Calculating boat speed

[Nordy]

Hello,
first as a newcomer I send greeting to all here.

I'm very interested in propeller physics and have created some formulas for thrust and torque to calculate speed of small gliding boats.

I use the wellknown formulas for thrust and torque and the wageningen b-series kt and kq coefficients.
Assuming kt and kq are linear around the max-speed point you can easily find two steady state formulas.
The thrust formula finds the needed advance ratio with respect to kt and kq latter depending on prop geometry (diameter, pitch/diameter ratio , blade number and expanded area ratio).
The torque formula delivers the needed engine revolution assuming a linear engine torque dependance.

In the case of optimizing a given prop you always know boat's speed and revolution you aren't satisfied with.
Ideally you know two boat and engine speeds, one for light and one for heavy loaded boat.
This has the big advantage you'll know the driving resistance of your boat and put it into the formula.
And you have some other boundary conditions for kt and kq to reach the performed speeds in calculation.

What you further must know is easy to have, outboard engine power at prop wheel and max power engine speed, gear ratio, propeller diameter, pitch, blade number and expanded area.

The third order b-series kt and kq polynomials and the formulas for thrust, torque, resistance and so on are caculated by excel.

All works well.

But I have the problem, calculated values of v max and n max are always too low.
A typical example:
A 5,50m rib reaches in practice 60 km/h, the engine speed is 5800.

The calculated speeds are 56 km/h and 5600 rpm.
The prop efficiency J/2Pi*Kt/kq is 79%, that's a common and very good value almost at the limit.

If I apply kt and kq multipliers to let the two formulas fulfill the boundaries (60km/h and 5800 rpm) the efficiency will rise to impossible 95 or more per cent.

Nevertheless varying prop geometry then will bring very reasonable results.

I understand the used prop will always differ from the B-series type and boat conditions differ as well from the wageningen free water test field.

That's why kt and kq multipliers will always have to be applied.

But I don't understand why it takes a 95 % or better efficiency to reach the performed speeds.
In some calculations I had the perpetuum mobile (Eta > 100%) !?

Has anybody an idea ?

Best greetings from snowy Germany

Peter

[RANCHI OTTO]

at 60 km/h the propeller having Wageningen profiles have a lost in efficiency and thrust very important due to the cavitation.

There are Kt,Kq vs J diagrams of these B-series propeller according to various sigma, so doing you can estimate the real thrust of the propeller in real working conditions

[Nordy]

Thank you Otto and best wishes to beautiful Triest.

I think the reason for the too little v max and n max may be a too high driving resistance in the formulas.

My formula is: R = 0,5*Ro*c*Aw*v^2, it's the well known drag resistance.

For steady state v max condition you can write:

Pe max = R*v max = 0,5*Ro*c*Aw*v max^3

c*Aw [m^2] = 2*Pe max [hp] / Ro [kg/m^3] / v max [km/h]^3 *1000*3,6^3/1,36

For a 90 hp outboarder and a measured v max of 59,8 km/h and Ro = 1000 kg/m^3 you get:

c*Aw = 0,0289 m^2 (c = drag coefficient, Aw = wetted Boat area)

Probably this value is too high.

Reducing it to 0,0263 and additional changing kq from original

Kq = 0,0971-0,0484*J to

Kq = 0,0971-0,0524*J and an unchanged

Kt = 0,5024-0,2816 *J

the formula delivers 59,8 km/h and 5800 rpm.

The efficiency is 89,7 % and still very high.

Do you think this is possible for a light inflated 5,50m rigid boat ?

The other data are:

Advance ratio J = 1,166
Bp = 4,33
Slippage = 20,3 % (including 3% wake)
Thrust = 3643 N and
Torque = 249 Nm

The propeller is a 3 x 13 x 19 with Ae/Ao=0,33.

I would deeply appreciate your opinion on this.

Peter

[RANCHI OTTO]

If I've good understood you are speaking about rib equipped with outboard engine...sorry but the propellers for outboard engines are quite different from the Wageningen B Series, I have open water tests for a lot of cavitating and subcavitating screws but not for outboardscresw.

