt1 Volt2 Nvolt -2.0 2.0 3 ! Dbet1 Dbet2 NDbet 1) Line 1 specifies flight velocities from Vel1 to Vel2 in Nvel samples. For the example line 1, the velocities are Vel = 0 2 4 6 8 10 12 (m/s) 2) Line 2 specifies prop rpms from Rpm1 to Rpm2 in Nrpm samples: Special action is taken depending on Nrpm... If Nrpm=0, then Voltages are set, Rpms are computed (Line 2 data is ignored) If Nrpm>0, then Rpms are set, Voltages are computed (Line 3 data is ignored) 3) Line 3 specifies motor voltages from Volt1 to Volt2, in Nvolt samples. This voltage is simply passed to SUBR.MOTORQ, and can represent any power control parameter, such as "throttle" for an IC engine. 4) Line 4 specifies blade pitch change, in degrees. This line is optional.