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:

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;

[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)

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