free internet rowing model (firm)

FREE INTERNET ROWING MODEL
(FIRM)
EXAMPLES: Pairs
March 25, 2015
FIRM IS RESEARCH CODE!
Please check all estimates generated by the program
against experimental results before committing any
time or funds to your project as no liability can be
accepted by Cyberiad.
c
2015
Cyberiad
All Rights Reserved
Contents
1 INTRODUCTION
1
2 W2-: Women’s Pairs
2
3 M2-: Men’s Pairs
7
1
INTRODUCTION
Two pairs examples are included in this version of FIRM. More will be added in future versions.
1
2
W2-: Women’s Pairs
The on-water trial for these two heavyweight female rowers, “Gigi” and “Qing”, was conducted over 2000m on a summer
morning. Air and water temperatures were not recorded: they were estimated as 15◦ C and 23◦ C respectively. Measured
values of rigging details, oar angles, gate normal forces, and their anthropometry were used as input to FIRM. Body angle
regimes were not recorded but were estimated by the author using a complicated fitting process.
Table 1: Summary of experimental results for this simulation: number of strokes, stroke rate, non-dimensional pull phase duration
(tp /ts ), minimum hull velocity (Umin ), maximum hull velocity (Umax ), and mean hull velocity (U ).
Item
Nstrokes
Rate (spm)
tp /ts
Umin (ms−1 )
Umax (ms−1 )
U (ms−1 )
Value
35.968
0.543
3.363
5.760
4.803
41
±0.315
±0.010
±0.046
±0.068
±0.055
Table 1 summarises the main quantities relating to the simulation for this crew. Values are given ± one standard deviation.
Table 2: Experimental oar-related values for this simulation: Minimum and maximum oar angles, and maximum gate normal force.
Name
Gigi
Qing
Min. Angle
(degrees)
Port Oar
Max. Angle
(degrees)
Max. FGn
(N)
-52.9±0.42
30.5±0.55
722.9±24.5
0.75
Min. Angle
(degrees)
-52.9±0.40
Starboard Oar
Max. Angle
Max. FGn
(degrees)
(N)
32.8±0.75 733.3±59.6
6
0.5
5.5
0.25
5
-0.25
U (ms-1)
a (g)
0
-0.5
-0.75
4.5
4
W2-: GQ
Exp.
Exp. Mean
± SD
Pred.
Crew
-1
-1.25
-1.5
0
0.1
0.2
0.3
0.4
0.5
t/ts
W2-: GQ
Exp.
Exp. Mean
± SD
Pred.
Crew
3.5
3
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
Figure 1: Hull propulsive acceleration and crew cg acceleration (left); hull velocity and crew cg velocity (right).
The hull propulsive acceleration is shown in the left panel of Fig. 1. Experimental data is shown as pink dots; the thick
black curve is the mean of the measured values and the thin lines are one standard deviation (SD) either side of the mean
curve. The green curve is FIRM’s prediction.
Hull propulsive velocity and the speed of the crew CG is shown in the plot at the right of Fig. 1.
The forces in the equations of motion are shown in the left panel of Fig. 2. Drag components during the stroke are in
the panel at the right.
Experimental oar azimuth angles and values used as input to FIRM are shown at the left of Fig. 3. Gate normal forces
are at the right of the figure.
Blade propulsive forces are shown at the left of Fig. 4. Dynamic oar lever ratios shown at the right of the figure include
the effect of variations in the location of the OBCP during the stroke.
Body angle regimes are shown in the two parts of Fig. 5. The angles are the same for both crew members in this
simulation.
2
250
120
Drag (N)
160
Force (N)
500
0
-250
0
0.1
0.2
0.3
0.4
0.5
t/ts
80
40
W2-: GQ
Fprop
Fboat
Fcrew
-Fdrag
Fsys
-500
W2-: GQ
Air
Viscous
Wave
Total
0
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
40
1000
20
750
0
500
W2-: GQ
(Seat 1) Gigi
(Seat 2) Qing
FGn (N)
ψxy (degrees)
Figure 2: Equation of motion forces (left) and drag components (right).
