Pacemaker Boats

[merwin10]

First of all let me apologize for the length of this post before hand - I have been getting several emails in regard to prop calculations - Let me start by saying that there will be contrary views of these calculations depending on the source - I have collect these formulas from several sources to include ABYC and USCG! I happen to like Michigan Wheels type calculations based on EAR (expanded area ratios) for figuring correct prop diameters -

Our boat here is a 36’ sports fish planning hull with 800 HP @ 4200 RPM coupled to a 2.59:1 transmission, the propeller shaft has two bearings and the boat is displacing 24,000 lbs., sound familiar -

First let’s figure out the engine torque –

Total HP @ RPM the formula uses a constant = 5252 times the HP divided by RPM –
5252 x 800 / 4200 = 1000 lbs. of Engine Torque

How we need to figure out shaft HP and torque after the transmission losses –
SHP = 0.97 x 800 = 776HP this is based on a 3% loss due to friction in the transmission –
There are two shaft bearings derated at 1.5% per bearing
0.015 x 2 = 3% loss due to shaft bearings –

Now we need to figure the shaft RPM –
Engine Rpm / Transmission Ratio = Shaft RPM (SRPM)
4200 ERPM / 2.59 = 1622 SRPM

Propeller torque -
Back to the torque formula but this time it is at the propellers –
5252 x 679SHP / 1699SRPM = 2099 lbs. of prop torque –

Now how much power is required to push our test 24,000 lbs boat forward at 25 knots – with a WOL (waterline overall length) of 34 feet –
First what is the Speed to Length Ratio –
25Knot / sqrt of 34’ = 4.287:1

Power to Weight Ratio -
How many pounds of displacement does each HP need to push –
24,000 / 776SHP = 31 pounds of displacement

Now we need to enter the EAR of the prop – 120 for trawler – 150 – planning – 190 for 50kts+ - 210 for racing – we are going to use 150 as our EAR –


Now figure the maximum speed given the EAR and the SHP –
150 / sqrt of 31 = 27 knots

So we now know the set up so far exceeds the 25 knot desired speed –

Now for the pitch calculation – what we know is that the desired speed is 25 knots and the Shaft RPM WOT is 1622 RPM – Since we want cruise speed which is about 80% of WOT or SRPM is 1622 x 0.8 = 1297SRPM @ 80% WOT

Next we need to get in common mode and since speed is in knots and rpm is in minutes we need to get on some common ground – So how many feet per minute is 25 knots
25 x 101.3 = 2533 feet per minute

So how many feet must the prop push the boat to attain the desired speed –
Desired Speed feet per minute / 80% SRPM = Feet per minute –
2533 / 1297 = 1.95 feet per minute

What pitch prop would achieve the 1.95 feet per minute – This is a theoretical number –
Feet per minute * 12 inches = Tpitch
1.95 * 12 = 23.43 inches of theoretical pitch –

Theoretical speed – (Tspeed)
Tpitch x 80% Srpm = inches of forward movement per minute –
23.43 x 1297 = 30388.71 then 30388.71 x 60 = 1823322.6 inches per hour – then 1823322.6 / 72913.38 = 25.066 knots

Propeller Slip –
Propeller slip changes for each boat and each propeller set on a boat – No two are the same – What we are looking for is a low number 10 to 20 % is reasonable – we will be using slip at WOT speed, as you know slip is not a constant factor but it does become smaller the faster you go! This has to do with basic physics – remember things in motion like to stay in motion hence things at rest what to rest! Hence you slip factor when you first engage your transmission is almost 100% because the boat is at rest and wants to stay there, so the propeller turns and slips thru the water while the boat starts to move!

SLIP -
(SOG/Tspeed) x 100 = % efficiency then 100 - % efficiency = slip
22 knots / 25.066 knots x100 = 87.97% efficient then 100 - 87.97% = 12.02 % Slip

Propeller Diameter –
This is the tricky one as you need enough blade area to create thrust whilst keeping the blade tip speed down as not to cause cavitation – Given a propeller turning at a given speed as you move away from the center the radius increases as does the distance at a point the blade will cavitate because of the speed it travels from the center – Higher pitch propellers tend to cavitate sooner than lower pitch propellers – The reason is the hydrofoil has more low pressure on the back of the blade – Furthermore, cavitation occurs quicker in lighter water than in denser water so the calculation has to consider the specific gravity of the water medium – This is determined by the hydrodynamic incidence law! Which is to complex to describe here –

Tip speed can be visualized by this formula –
PRPM x diameter / 336 Hence
1297 x 22 / 336 = 84.92 Tip MPH

One thing we do know is that tip speed decreases with diameter!
1297 x 20 / 336 = 77.20 Tip MPH

Hence by decreasing the diameter we decrease the tip speed thus reducing the possibility of propeller cavitation.

About the only other thing I can say about propeller diameter is if it fits try it – you need to work with a great prop shop – one that will let you try different propeller setups until you find the one that is right for your boat – All the calculations in the world will not be able to describe your boat in actual running conditions. It is not possible to calculate everything that effects the propellers movement –

Well I hope this LONG explanation is of some help –

Mike -
_________________
"Best part of Boating -- is the people you meet"

[neverending]

So how many feet must the prop push the boat to attain the desired speed –
Desired Speed feet per minute / 80% SRPM = Feet per minute –
2533 / 1297 = 1.95 feet per minute

What pitch prop would achieve the 1.95 feet per minute – This is a theoretical number –
Feet per minute * 12 inches = Tpitch
1.95 * 12 = 23.43 inches of theoretical pitch –

Mike,

I the above, "feet per minute" should read "feet per revolution".

Thanks for the great reference work.
_________________
Dennis Sherod