FREE INTERNET ROWING MODEL
(FIRM)
EXAMPLES: Single Sculls
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 W1x: Women’s Single Sculls
2.1
W1x exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
4
3 LW1x: Lightweight Women’s Single Sculls
8
4 M1x: Men’s Single Sculls
13
5 LM1x: Lightweight Men’s Single Scull
18
1
INTRODUCTION
Four single scull examples are included in this version of FIRM. More will be added in future versions.
1
2
W1x: Women’s Single Sculls
Many of the results for this sculler (who we have named Aage) have been used throughout the FIRM manual. Measured
values of rigging details, oar angles, gate normal forces, and her anthropometry were used as input to FIRM. Body angle
regimes for three complete strokes were extracted from videos taken during the trial and these were used to constrain the
angles predicted by the inverse kinematic procedures.
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
35.111
0.540
3.288
5.430
4.529
28
±0.214
±0.005
±0.063
±0.060
±0.061
Table 1 summarises the main quantities relating to the simulation for this sculler. 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
Aage
Port Oar
Max. Angle
(degrees)
43.2±0.33
Min. Angle
(degrees)
-59.8±0.43
Max. FGn
(N)
404.4±14.1
Min. Angle
(degrees)
-56.4±0.38
Starboard Oar
Max. Angle
Max. FGn
(degrees)
(N)
44.5±0.42 387.0±16.0
A blade loss factor of kloss = 0.015 has been used to bring FIRM predictions in line with the experimental mean speed
of U = 4.529ms−1 . Given the many uncertainties, this small 1.5% reduction seems quite acceptable. (Instead of using the
blade loss factor, we could have adjusted, for example, the oarhandle centre of effort, the viscous form factor, or the air drag
coefficients). A further justification for the small adjustments is that they are well within the standard deviations around
the means of the maximum gate normal forces given in Table 1.
1
6
W1x: Aage
Exp.
Exp. Mean
± SD
Pred.
Crew
5.5
0.5
5
a (g)
U (ms-1)
0
4.5
-0.5
4
W1x: Aage
Exp.
Exp. Mean
± SD
Pred.
Crew
-1
-1.5
0
0.1
0.2
0.3
0.4
0.5
t/ts
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.
The agreement is quite good, however, it should be kept in mind that it was achieved by using body angle regimes
specifically chosen to get that good agreement.
2
There is a small dip at about t/ts = 0.15 where the acceleration drops below zero. That, of course, must reduce the
boat speed, and this can be seen as a corresponding dip in the right panel of the figure. The cause of the dip is most
probably a question of rowing technique. FIRM has been able to reproduce the curve, but it cannot be used on its own to
suggest reasonable ways to correct the deficiency. That requires good coaching, and a more thorough biomechanical analysis.
Kleshnev [?] has examined similar “double peaks” in boat acceleration.
300
100
W1x: Aage
Fprop
Fboat
Fcrew
-Fdrag
Fsys
200
W1x: Aage
Air
Viscous
Wave
Total
75
Drag (N)
Force (N)
100
50
0
25
-100
-200
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 2: Equation of motion forces (left) and drag components (right).
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.
60
180
40
150
W1x: Aage
Knee
Hip
Neck
Shoulder
120
Joint Angle (degrees)
ψxy (degrees)
20
0
-20
90
60
30
-40
0
W1x: Aage
Exp. Port
Exp. Star
FIRM: Port
FIRM: Star
-60
-80
0
0.1
0.2
0.3
0.4
0.5
t/ts
-30
-60
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); joint angles (right)).
Experimental oar azimuth angles in the plot at the left of Fig. 3 have been shifted so they are referenced to the centre of
the pin. The continuous curves are the values used as input to FIRM.
Joint angle regimes are shown in the plot at the right of Fig. 3. Solid curves are the values used as input to FIRM.
Gate normal forces are shown at the left of Fig. 4. The curves are the values used as input to FIRM.
Oarblade propulsive forces are shown in the right panel of Fig. 4. These include the variation in the OBCP during the
stroke.
The x-wise velocities of the OHCE are shown at the left of Fig. 5. The velocity is negative during the drive because the
handle travels in the negative x-direction.
