# Turbulent boundary layer thickness

Can anyone explain how to calculate aproximate turbulent bbondary layer thickness, and explain how Reynolds numbers relate to turbulent boundary layer thickness ?

So far we have found a rule of thumb which states that boundary layer thickness equals 1% to 2% of the length of the wetted surface at 6 knots, but at higher speeds it must increase, does it increase in direct proportion to speed ?

I am wanting to estimate boundary layer thickness so that I can make appropriately sized vortex generators to reduce hull drag.

Thanks !

I thought I had a link to that but I cant find it…

from memory its about 3/4 inch…

Re numbers about 400,000 for 5m/s…

800,000 for 10m/s…I think

http://www.onemetre.net/Design/Design.htm

I could be way off…but for some reason, I have a good memory for useless figures such as these.

Yeah, Roy. I wondered about it for that reason too. As far as I know: Speedo “sharkskin” swimsuits would seem to have a lot of science in them, as Speedo has enough money and time and people to test that stuff (they’re claiming meaningful empirical timed results) and it’s a microscopically textured surface. Sharks shed the boundary layer with micro denticles, at the cost of outright top speed, but with payoff at bursts, and with surfboards being powered as they are, I think the boundary layer is a drag.

Someone is quoted talking (they admit to it being just theory) about boundary layer on hulls in TSJ as an advantageous thing. I don’t think it is.

I think a mild-sanded finish is probably better for bottoms, and I saw Steve Pirchner (or whatever his name is–“How to build your first surfboard”) say that rough sanded epoxy hotcoat finishes are good enough for waxless grip on top too, so I’m thinking rough has advantages besides my laziness.

But I reserve the right to change my minds, or having them changed by people.

For everything (well, nearly everything) you wanted to know about boundary layers (circa 1960 but still valid):

“Boundary Layer Theory” (635p)

by Herman Schlichting (translated by Dr. J. Kestin)

Fourth Edition (my copy…don’t know if there is a newer edition)

McGraw-Hill Series in Mechanical Engineering

McGraw-Hill Book Company, Inc. NY, London, Toronto

When I have a little time, I’ll reproduce some of the equations for boundary layer growth/thickness for flow acoss a thin flat sheet – an approximation to a surfboard bottom (note that the transition from a laminar bounday layer to a turbulent boundary layer is dependent on a lot of factors, including shape, roughness, ambient turbulence levels, etc.)

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I thought I had a link to that but I cant find it...

from memory its about 3/4 inch…

I think that is a reasonable ballpark figure for surfing speeds, near the tail, near the middle of the board.

Smaller further forward, closer to the rails. Under a rail fin it is closer to 1/4".

Thicker under concaves. Thinner under Vees.

I’m sure MTB will be back with full equations…mine are guesstimations from series of cutaway fins I’ve made.

…to continue from my previous post (my comments in […]):

[From Schlichting (1960) for laminar flow:

Let:

R* = 1/Reynolds number

T99 = thickness of the boundary layer at a distance

L from the leading edge of a flat plate (approximation to a surfboard)

v = kinematic viscosity of the fluid

then:]

T99/L = 5.0 x square-root(R*)

[But, as Schlichting notes:]

"It is impossible to indicate a boundary layer thickness in an unambiguous way, because the influence of viscosity in the boundary layer decreases asymptotically outwards. The parallel component of u [the along-plate component of the flow] tends asymptotically to U [the parallel component well forward of the beginning of the plate] of the potential flow. [We define a boundary layer thickness, T99, as the thickness] …for which u = 0.99 x U.

[Alternatively] A physically meaningful measure for the boundary layer thickness is the ‘displacement-thickness’, … which is that distance [TD] by which the external potential field of flow is displaced outwards as a consequence of the decrease in velocity in the boundary layer…

[The resulting boundary layer thickness, TD, is:]

TD/L = 1.72 x square-root(R*)

[or about 1/3 the thickness of the T99 boundary layer.]