-20
250
-40
0
W2-: GQ
(Seat 1) Gigi
(Seat 2) Qing
-60
0
0.1
0.2
0.3
0.4
0.5
t/ts
-250
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
Figure 3: Oar azimuth angles Ψxy (left); gate normal forces FGn (right).
Yawing moment lever arms and yawing moments are shown in the two parts of Fig. 6.
The OBCP trajectories in Fig. 7 have been plotted on the same side of the hull for clarity and comparison.
The OBCP trajectories in the yz-plane are shown in Fig. 8. For the purposes of this plot, the OBCP is assumed to be
at the geometric centre of the blade when it is out of the water.
The OBCP is below the water from about t/ts = 0.01 to t/ts ≈ 0.47. The latter value is the value entered in the main
input file.
3
250
2.31
W2-: GQ
(Seat 1) Gigi
(Seat 2) Qing
W2-: GQ
(Seat 1) Gigi
(Seat 2) Qing
2.3
200
Dynamic Oarlever Ratio
2.29
FBx (N)
150
100
50
2.28
2.27
2.26
0
2.25
-50
2.24
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
Figure 4: Blade propulsive forces FBx (left); dynamic oar lever ratios (right).
180
180
W2-: Qing
Knee
Hip
Neck
Shoulder
150
120
Joint Angle (degrees)
120
Joint Angle (degrees)
W2-: Gigi
Knee
Hip
Neck
Shoulder
150
90
60
30
90
60
30
0
0
-30
-30
-60
-60
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
Figure 5: Joint angles: Seat 2 (left): Seat 1 (right).
4
750
W2-: GQ
(Seat 1) Gigi
(Seat 2) Qing
3
W2-: GQ
(Seat 1) Gigi
(Seat 2) Qing
Total
Yawing Moment (Nm)
Yawing moment lever arm (m)
500
2
1
0
-1
250
0
-250
-2
-500
-3
-4
-750
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
Figure 6: Yawing moment lever arms Lyaw (left); yawing moments Myaw (right).
4
0.7
0.8
0.9
1
3.5
3.5
W2-: GQ
(Seat 2) Qing
W2-: GQ
(Seat 1) Gigi
Direction of
Direction of
Boat Travel
Lateral distance from hull centreline (m)
Lateral distance from hull centreline (m)
Boat Travel
3
Release
2.5
Catch
2
1.5
-2.75
-2.5
-2.25
-2
-1.75
3
Release
2.5
Catch
2
1.5
-2.75
-1.5
-2.5
-2.25
x (m)
-2
-1.75
-1.5
x (m)
0.2
0.2
0.1
0.1
zobcp (m. above water)
zobcp (m. above water)
Figure 7: OBCP trajectories in the xy-plane: Port side (left); Starboard side (right).
0
-0.1
0
-0.1
W2-: GQ
Waterplane
(Seat 2) Qing
-0.2
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
W2-: GQ
Waterplane
(Seat 1) Gigi
-0.2
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
Figure 8: OBCP trajectories in the yz-plane: Port side (left); Starboard side (right).
5
0.7
0.8
0.9
1
W2- : Gigi and Qing
Rate 36.0 spm
Speed 4.80 m/s
Work on
Oarhandles
B.
HANDLES
B/A
A.
MUSCULAR
EFFORT
694 W
100 %
Dead Mass 27.0 kg
Moving Mass 145.0 kg
Total Mass 172.0 kg
Net
Kinetic Energy
E.
542 W
SYSTEM
152 W
NOTE: B+F=D+H and C+E=D+G
MOMENTUM
78 %
E/A
22 %
Blade Efficiency
Mom. Efficiency
C/B = 85.5 %
F/E = 64.4 %
C.
F.
PROPULSION
463 W
FOOT BOARDS 98 W
(External)
C/A
67 %
F/A
14 %
D.
DRAG
Propelling Efficiency
D/(D+H) = 87.7 %
H.
BLADE 79 W
LOSSES
H/A
11 %
Lost to water
Work done
on shell
561 W
D/A
81 %
Transferred to air and water
I=D+G+H.
TOTAL
694 W
LOSS
I/A
100.0 %
Net Efficiency
D/(D+H)-G/A = 79.9 %
Figure 9: Power flow chart.
