b) that it should be reasonably straightforward for the rider to get on and off;
c) since the floats would be in the water only at low speeds, their hydrodynamic drag would be of little significance, but they would need to be resistant to impact damage.
In view of (c), inflatable cylindrical floats were chosen, which can also be very light.
They are 1.75m long by
0.31m diameter, i.e. with a buoyancy of 132kg each, so either on its own can support the entire weight of vessel and rider. The arrangement is shown, in stern view, in Figure 10a. Figure 10b shows how the overall upsetting torque, i.e. gmzmsin hydrostatic righting torque, varies with roll angle , as calculated for 68kg and 80kg riders.
The curves rising through the origin represent
unstable equilibrium in the vertical position, as expected. For a 68kg rider, the float touches the water at = 6.5°, and stable static equilibrium is reached at = 17.6°. The fact that the lobe of the 68kg curve below the -axis is larger than that above it gives ample security against overshoot
8.
CONCLUSIONS
A long narrow single-hulled vessel is likely to have low resistance to forward motion, and hence be economical on power, but it will be difficult to make it stable in roll. However several existing vessels have demonstrated that it is possible, with the use of a forward rudder, to make stable during
forward motion a vessel that, when
stationary, is highly unstable. A mathematical model of this phenomenon has been offered, together with some limited experimental confirmation with a particular vessel. The experimental results show the rudder giving rapid control
of yaw-rate, with a predicted by the theory. “gain” much as It seems likely, though before reaching another point of unstable
equilibrium at = 42°. The situation for an 80kg rider is perhaps more questionable in that respect.
unchecked, that it gives similarly rapid control of lateral velocity, and thus of the path taken by the vessel at the waterline. Given this, the control problem resembles that of keeping a bicycle upright. The mathematical model, as simulated, suggests that a simple control law relating rudder angle to roll and yaw rates should be adequate for stability. But since, as far as is known, vessels of this type have so far all been controlled by human riders, the only way to demonstrate the validity of such control laws is probably to build an automatically-steered vessel, with some form of gyroscopic sensor.
Since vessels of the type discussed can be kept upright by rudder control only when moving forward,
it is
necessary to include means for ensuring stability when stationary or going astern. Some ways of doing this have been outlined.
a c b
A single-hulled vessel so stabilised has a resistance advantage over a catamaran only if the control surfaces do not need to be so large as to nullify it. Theory suggests they do not, but more experimental evidence is needed on this.
Figure 10: Vessel of Figure 4 with above-surface outrigger floats. (a), stern view; (b) upsetting torque v. roll angle; (c) equilibrium position getting on or off
The vessel is also in stable equilibrium in the situation of Figure 10c, so there is no problem in getting on or off at a bank.
A useful refinement, particularly in a larger vessel, could be means to lower the floats, when stationary, to the point where the vessel would be in stable equilibrium at = 0°.
©2007: Royal Institution of Naval Architects
Vessels of this nature are probably only really suitable for inland or sheltered waters, but they do not necessarily have to be confined to small single-person boats, as they have been to date. The usual problem in giving a long thin hull to a conventional vessel lies in its strength, since the depth from deck to keel has to be small for the sake of stability. But if roll stability is secured as described above, this limitation disappears. The beam too can be increased, above the waterline, if extra lateral bending strength is needed.
9. ACKNOWLEDGMENTS
The vessels of Figures 3 and 4 were designed and developed
by England as part of their
undergraduates at Oxford University, project work,
under the
supervision of the author, and constructed by them and by technicians in the Department of Engineering Science. So many people have been involved over a period of years that it is impractical to name them all.
B-9
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54