[To be complete] We may at this point evaluate the ‘momentum thickness’ [TM, which is related to] …the loss of momentum in the boundary layer as compared with potential flow…[this calculation] gives:

TM/L = 0.664 x square-root(R*)

[At some Reynolds Number (i.e. at some point downstream from the leading edge, the laminar flow will change to turbulent. For a flat plate this transition can occur somewhere between a Reynolds Number of 2 x 10^5 and 10^6, depending on the smoothness of the plate and the degree of ambient turbulence in the flow. Once the boundary layer has change from laminar to turbulent, its thickness is related to the downstream distance and the Reynolds Number by the equation:]

TB99/L = 0.37 x (R*)^0.2

[Since the surf zone is virtually certain to have some degree of turbulence, let us assume that the boundary layer changes from laminar to turbulent at a Reynolds Number (based on the distance from the leading edge of the wetted area of the board) of 2 x 10^5. ‘Over the bottom’ speed measurements indicate typical speeds (in my area) of 15-20 mph (22-29 ft/sec). ‘Through the water’ speeds are likely to be less, so let’s assume a speed of 20 ft/sec (610 cm/sec). In that case, the downstream distance from the leading edge of the wetted surface of the board to the transition from laminar to turbulent flow will be about 3.3 cm (1.3) inches, and the T99 boundary layer thickness will be about 0.037 cm (and the displacement thickness, TD, of the boundary layer will be about 0.012 inches).

At a speed of 5 ft/sec (~paddling speed) the transition from laminar to turbulent flow will occur about 5 inches from the leading edge, and the boundary layer thickness (T99) at the transition point to turbulent flow will be about 0.05 inches from the leading edge.

Thus it would appear that boundary layer flow on the bottom of a board is generally turbulent–except, perhaps, in the outer region of slender (‘high’ aspect ratio) fins moving through the water at slow speeds.

Now let’s estimate the turbulent boundary layer thickness at the tail end of a board traveling at 20 ft/sec. Assuming a wetted length of 4’, or 490 cm (from the entry point on the ‘wave side’ of the board to the tail), the Reynolds Number will be about 30 x 10^6, and the thickness of the turbulent boundary layer at the tail of the board will be about 5.8 cm (or 2.3 inches)–about 1.2 percent of the wetted length).]

So do you agree that it makes sense to leave the bottom sanded as opposed to polished? I saw a board with golf ball style dimples in the bottom somewhere online, and I’ve seen sharkskin finishes mentioned for surfboards, the aforementioned swimsuits are almost universally used now, and of course, sharks, so it seems like a sanded finish would accomplish some of the same benefit?

From Wikipedia: At high Reynolds numbers, typical of full-sized aircraft, it is desirable to have a laminar boundary layer. This results in a lower skin friction due to the characteristic velocity profile of laminar flow. However, the boundary layer inevitably thickens and becomes less stable as the flow develops along the body, and eventually becomes turbulent, the process known as boundary layer transition. One way of dealing with this problem is to suck the boundary layer away through a porous surface (see Boundary layer suction). This can result in a reduction in drag, but is usually impractical due to the mechanical complexity involved.

At lower Reynolds numbers, such as those seen with model aircraft, it is relatively easy to maintain laminar flow. This gives low skin-friction, which is desirable. However, the same velocity profile which gives the laminar boundary layer its low skin friction also causes it to be badly affected by adverse pressure gradients. As the pressure begins to recover over the rear part of the wing chord, a laminar boundary layer will tend to separate from the surface. Such separation causes a large increase in the pressure drag, since it greatly increases the effective size of the wing section. In these cases, it can be advantageous to deliberately trip the boundary layer into turbulence at a point prior to the location of laminar separation, using a turbulator. The fuller velocity profile of the turbulent boundary layer allows it to sustain the adverse pressure gradient without separating. Thus, although the skin friction is increased, overall the drag is decreased. This is the principle behind the dimpling on golf balls, as well as vortex generators on light aircraft. Special wing sections have also been designed which tailor the pressure recovery so that laminar separation is reduced or even eliminated. This represents an optimum compromise between the pressure drag from flow separation and skin friction the induced turbulence. http://en.wikipedia.org/wiki/Boundary_layer

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So do you agree that it makes sense to leave the bottom sanded as opposed to polished? I saw a board with golf ball style dimples in the bottom somewhere online, and I’ve seen sharkskin finishes mentioned for surfboards, the aforementioned swimsuits are almost universally used now, and of course, sharks, so it seems like a sanded finish would accomplish some of the same benefit?

From Wikipedia: At high Reynolds numbers, typical of full-sized aircraft, it is desirable to have a laminar boundary layer. This results in a lower skin friction due to the characteristic velocity profile of laminar flow. However, the boundary layer inevitably thickens and becomes less stable as the flow develops along the body, and eventually becomes turbulent, the process known as boundary layer transition. One way of dealing with this problem is to suck the boundary layer away through a porous surface (see Boundary layer suction). This can result in a reduction in drag, but is usually impractical due to the mechanical complexity involved.