6
Air 14 %
Visc. 80 %
Wave 7 %
Velocity Efficiency
1-G/A = 92.2 %
G.
BODY FLEX 54 W
(Internal)
G/A
8%
Lost as heat, breath etc.
3
M2-: Men’s Pairs
The on-water trial for these two heavyweight male rowers, “Dazza” and “Robbo”, was conducted over 500m on a cold
winter morning. Air and water temperatures were not recorded: they were estimated as 9◦ C and 9◦ C respectively. Measured
values of rigging details, oar angles, gate normal forces, and their anthropometry were used as input to FIRM. Body angle
regimes were not recorded but were estimated by the author using a complicated fitting process.
Table 3: Summary of experimental results for this simulation: number of strokes, stroke rate, non-dimensional pull phase duration
(tp /ts ), minimum hull velocity (Umin ), maximum hull velocity (Umax ), and mean hull velocity (U ).
Item
Nstrokes
Rate (spm)
tp /ts
Umin (ms−1 )
Umax (ms−1 )
U (ms−1 )
Value
36.002
0.476
3.660
6.487
5.330
18
±0.296
±0.008
±0.090
±0.066
±0.074
Table 3 summarises the main quantities relating to the simulation for this crew. Values are given ± one standard deviation.
Table 4: Experimental oar-related values for this simulation: Minimum and maximum oar angles, and maximum gate normal force.
Name
Dazza
Robbo
Min. Angle
(degrees)
Port Oar
Max. Angle
(degrees)
-50.7±0.67
32.4±0.33
Max. FGn
(N)
Min. Angle
(degrees)
-57.1±0.60
Starboard Oar
Max. Angle
Max. FGn
(degrees)
(N)
30.8±0.38 1138.3±27.5
1351.4±37.7
1
7
6.5
0.5
6
a (g)
U (ms-1)
0
-0.5
5.5
5
4.5
M2-: DR
-1
Exp.
Exp. Mean
± SD
Pred.
Crew
-1.5
0
0.1
0.2
0.3
0.4
0.5
t/ts
M2-: DR
Exp.
Exp. Mean
± SD
Pred.
Crew
4
3.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
Figure 10: Hull propulsive acceleration and crew cg acceleration (left); hull velocity and crew cg velocity (right).
The hull propulsive acceleration is shown in the left panel of Fig. 10. Experimental data is shown as pink dots; the thick
black curve is the mean of the measured values and the thin lines are one standard deviation (SD) either side of the mean
curve. The green curve is FIRM’s prediction.
Hull propulsive velocity and the speed of the crew CG is shown in the plot at the right of Fig. 10.
The forces in the equations of motion are shown in the left panel of Fig. 11. Drag components during the stroke are in
the panel at the right.
Experimental oar azimuth angles and values used as input to FIRM are shown at the left of Fig. 12. Gate normal forces
are at the right of the figure.
Blade propulsive forces are shown at the left of Fig. 13. Dynamic oar lever ratios shown at the right of the figure include
the effect of variations in the location of the OBCP during the stroke.
Body angle regimes are shown in the two parts of Fig. 14. The angles are the same for both crew members in this
simulation.
7
750
250
M2-: DR
Fprop
Fboat
Fcrew
-Fdrag
Fsys
500
M2-: DR
Air
Viscous
Wave
Total
200
250
Drag (N)
Force (N)
150
0
100
-250
50
-500
-750
0
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
Figure 11: Equation of motion forces (left) and drag components (right).
40
1400
M2-: DR
(Seat 1) Dazza
(Seat 2) Robbo
1200
20
0
FGn (N)
ψxy (degrees)
1000
-20
800
600
400
-40
200
M2-: DR
(Seat 1) Dazza
(Seat 2) Robbo
-60
0
0.1
0.2
0.3
0.4
0.5
t/ts
0
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
Figure 12: Oar azimuth angles Ψxy (left); gate normal forces FGn (right).
Yawing moment lever arms and yawing moments are shown in the two parts of Fig. 15.
The OBCP trajectories in Fig. 16 have been plotted on the same side of the hull for clarity and comparison.
