Propeller Size Evaluation Part 3

In Part 1 of our search for the correct or optimum propeller size for Indra, we discovered what size propeller we had and the many "issues" with it. In Part 2 of our search we increased our knowledge of propellers enough to understand what pieces of information we needed for a propeller size calculation. In this post, Part 3, we discover a online propeller calculator and evaluate its methodology and recommendations.

A internet search on boat propeller size calculator revealed a few potential candidates.

• Boatdiesel.com - this website has a basic and advanced propeller size calculator but access is restricted to paid membership. Both propeller calculators appear to be based on the concepts and formulas in the Propeller Handbook by Dave Gerr and uses the Crouch or slip method to determine propeller recommendations.
• Castle Marine Ltd - had a very outdated pitch calculator based on Windows XP/Vista software. Since this version of Windows is ancient history, we did not use this program.
• Marine Propeller Calculator - they had a very rudimentary propeller calculator which did not consider any boat characteristic information.
• PropExpert software - on website Hydrocomp, Inc. it offered for sale, PropExpert a propeller sizing and analysis software product. However, as it was intended for sale to commercial entities like propeller shops, distributors, and manufacturers it was not likely priced for purchase by the average boat owner.
• Prop Scan software - on website Prop Scan it offers Prop Tools Propeller Sizing Software however this website is in the business of franchising the Prop Scan Business Opportunity and not selling software to the general public.
• Recreational Boat Building Industry (RBBI) - they had a very rudimentary Boat Propeller Calculator which did not consider any boat characteristic information.
• Surfbaud Freeware Propeller Calculator - on website Surfbaud Marine Propeller they have a Microsoft Excel spreadsheet called Propking in Excel and HTML formats that accepts user input to determine propeller size. Another smaller version of this Excel spreadsheet called propcalc.xls can be found by a search on the filename on the internet. This propeller calculator spreadsheet appears to be based on the concepts and formulas in the Propeller Handbook by Dave Gerr and uses the Crouch or slip method to determine propeller recommendations.
• Victoria Propeller Calculator - on website Vic Prop they have a publicly available and free to us propeller size calculator for displacement/semi-displacement hulls. This propeller calculator appears to be based on the concepts and formulas in the Propeller Handbook by Dave Gerr and uses the Crouch or slip method to determine propeller recommendations.

We selected the publicly available and free to use the Victoria Propeller Calculator to enter Indra's data and review its recommendations.

We first ran Indra's current boat characteristics with the replaced old Yanmar 3QM30H 30 hp engine specifications. The calculation recommended a 17" diameter by 9" pitch propeller versus the existing 18" diameter by 13" pitch propeller. Next we reran the calculation with the same boat characteristics and the currently installed Yanmar 4JH5E 53.1 hp engine specifications. The calculation recommended a 20" diameter by 11" pitch propeller versus the existing 18" diameter by 13" pitch propeller. These differing propeller size results indicated that Indra's current propeller size was likely not the optimum size for either engine. These results required a more in-depth, detailed review and understanding of how these recommendations were derived with the goal of determining what propeller size is "best" for Indra. What follows below is our review and analysis of the propeller calculator data output and recommendations.

We relied extensively on the methodology outlined in the Propeller Handbook by Dave Gerr to investigate the propeller selection question; it is important to note that we have different opinions on certain recommended methods put forth in the book. There is a revised 2018 second edition of this book, however, for reasons unknown, it was out-of-stock or out-of-print on each vendor site we located - the author and public would likely benefit if it was available as a electronic downloadable version (Kindle, etc.) instead of the current paperback edition format - in our opinion paper media does not fare well in the moist boat environment; we avoid it in most cases. To facilitate multiple test configuration scenarios we used Microsoft Excel to store equations and boat variables instead of using a basic calculator to repetitively perform the tedious manual entries and calculations.