The seat velocity is shown in the right panel of Fig. 5. It too is negative during the pull phase. At the release the seat
velocity slows down and remains at zero for a short time before the stern is pulled towards the rower during the recovery.
3
450
125
W1x: Aage
Exp. Port
Exp. Star
FIRM: Port
FIRM: Star
400
W1x: Aage
Port
Star
100
350
300
FBx (N)
FGn (N)
75
250
200
50
150
100
25
50
0
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
0.6
0.7
0.8
0.9
1
Figure 4: Gate normal forces FGn (left); blade propulsive forces FBx (right).
1.5
W1x: Aage
Port
Star
2
1
1
0.5
Seat velocity (m/s)
OHCE x-velocity (m/s)
3
0
0
-1
-0.5
-2
-1
-3
W1x: Aage
Hip (Seat)
-1.5
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
Figure 5: OHCE horizontal velocity (left); seat velocity (right).
Yawing moment lever arms are shown in the left plot of Fig. 6. These, and the yawing moments shown at the right of
the figure both contain the effects of the OBCP varying during the stroke.
Vertical oar angles are shown in the plot at the left of Fig. 7. The corresponding locations of the OBCP for both oars
are shown at the right. The vertical angles and vertical locations for both oars are identical, however, the azimuth angles are
different.
The OBCP is below the water from about t/ts = 0.01 to t/ts = 0.55. 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 trajectories of the joints are shown in the plot at the left of Fig. 8; trajectories of the segment and oar centres of
gravity are shown at the right.
The trajectory of the hip is a flat line because it is the same as that of the seat which does not move up or down during
the stroke. The trajectory of the sum of the CG is the black trace in the right-hand plot. It can be seen that the vertical
displacement is much less than the horizontal which justifies ignoring the vertical component in many models.
The OBCP trajectories in Fig. 9 have been plotted on the same side of the hull for clarity and comparison. Puddles are
most likely to be formed during the period immediately before the release.
2.1
W1x exercises
Once we have good agreement between FIRM predictions of hull propulsive acceleration and hull velocity, there are many
simple “what if” type questions we can ask. Most of the short exercises can be done by making very simple modifications to
4
3
400
W1x: Aage
Port
Star
W1x: Aage
Port
Star
Sum
300
200
1
Yawing Moment (Nm)
Yawing moment lever arm (m)
2
0
-1
100
0
-100
-200
-2
-300
-3
-400
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 6: Yawing moment lever arms (left); yawing moments (right).
12
0.2
10
0.1
zobcp (m. above water)
ψyz (degrees)
8
6
4
0
-0.1
2
W1x: Aage
Port
Star
0
0
0.1
0.2
0.3
0.4
0.5
t/ts
W1x: Aage
Waterplane
Port OBCP
Star OBCP
-0.2
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 7: Vertical oar angles Ψyz (left); OBCP trajectories in the yz-plane (right).
one of the input files.
Remember to restore the original value in the file before you try another example. The best method is to make a copy of
the line you want to modify, then use the # character to comment out the original line. After you finish the exercise, delete
the modified line, and remove the # character from the original line. (If you forget what modifications you made, delete the
entire FIRM directory and re-install it: that should only take a few seconds.)
Before making any modifications to the files, run FIRM for the original file and record the mean hull velocity that appears
on the Model Screen, or in the summary.csv file.
Exercise W1x 1.0: What is the predicted mean hull velocity at 20◦ C water and 20◦ C air temperature?
Hint: change the values near the start of the main input file, aage.in
Exercise W1x 1.1: What difference in time over 2000m does the change in mean velocity represent?
Exercise W1x 1.2: How many metres does the change in mean velocity represent?
Exercise W1x 2.0: When rowers resume training after a lay-off, they are usually not as strong as when they are at their peak.
What is the effect of reducing the maximum gate forces by 10%? Hint: Change the blade loss factor.
Exercise W1x 3.0: Although the boat used in this example is very similar to the actual boat used in the on-water trials, it
seems a little large for this rower. (Some people refer to this as “over-boating”). What is the effect of using a different hull,
for example the slightly shorter S075L101g1 hull?
