# Challenge to naval architects and marine engineers

Discussion in 'Props' started by sandhammaren05, Feb 8, 2022.

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### sandhammaren05Senior Member

For high performance propellers the blades are thin, especially near the leading edge, but not so thin that p(r,s) set on the mean camber surface coincides with p(r,s) as measured on the high pressure blade side. But regarding my problem posed, it doesn't matter if you think of the mean camber surface or the high pressure blade side. The same formula will apply in either case although the measurements will be different. We know because we've designed a surface piercing prop by specifying the numbers for the mean camber surface. One can get p(r,s) for any prop by an optical scan of the blade, as we've also recently done in an effort to discover the camber of a prop made elsewhere.

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### gonzoSenior Member

A section of a helix will have camber unless it had zero pitch ( a washer)

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### gonzoSenior Member

From the geometry perspective that is correct. However, the standard method of measuring propeller pitch uses the chord from the forward to the rear edge of the blade.

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### baeckmoHydrodynamics

No, that is wrong. A helix is a straight line that has been "wrapped" around an axis at radii that can be different at different positions. Note that constant radius is not a constraint per se. This is the case when you look at a diagonal flow impeller, f.i..

The constraint is whether the axial displacement (dL) of a point on the "screw" surface is constant with impeller rotation (dFi), or if it changes according to some (prescribed) requirement.

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### HeimfriedSenior Member

I have the sketch redrawn to better adapt it to the cylindrical coordinates, however I used x instead of z. All angles are used in radians. "r" is the constant radius of the given circular section, the section is expanded in a plane. The abscissa is in u = phi * r to give the dimension lenght, the ordinate is in x (lenght). The reference line for determining the camber is the mean pitch angle of this blade section
alpha = arctan(( x0 - xn) / (u0 - un)) .
tan(alpha) = ( x0 - xn) / (u0 - un)
The mean pitch of this section is P(m, s) = 2 * pi * r * tan(alpha).

The "small intervals" are not shown very small in the diagram in order to provide visible distances, angles etc.
In order to give the term "progressive" pitch an equivalent I will go along the section in the flow direction of the water, starting at u0, x0 (leading edge).
To shorten the formulas I will define P'(n) = P(n) / 2 * pi * r = tan(alpha(n)).
At the station u0 = r * phi(0) the gauge displays a x0, at the station u1 there is a x1.
The camber at the point(u1, x1) is cb1 = deltax1 * cos(alpha) = (x1 - xalphau1) * cos(alpha) = (x1 - u1 * tan(alpha)) * cos(alpha).
The local P'(1) = (x0 - x1) / (u0 - u1) = tan(alpha1).
At the station u2, x2 :
cb2 = (x2 - u2 * tan(alpha)) * cos(alpha) ; P'(2) = (x1 - x2) / (u1 - u2) = tan(alpha2).

The vertical distance between the x values (x(i) - x(i+1)) is increasing while the horizontal distance (u(i) - u(i+1)) remains constant, so the tan(alpha(i+1)) is increasing and the (local) pitch is increasing.

Last edited: Feb 10, 2022
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### gonzoSenior Member

I agree with your definition. I was trying to relate the claim of the helical propeller to a projection of a surface. Unless the OP makes a better description of what he means, It is impossible to understand what the question is about.

@ Heimfried: I understand the local pitch, which is the tangent to the curve. However, as it relates to a propeller blade, that is not the standard definition of pitch. Propeller pitch is based on the old comparison of a propeller to a screw. It does not work properly to explain slip or the effect of different foil profiles. Maybe pitch, like the definition of when a boat starts planing, should be considered as an arbitrary dimension.

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### jehardimanSenior Member

I think I see what is going on here based upon Sandies OP and his other thread comments. In SC and SP props realistically only the face is working, much like a wedge pushing on the water. For maximum efficiency, the blade needs to enter the undisturbed water at the speed of advance (Va) and end at the speed of advance plus the slip (Va+s). Using Heimfried's notation we need an alpha and a camber such that tan(alpha 1)*2*pi*r=Va and tan(alpha n)*2*pi*r=Va+s.

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### gonzoSenior Member

There was no mention that the question referred to ventilated or supercavitating propellers.

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### baeckmoHydrodynamics

It's a well known fact that in ventilated and cavitating flows, the leading edge has to operate with zero angle of attack (making low advance ratios problematic). In non-cavitating flows, part of the lift is generated by the leading edge due to the sudden change in direction from the positive angle of attack. For cavitating flow, the best L/D ratios are seen when the profile is loaded more towards the trailing edge, hence the positive effect of cupping. Ie, there can be no lift from AoA, all lift is from camber on pressure side. The original works by Tulin in USA and Posdunin in Russia pointed in that direction from the beginning.

We use this in turbopump and inducer design as well, where the initial part of the blade is "unloaded", it is just "shaping the flow".

Example 1: the Newton-Rader series "transcavitating" screws in original shape cavitated on the pressure side, close to the LE. The profile was arbitrarily filed, so that the LE mean chord was straightened.

Example 2: Russian supercavitating profiles having a straight "body" with sharp LE and an interceptor (see Aschkinadze, Sadovnikov et al).

Example 3: 3- and 5-term profiles reported by V.E. Johnson (Langley Tech rept R-93).

I think the issue in the "propeller heating-and-beating" society is about misuse and/or misunderstanding of the terminology combined with lacking understanding of scientific definitions.

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### jehardimanSenior Member

He did in this thread and in others, just not directly. Here "high performance" doesn't mean good engineering, just lots of horsepower.

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### sandhammaren05Senior Member

You clearly do not understand a helix or a helicoid. No curve has 'camber'. Why do you respond with total nonsense? Nothing better to do?

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### sandhammaren05Senior Member

Supercavitating props are of no interest for high performance: the lift coefficient would be too low and the drag due to the cavity too high. Progressive pitch is not found on blades with airfoil-type sections, it's found only on thin blades where the curvature is monotonic increasing from leading to trtailing edge on both blade sides.

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### sandhammaren05Senior Member

Wrong, high performance means good engineering at fixed horsepower, as in any APBA or UIM racing class. Or with a bass boat, e.g., with a motor of fixed hp.

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### sandhammaren05Senior Member

We have found that outboard castings, including racing props, whether heated and beaten or not, generally do not have a systematic camber in the sense of an empirically-well-defined camber over radial arcs at different radii. This is not surprising because hi performance props are generally designed by copying and slightly modifying a heat and beat prop. Our self-designed CNC prop has a simple camber built into the mean camber surface mathematically. As an offshoot of that work, we have an equation that expresses the slope dh/ds of the camber h(r,s) in terms of progressive pitch p(r,s). So the progressive pitch is in our case mathematically specified. Hans has recently used an optical scan on a prop that I beat on, with the intention of trying to see what camber I try to put in non-mathematically by using a brass hammer.

The CNC machine that cut the prop used the same program that Hans uses to print out 3D plastic models from his CAD program.

Racing is a great testing ground and is the final proving ground. One sets the leading edge for a particular speed, generally top speed. At lower speeds the angle of attack at the LE is positive. The extra camber greatly improves the acceleration at low and intermediate speeds. Cupping is generally necessary for acceleration, especially in a modified Le Mans start, just as dropping the flap on a wing is generally necessary for climbing. Generally, without a little cup in the right place, the required acceleration to be competitive is lost.

Last edited: Feb 11, 2022

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### gonzoSenior Member

I really have no idea what that means. Can you explain?
• Difference between heated and beaten or not
• systematic camber