## How fast can Relax sail?

In sailing it’s not unusual to find that changing course a little away from the direct line to your destination can give you more boat speed, as can sailing a little free of close hauled when you’re working to windward. Sometimes this can work to your advantage with the extra distance sailed being more than made up for by better boat speed, on other occasions the gain in speed isn’t enough and you end up taking longer than you needed.

Obviously, there’s plenty of things affecting the speed through the water, such as wind, waves, sails and their setting, and the helm. However, if you’ve ever wondered “should we be going faster?”, this might answer your question.

First, some definitions. The **rhumb line** is the straight line from the starting point to the destination, that is the shortest distance to the destination. **Course Offset** is the angle between our course and the rhumb line, which is the amount we’ve decided to sail away from the most direct course to gain some extra boat speed.

**Cross Track Error** (often abbreviated to XTE) is how far we are away from the rhumb line at any time.

The raw data transducers give:

- Compass heading
- Speed through the water (STW)
- Apparent wind speed (AWS)
- Apparent wind angle (AWA)

The GPS gives:

- Course over the ground (COG)
- Speed over the ground (SOG)

From these two sources, the following can be calculated:

- True wind speed (TWS)
- True wind angle (TWA)
- True wind direction (TWD)
- Velocity made good to windward or downwind (VMG)
- Velocity made good on course (VMC)

(VMC is your velocity towards a specific waypoint, and in these notes is assumed to be the windward or leeward mark. Not all systems will give VMC)

(Remember your maths? Speed is the rate along a path, whereas velocity is a vector defined as rate and direction)

## VMG

We are often interested in maximising our progress in an upwind or downwind direction. VMG is the velocity component of the boat in an upwind (or downwind) direction. The closer you sail to the wind, the slower you go until the boat comes head-to-wind and stops. Sail at 90 degrees to the wind on a reach and you will go fast, but your velocity upwind is now zero. Therefore, when heading upwind, there will be an optimum angle to sail at to maximise your upwind speed. The same applies downwind; there is an optimum angle to give the best downwind speed.

There is a problem with VMG – the helm can change the boat’s heading faster than its speed. Here’s an example:

Assume you want to sail due north, and the wind is also blowing from the north. Let’s say the boat is sailing optimally at 8 knots and at 30 degrees to the wind. If you head up by 20 degrees you are now heading almost in the correct direction and the VMG will instantly improve. Then the boat starts to slow down and your VMG decreases. The helm then bears away and the VMG drops even more, because your angle to the wind has dropped. The boat then picks up speed and the VMG increases.

Moral – don’t helm by steering to the VMG.

## VMC

Imagine the wind is blowing from the north, and the mark you are sailing towards is also due north. You can sail optimally at 30 degrees to the wind, which gives your best VMG. As you sail north at 30 degrees, you stay at your best VMG, but the velocity that you are making towards the mark gradually decrease. When you are abeam of the mark your speed towards it will be zero, and as you continue on your track your velocity towards the mark becomes negative. VMC therefore optimises your speed towards a mark. If you’ve put a waypoint into the chart plotter, the software may give you a VMC. (The Raymarine Axiom software uses the laylines function for this)

In a race with long legs, and a bit of common sense, VMG is going to be close to VMC

## Polar diagrams

VMG is also dependent on the yacht design and there are various ways of calculating it:

- Sail and record your boat speed and angle to the wind. Do this for all angles, and record lots of data.
- Velocity Prediction Programs (VPP) will be used by all yacht designers
- Computational Fluid Dynamics (CFD) is the expensive method of modelling VMG and is probably only going to be used in the design of grand prix racer type yachts.

The crossplot of speed and angle is presented as a polar diagram, with the data displayed for different wind speeds. Even if very high-quality, a set of polars can only reflect the computer model they started with, and express it in a set of targets unique to that boat. A different displacement, sailplan, alloy or carbon rig, shallow or deep keel type, or crew weight, will lead to more or less different results.

## Polar diagrams for Relax (X40)

The polar diagrams are for an X40, but I don’t know how the data was created or what the sail plan was.

In the plot below, the radial axes are True Wind Angle (TWA) and the vertical scale is boat speed. Plots normally have lines plotted for various True Wind Speeds (TWS). In this example, I’ve only plotted the curve for a TWS of 20 knots.

It’s easy to read – move your finger radially along any true wind angle. Stop when you reach the boat performance line associated with the true wind speed you are experiencing. Now, read back around the concentric boat speed circles to the vertical axis and read off the VMG for that given true wind angle and that given true wind speed.

The plot also shows the best VMG upwind and downwind. This point is shown where the graph changes from green to red, in this case sailing with a TWA of 36 degrees will give you a VMG of 7 knots. If you sail closer than 36 degrees to the wind, your upwind VMG will drop. Similarly, the best downwind VMG is 8.2 knots, achieved when the boat is at 172 degrees to the wind.

## The effect of wind speed

Everyone knows that if the wind strength increases you can point closer to the wind, but by how much? The series of plots below are in increments of 10 knots. (Note that the vertical axis does change) With 5 knots of wind, you should be sailing with a TWA of 45 degrees. When the wind increases to 15 knots you can make an angle of 39degrees.

## In conclusion

Since we know the optimum angle and VMG for any wind speed, the STW can be calculated, which is the VMG/cos(angle). The table below gives the numbers for different wind speeds, and the theoretical maximum STW. Now it’s just a matter of trimming and helming to get those speeds!

## 1 thought on “How fast can Relax sail?”

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Good article Alasdair – where did you get the polar analysis software from?

The next challenge is when the rhumb line is really a CTS due to the tide.