Stroke Metrics

For OTW stroke metrics, there are two interesting applications, RIM ( and Crewnerd (

Crewnerd gives a “check factor” metric of how well you are rowing. RIM has several metrics. Today I will discuss “stroke efficiency” and “check factor”.

I was interested to see what my model had to say about these metrics. Be aware that this post may tell as much about the imperfections of my model as about those two apps.

In this post I am going to look at the metrics for different force profiles during the stroke. These are the stroke force profiles I am using:

force curves

The ultimate efficiency measure of rowing is to get the maximum average boat speed at a given power. The below picture is a key picture calculates just that. The differences between the different stroke profiles are quite subtle.figure_1

So what does the graph tell us? First, that the differences in speed are very subtle. Still, it seems that red circles (T2) are the most efficient, lowest average power at a given average boat speed. Profile T5 seems to be the worst.

So how does Crewnerd’s “Check Factor” look like?


T5 is clearly the worst, giving the highest value of “check” at a given boat speed.

What is also clear is that to increase speed, one ends up inevitably with a higher value of “check”. Don’t try to minimize check at the cost of losing speed!

Now we turn to RIM. The RIM definition of “check” is just the difference between max and min boat speed.


So, at a given velocity, T2 is clearly the “lowest check” value and T5 the worst. It seems also RIM definition of “check” is useful.

RIM has another metric, “stroke efficiency”, defined as the integral of boat speed over one stroke, minus the integral of minimum boat speed. It measures how much further your stroke takes you compared to the minimum boat speed.


For this metric, higher is better. So again T5 scores the worst, and the best seems to be T3.

I think it is too early for conclusions, but here are some take away messages that I stick to for now:

  1. Expect any metric to change with boat speed and stroke rate. You should make sure you keep both constant if you try to optimize your stroke, which is difficult
  2. At given boat speed and stroke rate, the three tested metrics are consistent in the sense that optimizing them brings you to the most efficient power profile.

To be continued …


New Rowing Physics and Rowing Mechanics Forum

This blog with my attempts to model Rowing Physics has been collecting dust for a while. I intend to keep these pages for reference and will publish new blog posts whenever I develop new functions or improve it.

However, I would really love to move the discussion on Rowing Physics and the comparison of the different models out there to this new Forum:


We are starting to see the possibilities for low-cost easy-to-access empirical data driven approaches. This is very exciting. The above-mentioned blog is maintained by the developer of Rowing in Motion who is very active. Let’s all move to where the action is!!!

Carole McNally Memorial CTC and 2k tester

Featured image

Workout Summary – Feb 14, 2015
Workout Details

Fletcher Warming up, followed by a 2k, of which I rowed only the first 1402m at my estimated 2k pace. Predicted end time just under 7 minutes.

Comparisons (quick status update)

As a result of the differences found in this post, Bill Atkinson and I have been going through our detailed models. This has resulted in the correction of my model in two points:

  1. It is not necessary to define a virtual outboard to calculate the blade force. The blade force is simply given by the F_{\rm handle} l_{\rm in}/l_{\rm out}, independent of the amount of blade slip.
  2. I had an extra term \sin\alpha in the calculation of the blade effective area which upon closer study of the expressions for  lift and drag is not necessary. The coefficients already take into account the area effect of the attack angle.

Bill also provided me with a detailed list of input values and calculated results for his model. This enabled me to improve my input values to more closely match his.

Here’s the current comparison:

Figure 1: Updated power distribution for Sander's model

Here are Atkinson’s results:

Figure 2: Power distribution for Atkinson's model

This reduces the difference in blade dissipation to an acceptable 1% error, and the power difference at the oarlock, oarhandle, and power dissipated in drag on the shell are on the order of 5%. Now the biggest discrepancies are in the power dissipation in the rower’s body, and the related question of shell and rower kinetic energy exchange during the stroke.

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.

Drag revisited (2)

In this post, I postulated that skin drag amounts to about 80% of drag and simply divided the skin drag by 0.8 to obtain the total drag.

Bill Atkinson pointed me to this work by Tuck and Lazauskas. First of all, form drag is estimated there by an equation from a paper by Scragg:

C_f = k C_{\rm skin}


k = 0.0097(\theta_{\rm entry} + \theta_{\rm exit})

where \theta_{\rm entry} and \theta_{\rm exit} are the half angles (in degree) of the bow and stern, respectively. Tuck and Lazauskas do a complete modeling of wave drag as well, and come up with something that we could almost call a phase diagram for rowing shells. Looking at the figure 2b here, the wave drag is around 6% of total drag for shells optimized for racing speed, a Froude number around 2 in the figure. Of course, wave drag varies quite strongly with the shell’s velocity. However, the shell velocity varies during the stroke, and it seems a good approximation to use an average value for wave drag which is only a minor portion of the total drag. Doing the integrals to calculate the instantaneous value would slow down the simulation software too much, for a relatively small improvement in accuracy.

