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initial import of wingflexer.nas

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Thomas Albrecht 2015-01-14 19:13:01 +11:00
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# 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
# <rotate> 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 <rotate> 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() },
};