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I'm building an autonomous boat, to which I now add a keel below it with a weight at the bottom. I was wondering about the shape that weight should get. Most of the time aerodynamic shapes take some shape like this:

enter image description here

The usual explanation is that the long pointy tail prevents turbulence. I understand that, but I haven't found a reason why the front of the shape is so stumpy. I would expect a shape such as this to be way more aerodynamic:

enter image description here

Why then, are shapes that have good reason to be aero-/hydrodynamic/streamlined (wings/submarines/etc) always more or less shaped like a drop with a stumpy front?

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    $\begingroup$ Related: Why should the leading edge be blunt on low-speed, subsonic airfoils? $\endgroup$
    – Tanner Swett
    Aug 11, 2020 at 14:50
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    $\begingroup$ Why do ships have bulbous bows? $\endgroup$
    – CGCampbell
    Aug 11, 2020 at 21:05
  • $\begingroup$ Hi kramer65, and welcome to Physics Stack Exchange! I've removed a number of comments that were attempting to answer the question and/or responses to them. Commenters, please keep in mind that comments should be used for suggesting improvements and requesting clarification on the question, not for answering. $\endgroup$
    – David Z
    Aug 11, 2020 at 22:33
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    $\begingroup$ en.wikipedia.org/wiki/Nose_cone_design $\endgroup$
    – Steve
    Aug 12, 2020 at 1:18
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    $\begingroup$ On second thought I believe my comment does address the question. Dragging a keel model through water in an A/B comparison of your two shapes should show the 'stumpy' having significantly less turbulence; in addition, doing it manually will cause the model to 'sniff out' the optimal position to minimize turbulence. No need to run mathematical simulations for a simple yes/no question. You can test it in the bathtub. — Unless you wanted to optimize the shape, but you didn't ask about that. $\endgroup$
    – Timm
    Aug 18, 2020 at 23:59

4 Answers 4

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You are correct if your boat will only travel in a straight line.

In real life the motion of the boat will often have a yaw angle, so that it is moving slightly "sideways" relative to the water. For example it is impossible to make a turn and avoid this situation.

If the front is too sharp, the result will be that the flow can not "get round the sharp corner" to flow along both sides of the boat, without creating a lot of turbulence and waves which increase the drag on the boat.

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    $\begingroup$ Also, prevailing wind conditions in real life create an effective 'yaw', that is complex and changing. $\endgroup$
    – Lamar Latrell
    Aug 11, 2020 at 21:18
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    $\begingroup$ I would argue that your first sentence is incorrect, and that's the prime theme of my own answer. However, my answer doesn't emphasize that the performance with yaw angle included is the more important advantage of the rounded leading edge. $\endgroup$
    – D. Halsey
    Aug 12, 2020 at 15:42
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Any speculation about what shape might be best is meaningless without specifying the flow conditions. For the keel on a boat, the main one is the Reynolds Number, a parameter that is proportional to the the length multiplied by the speed.

In most low-speed applications, a sharp leading-edge is not the best. With any incidence, the flow will tend to separate too readily, but even when going straight through the fluid there are velocity gradients that need to be considered. The flow increases and then decreases in speed as it moves along the keel, and the drag that this causes depends on the details of the viscous boundary layer development.

The figure below (which I generated using a readily available analysis code) shows some approximate optimizations of 2D foil sections at several different values of Reynolds Number. The best shapes at the highest speeds (at the top of the figure) have smaller leading-edge radii than the low-speed ones (at the bottom), which are extremely blunt. enter image description here

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    $\begingroup$ The trailing edge angle of most shapes is too blunt to be optimal. Only the topmost one looks fine. $\endgroup$
    – Peter Kämpf
    Aug 11, 2020 at 15:19
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    $\begingroup$ @ Peter Kämpf I put "optimum" in quotes in the figure & called the results "approximate" in the text because these were not totally converged optimizations & I am also suspicious of the trailing-edge angles. That said, I'm not convinced that cusped trailing edges are desirable at the smallest Reynolds numbers. Since the question is mainly about the leading-edge shapes, I decided to go ahead & show the se results. $\endgroup$
    – D. Halsey
    Aug 11, 2020 at 15:35
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    $\begingroup$ Could you name your "readily available analysis code"? $\endgroup$
    – Nobody
    Aug 12, 2020 at 9:54
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    $\begingroup$ @ Nobody I used XFOIL for the flow-analysis portion of the procedure. This was combined with a code of my own to generate airfoil shapes from a small number of parameters, and a crude optimizer looping through many shapes in a Windows Powershell script. XFOIL is a well-known potential-flow/boundary-layer code from MIT that has been thoroughly validated and compares favorably with more involved NS solvers (at least for 2D airfoil cases). pennstate.pure.elsevier.com/en/publications/… $\endgroup$
    – D. Halsey
    Aug 12, 2020 at 15:31
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    $\begingroup$ What parametrisation scheme did you use for the airfoils? $\endgroup$
    – GodotMisogi
    Aug 13, 2020 at 4:03
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As mentioned above, indeed, this shape is more aerodynamic when parallel to the vector field (flow direction) in particular. You see this shape often on long distance Kayaks and Canoes that move in relatively straight lines. But this shape is certainly not ideal for changing directions, as the drag will be greater than with your first shape.

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One way of looking at the problem is to consider the pressures over the surface. Streamlines curling outwards tend to indicate high pressure pushing water away, streamlines curling inwards indicate low pressure drawing water in.

A reflex curve at the front, as in your second image, gives high pressure across much of the frontal area, causing high drag. A blunt curve, as in your first image, gives high pressure over only a small area and low pressure around the outer forebody, actually drawing the craft forwards. The long tail behind reduces the inward curl, and hence suction, which would drag it back.

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    $\begingroup$ The problem with looking at it this way is that everything you say applies equally well to inviscid flow results, which would have zero drag (in 2D). To explain the drag results, you need to show how the boundary layers create a fore & aft assymetry in the pressures. $\endgroup$
    – D. Halsey
    Aug 12, 2020 at 15:35
  • $\begingroup$ @D.Halsey Yes I missed that bit out. It is of course the reason why the pressures cause drag in the way they do. However since the question confines itself by default to streamlined shapes in viscous flow, it seemed not so much a problem as a complication not worth embroidering on. $\endgroup$
    – Guy Inchbald
    Aug 12, 2020 at 20:09
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    $\begingroup$ The notion of the low-pressure area drawing the craft forward might I think be best understood by recognizing that a blunt edge will put more energy into the water than would a pointier edge, but when using a pointier edge, a bigger fraction of the energy put into the water will be carried away in the form of a wave; any energy which is thus carried away is lost to the boat. The blunter edge will cause more energy to be initially transferred to the water, but less to be carried away, leaving more to be transferred back to the boat. $\endgroup$
    – supercat
    Aug 12, 2020 at 21:43
  • $\begingroup$ Another complication I have not mentioned is that a pressure "bubble" distant from the surface will bend streamlines nearer in. For example the typical outward curl at the trailing edge is cause by such a low-pressure bubble; there is no high-pressure zone creating forward thrust back there! Nevertheless, the principle remains a useful guide. $\endgroup$
    – Guy Inchbald
    Aug 17, 2020 at 10:51

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