Hint: change the line in the Hull Filename block of the file aage.in from
hulls/S080L106a1.csv
5
1
W1x: Aage
Knee
Hip
Neck
Port Hand
Star Hand
0.8
z-ordinate of CG relative to ankle (m)
z-ordinate of joint relative to ankle (m)
1
0.6
0.4
0.2
0
-1.6
W1x: Aage
Shank
Thigh
Torso
Head
Upper Arm
Forearm
Port Oar
Star Oar
Sum
0.8
0.6
0.4
0.2
-1.2
-0.8
-0.4
0
0.4
0
-1.6
0.8
-1.2
-0.8
x-ordinate of joint relative to ankle (m)
-0.4
0
0.4
0.8
x-ordinate of CG relative to ankle (m)
Figure 8: Joint trajectories (left); trajectories of centres of gravity (right).
2.8
W1x: Aage
Port
Star
Lateral distance from hull centreline (m)
2.6
Direction of
2.4
Boat Travel
2.2
2
Release
Catch
1.8
1.6
-2.8
-2.6
-2.4
-2.2
-2
-1.8
-1.6
-1.4
-1.2
x (m)
Figure 9: OBCP trajectories in the xy-plane.
to
hulls/S075L101g1.csv
Exercise W1x 3.1: Examine the effect of changing the dimensions of the S080L106a1.csv hull. For example, change the length
of the hull from 7.90 to 7.80. What is the effect on mean hull speed? How does it affect transverse stability (i.e. on GMT0 )?
Exercise W1x 3.2: Make the S080L106a1.csv hull narrower by reducing the overall beam from 0.275m to 0.270m. What is
the effect on mean hull speed and transverse stability?
Exercise W1x 4.0: What is the effect on hull velocity of increasing the hull weight by 1, 2, or 3 kgs?
Hint: change the values in the hull input file.
Exercise W1x 5.0: What is the effect of increasing the rower’s weight by 1, 2 and 3 kgs?
Hint: change the values of the rower’s weight in the anthro.csv input file.
Exercise W1x 5.1: Is the effect exactly the same as increasing the hull weight by the same amount, for example, by carrying
large bottles of water?
Exercise W1x 6.0: Look up the world’s best time for this event in the Appendix to the FIRM manual. Now change the gate
forces for this sculler, run FIRM and note the new mean hull velocity. What percentage increase in force is required for Aage
to equal the world record time?
6
W1x: Aage
Rate 35.1 spm
Speed 4.53 m/s
A.
MUSCULAR
EFFORT
Work on
Oarhandles
B.
HANDLES
B/A
316 W
398 W
100 %
Dead Mass 14.0 kg
Moving Mass 76.2 kg
Total Mass 90.2 kg
Net
Kinetic Energy
E.
82 W
SYSTEM
MOMENTUM
E/A
21 %
Mom. Efficiency
F/E = 71.9 %
F.
FOOT BOARDS 59 W
(External)
F/A
15 %
NOTE: B+F=D+H and C+E=D+G
79 %
Blade Efficiency
C/B = 80.5 %
C.
PROPULSION
254 W
C/A
64 %
D.
DRAG
Propelling Efficiency
D/(D+H) = 83.6 %
H.
BLADE 62 W
LOSSES
H/A
15 %
Lost to water
Work done
on shell
313 W
D/A
79 %
Transferred to air and water
I=D+G+H.
TOTAL
398 W
LOSS
I/A
100.0 %
Net Efficiency
D/(D+H)-G/A = 77.8 %
Figure 10: Power flow chart.
7
Air 11 %
Visc. 82 %
Wave 7 %
Velocity Efficiency
1-G/A = 94.2 %
G.
BODY FLEX 23 W
(Internal)
G/A
6%
Lost as heat, breath etc.
3
LW1x: Lightweight Women’s Single Sculls
The on-water trial for this lightweight sculler, “Lara”, was conducted over 500m. Air and water temperatures were not
recorded: they were estimated as 10◦ C and 10◦ C respectively. Measured values of rigging details, oar angles, gate normal
forces, and her 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
27.902
0.453
2.861
4.540
4.061
34
±0.248
±0.005
±0.030
±0.034
±0.022
Table 3 summarises the main quantities relating to the simulation for this sculler. 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
Fgn .