The OBCP trajectories in the yz-plane are shown in Fig. 17. For the purposes of this plot, the OBCP is assumed to be
at the geometric centre of the blade when it is out of the water.
The OBCP is below the water from about t/ts = 0.01 to t/ts ≈ 0.47. The latter value is the value entered in the main
input file.
8
450
2.32
M2-: DR
(Seat 1) Dazza
(Seat 2) Robbo
400
350
Dynamic Oarlever Ratio
2.3
300
FBx (N)
M2-: DR
(Seat 1) Dazza
(Seat 2) Robbo
2.31
250
200
150
2.29
2.28
2.27
2.26
100
2.25
50
0
2.24
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
Figure 13: Blade propulsive forces FBx (left); dynamic oar lever ratios (right).
180
180
M2-: Robbo
Knee
Hip
Neck
Shoulder
150
120
Joint Angle (degrees)
120
Joint Angle (degrees)
M2-: Dazza
Knee
Hip
Neck
Shoulder
150
90
60
30
90
60
30
0
0
-30
-30
-60
-60
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
Figure 14: Joint angles: Seat 2 (left): Seat 1 (right).
4
1500
M2-: DR
(Seat 1) Dazza
(Seat 2) Robbo
3
M2-: DR
(Seat 1) Dazza
(Seat 2) Robbo
Total
Yawing Moment (Nm)
Yawing moment lever arm (m)
1000
2
1
0
-1
500
0
-500
-2
-1000
-3
-4
-1500
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
Figure 15: Yawing moment lever arms Lyaw (left); yawing moments Myaw (right).
9
0.7
0.8
0.9
1
3.5
3.5
Direction of
Direction of
Boat Travel
Lateral distance from hull centreline (m)
Lateral distance from hull centreline (m)
Boat Travel
3
Release
2.5
Catch
2
M2-: DR
(Seat 2) Robbo
1.5
-2.75
-2.5
-2.25
-2
-1.75
3
Release
2.5
Catch
2
M2-: DR
(Seat 1) Dazza
1.5
-2.75
-2.5
-1.5
-2.25
x (m)
-2
-1.75
-1.5
x (m)
0.2
0.2
0.1
0.1
zobcp (m. above water)
zobcp (m. above water)
Figure 16: OBCP trajectories in the xy-plane: Port side (left); Starboard side (right).
0
-0.1
0
-0.1
M2-: DR
Waterplane
(Seat 2) Robbo
-0.2
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
0.7
0.8
0.9
M2-: DR
Waterplane
(Seat 1) Dazza
-0.2
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
0.6
Figure 17: OBCP trajectories in the yz-plane: Port side (left); Starboard side (right).
10
0.7
0.8
0.9
1
M2- : Dazza and Robbo
Dead Mass 27.0 kg
Rate 36.1 spm
Moving Mass 191.0 kg
A.
Speed 5.33 m/s
Total Mass 218.0 kg
MUSCULAR 1205 W
Work on
Net
EFFORT
Oarhandles
Kinetic Energy
100 %
B.
E.
HANDLES 912 W
SYSTEM
292 W
NOTE: B+F=D+H and C+E=D+G
MOMENTUM
B/A
76 %
E/A
24 %
Blade Efficiency
Mom. Efficiency
C/B = 77.3 %
F/E = 71.0 %
C.
F.
PROPULSION
706 W
FOOT BOARDS 207 W
(External)
C/A
59 %
F/A
17 %
D.
DRAG
Propelling Efficiency
D/(D+H) = 81.5 %
H.
BLADE 207 W
LOSSES
H/A
17 %
Lost to water
Work done
on shell
913 W
D/A
76 %
Transferred to air and water
I=D+G+H.
TOTAL 1205 W
LOSS
I/A
100.0 %
Net Efficiency
D/(D+H)-G/A = 74.5 %
Figure 18: Power flow chart.
11
Air 13 %
Visc. 79 %
Wave 7 %
Velocity Efficiency
1-G/A = 93.0 %
G.
BODY FLEX 85 W
(Internal)
G/A
7%
Lost as heat, breath etc.