by Lester Gilbert
Toward the end of our experiments in the towing tank we
wondered if we could measure differences in hull drag due to small
irregularities on the hull. One case concerned the application of a thin tape to
mark the waterline, and we used a 10-Rater (10R) hull for this experiment,
illustrated in Figure 1. Another case involved taking a well-used fin and
fairing its leading edge. For this we towed a Marblehead.
At low speeds the viscosity of the fluid is a dominant
factor, which tends to damp out any irregularities that occur in the flow along
a surface or past an obstruction. This is why laminar flow occurs at low
speeds—imagine molasses flowing out of a can onto a spoon. Even sharp corners do
not cause lasting turbulence in the flow, which recovers from the local
disturbance and remains very stable downstream. At higher speeds fluids become
relatively less viscous and when disturbed from their laminar flow state, will
remain turbulent—imagine the upward flow of smoke from a cigarette in a room
with no drafts. The flow is smooth and streamlined for some distance, and then
it becomes turbulent, never to recover the streamlined flow again. At still
higher speeds the flow will be turbulent virtually from the outset.
10R waterline marksOne kind of boundary layer trip is the thin tape used to mark waterline endings in classes such as the 10R, A, and M. We towed a 10R hull with two normal waterline marks and then with no waterline marks. We used two FWD weights to give two towing speeds, low and high, such that the hull reached velocities of approximately 0.4 m/s and 0.9 m/s respectively.
Effect of waterline marksThe timed run took somewhere around 8 seconds and 19 seconds for the high and low FWD towing forces. Three runs were made for each towing speed, for each configuration of the marks, giving a total of 12 runs. The time for the three runs was averaged, converted to an average velocity, and the percentage change in velocity for that towing force was calculated—a “delta %” relative to the lowest velocity recorded. The measurement error for each delta was estimated as a standard error, and it is worth noting that the standard error of the delta (velocity change) was of the order of 0.2%. That is, using classical statistics, we can be 95% confident that a delta of, say, 1% in average velocity is indeed somewhere between 1.4% and 0.6% (plus and minus two standard errors). The resulting graph is shown in Figure 2.
We can see from Figure 2 that, at the high towing speed,
having no waterline marks allowed the hull to run faster by around 0.62%. This
difference is statistically significant, as may be seen by the fact that the
error bars are reasonably shorter than the differences they calibrate. On the
other hand, at low towing speed, the difference in hull velocity is not
significant, and having waterline marks did not seem to affect hull speed. Did
you expect any of that?
What is happening here? Probably at the lower speed the limit
mark is tripping the flow at the bow into turbulent flow, but the flow is
sufficiently robust for it to recover its laminar state very quickly. So there
is little or no measureable increase in drag. At the stern the flow will
probably be turbulent anyway and the aft limit mark will not have much
disturbing effect on the flow. At the higher speed the flow is less robust (the
water is less relatively viscous), and trip of the flow into turbulence is
somewhat longer lasting. The increase in drag, however, is much less than would
be expected if the flow were to be changed fully from laminar to turbulent.
Marblehead fin leading edgeTo look at another kind of hull irregularity, we towed a Marblehead hull with a fin in its original condition, and then with its leading edge faired nicely with some wet-and-dry, 800 grit sandpaper. We used two FWD weights resulting in two towing speeds, low and high, such that the hull reached velocities of approximately 0.4 and 1.0 m/s respectively.
Effect of faired fin leading edgeThe timed run took somewhere around 7 and 17 seconds depending on the FWD towing force. Three runs were made for each towing speed, for each fin condition, giving a total of 12 runs. The time for the three runs was averaged, converted to an average velocity, and the percentage change in velocity for that towing force was calculated—a “delta %.” The measurement error for each delta was estimated as a standard error, and it is worth noting that the standard error of the delta (velocity change) was of the order of 0.2%. That is, using classical statistics, we can be 95% confident that a delta of, say, 0.4% in average velocity is indeed somewhere between 0% and 0.8% (plus and minus two standard errors). The resulting graph is shown in Figure 3.
We can see from Figure 3
that the differences in hull velocity, around 0.27%, were within measurement
error (the error bars overlap), and could not be called significant. Did you
Discussion and conclusionsWe see that waterline measurement marks have slowed the 10R hull by around 0.6% at high speed, while there is no significant effect at low speed. We see that fairing a rough leading edge of a Marblehead fin did not show a measurable effect at either speed.
Those of you with a
statistical background might like to know that the p value of the difference was
0.09. Not quite the conventional 0.05, but, ah, suggestive. And we know that the
little things add up.
AcknowledgementsThese experiments would not have been possible without Graham Bantock’s enthusiasm and knowledge, or without the support of the University of Southampton.
©2023 Lester Gilbert