Name
Max. FGn
(N)
354.3±10.4
Min. Angle
(degrees)
-60.3±0.56
0.6
4.75
0.4
4.5
0.2
4.25
0
4
U (ms-1)
a (g)
Lara
Port Oar
Max. Angle
(degrees)
43.2±0.48
Min. Angle
(degrees)
-62.9±1.19
-0.2
-0.4
Starboard Oar
Max. Angle
Max. FGn
(degrees)
(N)
44.0±0.47 362.7±12.9
3.75
3.5
-0.6
3.25
LW1x: Lara
Exp.
Exp. Mean
± SD
Pred.
Crew
-0.8
-1
0
0.1
0.2
0.3
0.4
0.5
t/ts
LW1x: Lara
Exp.
Exp. Mean
± SD
Pred.
Crew
3
2.75
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: 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. 11. 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.
The most notable feature of the hull speed curve in the plot at the right of Fig. 11 is the long, relatively constant region
during the recovery. This behaviour is not evident in other classes of rowing; it might be peculiar to this particular lightweight
sculler, or to lightweight women sculling at relatively low rates and with short drive phase durations.
The forces in the equations of motion are shown in the left panel of Fig. 12. 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 in the plot at the left of Fig. 13.
Estimated joint angle regimes used as input to FIRM are shown in the plot at the right of Fig. 13.
8
300
60
LW1x: Lara
Fprop
Fboat
Fcrew
-Fdrag
Fsys
200
LW1x: Lara
Air
Viscous
Wave
Total
50
40
Drag (N)
Force (N)
100
30
0
20
-100
10
-200
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
0.6
0.7
0.8
0.9
1
Figure 12: Equation of motion forces (left) and drag components (right).
60
180
40
150
LW1x: Lara
Knee
Hip
Neck
Shoulder
120
Joint Angle (degrees)
ψxy (degrees)
20
0
-20
90
60
30
-40
0
LW1x: Lara
Exp. Port
Exp. Star
FIRM: Port
FIRM: Star
-60
-80
0
0.1
0.2
0.3
0.4
0.5
t/ts
-30
-60
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
t/ts
Figure 13: Oar azimuth angles Ψxy (left); joint angles (right)).
Gate normal forces are shown at the left of Fig. 14. The curves are the values used as input to FIRM.
Oarblade propulsive forces are shown in the right panel of Fig. 14. These include the variation in the OBCP during the
stroke.
The x-wise velocities of the OHCE are shown at the left of Fig. 15. The velocity is negative during the drive because the
handle travels in the negative x-direction.
The seat velocity is shown in the right panel of Fig. 15. It too is negative during the pull phase. At the release the seat
velocity slows down and remains at zero for a very short time before the stern moves towards the rower during the recovery.
Yawing moment lever arms are shown in the left plot of Fig. 16. These, and the yawing moments shown at the right of
the figure both contain the effects of the OBCP varying during the stroke. The nett yawing moment is quite small for this
sculler.
Vertical oar angles are shown in the plot at the left of Fig. 17. The corresponding locations of the OBCP for both oars
are shown at the right. The vertical angles and vertical locations for both oars are identical, however, the azimuth angles are
different.
The OBCP is below the water from about t/ts = 0.01 to t/ts = 0.45; the latter value was specified in the main input file.
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 trajectories in Fig. 18 have been plotted on the same side of the hull for clarity and comparison. Puddles are
most likely to be formed during the period immediately before the release.
9
400
125
LW1x: Lara
Exp. Port
Exp. Star
FIRM: Port
FIRM: Star
350
LW1x: Lara
Port
Star
100
300
250
FBx (N)
FGn (N)
75
200
150
50
100
50
25
0
-50
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
0.6
0.7
0.8
0.9
1
Figure 14: Gate normal forces (left); blade propulsive forces (right).
1.5
LW1x: Lara
Port
Star
2
1
1
0.5
Seat velocity (m/s)
OHCE x-velocity (m/s)
3
0
0
-1
-0.5
-2
-1
-3
LW1x: Lara
Hip (Seat)
-1.5
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
Figure 15: OHCE horizontal velocity (left); seat velocity (right).