As far as the bow and stern angles are concerned, I collected data from boat manufacturers sites about the boat length, beam and draft as a function of the displacement.The results are depicted in figure 1. The solid line is a linear fit, showing that all boats are basically of (more or less) the same shape. Assuming a parabolic boat shape, the bow half angle would be 8 degrees, with an elliptic shape around 6.3 degrees. This would give a value of k between 0.12 and 0.15. So, the total drag (wave drag, skin drag and form drag) would be about 1.2 to 1.22 times the skin drag. Or, in other words, skin drag accounts for about 82% of the total drag.


Figure 1 Shell length vs beam (both in m) for Vespoli and Empacher shells

Regarding the scaling equation used for different boat types, it is clear that if all boats are basically scaled versions of the same shape, then beam, draft and length should be proportional to the 1/3 power of displacement. This is clearly shown in figures 2 and 3.


Figure 2: Beam as a function of displacement for different makes and types of shell.


Figure 3: Shell length vs displacement for different makes and types of rowing shells

Finally, figure 4 shows the wetted area as quoted on various manufacturer’s websites as a function of the displacement. The solid line shows the \propto D^{2/3} scaling that I use in my model.

Figure 4: Wetted area as a function of displacement for rowing shells of various manufacturers

So, in conclusion, the mystery isn’t a mystery any more. The lower value quoted by Slasias and Tullis is just the skin drag portion calculated from a 5m² wetted area. In reality, the wetted area of a four is slightly higher, and one has to add 20% for wave drag and form drag. Looking at the scatter of the data in the various graphs, I would also say that the accuracy of my model is good within about 10%, not better. This is not a disaster, as the relative results predicted by the model are still valid. Finally, boat design is found to be extremely important, as a 5% reduction of skin drag can means a mean velocity increase of 2.6%. This amounts to more than 2 seconds per 500m for an eight.

Drag revisited

A discussion on the Concept 2 UK Forum reminded me of the unsolved mystery of the amount of drag experienced by a rowing shell. So I went back to my old textbook on Fluid Mechanics (Robert A. Granger, “Fluid Mechanics”, Dover 1995). Assuming fully turbulent boundary layer flow, the drag coefficient for skin drag is a function of the shell’s velocity or Reynold’s number. Granger recommends the following equation:

C_{D_f} = \frac{0.455}{(\log R_l)^{2.58}}

for Reynold’s numbers R_l larger than 10^7. The  International Towing Tank Conference (ITTC) recommends a slightly different equation:

C_{D_f} = \frac{0.075}{(\log R_l - 2)^2}.

For a single with a length of 8.2m and a velocity of 8.42 m/s (1:43 per 500m), the Reynold’s number amounts to 3.3\times 10^7 for water of 10 degrees C. This gives C_{D_f} = 2.459 \times 10^{-3} with the ITTC equation. Assuming the wetted area for a single with a rower weighing 80kg to be 2.25 m² as claimed by Cambridge Racing Shells to be the value for a Fluidesign single, I obtain \alpha_{\rm skin} = 2.77 N s²/m². Using Granger’s equation, I get 2.81 N s²/m². For a four with a wetted surface of 6 m², I get 6.7 N s²/m² using the ITTC equation.

Skin drag is not the only form of drag. There is also form drag and wave drag. It is said that skin drag accounts for about 80% of the drag (Ana Dudhia). So, dividing my number by 0.8 I get a value of \alpha amounting to 3.51 for the single scull at race speed. Pretty close to the value I have used so far. The difference is a slight dependence on the shell’s velocity for the value of \alpha. In figure 1, the drag force using the ITTC equation is compared with the simplified method of taking constant drag coefficient, for a single scull with a rower weighting 80kg (wetted surface of 2.25 m²). The differences are small but at maximum velocity they can be of the order of 10%.

Figure 1: Drag Force vs velocity for a single scull with a rower of 80kg. Green line: Constant drag coefficient approximation. Blue line: ITTC 1957 drag coefficient

The division by 0.8 to account for other forms of drag seems a bit arbitrary. Interestingly, when I try to validate the model on the Lucerne 2010 (no wind) boat speed and ergometer scores of Ondřej Synek, the 2010 world champion in the single, I get a consistent story. Synek’s Lucerne achievement was a power of 586W on the 2k (calculated using the ITTC equation value for drag). Assuming 25W is consumed in moving a 98kg heavy athlete up and down the Concept 2 slide, the remaining ergometer power of 561W corresponds to a 2000m time of 5:42 on the ergometer. Synek is known to have rowed 5:41.8 (Czech National record).

As Bill Atkinson rightly pointed out, the scaling equation I used to calculate for different boat types, depends heavily on the wetted shape. I took the \propto m^{2/3} intuitively without giving it much thought, except that Anu Dudhia uses it here. The numbers given for wetted area on the CRS site seem to confirm this. Also, my validation with the 2010 Lucerne results gives confidence, but, admittedly, I have not given it enough thought from the basic physics side. To be continued …