Comparing Engine Efficiency At Various Boat Speeds

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jimh posted 12-12-2012 11:10 PM ET (US)
Comparing Engine Efficiency At Various Boat Speeds
Previously the rated horsepower of an engine and its rate of fuel consumption when running at full throttle have been used to calculate the efficiency of the engine in converting fuel to horsepower. This is known as the brake specific fuel consumption or BSFC. Because we typically only knew the engine horsepower with any accuracy at one speed--full throttle--we could not calculate the BSFC at other engine speeds. This analysis now presents a method for deducing the engine power at various speeds and then using that to calculate the BSFC.
The key to the method is to determine the engine horsepower at some intermediate speed, other than at full throttle. Naval architects have determined with reasonable certainty that the relationship between the speed of revolution of a propeller and the horsepower needed to turn it can be expressed by
HP = C x RPM^2.7
Using the rated horsepower of an outboard engine and the maximum speed it can reach when turning a propeller, we can find a value for C. With a value for C we can then solve for horsepower at any engine speed using the above relationship.
From my own experience, I have an outboard engine rated to deliver 225-HP. At full throttle, with the load of my boat and propeller, the engine turns at 5,600-RPM. (The boat speed will be about 42-MPH and the fuel economy about 1.9-MPG. This is a fuel flow of 22.1-GPH. We'll use these later) Because of gear reduction the propeller turns 1.85-times slower, or 3,027-RPM. Now we solve for C
C = HP / RPM^2.7
C = 225 / 3027^2.7
C = 1.018138 x 10^-7
With this relationship we can now solve for horsepower at any propeller shaft speed. From my experience a good cruising speed--where fuel economy peaks--is typically at an engine speed of 3,900-RPM, corresponding to a propeller shaft speed of 2,108-RPM. (At this speed with my boat and propeller we typically are making 27-MPH with a fuel economy of 2.7-MPG. This is a flow rate of 10-GPH. We'll use these later.) We can solve for horsepower:
HP = 1.018138 x 10^-7 x 2108^2.7
HP = 96-HP
Since we have a good estimate of horsepower, and we know the fuel flow, we can find the engine brake specific fuel consumption at this speed:
BSFC = 10-gallons/96-HP-hour x 6.25-lbs/1-gallon
BSFC = 0.65-lbs/HP-hour
Now we compare to wide-open throttle:
BSFC = 22.1-gallons/225-HP-hour x 6.25-lbs/1-gallon
BSFC = 0.61-lbs/HP-hour
The calculation clearly show the engine is running more efficiently at full throttle than at cruise, although by only a small fraction of improvement. These calculations do show that there is nothing magic about running a big engine at partial throttle in producing more efficiency in the engine. (By the way, on my engine there is a measure of the throttle position; at the 3,900-RPM setting, and it is typically about 35-percent of maximum throttle.)
From this analysis I don't see anything special about the fuel economy that might result from running a really big engine at partial throttle. The engine seems to be doing about the same job of converting fuel to horsepower at both settings of the throttle. This is contrary to a frequently repeated notion that fuel economy will be enhanced if one gets a big engine and runs it at partial throttle all the time.
How did this notion of a big engine being more fuel efficient come about? It was probably from a bad assumption that the boat's fuel economy was a measure of engine efficiency. The two are different.
Do not confuse the boat's fuel economy in miles per gallon with the engine's rate of converting fuel into horsepower. The fuel economy of the boat tends to peak at a particular speed as a result of many factors, including hull design, water drag, wind drag, propeller efficiency, and so on. It is common to see that boat MPG will peak shortly after the boat gets on a plane and is running nicely with less hull drag. As speed is increased other factors tend to reduce the fuel economy, but from this analysis it does not appear that the engine efficiency is causing a decline in boat MPG from the lower throttle to wide-open throttle. The BSFC of the engine is in the same range at both boat speeds. We know that wind resistance increases rapidly with speed. There are many equations for computing wind load as a function of wind velocity. They tend to in calculate the wind load as a function of the wind velocity squared. Hydrodynamic drag probably does, too. (I am not a naval architect so I don't have a handy formula for that.) In any case, we see that many factors are in play for determining the particular speed a boat will run on plane at best efficiency. It is not reasonable to assume because the fuel efficiency (MPG) of the boat peaked in a certain range there must have been a corresponding peak in the engine efficiency at converting fuel to horsepower at that same engine speed range.