300
LW1x: Lara
Port
Star
2
200
1
100
Yawing Moment (Nm)
Yawing moment lever arm (m)
3
0
-1
-2
LW1x: Lara
Port
Star
Sum
0
-100
-200
-3
-300
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
Figure 16: Yawing moment lever arms (left); yawing moments (right).
10
0.6
0.7
0.8
0.9
1
8
0.1
zobcp (m. above water)
4
0
-0.1
2
LW1x: Lara
Port
Star
0
0
0.1
0.2
0.3
0.4
0.5
t/ts
LW1x: Lara
Waterplane
Port OBCP
Star OBCP
-0.2
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 17: Vertical oar angles Ψyz (left); OBCP trajectories in the yz-plane (right).
2.6
Lateral distance from hull centreline (m)
ψyz (degrees)
6
LW1x: Lara
Port
Star
Direction of
2.4
Boat Travel
2.2
2
Release
1.8
Catch
1.6
-2.8
-2.6
-2.4
-2.2
-2
-1.8
-1.6
-1.4
x (m)
Figure 18: OBCP trajectories in the xy-plane.
11
-1.2
0.7
0.8
0.9
1
LW1x
: Lara
Rate 27.9 spm
Speed 4.07 m/s
A.
MUSCULAR
EFFORT
Work on
Oarhandles
B.
HANDLES
B/A
223 W
268 W
100 %
Dead Mass 14.0 kg
Moving Mass 62.0 kg
Total Mass 76.0 kg
Net
Kinetic Energy
E.
45 W
SYSTEM
MOMENTUM
E/A
17 %
Mom. Efficiency
F/E = 77.5 %
F.
FOOT BOARDS 35 W
(External)
F/A
13 %
NOTE: B+F=D+H and C+E=D+G
83 %
Blade Efficiency
C/B = 76.4 %
C.
PROPULSION
171 W
C/A
64 %
D.
DRAG
Propelling Efficiency
D/(D+H) = 79.5 %
H.
BLADE 53 W
LOSSES
H/A
20 %
Lost to water
Work done
on shell
205 W
D/A
77 %
Transferred to air and water
I=D+G+H.
TOTAL
268 W
LOSS
I/A
100.0 %
Net Efficiency
D/(D+H)-G/A = 75.8 %
Figure 19: Power flow chart.
12
Air 11 %
Visc. 81 %
Wave 9 %
Velocity Efficiency
1-G/A = 96.2 %
G.
BODY FLEX 10 W
(Internal)
G/A
4%
Lost as heat, breath etc.
4
M1x: Men’s Single Sculls
The on-water trial for this sculler, “Stevo”, was conducted over 500m. Air and water temperatures were not recorded:
they were estimated as 22◦ C and 22◦ C respectively. Measured values of rigging details, oar angles, gate normal forces, and
his anthropometry were used as input to FIRM. Body angle regimes for 2 complete strokes were extracted from videos taken
during the trial.
Table 5: 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
34.991
0.497
3.431
5.819
4.942
42
±0.205
±0.004
±0.079
±0.080
±0.071
Table 5 summarises the main quantities relating to the simulation for this sculler. Values are given ± one standard
deviation.
Table 6: Experimental oar-related values for this simulation: Minimum and maximum oar angles, and maximum gate normal force.
Name
Stevo
Port Oar
Max. Angle
(degrees)
41.7±0.92
Min. Angle
(degrees)
-64.7±0.50
Max. FGn
(N)
538.8±24.5
Min. Angle
(degrees)
-61.3±0.55
6.5
0.8
6
0.4
5.5
0
5
a (g)
U (ms-1)
1.2
-0.4
-0.8
Starboard Oar
Max. Angle
Max. FGn
(degrees)
(N)
43.3±0.49 602.9±26.9
M1x: Stevo
Exp.
Exp. Mean
± SD
Pred.
Crew
4.5
4
M1x: Stevo
Exp.
Exp. Mean
± SD
Pred.
Crew
-1.2
-1.6
0
0.1
0.2
0.3
0.4
0.5
t/ts
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 20: 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. 20. 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 and crew CG velocities are shown at the right. Maximum gate normal
forces were increased by 1% to make measured and predicted predicted mean velocity coincide more closely.