For Indra, we entered the following values into the propeller size calculator online form:

• Waterline length of vessel: 31.24 Feet - True North 34 specifications state waterline length is 30.5 feet. The Actual Loaded Waterline Length is 31 ft 2.85 inches due to added displacement weight resulting in Indra resting lower in the water.
• Beam at the waterline: 10.71 Feet - True North 34 specifications state beam is 11.0 feet. The Actual Beam Loaded Waterline Length is 10 ft 8.5 inches due to the curvature of the hull.
• Molded hull draft (excluding keel): 3.89 Feet - True North 34 specifications state draft is 5.5 feet. Loaded draft is 5 ft 10.8 in. Loaded draft without keel is 3 ft 10.67 inches - we calculated this value from scaled drawings. Do not see a feasible method to physically and accurately measure this value other than from a scaled drawing.
• Vessel displacement weight: 33500 Pounds - True North 34 specifications state displacement weight is 26,000 pounds. We used the actual indicated weight of a different, fully equipped True North 34 during its haul out as it hung in the travel lift's slings. This was about 32,500 lbs, however Indra has a larger engine, hardtop, wind vane, solar array, and likely more stuff aboard, so increased estimated weight to 33,500 pounds.
• Number of engines (Shaft lines): 1 - Only one diesel engine installed.
• Maximum rated horsepower of each engine: 53.1 hp - Obtained from Yanmar's 4JH5E engine specifications and installed engine identification plate - 39.6 kW = 53.1 hp.
• Maximum rated engine R.P.M.: 3000 RPM - Obtained from Yanmar's 4JH5E engine specifications and installed engine identification plate - the min⁻¹ term is the same as RPM.

• Gear ratio: 2.61 - Obtained from Yanmar's KM35P gearbox/transmission specifications and installed identification plate.

• Number of shaft bearings between the gear box and the propeller: 1 - Indra has only one cutless bearing installed on the propeller shaft; did not increase to 2 for the stuffing box shaft gland as instructions stated not to.
• Desired maximum speed: 6.5 Knots - As we already have a engine and Indra's speed is limited by her loaded waterline length this question was really not applicable.

With the information filled in we clicked the Calculate button and the results were displayed. The Data Input box listed the same input values and calculated the maximum shaft RPM. As I intended to verify (scrutinize) the calculated results, I researched the likely equations in the Propeller Handbook and manually calculated the results to see how close they were.

• Propeller Drive Shaft Revolutions Per Minute (RPM) = Maximum Engine Revolutions Per Minute (RPM) / Transmission Gear Reduction Ratio.
• Maximum Propeller Drive Shaft RPM = 3,000 RPM / 2.61 Gear Ratio = 1,149.43 RPM - result closely matches the displayed value of 1149 RPM.

The Horsepower Calculations box re-displayed the previously entered engine horsepower of 53.1 hp and calculated the total available torque ft/lbs at the engine.

• Torque (T) in Ft/Lbs = (5,252 x Horsepower (hp)) / Revolutions Per Minute (RPM)
• Torque (T) = (5252 x 53.1 hp) / 3000 RPM = 92.96 ft/lbs - result closely matches the displayed value of 93 ft/lbs.
• The number 5,252 in the equation is a constant value derived from 1.0 hp = 550 Foot-Pounds per Second, which is then divided by the circumference of a circle 2π divided by 60 seconds per minute. The 5252 constant = 550 ft lbs/sec / (2π / 60 sec) = 5252.113.

The total available torque of 92.96 ft/lbs at 3,000 rpm from the engine was compared to the Yanmar 4JH5E torque curve and it appeared to be reasonably close.

The Horsepower Calculations box displayed 3% hp loss at gearbox and 1.5% hp loss at shaft bearing. The Propeller Handbook by Dave Gerr stated the same horsepower loss percentages for the gearbox and shaft bearing but did not elaborate on the rationale that determined these horsepower loss percentages.

• Gearbox/Transmission Horsepower Loss = Fuel Stop Power Brake Horsepower x 3% = 53.1 hp x 0.03 = 1.593 hp - result closely matches the displayed value of 1.6 HP.
• Shaft Bearing Horsepower Loss = Fuel Stop Power Brake Horsepower x 1.5% = 53.1 hp x 0.015 = 0.7965 hp - result closely matches the displayed value of 0.8 HP.

