Details and Model
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:
C1 = a composed coefficient [Ns2/m2]
Replace z by x:
This is the basic equation for the simulation model.
The SIMULINK model then becomes:
The SIMULINK model
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
axis([0 T 2 6])
title('boat speed during recover')
col(1)='w'; col(2)='r'; col(3)='b';
% loop for three cases
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
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
end % end i
fprintf(1,'*************** final results ***************\n')
fprintf(1,'%8.4f %8.4f %8.4f \n',...
dist(ii), Vf(ii), E(ii))
end; % ( end ii)