The forces in the equations of motion are shown in the left panel of Fig. 21. Drag components during the stroke are in
the panel at the right.
Experimental oar azimuth angles in the plot at the left of Fig. 22 have been shifted so they are referenced to the centre
of the pin. The continuous curves are the values used as input to FIRM.
Gate normal forces are shown at the left of Fig. 23. The curves are the values used as input to FIRM.
Oarblade propulsive forces are shown in the right panel of Fig. 23. These include the variation in the OBCP during the
stroke.
13
400
120
M1x: Stevo
Fprop
Fboat
Fcrew
-Fdrag
Fsys
300
M1x: Stevo
Air
Viscous
Wave
Total
100
200
Drag (N)
Force (N)
80
100
0
60
40
-100
20
-200
-300
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 21: Equation of motion forces (left) and drag components (right).
60
180
40
150
M1x: Stevo
Knee
Hip
Neck
Shoulder
120
Joint Angle (degrees)
ψxy (degrees)
20
0
-20
90
60
30
-40
0
M1x: Stevo
Exp. Port
Exp. Star
FIRM: Port
FIRM: Star
-60
-80
0
0.1
0.2
0.3
0.4
0.5
t/ts
-30
-60
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 22: Oar azimuth angles Ψxy (left); joint angles (right)).
The x-wise velocities of the OHCE are shown at the left of Fig. 24. The velocity is negative during the drive because the
handle travels in the negative x-direction.
The seat velocity is shown in the right panel of Fig. 24.
Yawing moment lever arms are shown in the left plot of Fig. 25. These, and the yawing moments shown at the right of
the figure both contain the effects of the OBCP varying during the stroke.
Vertical oar angles are shown in the plot at the left of Fig. 26. The corresponding locations of the OBCP for both oars
are shown at the right. The vertical angles and vertical locations for both oars are identical, however, the azimuth angles are
different.
The OBCP is below the water from about t/ts = 0.01 to t/ts = 0.497. 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 trajectories in Fig. 27 have been plotted on the same side of the hull for clarity and comparison.
14
700
200
M1x: Stevo
Exp. Port
Exp. Star
FIRM: Port
FIRM: Star
600
M1x: Stevo
Port
Star
150
400
FBx (N)
FGn (N)
500
300
100
200
50
100
0
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
0.6
0.7
0.8
0.9
1
Figure 23: Gate normal forces FGn (left); blade propulsive forces FBx (right).
3
1.5
M1x: Stevo
Port
Star
M1x: Stevo
Hip (Seat)
1
2
Seat velocity (m/s)
OHCE x-velocity (m/s)
0.5
1
0
0
-0.5
-1
-1
-2
-1.5
-3
-2
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
Figure 24: OHCE horizontal velocity (left); seat velocity (right).
3
500
M1x: Stevo
Port
Star
2
300
200
1
Yawing Moment (Nm)
Yawing moment lever arm (m)
M1x: Stevo
Port
Star
Sum
400
0
-1
100
0
-100
-200
-300
-2
-400
-3
-500
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
Figure 25: Yawing moment lever arms (left); yawing moments (right).
15
0.6
0.7
0.8
0.9
1
10
0.2
8
zobcp (m. above water)
6
4
0
-0.1
2
M1x: Stevo
Port
Star
0
0
0.1
0.2
0.3
0.4
M1x: Stevo
Waterplane
Port OBCP
Star OBCP
-0.2
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 26: Vertical oar angles Ψyz (left); OBCP trajectories in the yz-plane (right).
2.8
M1x: Stevo
Port
Star
2.6
Lateral distance from hull centreline (m)
ψyz (degrees)
0.1
Direction of
2.4
Boat Travel
2.2
2
Release
Catch
1.8
1.6
-2.8
-2.6
-2.4
-2.2
-2
-1.8
-1.6
-1.4
x (m)
Figure 27: OBCP trajectories in the xy-plane.
16
-1.2
0.7
0.8
0.9
1
M1x: Stevo
Rate 35.0 spm
Speed 4.94 m/s
Work on
Oarhandles
B.