So the total horsepower loss is 1.593 hp plus 0.7965 hp which equals 2.3895 hp.

A review of the Yanmar engine specifications power curve (see below) revealed a dashed line that represents power loss and available power output at the propeller shaft. These power curves were likely based on the Yanmar 4JH5E engine as originally configured and tested with the originally equipped 80 Amp alternator. We replaced the original 80 Amp alternator with a 150 Amp alternator. The alternator manufacture estimated that for each 25 Amps it would require 1 hp of engine power. Therefore, 150 Amp minus 80 Amp then divided by 25 Amps per 1 hp yielded an additional horsepower loss of 2.8 hp not accounted for or asked for in the online calculation. Replacing a low-amperage alternator with a higher output amperage alternator is commonplace today amongst boat owners; propeller calculations should account for this item as the horsepower loss is significant the larger the alternator amperage size is. The online calculation also does not request input for other potential engine driven ancillary equipment that would reduce the total available horsepower to the propeller/shaft even further.

The Yanmar engine specifications state the maximum horsepower output at the propeller when the engine is at its maximum rating is 50.96 hp indicating a loss of 2.14 hp by the gearbox. This gearbox loss of 2.14 hp is higher than the propeller calculation estimate at 3% of maximum rated engine horsepower which equals 1.593 hp. The gearbox loss of 2.14 hp is equivalent to 4.03% of maximum rated engine horsepower.

So Indra's actual total horsepower loss is 5.74 hp based on 2.14 hp due to the gearbox, 2.8 hp due to the alternator, and 0.80 hp due to the cutless bearing. The actual total horsepower loss is 3.3505‬ hp higher than the propeller calculator estimates.

The Horsepower Calculations box displayed the total horsepower available at the propeller.

• Propeller Shaft Horsepower = Fuel Stop Power Brake Horsepower - Total Horsepower Losses (gearbox, bearing, alternator, etc.).
• Propeller Shaft Horsepower = 53.1 hp - 1.593 hp - 0.7965 hp = 50.17 hp. The Horsepower Calculations box displayed 50.7 HP versus the manual calculation of 50.17 hp which indicates the calculation has induced rounding errors.
• The corrected Propeller Shaft Horsepower with Indra's actual total horsepower losses is 53.1 hp - 5.74 hp = 47.36 hp - a notable difference from result of 50.7 HP.

The Horsepower Calculations box displayed the total torque in ft/lbs available at the propeller.

• Torque (T) in ft/lbs = (5,252 x Horsepower (hp)) / Maximum Propeller Drive Shaft RPM
• Torque (T) in ft/lbs = (5252 x 50.17 hp) / 1149.43 RPM = 229.24 ft/lbs. The Horsepower Calculations box displayed 232 ft/lbs versus the manual calculation of 229.24 ft/lbs; the difference is likely due to induced rounding errors.
• The corrected Torque with Indra's actual total horsepower losses is - Torque (T) in Ft/Lbs = (5252 x 47.36 hp) / 1149.43 RPM = 216.40 ft/lbs - a notable difference from result of 232 ft/lbs.

The Speed & Power Calculations box displayed the estimated displacement hull speed.

• Theoretical Maximum Hull Speed in Knots = Speed to Length Ratio x (Loaded Waterline Length in Feet)^0.5
• Theoretical Maximum Hull Speed = 1.34 x (31.24 ft)^0.5 = 7.489 Knots - result closely matches the displayed value of 7.49 Knots.

The Speed & Power Calculations box displayed the minimum horsepower required at the propeller for the theoretical maximum hull speed of 7.49 knots which has a Speed to Length Ratio of 1.34.

• Theoretical Maximum Hull Speed Minimum Required Propeller Shaft Horsepower = Displacement in Pounds / (10.665 / Speed to Length Ratio)³
• Minimum Required Propeller Shaft Horsepower = 33500 lbs / (10.665 / 1.34)^3 = 66.45 HP - a notable difference from result of 73.1 HP. The reason for the difference in values was not determined. As Indra's 53.1 hp engine will not support a speed of 7.49 knots, this difference is of no concern.

