Recover

Details and Model

For an introduction to the problem we refer to Recover, Summary and Results.

**2 Derivation of the equations.**

m_{1}= mass of the boat + that part of the mass of the sculler that does
not move

with respect to the boat + hydrodynamic added mass

m_{2}= 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 m_{2} with respect to the mass m_{1}

z = absolute
coordinate of the joint centre of mass of m_{1} and m_{2}

y = 0 when the mass m_{1} is in the catch position (unlike in Simulation of Rowing)

The relation between x, y and z is given by:

_{}

and:

_{}

_{}_{}

_{}

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 v_{m}. The initial seat speed for the three
modes is v_{o} (i) = [-v_{m}
-2v_{m} 0].

The inital hull
speed V_{o}(i) at the start of the simulation follows from the
conservation of momentum

_{}

The simulation
ends with the hull speed V_{e}(i) and the seat speeds

v_{e}(i)
= [-v_{m} 0 -2v_{m}].

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)