# wingflexer.nas - A simple wing flex model. # # Copyright (C) 2014 Thomas Albrecht # # This program is free software; you can redistribute it and/or # modify it under the terms of the GNU General Public License as # published by the Free Software Foundation; either version 2 of the # License, or (at your option) any later version. # # This program is distributed in the hope that it will be useful, but # WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; if not, write to the Free Software # Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. # # --> # g # +-----+ +-----+ # <--- | m_w |---/\/\/\---| | # +-----+ +-----+ # Lift wing spring fuselage # force mass # # We integrate # # .. k d . 0.5*F_L .. # 0 = -z + --- z + ---- z - ------- - g - z_f # m_w m_w m_w # # where # # z : deflection # k : wing stiffness # d : damping # m_w = m_dw + fuel_frac * m_fuel # Total wing mass. Because the fuel is distributed over the wing, we use # a fraction of the fuel mass in the calculation. # 0.5*F_L : lift force/2 (we look at one wing only) # .. # z_f : acceleration of the frame of reference (fuselage) # # and write the deflection (z + z_ofs) in meters to /sim/model/wing-flex/z-m. # The offset z_ofs is calculated automatically and ensures that the dry wing # (which still has a non-zero mass) creates neutral deflection. # # Discretisation by first order finite differences: # # z_0 - 2 z_1 + z_2 k d (z_0 - z_1) 1/2 F_L .. # ----------------- + --- z_1 + --- ----------- - ------- - g - z_f = 0 # dt^2 m_w m_w dt m_w # # It is convenient to divide k and d by a (constant) reference mass: # # K = k / m_dw # D = d / m_dw # # To adapt this to your aircraft, you need m_w, K, D. # How to estimate these? # # 1. Assume a dry wing mass m_dw. Research the wing fuel mass m_fuel. # # 2. Obtain estimates of # - the deflection z_flight in level flight, e.g by comparing photos # of the real aircraft on ground and in air, # - the wing's eigenfrequency, perhaps from videos of the wing's oscillation in # turbulence, # - the deflection with full and empty tanks while sitting on the ground. # # 3. Compute K to match in flight deflection with full tanks: # K = g * (m_ac / 2 - (fuel_frac * m_fuel)) / (z_in_flight / z_fac) / m_dw # # where # m_ac : aircraft mass # g : 9.81 m/s^2 # z_fac: scaling factor for the deflection, start with 1. # # 4. Compute the eigenfrequency of this system for full and empty wing tanks: # f_full = sqrt(K * m_dw / (m_dw + fuel_frac * m_fuel)) / (2 pi) # f_empty = sqrt(K) / (2 pi) # # Ideally we want our model to match the eigenfrequency, the deflection # while sitting on the ground with full or empty tanks, and the deflection # during a hard landing. Getting real-world data for the latter is difficult. # # There's a python script wingflexer.py which assists you in tuning the parameters. # # Here are some relations: # - a lower wing mass increases the eigenfrequency, and weakens the touchdown bounce # - a higher stiffness K reduces the deflection and increases the eigenfrequency # # The 787 is known for its very flexible wings; the deflection in # unaccelerated flight is quoted as z = 3 m. One wing tank of FG's 787-8 holds # 23,000 kg of fuel. Because the fuel is distributed over the wing, we use a # fraction of the fuel mass in the calculation: fuel_frac = 0.75. For the same reason # we don't use the true wing mass, but rather something that makes our model look # plausible. # # So assuming a wing mass of 12000 kg, we get K=25.9 and f_empty = 0.5 Hz. # That frequency might be a bit low, videos of a 777 wing in turbulence show about # 2-3 Hz. (I didn't research 787 videos). # # To increase it, we could either reduce m_dw or increase K. A lower m_dw results # in a rather weak bounce on touchdown which might look odd. A higher K reduces # the deflection z_flight, but we can simply scale the animation to account for # that. We'll multiply the deflection z by a factor z_fac to get an angle for the # animation later on anyway. So repeat 3. and 4. using e.g. z_fac = 10. # Now K = 259 and f_empty=2.6 Hz. While our model spring now only deflects # to 0.3 m instead of 3 m, the animation scale factor will make sure the wing # bends to 3 m. This way, we can match both eigenfrequency and observed deflection, # and still get a realistic bounce on touch down. Finally, adjust D such that an # impulse is damped out after about one or two oscillations; D = 12 seems to work # OK in our example. # # It's difficult to get real-world data on the deflection during touchdown. # Touchdown at more than 10 ft/s is considered a hard landing. There's a video of # a hard landing of an A346 (http://avherald.com/h?article=471e70e9), showing the # wings bend perhaps 1 m. But I couldn't find any data for the acceleration over # time during a hard landing. # # To assist you in tuning