The Speed & Power Calculations box displayed the HP required at the propeller for desired 6.5 knots speed.

• Propeller Shaft Horsepower = Displacement in Pounds / (10.665 / (Hull Speed in Knots / (Loaded Waterline Length in Feet)^0.5))³
• Propeller Shaft Horsepower = 33500 lbs / (10.665 / (6.5 kts / (31.24 ft)^0.5))^3 = 43.43 hp - result closely matches the displayed value of 43 HP.

The Speed & Power Calculations box displayed the maximum speed in Knots with existing 53.1 horsepower.

• Knots = (10.665 / (Displacement in Pounds / (Fuel Stop Power Brake Horsepower - Total Horsepower Losses)) ^1/3) x (Loaded Waterline Length in Feet)^0.5
• Knots = (10.665 / (33500 / (53.1 hp - 2.3895 hp))^1/3) x (31.24 ft)^0.5 = 6.8445 - result closely matches the displayed value of 6.81 Knots.
• The corrected Knots with Indra's actual total horsepower losses is = (10.665 / (33500 / (53.1 HP - 5.74 hp))^1/3) x (31.24 ft)^0.5 = 6.6902 Knots.

The Speed & Power Calculations box Notes stated the propeller sizing calculations are based on 90% of full RPM to provide engine reserve power for variable loading in the vessel. It was recommended in the Propeller Handbook by Dave Gerr that propeller diameter be calculated at 100% of engine maximum RPM and propeller pitch be calculated at 90% of engine maximum RPM.

The Propeller Size Calculations box calculated a recommended size in diameter and pitch for a 2, 3, and 4 blade propeller.

Propeller Size Diameter Calculations based on 100% Engine Horsepower and RPMs:

• Three Bladed Propeller Diameter in Inches = (632.7 x (Propeller Shaft Horsepower)^0.2) / Propeller Shaft Revolutions Per Minute (RPM)^0.6
• Three Bladed Propeller Diameter = (632.7 x 50.17^0.2) / 1149.43^0.6 = 20.1835 Inches - result closely matches the displayed value of 20.4.
• Corrected Three Bladed Propeller Diameter with Indra's actual total horsepower losses is = (632.7 x 47.36 hp^0.2) / 1149.43^0.6 = 19.9522 inches or standard propeller diameter size 20 Inch.

• Two-Bladed Propeller Diameter = Three-Bladed Propeller Diameter x Two-Bladed Propeller Diameter Conversion Factor
• Two-Bladed Propeller Diameter Conversion Factor is 1.05 - reference the Propeller Handbook by Dave Gerr, Table 5-2.
• Two-Bladed Propeller Diameter = 20.1835 x 1.05 = 21.1927 Inches or standard propeller diameter size 21 Inch.

• Four-Bladed Propeller Diameter = Three-Bladed Propeller Diameter x Four-Bladed Propeller Diameter Conversion Factor
• Four-Bladed Propeller Diameter Conversion Factor is 0.94 - reference the Propeller Handbook by Dave Gerr, Table 5-2.
• Four-Bladed Propeller Diameter = 20.1835 x 0.94 = 18.9725 Inches or standard propeller diameter size 19 Inch.

Propeller Size Pitch Calculations based on 90% Engine Horsepower:

1. 90% Engine Horsepower = 0.90 x (Fuel Stop Power Brake Horsepower - Total Horsepower Losses)
   1. 90% Engine Horsepower = 0.90 x (53.1 hp - 2.3895 hp) = 45.639 hp
2. 90% Maximum Propeller Drive Shaft RPM = 0.90 x Maximum Propeller Drive Shaft RPM
   1. 90% Maximum Propeller Drive Shaft RPM = 0.90 x 1149.43 RPM = 1034.487‬ RPM
3. Knots @ 90% = (10.665 / (Displacement in Pounds / (90% Engine Horsepower)) ^1/3) x (Loaded Waterline Length in Feet)^0.5
   1. Knots @ 90% = (10.665 / (33500 lbs / 45.639 hp)^1/3) x (31.24 ft)^0.5 = 6.608 Knots
4. Propeller Slip = 1.4 / (Knots @ 90%)^0.57
   1. Propeller Slip = 1.4 / (6.608 kts)^0.57 =0.4772
5. Three Bladed Propeller Pitch in Inches = (12 in/ft x (Knots @ 90%) x 101.3 kts/ft/min) / 90% Maximum Propeller Drive Shaft RPM) x (1.0 + Propeller Slip)
   1. Three Bladed Propeller Pitch in Inches = (12 in/ft x (6.608 kts) x 101.3 kts/ft/min) / 1034.487 RPM) x (1.0 + 0.4772) = 11.4703 Inches or standard propeller pitch size of 11 Inch.
   2. Pitch values should be rounded down unless the decimal is 0.7 or greater.

