Landing in a Crosswind
A&AE 421
Landing In a Crosswind
Homework: Due Wednesday 11/1/06
You have been e-mailed the Matlab code contained in this document. For the Cessna 182 aircraft given on pages 480-482 of Roskam, find the following for the approach flight condition. Watch your units.
1. Plot rudder deflection, aileron deflection, and bank angle versus sideslip angle () for up to 12 degrees. Also plot these quantities versus crosswind (knots). Hint. The code is set up to make these plots but for a different aircraft. You need only change the vehicle specific constants in the Matlab code to those for the Cessna 182.
2. How much rudder deflection is required to land in a 10 knot crosswind using the conventional method?
3. What would the crab angle be if the pilot of the Cessna chose to land in a 10 knot crosswind with a crab angle?
Lesson Objectives:
What are the control techniques for landing in a crosswind?
Landing with a crab angle (B-52), see sketch 12
requires special landing gear
Conventional method (most airplanes), see sketch 2
What are the control power implications of landing in a crosswind?
for design of the rudder and aileron
What do the Military Specifications on Flying Qualities say about landing in a crosswind?
(portions of this document are attached)
What are typical values of crosswind to use in designing control surfaces?
What are the allowable control forces for landing in a crosswind?
Solution Technique:
The analysis required for this involves finding the steady-state solution to the Lateral-Directional equations of motion (roll, yaw and side-force equations of motion). See attached MATLAB code.
See section 4.2.6 of Roskam (Lateral-Directional Stability and Control Characteristics for Steady State, Straight Line Flight), pp 216-218.
Landing in a Crosswind Using a Crab Angle
Landing in a Crosswind with Sideslip
(Conventional method)
Crosswind effects plotted versus sideslip angle (beta, degrees)
Crosswind effects plotted versus crosswind component (knots)
% Investigation of lateral-directional trim in a crosswind
% See page 223 of Roskam for aircraft data
%
clear
disp(' ')
disp(' Start here')
disp(' ')
%
% INPUTS
%
W=8750 % pounds
rho=.002378 % slugs/ft^3
U1=270 % ft/sec
S=253 % ft^2
LT1=0 % ft-lbf
NT1=0 % ft-lbf
DND1=0 % ft-lbf
b=38 % ft
Cyb=-.0105 % per degree
Cyda=0 % per degree
Cydr= .0021 % per degree
Clb=-.0029 % per degree
Clda=.0024 % per degree
Cldr=.0002 % per degree
Cnb=.0018 % per degree
Cnda=.0005 % per degree
Cndr=-.001 % per degree
gamma=0 % degree
deltabeta=1 % degree
nbeta=12
%
% Problem statement
% Given beta, find phi(deg), da(deg) and dr(deg)
% x=sin(phi),da,dr
% Ax=B*beta
%
% Set up dimensions
%
BETA=zeros(1,nbeta);
DA=zeros(1,nbeta);
DR=zeros(1,nbeta);
PHI=zeros(1,nbeta);
xwindkn=zeros(1,nbeta);
%
% Compute intermediate items
%
d2r=pi/180
qbar=.5*rho*U1*U1
U1knots=U1*.5925 % knots
a1=[W*cos(gamma*d2r)/(qbar*S), 0, 0]'
a2=[Cyda, Clda, Cnda]'
a3=[Cydr, Cldr, Cndr]'
A=[a1 a2 a3]
B=[-Cyb; -Clb; -Cnb]
AIB=inv(A)*B;
%
for i=0:nbeta-1
beta=i*deltabeta;
x=AIB*beta;
PHI(i+1)=asin(x(1))/d2r;
DA(i+1)=x(2);
DR(i+1)=x(3);
BETA(i+1)=beta;
end
windkn=sin(BETA*d2r)*U1*.5925
%
% Plot results vs beta
%
figure(1)
subplot(3,1,1)
plot(BETA,DR)
heading=['Landing in a crosswind, U1= ',num2str(U1knots),' knots, right sideslip (beta+)']
title(heading)
ylabel2('rudder (deg)')
text2(.05,.8,'Dr+ means trailing edge left, push left pedal, nose left of wind, wind hits on the right side')
%
subplot(3,1,2)
plot(BETA,DA)
ylabel2('aileron (deg)')
text2(.05,.8,'Da+ means right aileron up, push stick right')
%
subplot(3,1,3)
plot(BETA,PHI)
text2(.05,.6,'Right wing down, right bank angle')
ylabel2('phi (deg)',-.10,.9)
xlabel('beta (deg)')
%
% Plot results vs crosswind velocity in knots
%
figure(2)
subplot(3,1,1)
plot(windkn,DR)
title(heading)
xlabel('crosswind (knots)')
ylabel2('rudder (deg)')
text2(.05,.8,'Dr+ means trailing edge left, push left pedal, nose left of wind, wind hits on the right side')
text2(.05,.65,'Crosswind=U1*sin(beta)')
%
subplot(3,1,2)
plot(windkn,DA)
xlabel('crosswind (knots)')
ylabel2('aileron (deg)')
text2(.05,.8,'Da+ means right aileron up, push stick right')
%
subplot(3,1,3)
plot(windkn,PHI)
xlabel('crosswind (knots)')
text2(.05,.6,'Right wing down, right bank angle')
ylabel2('phi (deg)',-.10,.9)
