# Stroke Profile III – realistic force profiles

In the two previous posts, I have looked at hypothetical force profiles. Here I present the simulation results on more realistic ones.

Figure 1: Force profiles used to simulate more realistic rowing styles

Figure 1 shows the profiles used in the simulation. As you can see, all are defined by two points (x1,F1) and (x2,F2). The first point defines the handle position at maximum leg force. From that point on, the force can stay on a plateau or go downhill immediately. This is defined by the second point (x2, F2).  The force curves look more or less like what can be observed on a Concept2 ergometer screen. One could interpret the differences as differences in style, and perhaps also body proportions. For example, T3 could be a rower with shorter legs and a longer torso compared to T2. T5 is equal to “trapezium” in my two previous posts.

Figure 2: Mean boat velocity vs rower power for different force curves

Figure 2 shows the mean boat velocity achieved for a rower in the single, using standard rigging (catch angle 63 degrees). Each data point represents a different stroke rate, increasing from 25 spm to 35 spm in steps of one stroke per minute. Again, the differences are small. The most efficient strokes seem to be T2 and T5. T3 seems to be the most inefficient. It is interesting to look at the difference between T2 and T3. It seems like keeping a strong stroke as long as possible pays off. This is in agreement with common coaching practices.

Figure 3: Mean boat velocity vs rower power, smaller catch angle

Figure 3 shows the same plot as figure 2, with a changed rigging. The rower has moved the footboard towards the bow and reduced the catch angle to 43 degrees.  Still, the rowing style “T2” is the most efficient, although the differences are reduced. In conclusion, a flatter force profile leads to more efficient rowing, independent of the catch angle, although smaller catch angles are more forgiving.

The differences between T2 and T3 are that the short-legged rower T3 has to push harder in the beginning of the stroke to reach the same velocity. He therefore loses more energy due to blade slip. The more balanced stroke of T2 wins.

# Stroke force profile II – a detailed look

In the previous post, I wondered about the differences in rower power for the different stroke profiles. Here’s a comparison between an ideal “flat” profile and the “trapezium” profile from the previous post.

Figure 1: Energy consumed during one stroke of "trapezium" style rowing

The red line in figure 1 is the energy used at the oarlock to accelerate the boat. The black line is energy dissipated at the blade (creating puddles). This rower is doing 35 spm and rowing 1:57 per 500m.

Figure 2 shows the same plot for the “flat” stroke profile. The mean boat speed achieved is almost the same, 1:57 per 500m at 35 spm. However, the energy consumed is higher. The “trapezium” sculler is rowing at 507W, while the “flat” sculler is rowing at 531W. So, where’s the difference?

Here’s a table with some data:

So, indeed the robot rowing a “flat” stroke force profile wastes more energy at the blade. However, he also puts more energy into the propulsion of the boat … at the same average speed. How is that possible? Is he more inefficient? First, I looked at the maximum and minimum boat speeds, and it seemed that the “trapezium” rower had a more unbalanced stroke, with larger speed differences during the stroke. Also, the mean square deviation from the mean velocity (a very very mean paramater) is higher. However, the mean $v^3$ which is proportional to the energy lost in drag is higher for the “flat” rower. Especially, during the recovery, the “flat” rower dissipates more energy at the hull through drag than the “trapezium” rower.

Let’s not forget that we used some extreme force profiles, which are never seen in real rowing. In reality, force profiles for different rowing styles will be closer to each other. I have a suspicion that physiology plays a larger role here than physics. It will be the movement which is most efficient and/or most powerful for the body which will make the difference. Another source of inaccuracy might be that my model does not take into account a pitching movement of the boat (around the lateral axis) which might be a source of additional energy dissipation.

# Force profile – surprising results

In the previous post, I looked at the influence of different recovery styles. Now, it’s time to look at the influence of the force profile during the stroke. I varied the force profile of the applied force during the stroke, keeping stroke length constant, and scaling the maximum force such that the average handle force per stroke remains constant. Figure 1 shows the different force profiles that I tried. The system used for the simulations was a single scull with a 80kg rower and fairly standard rigging. Catch angle -63 degrees, finish angle 43 degrees (zero being sculls perpendicular to the boat’s long axis).

Figure 1 shows the various stroke profiles that I tested. I used extreme, unrealistic profiles on purpose. We’re still in validation mode so consider the results more as a test of the simulation than an exercise using realistic stroke profiles. No sculler will be able to pull a force profile like “strong finish” in figure 1. Once we have confidence in the simulations and a feeling for the error margins, we can look at realistically achievable force profile variations.

Figure 2 shows the results. As said, I kept the average handle force per stroke constant and increased the stroke frequency from 25spm to 35spm for the five different force profiles. The duration of the stroke is a function of the force profile and of the boat velocity at the catch, so the recovery speed, or ‘the rhythm’ will be different for the different rowing styles, even when rowing at the same stroke frequency.

Figure 2: Mean velocity vs power for different force profiles (stroke frequency varying between 25spm and 35spm)

Interestingly, all force profiles except “strong catch” seem to fall around a common Power-velocity curve, although the stroke frequency needed to achieve a certain power varies. Apparantly, some force profiles are “heavy” strokes where the rower achieves a higher average power with a lower stroke frequency. It’s a bit puzzling to me to see such large differences in power at the same stroke frequency for the different force profiles. My working assumption right now is that the constant average handle force in figure 1 is really a “stroke length average” and not a time average, but I am not 100% sure that this is the right explanation. I need to dive into my model to find the explanation.

The “strong catch” curve is the outsider. Higher end speeds are achieved, at relatively low frequency, however at the cost of much higher power. So, is this a “heavy, inefficient” stroke? The equations for drag and lift are symmetric around the 0 degree oar angle point. However, the scull arc in my example is not symmetric around 0. So, I performed an additional set of simulations where I moved the foot board towards the bow in such a way that the catch angle is now only -43 degrees and the finish angle is 63 degrees. The results can be seen in figure 3.

Figure 3: Velocity vs power. Same as figure 2, but with a lower catch angle

Indeed, the “strong finish” stroke has now become the most inefficient one. Looking at Van Holst, figure 4.3 here, the cause of this is that the rowing is pulling hard in the part of the stroke where the blade efficiency is low. We’ll look at this conclusion again in a subsequent post on catch angle dependence.

Note to self: In another subsequent post, I need to look deeper into the power differences for the different stroke force profiles.

# Cas Rekers passed away

I haven’t known him personally, but I remember Cas demonstrating his RowPerfect on the Bosbaan some twenty years ago. I think he greatly stimulated the development of rowtrainers, and managed to build and market a rowtrainer that comes remarkably close to the feeling of rowing on water.

Here’s the equation that describes what his RowPerfect did better than the competition:

$m_c (v_t + v_b - v_c) + m_b (v_t + v_b) = m_c v_t + m_b v_t$.

A beautiful In Memoriam written by Carl Douglas.