• Two-Bladed Propeller Pitch = Three-Bladed Propeller Pitch x Two-Bladed Propeller Pitch Conversion Factor
• Two-Bladed Propeller Pitch Conversion Factor is 1.01 - reference the Propeller Handbook by Dave Gerr, Table 5-2.
• Two-Bladed Propeller Pitch = 11.4703 Inches x 1.01 = 11.585 Inches or standard propeller pitch size of 11 Inch.

• Four-Bladed Propeller Pitch = Three-Bladed Propeller Pitch x Four-Bladed Propeller Pitch Conversion Factor
• Four-Bladed Propeller Pitch Conversion Factor is 0.98 - reference the Propeller Handbook by Dave Gerr, Table 5-2.
• Four-Bladed Propeller Pitch = 11.4703 Inches x 0.98 = 11.2409 Inches or standard propeller pitch size of 11 Inch.

Propeller Size Pitch Calculations based on 90% Engine Horsepower with Indra's actual total horsepower losses:

1. 90% Engine Horsepower = 0.90 x (Fuel Stop Power Brake Horsepower - Total Horsepower Losses)
   1. 90% Engine Horsepower = 0.90 x (53.1 hp - 5.74 hp) = 42.624 hp
2. 90% Maximum Propeller Drive Shaft RPM = 0.90 x Maximum Propeller Drive Shaft RPM
   1. 90% Maximum Propeller Drive Shaft RPM = 0.90 x 1149.43 RPM = 1034.487‬ RPM
3. Knots @ 90% = (10.665 / (Displacement in Pounds / (90% Engine Horsepower)) ^1/3) x (Loaded Waterline Length in Feet)^0.5
   1. Knots @ 90% = (10.665 / (33500 lbs / 42.624 hp)^1/3) x (31.24 ft)^0.5 = 6.4593 Knots
4. Propeller Slip = 1.4 / (Knots @ 90%)^0.57
   1. Propeller Slip = 1.4 / (6.4593 kts)^0.57 =0.4834
5. Three Bladed Propeller Pitch in Inches = (12 in/ft x (Knots @ 90%) x 101.3 kts/ft/min) / 90% Maximum Propeller Drive Shaft RPM) x (1.0 + Propeller Slip)
   1. Three Bladed Propeller Pitch in Inches = (12 in/ft x (6.4593 kts) x 101.3 kts/ft/min) / 1034.487 RPM) x (1.0 + 0.4834) = 11.2592 Inches or standard propeller pitch size of 11 Inch.
   2. Pitch values should be rounded down unless the decimal is 0.7 or greater.

So to summarize the results, both the Propeller Handbook by Dave Geer and the Victoria Propeller Ltd online propeller size calculator recommended for Indra a 20" diameter by 11" pitch three blade propeller. Despite the difference in total horsepower calculation and some minor numerical rounding errors, the end result was the same size propeller recommendation. The important item to realize is the method of pitch calculation is based on 90% of maximum horsepower/RPM and this methodology favors a slightly over pitched propeller. The other contention we have with this method, besides total horsepower calculation, is the overall basis for calculations is based on 100% of the engine's maximum ratings which is limited to 5% of engine operational time. We are of the opinion that calculations should be based on the other 95% factor which equates to the normal engine range for everyday use. Whether this difference in opinion results in a different size propeller is what the next post, Part 4, will try to determine.