Chapter 7       Leeway and the thrust versus speed graph for a model yacht

Having laid out the “theory” needed to explain model yachts I have to break into the complex interaction between the several parts of a racing yacht to start the process of explaining how they all work together.

It turns out that most things fall into place from an explanation of how the forces exerted by the sails act to drive a yacht when it is beating as close as possible to the wind. An essential preliminary to that is a knowledge of the leeway that a yacht may have when it is beating. I decided to fit an electrically driven airscrew to my 27² yacht to simulate the sails. The motor was a standard Speed 660 and the propeller was 6² in diameter by 5.5² pitch using a 7 cell pack of Nicads. Picture 7-1 shows the test rig on the yacht and it is evident that the propeller is set almost transversely. In fact the angle of the motor could be changed remotely from 85° to 70° to the centre line of the yacht as shown in pictures 7-2a, b, and c. A little trigonometry was all that was needed to calculate the transverse components and the forward components as percentages of the propeller thrust. These are given in Table 7-3.

It was most instructive. The boat handled just like an ordinary power-boat. Picture 7-3 shows the yacht on the lake probably at nearly maximum revs and the propeller at more than 70°.

Having seen figures of 10° quoted for leeway I expected to be able to see the leeway easily. In fact it was hard to see any leeway at all. At best the leeway appeared to be just a few degrees, perhaps as little as 3°. Fins and rudders appear to be very good at their job.

The fact that the airscrew drove the yacht was not a surprise but the speed that could be attained with the propeller at 85° certainly was. It was immediately evident that the yacht was extremely easy to drive. This showed that a beating yacht needs only a small drive to achieve sufficient speed for it to tack through head to wind.

It was now obvious that a second series of tests was required  to relate the speed of the yacht to the thrust of the propeller. In fact I had already measured the thrust produced by the motor at various speeds so all that was needed was to set the motor axis along the centreline of the hull and try again. Graph 7-5 shows the thrust in grammes versus speed. The circles are the experimental points and the solid line is a simple mathematical curve[1] passing through most of them.

With this graph available and a portable tachometer designed for the purpose the prop speed could be set and the yacht timed over a measured course. As a side benefit these tests permitted photographs to be taken of the wave pattern at each thrust.

The result is shown in Graph 7-6. Again the experimental points are circles and a curve[2] is fitted through them. I found it to be difficult to describe the implications of this curve because it does not reach its maximum. However the critical speed of 3.4 feet/second for a 27² hull makes a convenient reference speed. It is the dotted line

I repeated the tests above for an A boat (a Sweet) using a geared Astro 15 motor driving a 17² propeller. The outcome is shown in Graph 7-7. Using the waterline length of 55² the critical speed is 4.85 feet/second. The graph has the same shape as that for the 27² yacht so presumably metre boats and Marbleheads also have the same shape.

For any yacht the drive produced by the sails and the resulting speed are linked by this graph[3]. One statement shows the importance of this graph. A speed equal to 50% of the critical speed can be produced by a thrust that is only 13% of the thrust required to produce the critical speed. This tells us that we have to look for a mechanism by which a sailing rig moving at an angle upwind can produce a small force and then beating against the wind is possible at a speed which permits tacking through head to wind.

[1] It is the graph of thrust = 0.000000189 (rpm)2.35

[2] It is speed = 5.8 (thrust)1/2.8

[3] I know that this graph is readily available for full sized yachts but it is given as a drag versus speed graph. I did not spot the equality between drag and thrust and its significance escaped me.