HANDLES
B/A
A.
MUSCULAR
EFFORT
578 W
100 %
Dead Mass 14.0 kg
Moving Mass 97.9 kg
Total Mass 111.9 kg
Net
Kinetic Energy
E.
462 W
SYSTEM
116 W
NOTE: B+F=D+H and C+E=D+G
MOMENTUM
80 %
E/A
20 %
Blade Efficiency
Mom. Efficiency
C/B = 77.9 %
F/E = 75.8 %
C.
F.
PROPULSION
360 W
FOOT BOARDS 88 W
(External)
C/A
62 %
F/A
15 %
D.
DRAG
Propelling Efficiency
D/(D+H) = 81.4 %
H.
BLADE 102 W
LOSSES
H/A
18 %
Lost to water
Work done
on shell
448 W
D/A
77 %
Transferred to air and water
I=D+G+H.
TOTAL
578 W
LOSS
I/A
100.0 %
Net Efficiency
D/(D+H)-G/A = 76.6 %
Figure 28: Power flow chart.
17
Air 10 %
Visc. 82 %
Wave 8 %
Velocity Efficiency
1-G/A = 95.2 %
G.
BODY FLEX 28 W
(Internal)
G/A
5%
Lost as heat, breath etc.
5
LM1x: Lightweight Men’s Single Scull
The on-water trial for this lightweight sculler, “Karl”, was conducted over 500m during an early autumn morning.
Measured values of rigging details, oar angles, gate normal forces, and his anthropometry were used as input to FIRM.
Body angle regimes were not recorded but were estimated by the author using a complicated fitting process. Air and water
temperatures were not recorded: they were estimated as 10◦ C and 15◦ C respectively. A 1.155 ms−1 head wind has been
assumed.
Table 7: 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
34.272
0.545
3.374
5.487
4.529
25
±0.269
±0.005
±0.055
±0.060
±0.054
Table 7 summarises the main quantities relating to the simulation for this sculler. Values are given ± one standard
deviation.
Table 8: Experimental oar-related values for this simulation: Minimum and maximum oar angles, and maximum gate normal force
Fgn .
Name
Karl
Port Oar
Max. Angle
(degrees)
45.0±0.68
Min. Angle
(degrees)
-64.5±0.76
Max. FGn
(N)
461.3±16.0
Min. Angle
(degrees)
-58.9±0.85
Starboard Oar
Max. Angle
Max. FGn
(degrees)
(N)
47.7±0.57 439.0±11.6
A useful exercise would be to set the wind speed to zero and kloss to about 0.06. The mean hull speed for that case
should be similar to the one where a head wind was used.
0.6
6
0.4
5.5
0.2
5
U (ms-1)
a (g)
0
-0.2
4.5
-0.4
4
-0.6
LM1x: Karl
Exp.
Exp. Mean
± SD
Pred.
Crew
-0.8
-1
0
0.1
0.2
0.3
0.4
0.5
t/ts
LM1x: Karl
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 29: 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. 29. 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.
The forces in the equations of motion are shown in the left panel of Fig. 30. 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 in the plot at the left of Fig. 31.
Estimated joint angle regimes used as input to FIRM are shown in the plot at the right of Fig. 31.
18
300
100
200
LM1x: Karl
Air
Viscous
Wave
Total
80
100
Drag (N)
Force (N)
60
0
40
-100
LM1x: Karl
Fprop
Fboat
Fcrew
-Fdrag
Fsys
-200
-300
0
0.1
0.2
0.3
0.4
0.5
t/ts
20
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
0.6
0.7
0.8
0.9
1
Figure 30: Equation of motion forces (left) and drag components (right).
60
180
LM1x: Karl
Exp. Port
Exp. Star
FIRM: Port
FIRM: Star
40
LM1x: Karl
Knee
Hip
Neck
Shoulder
150
120
Joint Angle (degrees)
ψxy (degrees)
20
0
-20
90
60
30
-40
0
-60
-30
-80
-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
Figure 31: Oar azimuth angles Ψxy (left); joint angles (right)).
Gate normal forces are shown at the left of Fig. 32. The curves are the values used as input to FIRM.
