# Quantify the Coxswain's Work

In rowing, having the correct heading is crucial. How much can a boat steer off course before it affects performance? In this post we share some data from the Navy-Princeton Cup of April 6, 2024, to explain how you can use our tool to measure this.

In rowing, boats usually race 2000 m in a buoyed course where each boat should remain within an at least 12.5 m wide lane (https://worldrowing.com/technical/rules/). Most US collegiate courses do not have buoy lines or lanes. Instead, the crews point at a marker 2000 m away.

*This picture shows the markers from the Navy-Princeton Cup: they are the barely visible bright orange pixels in the center of the picture.*

The first to cross the finish line wins the race. In tight races, the winning boat may be only a few tens of centimeters ahead of the second place. It is generally assumed that steering off-course (meaning the boat is still inside its lane but tends to go towards its left or right side) is very bad and may cost a boat the crucial few centimeters to win the race or become second. But how bad is it really to come off course?

I start with a mathematical analysis, show three real-world examples from @tigerheavies from the Navy-Princeton Cup of April 6, 2024, in Annapolis, MD, recorded with our rowing analysis system, and finish with a quote from Greg Hughes, head coach of the @tigerheavies.

I'd like to express big thanks to the team and Greg for allowing us to publish their race data.

## The mathematical solution

Mathematically speaking, it is straightforward to compute how much distance is lost by coming off course. Let's assume that over a course distance of 100 m the boat steers 3 m too much to the left. In a buoyed course, this is already a lot and the rowers should definitely be aware of this. In the setting of the Navy-Princeton Cup, especially with strong currents and winds, a deviation of 3 m is almost impossible to notice.

*Illustration of 3 m deviation to the right over a distance of 100 m. The dashed lined to the left and right indicate the buoy line and the boat moves from the "bottom" to "top".*

What is the total distance they travelled? According to Pythagoras it is the square root of
(100^{2} + 3^{2}) = 100.045 m. Using trigonometry, the heading deviation, indicated
in the above figure by alpha, is 1.718°.

So, coming 3 m off course over 100 m only adds 4.5 cm of additional distance! This is not much and, I believe, could definitely be ignored as relevant to performance (of course the boat may want to come back to the center again. If it does this over the next 100 m then another 4.5 cm get added).

### The influence of the fastness of deviation

Where things get interesting is how rapid the boat comes off course, or once it is off course takes to come back to the center of the lane. Let's assume that, instead of over 100 m the boat only takes 50 m to come 3 m off course.

We get to a total distance covered of square root of (50^{2} + 3^{2}) = 50.090 m. The
heading deviation is 3.434°. Now the boat does an additional distance of 9 cm instead of 4.5 cm.
Twice as much. If it goes back with the same "speed" the boat "lost" 18 cm of
distance. Now, this starts to become relevant to performance.

On the other hand, if we allow the boat to take 200 m to deviate 3 m (or come back from this 3 m
deviation to the center) then the total distance covered is the square root of
(200^{2} + 3^{2}) = 200.022 m. The boat only makes an additional 2.2 cm distance.

### The mathematical take home message

Coming off course may not be bad and not add much extra distance. As long as it happens slowly. If a boat is noticing that it's coming off course don't correct too fast: come back to the center as slowly as possible, or even not at all.

## The real world: Navy-Princeton Cup 2024

TIn the real-world things are never as easy as in mathematical models. A boat never steers constantly in the same direction for a long distance. Instead, rowers (or the coxswain) notice that they are about to come off course and do some active corrections. Or they need to constantly correct their heading because of some side winds or currents, probably even changing over time.

For this purpose, our rowing analysis app shows the number of meters a boat comes off course for every instance of time, 200x per second. Moreover, the exact position of every stroke start is shown with color-coded dots: green if course deviation is less than 2° and yellow/orange if it is over 2°. If a boat kept a 2° heading deviation over 100 m it has to cover an additional distance of 6.1 cm.

### The "good" example with calm conditions

Let's start with a "good" example. There was no wind and the water was calm. It is an older recording from an M8+ boat of @tigerheavies with an average pace of 1:28.58 / 500 m and a linear distance of 1500 m. The effectively covered distance was 1500.2 m. The boat was never further away from the perfect line than 1.5 m. But there was a phase towards the end where the boat "drifted" from being 1.5 m too much to the right to 1.5 m too much to the left, resulting in a total sideways change of 3 m.

Very typical for real-life situations, the sideways deviations changed over time but were always green, not adding too much extra distance. There were a few moments of larger deviation (light green), but nothing to be too much concerned. The extra distance the boat had to cover was 20 cm. Interesting would be to discuss this plot with the coxswain: what steering or commands did he provide to the boat which caused these sometimes "sudden" steering changes?

### Navy-Princeton Cup 2024: very tough conditions

The conditions could be described as *"10-14mph cross to cross tailwind with significant chop and
whitecaps at points"*. Three boats "classes"/races HM1V – HM2V – HM3V were recorded, with
the starts spaced 30-45 minutes. Princeton won all these races against the Navy (all results:
https://www.row2k.com/...)

#### HM1V

A large gust hit the crew just before the start command, pushing them off point at a point when they had no time to correct before the start. What can be seen in the above plot is the crew's effort to correct this being pushed off. It took them the first 300 m to get all sorted out.

Despite all this, they only covered 0.5 m extra. Over 80% of it was happening in this first crucial part of the race. Afterward they were doing extremely well, considering the challenging conditions.

Race video: https://www.youtube.com/watch?v=Fgr32xiMpB8

#### HM2V

Again, we can see some struggles at the start but also much more sideways deviation caused by the wind and currents until 1400 m. At this point the boat crossed under a bridge, the shore became closer and parallel to the racecourse allowing for an easier reference. They covered 1.0 m extra.

*Satellite image of the boat's position for the HM2V boat, with color-coded speed. The bridge was approximately 1550 m from the start.*

Race video: https://www.youtube.com/watch?v=ueaTk-g_Hbw

#### HM3V

Similar to HM2V, the boat was considerably deviated to the left. Most deviation happened during the first 7 strokes. Corrections were slower, adding less extra distance than for HM2V. Nevertheless, they covered 1.0 m extra, mostly from these first 7 strokes.

Race video: https://www.youtube.com/watch?v=z8gDRaT0Vi0

### The real-world take-home message

In these very challenging conditions, it is almost impossible to keep correct heading and minimize sideways deviation during the start phase. The coxswains did an amazing steering job, but one can see the differences in level between HM1V, HM2V, and HM3V.

Rapid corrections and fast changing sideways deviations are responsible for extra distance. Slow corrections and adjustments don't cause much extra distance, even if the boat comes far off course.

These visualizations are only a first version and demonstrate one possible application of our sensor system. We are continuing to explore and find even better ways to visualize performance and add value to coaches, rowers, and coxswains.

In the words of Greg Hughes, head coach of @tigerheavies: