Tripping the Boundary Layer

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.

Figure 1. Ten-Rater hull in the towing tank.

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.

So the question is, will any irregularity in the forward surface of the hull or fin cause the expected laminar flow to be tripped to turbulent flow and cause a jump in frictional drag? Or will the flow recover its laminar nature and show negligible drag increase?

10R waterline marks

One 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.

As is traditional with these experimental reports, just before you see the results, what are your expectations? Do you think that a thin waterline tape on the hull at the bow, about 6 mm wide, 50 mm long, and 0.15 mm thick, and another longer one at the stern would measurably slow the boat? Do you think the boat would be slowed down equally across the different towing speeds? Or do you think the boundary layer trip would slow the boat down more at low towing speed than at high speed? And if you don’t have a thought right now, heck, don’t peek; give it a go. OK? Here are the interesting results… I say interesting, because we took the same test ourselves before the experiment and agreed that any difference in drag would not be measurable. We were wrong!

Effect of waterline marks

The 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.

Figure 2. Change in hull velocity at two towing speeds with different waterline ending marks.

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.

To 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.

Again, just before you see the results, what are your expectations? Do you think that a somewhat rough leading edge on the fin would measurably slow the boat? Do you think the boat would be slowed down equally across the different towing speeds? Or do you think the leading edge (LE) roughness would slow the boat down more at low towing speed than at high speed? And if you don’t have a thought right now, c’mon, we’ve given some strong hints. OK? Here are the interesting results… I say interesting, because I took the same test myself before the experiment, and thought that it was a no brainer, a faired LE would make a measurable change to the drag. Was I wrong?

Effect of faired fin leading edge

The 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.

Figure 3. Change in hull velocity at two towing speeds with original and faired fin.

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 guess that?

Discussion and conclusions

We 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.

It seems that it would be worth painting your waterline marks onto your hull rather than using a tape, even a thin tape. That surprised us. The size of the effect is, of course, small and can only show up in the highly controlled conditions of a towing tank—flat water, upright towing, no other forces, measuring to 1/100 s. It would be the equivalent of 60 cm over a run of 100 m—less than half a boat length for a 10R, but worth having.

On the other hand, don’t let the lack of a significant difference due to a fin’s rough or smooth leading edge fool you. Although the fin was well used, only Graham noticed that its edge was a little rough and needed cleaning up. Me, I didn’t notice. The results are suggestive, if not conclusive—fairing the LE made a fractional difference of 0.27% at high speed. The tests were all made with no side force, equivalent to sailing downwind, and it may be that the difference would be larger where the fin operates at an angle of attack (leeway) in order to develop lift.

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.

Acknowledgements

These experiments would not have been possible without Graham Bantock’s enthusiasm and knowledge, or without the support of the University of Southampton.