At lower Reynolds numbers, such as those seen with model aircraft, it is relatively easy to maintain laminar flow. This gives low skin-friction, which is desirable. However, the same velocity profile which gives the laminar boundary layer its low skin friction also causes it to be badly affected by adverse pressure gradients. As the pressure begins to recover over the rear part of the wing chord, a laminar boundary layer will tend to separate from the surface. Such separation causes a large increase in the pressure drag, since it greatly increases the effective size of the wing section. In these cases, it can be advantageous to deliberately trip the boundary layer into turbulence at a point prior to the location of laminar separation, using a turbulator. The fuller velocity profile of the turbulent boundary layer allows it to sustain the adverse pressure gradient without separating. Thus, although the skin friction is increased, overall the drag is decreased. This is the principle behind the dimpling on golf balls, as well as vortex generators on light aircraft. Special wing sections have also been designed which tailor the pressure recovery so that laminar separation is reduced or even eliminated. This represents an optimum compromise between the pressure drag from flow separation and skin friction the induced turbulence. http://en.wikipedia.org/wiki/Boundary_layer

I wouldn’t use a dimpled or rough surface on the bottom of a surfboard for the purpose of tripping laminar flow into turbulent flow. As the text you quoted indicates, that is normally only beneficial where the flow will be encountering adverse pressure gradients and a turbulent boundary layer would reduce the region of separated flow–e.g. with ‘blunt’ aft bodies such as a golf ball and the human body (a fish, or a shark, although streamlined, may be an entirely different situation because of the curvature of the body and the generation of eddies while swimming and maneuvering). On the other hand, the flow on the bottom of a planing surfboard is normally subject to a positive pressure gradient and the flow should not be prone to separation. One might argue that if there is substantial kick in the tail of the board, an adverse pressure gradient might occur (especially during nose riding). But the speeds and wetted length are sufficiently large in that case that the boundary layer in that area is already turbulent. This is allegedly one of the reasons why fast moving dimpled balls substantially larger in diameter than a golf ball apparently do not exhibit an advantage over a smooth one.

On the other hand, some surfboard fins with a small chord lengths, operating at slow speeds and at a high AOA, might benefit from vortex generators (e.g. a sanded surface) near the leading edge under those conditions (assuming that you don’t want the fin to be operating in a controlled skid during some maneuver).

As far as whether a sanded surface might have an advantage over a smooth surface for some other reason, the only possible mechanism that comes readily to mind is that perhaps when traveling at speed over a sea surface populated with capillary waves sufficient air might be momentarily trapped in a sufficient number of roughness “pockets” to in effect reduce the average viscosity of the boundary layer. But whether or not this would happen (or to a significantly large extent so as to make a difference), I don’t know. For example, it would certainly depend on the rate of entrainment of air out of the ‘scratches/depressions’ versus the rate of supply (from the troughs of the capillary waves), the ‘volume’ of the ‘scratches/depressions’ per unit wetted area of the board, etc.), and the magnitude of the increase of surface friction from the roughness (even if the roughness lies within the boundary layer, it still increases the skin friction drag to some degree) versus the reduction in drag associated with the decreased viscosity.

Thnkyou MTB, that’s exactly what I’m after.

A couple of questions:

Although most of what I have read about vortex generators assumes that their purpose is to prevent or reduce boundary layer separation, isn’t it the case that they can also be used to control turbulent boundary layer thickness and growth ? My idea is to make vortex generators which are less than a third of the height of the turbulent boundary layer, in the hope that they will reduce friction between layers and reduce the overall height of the boundary layer on the bottom of the surfboard.

Roy

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I thought I had a link to that but I cant find it…

from memory its about 3/4 inch…

Re numbers about 400,000 for 5m/s…

800,000 for 10m/s…I think

http://www.onemetre.net/Design/Design.htm

I could be way off…but for some reason, I have a good memory for useless figures such as these.

Thanks craftee, that’s an interesting site, am intrigued by the boat design tool which uses circular arcs and which has a rocker drawing tool, downloaded it but don’t have the programme to open it, it’s a ‘spreadsheet’ and seems to be rather a small file for a design programme do you know anything about it ?