parameters for the touchdown bounce we can give our # wing mass the touchdown vertical speed via /sim/model/wing-flex/sink-rate_fps. # # Our model outputs the deflection in meters, but the animation expects an # angle. It is up to you calculate an appropriate factor, depending on your wing # span and number of segments in the animation. Also don't forget to include z_fac. # # To use this with your JSBSim aircraft, use # # io.include("Aircraft/Generic/wingflexer.nas"); # WingFlexer.new(1, K, D, mass_dry_wing_kg, # fuel_fraction, fuel_node_left, fuel_node_right); # # with apropriate parameters. # # Yasim does not write the lift to the property tree. But you can create a helper # function which computes the lift as # lift_force_lbs = aircraft_weight_lbs * load_factor - total_weight_on_wheels_lbs # and write lift_force_lbs to /fdm/jsbsim/forces/fbz-aero-lbs (or another location # passed to WingFlexer.new() as lift_node). # # TODO # - write Yasim helper # - perhaps use analytical solution of ODE # - input for fuselage acceleration should rather be acceleration at CG -- find property io.include("Aircraft/Generic/updateloop.nas"); var WingFlexer = { parents: [Updatable], # FIXME: these defaults make the 787-8 wing flex look realistic, which is certainly not # the most generic airliner wing. Once someone obtains a set of parameters for e.g. # the 777, use them here. new: func(enable = 1, K=259., D=12., mass_dry_wing_kg = 12000., fuel_fraction = 0.75, fuel_node_left = "consumables/fuel/tank/level-kg", fuel_node_right = "consumables/fuel/tank[1]/level-kg", node = "sim/model/wing-flex/", lift_node = "fdm/jsbsim/forces/fbz-aero-lbs") { var m = { parents: [WingFlexer] }; m.node = node; m.m_dw = mass_dry_wing_kg; m.k = K * m.m_dw; m.d = D * m.m_dw; m.fuel_frac_on_2 = fuel_fraction / 2.; # so we don't have to divide each frame m.fuel_node_left = fuel_node_left; m.fuel_node_right = fuel_node_right; m.lift_node = lift_node; m.loop = UpdateLoop.new(components: [m], enable: enable); return m; }, reset: func { me.z = 0.; me.z1 = 0.; me.z2 = 0.; setprop(me.node ~ "z-m", 0.); setprop(me.node ~ "mass-wing-kg", me.m_dw); setprop(me.node ~ "K", me.k/me.m_dw); setprop(me.node ~ "D", me.d/me.m_dw); setprop(me.node ~ "fuel-fac", me.fuel_frac_on_2 * 2); setprop(me.node ~ "sink-rate_fps", 0.); me.g_on_2_times_LB2KG = getprop("/environment/gravitational-acceleration-mps2") / 2. * globals.LB2KG; me.calc_z_ofs(); setlistener(me.node ~ "mass-wing-kg", func(the_node) { me.m_dw = the_node.getValue(); me.calc_z_ofs(); }, 0, 0); setlistener(me.node ~ "K", func(the_node) { me.k = the_node.getValue() * me.m_dw; me.calc_z_ofs(); }, 0, 0); setlistener(me.node ~ "D", func(the_node) { me.d = the_node.getValue() * me.m_dw; }, 0, 0); setlistener(me.node ~ "fuel-fac", func(the_node) { me.fuel_frac_on_2 = the_node.getValue() / 2.; }, 0, 0); # The following helped me getting wing flex look OK. It's no longer # needed once you get the parameters right, so it's disabled by default. # Look for DEV to re-enable. # Include z-fac here, so you don't have to adjust the animation .xml # setprop(me.node ~ "z-fac", 3.); # me.last_dt = 1/30.; # me.max_z = 0.; # setlistener(me.node ~ "sink-rate_fps", func(the_node) { # var dz = me.last_dt * the_node.getValue() * globals.FT2M; # me.z0 = me.z1 - dz; # me.z2 = me.z1 + dz; # me.max_z = 0.; # }, 1, 0); }, calc_z_ofs: func() { print ("wingflex: calc z_ofs"); me.z_ofs = getprop("/environment/gravitational-acceleration-mps2") * me.m_dw / me.k; }, update: func(dt) { # limit time step to avoid numerical instability if (dt > 0.2) dt = 0.2; # DEV: # me.last_dt = dt; # fuselage z (up) acceleration in m/s^2 # we get -g in unaccelerated flight, and large negative numbers on touchdown var a_f = getprop("accelerations/pilot/z-accel-fps_sec") * globals.FT2M; # lift force. Convert to N and use 1/2 (one wing only) var F_l = getprop(me.lift_node) * me.g_on_2_times_LB2KG; # compute total mass of one wing, using the average fuel mass in both wing tanks. # The averaging factor 0.5 is lumped into fuel_frac_on_2 me.m = me.m_dw + me.fuel_frac_on_2 * (getprop(me.fuel_node_left) + getprop(me.fuel_node_right)); # integrate discretised equation of motion # reverse sign of F_l because z in JSBsim body coordinate system points down me.z = (2.*me.z1 - me.z2 + dt * ((me.d * me.z1 + dt * (-F_l - me.k * me.z1))/me.m + dt * a_f)) / (1. + me.d * dt / me.m); me.z2 = me.z1; me.z1 = me.z; me.z += me.z_ofs; # output to property setprop(me.node ~ "z-m", me.z); # DEV: scale output and log max deflection # var z_fac = getprop(me.node ~ "z-fac"); # if (me.z * z_fac < me.max_z) me.max_z = me.z * z_fac; # print (sprintf(" z %4.2f max %4.2f m %7.1f", me.z * z_fac, me.max_z, me.m)); # setprop(me.node ~ "z-m", me.z * z_fac); }, enable: func { me.loop.enable() }, disable: func { me.loop.disable() }, };