[jehardiman]

Nordy;

Ranchi Otto is correct about the prop differences. Most high speed props have a different blade loading curve, area development, and a non constant pitch (tips twisted off) to optimize blade loading which increases thrust for a given diameter. Using Lerbs's 1952 paper it is fairly easy to develop your own prop calculator. Additionally, I think you have underestimated the Taylor Wake fractions (yes, they apply to outboards on RIB's and no, most people don't measure them because it is cheaper/eaiser to tweak the props). You have very little wake adaptation in your analysis, which would change J significantly. Get a good book/paper on propellers in wakes (try one of Morgan's or Kerwin's) and you will see that it is possible to get an apparent efficiency as high as 130% or so with a well adapted prop.

[Nordy]

Hello Jehardiman,

thank you for your advice.

But I believe the problem is not to be seen in the differences between the Wageningen B-series-propellers and the actual 3 x 13 x 19 prop of that Honda 90hp in the analysis or in its non constant pitch.

I assume this because the calculated open water efficiency is near the limit of 80 %.
That means there is no more potential for further thrust increase by propeller means in open water.

Or have you heard that someone had ever measured open water efficiencies of > 80 % ?
It is the absolute limit isn't it ?

I must correct my former statements on driving resistance.
I now think c *Aw, which is needed in the staedy state thrust formula, is correctly enough determined by means of v max mesuring, as long as you consider rather small variations of v max.

Wake fraction:
I chose very low 3 % for it (the Taylor wake factor) because the boat in question is an 5,50 m inflated rib, a fast glider, which is rather light and has a weight/power ratio of only 10 kg/hp.
Enlarging wake fraction would increase the discrepancy, I tested it.
And I read this value would be adequate for such a boat.

You say one might get an apparent efficiency of 130 %.

I suppose you mean hull efficiency:

Eta Hull = (1-t)/(1-w) t=thrust deduction factor, w = taylor wake factor

Since w usually is > t both being < 1 eta hull is often > 1 or > 100%.
But Eta hull is only one of three efficiencies.
The sum formula for the overall efficiency is:

Eta propulsive = Eta open * Eta rotative * Eta hull

Eta open is the known open water efficiency (< = 0,8) of the B-series propellers and the one missing is Eta rot, that maybe > 1 - 1,1 for single screws.
Eta rot means that the flowing water may transfer its roational energy onto
the propeller.

And that's the point !

In my calculations I neglected this effect so far calculating with 1,0 the whole time.

If I choose 1,1 both speeds - v and n - increase considerably, so only a little
difference between practice and analysis is left, that my be closed by
proper kt and kq multiplification but at the expense of a open water efficiency beyond 80 %, near 85 % I think.

Strongly taken this is unrealistic and false because Eta open would never be > 80 % in open water testing.
But it only compensates for effects which are not under the control of the formulas.

The important thing is I hope you agree with me that prop-gemetry variations which may lead to a better speed and acceleration performance are controlled by the analysis in a correct way and it does I checked this.

As for t the thrust deduction factor I calculate with 0.
What do you think about this ?
Do you think there is noticeable thrust deduction with small inflated boats having a deep sharp rigid hull ?

Greeting from very cold Germany

Peter

[jehardiman]

Don't get so wrapped up about efficiency. The 130% number I quoted above was based upon a ~93% open water efficient cr-prop set recovering about 1/2 the wake energy. Totally unusable except for the designed purpose which was a about 200 Newtons of thrust at 6 knots with about 500 watts of power as the diameter was almost 1m and the blade cord was about 4 cm. The right side of the efficiency curve was precipitous to say the least!

Remember that for high-speed propellers, they are not designed like the B-series. There is cupping, which increases the apparent pitch, there is high blade loading cavitation features and phantom blade area effects, bound vortex and aeration lubrication.

Here is a quick check for wake. Do a 2-D transverse model of the stern profile at running depth. Using an e^x approximation for boundary layer velocity growth, see how wide the boundary layer must become until the energy expended to propel the RIB is equal to the energy in the boundary layer velocity. This will give you an approximation of the wake velocities.