## Yamaha’s “logical boat speed” formula

Optimizing the performance of Boston Whaler boats
OldKenT
Posts: 80
Joined: Sun Mar 06, 2016 1:18 pm

### Yamaha’s “logical boat speed” formula

I have recently repowered my 1985 17-foot Newport with a new Yamaha F70LA, using the excellent advice given on this forum, and am now testing the initial prop selection – an aluminum Yamaha K-series 13-5/8” X 14” – and, of course, comparing speeds and RPMs to those posted on this site for that motor on other 1980s 17-foot hulls with other props.

In the process of trying to understand how all of this works and whatever else I need to consider, I came across an online version of Yamaha’s 2012 Rigging Guide which identifies a “logical boat speed” formula in the portion of the Guide which addresses the different types of Yamaha propellers then available. After applying it to the results I got with my current prop, it seems to me to make sense, and since I have not seen this formula expressed this way previously on this web site, I am posting it in the hope that others will comment or find it useful. So, at the risk of presenting something that is so obvious that everyone here, except me, already knew it, here is the formula stated in the Yamaha Rigging Guide for calculating “logical boat speed”:

“Boat speed (km/h) = propeller pitch (inch) X engine speed (r/min) X .001524 X propeller efficiency / gear ratio.”

The Guide also states “Propeller efficiency = Actual advancing distance when propeller rotated one time / Logical advancing distance when propeller rotated one time.”

The online Mercury propeller slip caIculator asks for the same information - your propeller pitch, RPMs, speed, and gear case ratio to determine slip. So, I understand the Yamaha formula to mean that if a propeller is 100% efficient (which would be expressed in the formula as an efficiency of 1.00), the maximum possible boat speed under ideal conditions for any prop of any pitch at any engine speed will be determined by the formula, and that any loss in propeller efficiency – i.e., slip – will be reflected in a reduced top speed.

I think I have correctly determined that the formula constant of .001524 is used to convert one inch per engine revolution per minute to kilometers per hour, and therefore that a constant of .00094697 would be used to convert one inch per engine revolution per minute to miles per hour.

Applying this formula to my results with my new outboard and prop yields:
14” pitch X 6200 RPMs = 86,800 X .001524 = 132.28 / 2.33 = 56.77 kilometers per hour, which converts to 35.27 MPH top speed, assuming 100% propeller efficiency.
Or, using the MPH constant:
14” pitch X 6200 RPMs = 86,800 X .00094697 = 82.197 / 2.33 = 35.27 MPH top speed at 100% efficiency.

Dividing my GPS-determined top speed of 32.2 MPH with two people and a dog on board my Newport, and my 33.4 MPH top speed with one person, by the theoretical top speed of 35.27 MPH at 6200 RPMs yields a propeller efficiency of 91.3% and 94.7%, respectively. I expect the difference is slip and other factors. I would be interested to hear other thoughts on this.

Thanks to Jim and others for the terrific reference materials and advice offered on this site.
Ken

Phil T
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### Re: Yamaha’s “logical boat speed” formula

Ken -

Any chance you can share the link to the rigging guide for future reference?

What is your mounting position of the motor.
Member since 2003
1992 Outrage 17, 1992 Evinrude 115

OldKenT
Posts: 80
Joined: Sun Mar 06, 2016 1:18 pm

### Re: Yamaha’s “logical boat speed” formula

Phil,
Here is the link to the Guide: http://gfretwell.com/ftp/Rigging%20guide%202012.pdf
Section 2 of the Guide identifies Yamaha propellers and WOT Operating Range for Yamaha outboards as of 2012, and the formula I mentioned is on page 4 in that section, so the page number is marked as 2-4.
My outboard is mounted 2 holes up, using the notations in Jim's article. I asked for an aluminum prop, and the dealer recommended starting with the 13-5/8" X 14" which is now installed. If you use the Yamaha online prop selector and put in that the boat is a center console, that the outboard is an F70, and the goal is all around good performance, this prop is one of those recommended as a starting point.

The "logical boat speed" formula seems to me to be easy to use and it should accurately determine top end speed under ideal conditions assuming that a prop is 100% efficient. Of course, no props are 100% efficient, but the formula gives a basis for determining what is potentially achievable with each prop pitch, gear case ratio, and maximum RPMs. Does that sound right to you?
Ken

Yellowjacket
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Joined: Mon Jul 31, 2017 9:33 am

### Re: Yamaha’s “logical boat speed” formula

What the Yamaha site is calling "efficiency" is really just slip. Mercury is calling it slip, which is what it is. Yamaha is calling it "efficiency", but it really isn't efficiency. The folks at Yamaha may want to "dumb it down" for public consumption but what they are calculating is prop slip.