Oarblade propulsive forces are shown in the right panel of Fig. 32. These include the variation in the OBCP during the
stroke.
The x-wise velocities of the OHCE are shown at the left of Fig. 33. The velocity is negative during the drive because the
handle travels in the negative x-direction. The seat velocity is shown in the right panel.
Yawing moment lever arms are shown in the left plot of Fig. 34. These, and the yawing moments shown at the right of
the figure both contain the effects of the OBCP varying during the stroke. The nett yawing moment is quite small for this
sculler.
Vertical oar angles are shown in the plot at the left of Fig. 35. The corresponding locations of the OBCP for both oars
are shown at the right. The vertical angles and vertical locations for both oars are identical, however, the azimuth angles are
different.
The OBCP is below the water from about t/ts = 0.01 to t/ts = 0.54; the latter value was specified in the main input file.
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 trajectories in Fig. 36 have been plotted on the same side of the hull for clarity and comparison.
19
500
150
LM1x: Karl
Exp. Port
Exp. Star
FIRM: Port
FIRM: Star
400
LM1x: Karl
Port
Star
125
100
FBx (N)
FGn (N)
300
200
75
50
100
25
0
0
-100
-25
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
0.6
0.7
0.8
0.9
1
Figure 32: Gate normal forces (left); blade propulsive forces (right).
1.5
LM1x: Karl
Port
Star
2
1
1
0.5
Seat velocity (m/s)
OHCE x-velocity (m/s)
3
0
0
-1
-0.5
-2
-1
-3
LM1x: Karl
Hip (Seat)
-1.5
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
Figure 33: OHCE horizontal velocity (left); seat velocity (right).
3
400
LM1x: Karl
Port
Star
LM1x: Karl
Port
Star
Sum
300
200
1
Yawing Moment (Nm)
Yawing moment lever arm (m)
2
0
-1
100
0
-100
-200
-2
-300
-3
-400
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
Figure 34: Yawing moment lever arms (left); yawing moments (right).
20
0.6
0.7
0.8
0.9
1
10
0.1
8
zobcp (m. above water)
6
4
0
-0.05
2
LM1x: Karl
Port
Star
0
0
0.1
0.2
0.3
0.4
LM1x: Karl
Waterplane
Port OBCP
Star OBCP
-0.1
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 35: Vertical oar angles Ψyz (left); OBCP trajectories in the yz-plane (right).
LM1x: Karl
Port
Star
2.6
Lateral distance from hull centreline (m)
ψyz (degrees)
0.05
Direction of
2.4
Boat Travel
2.2
2
Release
1.8
Catch
1.6
-2.8
-2.6
-2.4
-2.2
-2
-1.8
-1.6
-1.4
x (m)
Figure 36: OBCP trajectories in the xy-plane.
21
-1.2
0.7
0.8
0.9
1
LM1x
: Karl
Rate 34.3 spm
Speed 4.53 m/s
A.
MUSCULAR
EFFORT
Work on
Oarhandles
B.
HANDLES
B/A
347 W
436 W
100 %
Dead Mass 14.0 kg
Moving Mass 75.0 kg
Total Mass 89.0 kg
Net
Kinetic Energy
E.
89 W
SYSTEM
MOMENTUM
E/A
20 %
Mom. Efficiency
F/E = 72.6 %
F.
FOOT BOARDS 65 W
(External)
F/A
15 %
NOTE: B+F=D+H and C+E=D+G
80 %
Blade Efficiency
C/B = 77.7 %
C.
PROPULSION
269 W
C/A
62 %
D.
DRAG
Propelling Efficiency
D/(D+H) = 81.2 %
H.
BLADE 77 W
LOSSES
H/A
18 %
Lost to water
Work done
on shell
334 W
D/A
77 %
Transferred to air and water
I=D+G+H.
TOTAL
436 W
LOSS
I/A
100.0 %
Net Efficiency
D/(D+H)-G/A = 75.6 %
Figure 37: Power flow chart.
22
Air 17 %
Visc. 77 %
Wave 6 %
Velocity Efficiency
1-G/A = 94.4 %
G.
BODY FLEX 24 W
(Internal)
G/A
6%
Lost as heat, breath etc.