# Comparisons … and questions

It has been silent on this blog for too long. It’s been a busy time for me, both at home and at work.

And I had another excuse. Bill Atkinson asked me to add my model to the comparison between Van Holst and Atkinson. It turned out the numbers didn’t compare too well. So I went through my code again and again to find discrepancies. Unfortunately, I didn’t find any. This evening, I went through everything again in a final effort to understand the difference between my model and the two others.

I give up. It doesn’t make sense to keep looking myself, to stubbornly restrict my thinking power to only my (limited) brain. Are we in the age of open source and web 2.0 and on-line collaboration or not? It’s time to show the unfinished work and let it be criticized in the open. So, here we go.

 inputs value unit remarks Mass of rower 90 kg Mass of shell 14 kg Peak blade force 368 N Trapezium profile (function of oar angle) Oar outboard 2 m Catch angle -1.18 rad Release angle 0.68 rad Stroke length 1.37 m Rating 29.4 stroke/min Blade area surface 0.142 m^2 sum of 2 scull blades Hull resistance factor (varies) ITTC approximation Blade lift/drag coeff (varies) simplified flat plate results value unit average shell velocity 4.75 m/s minimum shell velocity 3.3 m/s shell velocity at release 5.25 m/s recovery time 1.3 s Total power 547 W

The chart in figure 1 gives the power distribution. All values are in Watt, averaged over the stroke. The numbers in bold are direct outputs of my model. The other numbers are calculated. So, blade losses are calculated directly from the blade force and blade slip. Drag losses are calculated directly from the drag force and hull velocity. The power going into “momentum” is calculated directly from the acceleration of the rower’s mass, and the power at the oarlock is calculated from the propulsive force and boat velocity.

Figure 1: Power Distribution (updated)

For comparison, here’s the same chart for Marinus van Holst’s model (data taken from Atkinson’s site):

Figure 2: Power distribution according to Van Holst

Figure 3 shows the same chart for Atkinson’s model:

Figure 3: Power distribution according to Atkinson

Atkinson calls one of the cells “Footboard”. In my model, I have access to the energy “stored” in kinetic energy (rower and shell – as in excess of the average system velocity), but I am not able to calculate directly the power exercised “at the footboard”. This is the reason for the question mark behind “footboard” in figure 1. I have estimated the power dissipated in the rower’s body using Van Holst’s explanation, see figure 2 and the explanation just below it here.

Clearly, the numbers are different. I am especially concerned by my inability to achieve the same value for blade losses, where Atkinson and Van Holst agree. Time to consult the community …

Well, that didn’t hurt, didn’t it? Not yet.

Update 15 April 2011

Bill Atkinson pointed me to the same issue as Martijn has done a long time ago. In my equation for drag and lift, I multiplied the blade area A with the sine of the angle of attach $\sin\alpha$, which was wrong. I’ve corrected for this and updated the numbers in figure 1.