jimh posted 12-13-2012 09:34 AM ET (US)
We can also approach the estimate of horsepower used to obtain a particular boat speed by calculating it based on the boat speed. We know from Crouch the relationship between boat speed and horsepower is
MPH = C x (HP/LBS)^0.5
and we can compute the horsepower with the same data used above. First we find the factor C for a weight of 4,600-lbs at our top speed of 42-MPH with 225-HP:
C = MPH / (HP/LBS)^0.5
C = 42 / (225/4600)^0.5
C = 189.9
Then we calculate HP at 27-MPH
HP = WT x (MPH/C)^2
HP = 4600 x (27/189.9)^2
HP = 93
We compare this with the horsepower calculated with the propeller curve method and find good agreement: 93-HP versus 96-HP. This tends to verify the two methods.
Now we look at the BSFC with this new value:
BSFC = (10-gallon/93-HP-hour) x 6.25-lbs/1-gallon = 0.67-lbs/HP-hour
The BSFC is higher than estimated before. This again shows that running the engine at a reduced throttle setting is no guarantee that the efficiency of the engine will be higher.
Jerry Townsend posted 12-13-2012 02:48 PM ET (US)
Jim - we have been down this road before - the units on both sides of the equation have to be consistant.
Further, extrapolating from Naval prop performance to our application is not appropriate in my mind. That is, the Naval props are turning at vastly different RPMs and as such are operating in a significantly different fluid environment. ---- Jerry/Idaho
jimh posted 12-13-2012 11:48 PM ET (US)
Jerry--The unit conversion is handled by the C factor in each case. Both of the formulas used are not mine but are in wide use in Naval Architecture.
Propeller power curve loading seems to agree with Crouch with less than 3-percent variance. That is quite good in my mind.
You should not hold back on explaining better methods. I look forward to hearing about other ways to calculate the horsepower being delivered by an outboard engine when operating at various speeds and loads.

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Author	Topic: Comparing Engine Efficiency At Various Boat Speeds
jimh	posted 12-12-2012 11:10 PM ET (US) Comparing Engine Efficiency At Various Boat Speeds Previously the rated horsepower of an engine and its rate of fuel consumption when running at full throttle have been used to calculate the efficiency of the engine in converting fuel to horsepower. This is known as the brake specific fuel consumption or BSFC. Because we typically only knew the engine horsepower with any accuracy at one speed--full throttle--we could not calculate the BSFC at other engine speeds. This analysis now presents a method for deducing the engine power at various speeds and then using that to calculate the BSFC. The key to the method is to determine the engine horsepower at some intermediate speed, other than at full throttle. Naval architects have determined with reasonable certainty that the relationship between the speed of revolution of a propeller and the horsepower needed to turn it can be expressed by HP = C x RPM^2.7 Using the rated horsepower of an outboard engine and the maximum speed it can reach when turning a propeller, we can find a value for C. With a value for C we can then solve for horsepower at any engine speed using the above relationship. From my own experience, I have an outboard engine rated to deliver 225-HP. At full throttle, with the load of my boat and propeller, the engine turns at 5,600-RPM. (The boat speed will be about 42-MPH and the fuel economy about 1.9-MPG. This is a fuel flow of 22.1-GPH. We'll use these later) Because of gear reduction the propeller turns 1.85-times slower, or 3,027-RPM. Now we solve for C C = HP / RPM^2.7 C = 225 / 3027^2.7 C = 1.018138 x 10^-7 With this relationship we can now solve for horsepower at any propeller shaft speed. From my experience a good cruising speed--where fuel economy peaks--is typically at an engine speed of 3,900-RPM, corresponding to a propeller shaft speed of 2,108-RPM. (At this speed with my boat and propeller we typically are making 27-MPH with a fuel economy of 2.7-MPG. This is a flow rate of 10-GPH. We'll use these later.) We can solve for horsepower: HP = 1.018138 x 10^-7 x 2108^2.7 HP = 96-HP Since we have a good estimate of horsepower, and we know the fuel flow, we can find the engine brake specific fuel consumption at this speed: BSFC = 10-gallons/96-HP-hour x 6.25-lbs/1-gallon BSFC = 0.65-lbs/HP-hour Now we compare to wide-open throttle: BSFC = 22.1-gallons/225-HP-hour