Recover
Details and Model
1 Introduction
For an introduction to the problem we refer to Recover, Summary and Results.
2 Derivation of the equations.
m1= mass of the boat + that part of the mass of the sculler that does not move
with respect to the boat + hydrodynamic added mass
m2= that part of the mass of the sculler that moves with respect to the boat
x = absolute coordinate of the boat
y = relative coordinate of the mass m2 with respect to the mass m1
z = absolute coordinate of the joint centre of mass of m1 and m2
y = 0 when the mass m1 is in the catch position (unlike in Simulation of Rowing)
The relation between x, y and z is given by:
and:
The equation of motion is:
F = the external force on the system in +x direction, in
this case only the resistance of the hull in the water
C1 = a composed coefficient [Ns2/m2]
Replace z by x:
Rearranging yields:
This is the
basic equation for the simulation model.
with:
The SIMULINK model then
becomes:
Fig
2.2 The
SIMULINK model
vv
3 Initial
value and final value of hull speed.
Already defined is the mean seat speed vm. The initial seat speed for the three modes is vo (i) = [-vm -2vm 0].
The inital hull speed Vo(i) at the start of the simulation follows from the conservation of momentum
The simulation ends with the hull speed Ve(i) and the seat speeds
ve(i) = [-vm 0 -2vm].
The final hull speed, when the seat has come to rest follows then from:
The energy outflow during the recover is calculated from
3 Running the program
The SIMULINK model is run from a Matlab shell. The code of the shell is presented below.
% file reccalc.m c:\aaa\roeilift\recover\reccalc.m
% Analysis of
boatspeed during the recover under the influence
% of different
sliding speeds.
% input data
m1 = 45; % [kg]
boat mass
m2 = 65; % [kg]
mass moving in the boat
C = 2.5; %
[N.s2/m2] reistance of hull
s = 0.9; % [m]
sliding length
T = 1.0; % [s]
duration of recover
Vb = 4.0; % [m/s]
boatspeed at the end of the pull through
%
% initial
calculations
%
m = m1+m2;
A = m2/m;
B = C/m;
vm = s/T; % [m/s]
mean sliding speed for all cases
yddot = [0 +2*vm/T
-2*vm/T]; % sliding acceleration case 1,2 and 3
v00 = [-vm -2*vm
0]; % [m/s] initial sliding speed case 1, 2 and 3
vee = [-vm 0
-2*vm]; % [m/s] final sliding speed, case 1, 2 and 3
%
%prepare graph
%
figure
axis([0 T 2 6])
hold on
grid
xlabel('time [s]')
ylabel('velocity
[m/s]')
title('boat speed
during recover')
col(1)='w';
col(2)='r'; col(3)='b';
%
% loop for three
cases
%
for i=1:3;
v0 = v00(i); %
selection of initial sliding speed
V0 = (m*Vb -
m2*v0)/m; % boat speed at start of recover
D = yddot(i)*m2/m;
% call simulink
model recsim
[t,x,y]=rk45('recsim',T)
figure(1)
plot(tout,xdotout,col(i));
n=length(xout);
dist(i)=xout(n); %
[m] distance covered during recover
%
% calculating
boatspeed after halt at the front stops
%
Vf(i)=xdotout(n)+A*vee(i);
% [m/s] final boatspeed
%
%energy flow out
during recover
%
E(i)=
0.5*m*(Vb^2-Vf(i)^2); % [J]
%
% output to screen
% pause(10)
end % end i
fprintf(1,'*************** final results ***************\n')
for ii=1:3;
fprintf(1,'%8.4f %8.4f
%8.4f \n',...
dist(ii), Vf(ii), E(ii))
end; % ( end ii)