Actual prop efficiency is the propulsive force multiplied by the speed (converted to hp) divided by the actual shaft horsepower delivered at the shaft. Since that data is hard to get it's hard to calculate actual propeller efficiency and for that reason it isn't calculated very often. Real prop efficiency is down in the 75% range or sometimes even lower. Also, there is not such thing as a prop with no slip. Since you're dealing with a fluid there has to be some slip.

The size of prop has a lot to do with slip. Put on a bigger prop with more surface area and you get less slip. That doesn't mean you'll go faster, because that larger prop with more surface area may have more drag and actually might have poorer propulsive efficiency. Prop slip is a measure of how highly loaded the blades are, and as you go faster, blade loads go down for a constant horsepower, so the more lightly loaded the prop is , the lower the slip is going to be. Not rocket science.

Determining prop slip is important and assuming no prop slip you'll get the theoritical top speed, so that's a good guide as to how fast it is possible to go and setting an initial prop pitch to get you in the ball park.

The slip you are seeing is pretty low at the lightest load. Any time you can get down to 5 or 6% slip you're doing fine. So long as you are pulling max rpm you're probably in a good place with that kind of slip number. 10% slip at higher loads is to be expected. You can reduce slip by adding more prop surface area, but as I noted it probably won't make you go any faster, you'll get less slip, but the motor would bog down and then you'd need a lower pitch to get the rpm back up and you'll likely end up in pretty much the same place, plus or minus one or two mph.

jimh
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### Re: Yamaha’s “logical boat speed” formula

The Yamaha "formula" is not particularly special. It just describes the basics of propeller operation. See

http://continuouswave.com/whaler/reference/prop1.html

for a similar explanation I offered about 19 years ago.

As YELLOWJACKET notes above, the difference between theoretical speed of advance of a propeller calculated by pitch and rotation speed and the actual boat speed obtained is due to the SLIP of the propeller.

The value of SLIP is usually calculated by subtracting the OBSERVED SPEED from the SPEED OF ADVANCE, dividing the result by the SPEED OF ADVANCE, and expressing it as a percentage. This is the propeller designer's definition of slip. A propeller working effectively will usually at its higher speed ranges have a SLIP of less than ten-percent.

The actual pitch of a propeller blade in today's world of modern propellers is a somewhat arbitrary notation, as many propellers have blades that contain a progressive pitch, that is, the blade pitch is not completely constant and uniform but changes along the blade as the blade extends from the root of the propeller to the blade tip. The pitch designation then becomes somewhat of an average or an equivalence to compare among propeller of similar blade construction. Some propellers behave as if their pitch were greater than their declared or marked pitch, and computation of a SLIP value often results in the SLIP being a negative number--an impossibility.

The mathematics involved are trivial. See the linked article above for a verbose explanation.

In 2000 I posted the following comment in a follow-up to my article linked above to further explain the notion of SLIP:

Quoting William G. Van Doren from Oceanography and Seamanship ( an excellent book ):
"Contrary to popular opinion, a propeller does not screw itself through the water, but, rather, flies through it. Like an airplane wing, the propeller blades are shaped hydrofoils, and are designed to have a maximum lift (thrust) to drag ratio when operated at the proper angle of incidence (THETA) to the relative flow. This angle... is shown in [illustration not reproduced here].

"When rotating in a real fluid, owing to flow advance in developing thrust, the propeller does not advance by (PITCH feet per revolution) but by some smaller distance....

"The distance....by which a working propeller lags behind the advance it would have if delivering no thrust is called slip.

"...the working propeller's effective incidence angle is...[much math omitted] in plain English,

angle of incidence = pitch angle - ARCTAN(inflow_velocity/angular_velocity).

For the complete math and illustrations, see p.299-303.

jimh
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### Re: Yamaha’s “logical boat speed” formula

Further to the Yamaha formula: I absolutely dislike its method of unit conversion by employing some decimal factor. That has no value for me. Unit conversion is a much better method of handling problems like the disparate units involved in propeller calculations, where distances are measured in different units like inches, miles, nautical miles, or kilometers. For an example of the proper way to handle unit conversion, see my article at

http://continuouswave.com/whaler/reference/prop1.html

and read the section under the heading of UNIT CONVERSION which demonstrates the proper approach to handling conversion of different unit dimensions.