x 6.25-lbs/1-gallon BSFC = 0.61-lbs/HP-hour The calculation clearly show the engine is running more efficiently at full throttle than at cruise, although by only a small fraction of improvement. These calculations do show that there is nothing magic about running a big engine at partial throttle in producing more efficiency in the engine. (By the way, on my engine there is a measure of the throttle position; at the 3,900-RPM setting, and it is typically about 35-percent of maximum throttle.) From this analysis I don't see anything special about the fuel economy that might result from running a really big engine at partial throttle. The engine seems to be doing about the same job of converting fuel to horsepower at both settings of the throttle. This is contrary to a frequently repeated notion that fuel economy will be enhanced if one gets a big engine and runs it at partial throttle all the time. How did this notion of a big engine being more fuel efficient come about? It was probably from a bad assumption that the boat's fuel economy was a measure of engine efficiency. The two are different. Do not confuse the boat's fuel economy in miles per gallon with the engine's rate of converting fuel into horsepower. The fuel economy of the boat tends to peak at a particular speed as a result of many factors, including hull design, water drag, wind drag, propeller efficiency, and so on. It is common to see that boat MPG will peak shortly after the boat gets on a plane and is running nicely with less hull drag. As speed is increased other factors tend to reduce the fuel economy, but from this analysis it does not appear that the engine efficiency is causing a decline in boat MPG from the lower throttle to wide-open throttle. The BSFC of the engine is in the same range at both boat speeds. We know that wind resistance increases rapidly with speed. There are many equations for computing wind load as a function of wind velocity. They tend to in calculate the wind load as a function of the wind velocity squared. Hydrodynamic drag probably does, too. (I am not a naval architect so I don't have a handy formula for that.) In any case, we see that many factors are in play for determining the particular speed a boat will run on plane at best efficiency. It is not reasonable to assume because the fuel efficiency (MPG) of the boat peaked in a certain range there must have been a corresponding peak in the engine efficiency at converting fuel to horsepower at that same engine speed range.
jimh	posted 12-13-2012 09:34 AM ET (US) We can also approach the estimate of horsepower used to obtain a particular boat speed by calculating it based on the boat speed. We know from Crouch the relationship between boat speed and horsepower is MPH = C x (HP/LBS)^0.5 and we can compute the horsepower with the same data used above. First we find the factor C for a weight of 4,600-lbs at our top speed of 42-MPH with 225-HP: C = MPH / (HP/LBS)^0.5 C = 42 / (225/4600)^0.5 C = 189.9 Then we calculate HP at 27-MPH HP = WT x (MPH/C)^2 HP = 4600 x (27/189.9)^2 HP = 93 We compare this with the horsepower calculated with the propeller curve method and find good agreement: 93-HP versus 96-HP. This tends to verify the two methods. Now we look at the BSFC with this new value: BSFC = (10-gallon/93-HP-hour) x 6.25-lbs/1-gallon = 0.67-lbs/HP-hour The BSFC is higher than estimated before. This again shows that running the engine at a reduced throttle setting is no guarantee that the efficiency of the engine will be higher.
Jerry Townsend	posted 12-13-2012 02:48 PM ET (US) Jim - we have been down this road before - the units on both sides of the equation have to be consistant. Further, extrapolating from Naval prop performance to our application is not appropriate in my mind. That is, the Naval props are turning at vastly different RPMs and as such are operating in a significantly different fluid environment. ---- Jerry/Idaho
jimh	posted 12-13-2012 11:48 PM ET (US) Jerry--The unit conversion is handled by the C factor in each case. Both of the formulas used are not mine but are in wide use in Naval Architecture. Propeller power curve loading seems to agree with Crouch with less than 3-percent variance. That is quite good in my mind. You should not hold back on explaining better methods. I look forward to hearing about other ways to calculate the horsepower being delivered by an outboard engine when operating at various speeds and loads.