This is the page it’s called ‘hull design with arcs’

http://www.onemetre.net/Design/Design/Design.htm

Regards,

Roy

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Thus it would appear that boundary layer flow on the bottom of a board is generally turbulent–except, perhaps, in the outer region of slender (‘high’ aspect ratio) fins moving through the water at slow speeds.

If you watch the underwater shots of “New Emissions of Light and Sound” you will see that there is no turbulent flow (or very, very little) on the bottom of the board, but there only about 1.5’ of wetted length for most of the shots.

many of us that ride hulls tend to sand the bottom of our boards.

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If you watch the underwater shots of “New Emissions of Light and Sound” you will see that there is no turbulent flow (or very, very little) on the bottom of the board, but there only about 1.5’ of wetted length for most of the shots.

How can you see/verify the lack of turbulence (without aeration) in a transparent medium?

Additionally, boundary layer seperation (and its associated turbulence) is a very small-scale (but with big effects) phenemenon; not something that can be analyzed by the naked eye, and certainly not from a distance.

As much as I like the look of pretty, shiny boards, I think that sanded boards work better, though I have no empirical proof.

I once block-sanded (with 40 grit!) the bottom of a board that I didn’t particularly care about, leaving long scratches parallel to the stringer. It seemed a tad bit drivier and more solid than before, but that could’ve been my imagination (it was certainly weaker!).

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If you watch the underwater shots of “New Emissions of Light and Sound” you will see that there is no turbulent flow (or very, very little) on the bottom of the board, but there only about 1.5’ of wetted length for most of the shots.

How can you see/verify the lack of turbulence (without aeration) in a transparent medium?

Additionally, boundary layer seperation (and its associated turbulence) is a very small-scale (but with big effects) phenemenon; not something that can be analyzed by the naked eye, and certainly not from a distance.

How can you not see the difference between turbulent and laminar flow? They are very distinct, correct?

And, if they are not distinct to the naked eye, how do you know if the flow is turbulent rather than laminar?

sheesh. in a transparent medium like water you can’t tell at all whether the flow is laminar or turbulent. you can’t tell at all just by looking at it. of course, that doesn’t mean it doesn’t happen.

And I suspect the differences in most situations are not going to be noticeable. There’s too much else going on.

“Wise to learn from your mistakes. But wiser still to learn from the mistakes of others.”

Making it Fast - a matter of finish

This is where I just have to trust the generations of scientists who’ve studied the subject - dedicated their lives to topic. Just because I can’t see it don’t mean it aint happenin’. I can’t see bacteria, either, but it can kill me.

That’s the purpose of science… to make explanations and predictions. If you know the scientific principles at work, you can apply them to any situation. I think this is one.

How thick does the boundary layer have to be to be effective? We’re talking angstroms here. You can’t see anything on that scale.

Scientists make observations. (bacteria can be observed)

Who are these generations of scientists who have decided that there is turbulent boundary layer flow, on a surfboard hull operating on on breaking ocean waves, rather than laminar boundary layer flow?

Also, it is easy to observe turbulent flow as it comes off the rail, or turbulent flow from the wave breaking, or turbulent flow coming of the fin tip, so why is it hard to observe the turbulence on the hull?

Why does this turbulence manifest itself so differently, than all the other turbulence that can be easily observed and distinguished, that it cannot be observed and distinguished?

I don’t know any scientist that says there’s a “turbulent boundary layer flow” under a surfboard. I was referring to generations of scientists who’ve studied physics as they relate to aerodynamics and hydrodynamics. The bible on this topic was written in the '60’s, I think. So that qualifies as at least two generations. But even ancient civilizations (particularly the Romans, I’m told… by an Italian!) have studied how water and air flow, and applied even those crude, basic, but relevant observations and principles to their daily lives.

I think people here are talking about the inherent difficulty in making the kinds of observations required to study turbulence under a hull, especially on the scale needed to study sanded vs. polished surfaces, due to the scale. I agree. I think we’re really talking about water movement measured in really tiny units - microns? angstroms? What’s the distance across a scratch created by 400 or 600 grit paper? All of this in light of the fact that it’s difficult to recreate a wave-board interactions in a controlled environment to begin with. Maybe the lab will have to be brought to the surf instead of the surf to the lab.

But I think that it’s only a matter of time until somebody puts the money and effort into developing the instruments and technology required to make those kinds of observations.