Results with new CD
an CL values.
Octobre 2007
2. Result of a single variation
1. Introduction
This I a repetition of “Results” but now with the functions for CD and CL as publisshed by Caplan and Gardner:
Journal of Sports Sciences, April 2007; 25(6): 643-650
Nicholas Caplan & Trevor N. Gardner,
"A fluid dynamic investigation of the Big Blade and
Macon oar blade
designs in rowing propulsion"
For a download of this article go to: http://www.mediafire.com:80/?sharekey=8b46b928e2e521fc8ab8b2f348899ad000ca1676f8ccbcd6
See also Lift and Drag on this website.
The results are presented without much comment. Just compare with Results.
A few remarks: The following graphs are smoother than the ones in Results because of the smoother functions for CD and CL. The overall efficiency is just somewhat better: 0.751 against 0.769 and this results in an improved 2000m time: 436.5s against 450.2s. In real racing a considerable difference but don’t forget we have no choice. We cannot make a choice between Hoerner and Caplan & Gardner forces but only wonder who is right. The difference is of interest only for those who make calculations not for real life rowing.
Finally we observe in Fig 2.4 that the minimum instantaneous propulsion efficiency has increase from abt 0.63 to abt 0.68 and the minimum has shifted from an oar angle
-0.2 to -0.4rad.
2. Results of a single simulation
The input data specified in Table 2.1 is the same as in Results with the exception of C2 = 1.0. This now means the maximum lift coefficient CL =1.0 at 45o angle of attack and with CD = 2.0 as maximum drag coefficient at 90o. These maximum values have been chosen somewhat lower than Caplan and Gardner in their paper because these values are considered too high.
------- input data --------
|
m1 |
m2 |
Fbl |
L |
fi1 |
fi2 |
sl |
TR |
CANT |
|
kg |
kg |
N |
m |
rad |
rad |
m |
s |
rad |
|
30.0 |
70.0 |
350 |
1.80 |
-1.10 |
0.60 |
0.80 |
1.10 |
0.00 |
|
area |
C1 |
C2 |
spr |
|
m2 |
N.s2/m2 |
- |
m/sec |
|
0.130 |
3.50 |
1.00 |
-1.45 |
------- results -------
|
Ebls |
Exs |
Er |
Et |
eff |
T |
|
J |
J |
J |
J |
- |
s |
|
163.93 |
618.17 |
22.21 |
804.31 |
0.769 |
1.86 |
|
SR |
T2000 |
Prow |
Poar |
vel |
|
m-1 |
sec |
W |
W |
m/s |
|
32.21 |
450.2 |
431.73 |
337.60 |
4.443 |
|
Table 2.1 Input and results |
||||
|
m1= |
mass of the boat + that part of the mass of the rower 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 |
|
Fbl = |
force perpendicular on blade |
|
L= |
distance thole pin to point of application of force on blade |
|
fi1= |
value of j at the catch |
|
fi2= |
value of j at the finish |
|
sl = |
distance covered by m2 with respect to m1 (sliding length) |
|
TR= |
time for the recover |
|
area= |
area of two blades |
|
C1= |
resistance coefficient of boat hull |
|
C2= |
adjustment of lift and drag coefficient of blade |
|
spr = |
maximum seat speed during recover (follows from sl and TR) |
|
Ebls= |
energy delivered at the blade |
|
Exs= |
energy dissipated by boat resistance |
|
Er= |
kinetic energy of rower lost during recover |
|
Et= |
sum of Ebls, Exs and Er |
|
eff= |
overall efficiency |
|
T= |
time for one stroke |
|
tmp= |
stroke rate |
|
T2000= |
time to cover 2000m |
|
Prow= |
energy flow (power) to be delivered to the system |
|
vel= |
mean velocity of the boat |
|
Table 2.2 Explanation of used names |
|
|
|
|
Fig 2.1 |
|
|
|
Fig 2.2 Blade Trajectory |
|
|
|
Fig 2.3 Oar velocity as function of oar angle |
|
|
|
Table 2.4 Instantaneous propulsion efficiency |
