Planing boat range

I was trying to come up with a simple way to calculate planing boat range and came up with a formula that says, planing range only depends is speed and % fuel/to displacement. Does this make sense?

Crouch's formula says speed = c / sqrt(displacement/hp) and it appears roughly correct for most planing boats on the market, where c varies between 170 and 190 if displacement is in lb. Say c = 180, fuel (diesel) is x% of displacement and 1 gph gives you 18 hp/hour, 1 gallon = 7.1 lb diesel.

nmpg = 18*180*180 / (speed*disp)
nmpg = 18*180*180 / (speed*(gallons*7.1/x%) )
range = nmpg * gallons = 18*180*180/7.1*x%/speed = 91600*x%/speed
range = approx. 92,000*x%/speed and
x% = range*speed/92,000

For a typical cruiser, x% = 10% (fuel to displacement), speed is 20 knots, range = 460 nm, which makes sense. May be a little high. Clearly, a lot of approximations but at the end, range at a given speed depends only on fuel to displacement ratio. If one wants to design a boat with a 2,200 nm range at 20 knots, the boat needs to hold fuel = 48% of displacement.

Fuel % of displacement at planing speeds for 2,200 nm range
15 knots, x% = 2,200 x 15/90,000 = 36%
20 knots, x% = 48%
25 knots, x% = 60%
30 knots, x% = 72%

Any thoughts?

 

A bit hard to read, but what you are suggesting is the amount of fuel needed as a function of vessel displacement for a given range.

I don’t know many cruisers that can get 460nm running 20kts at displacement of say 9000 lbs and fuel of say 150 gallons. Usually most vessels are getting 1 mpg or in diesel maybe 2. I’d say you’ve oversimplified something.

 

It is missing a lot of important parameters. For example, if it has a flat, round or deep vee bottom. At higher speeds aerodynamic resistance becomes significant. At the same displacement, an ultraligh boat will have a larger volume than a heavy metal boat. The heavy boat will have much less resistance. There are many more which affects fuel efficiency.

 

The aim of the exercise is laudable but there are other factors to take into account as has been posted.For instance not all engines have the same level of thermal efficiency and a modern turbocharged diesel with electronic management will do better than those huge petrol engines that our American friends are so fond of,so I would agree that you need a factor in the calculation for an engine constant.I have no idea how you would derive enough information to arrive at suitable figures.The reference to Crouch also reminds me that there are hull factors that have to be taken into account,so perhaps the Crouch formula would be a good starting point but with a ratio of fuel/displacement that is constantly changing,wouldn't that factor also have to be taken into account or would the average of the initial and final ratios be sufficient?I suppose the ratios could be 1/5 th displacement to almost zero.

 

Fair points. I started this exercise because I was sick of reading articles that claim improved hulls, whatever, when in reality the differences are very small. Some factors matter and others cancel out. Specifically:

1) Different hull forms have a different constant in the Crouch formula but I reverse calculate this constant based on published max speed/hp/displacement. The constants are very close for different boats. Transom angle matters but heavy vs. light does not.

2) Transom angle is important. Shallow-v hulls have better fuel economy because you have less wetted surface in low to moderate seas. How much less could be calculated. Deep-v hulls have lower fuel economy but better comfort in heavy seas. If wetted surface drag is 50% (guess) of resistance and the difference of surface (cosine of transom angle) is 9% between 25 degree v and 5 degree v, then the impact is 4-5% on the fuel economy. Important but not significant.

3) Diesel efficiency, yes, it matters a bit. 18-20 hp/gallon, some do a little bit less, others a little bit more. It is a 10% difference but much smaller over time, meaning diesel engines from the 80's will get 17-18, turbodiesels from the 90's 18-19 and electronically controlled engines from the 2000's will get 19-20 with some doing 20.5. Larger engines are also slightly more efficient than smaller engines.

3) The point that fuel starts at 10% of displacement and is close to 0% at max range I had overlooked. This would increase the range, you need integration math to calculate it correctly. At the same time sea state and waves will decrease the range, so these two cancel each other out.

4) Propeller sizing. Since most boats have dry vs. fully laden displacement difference of 10-15% (fuel, water, gray water), the propellers sizing can be constant, optimized for the fully laden state. If fuel for a long-range (planing) cruiser is a much higher percentage, say 30-40%, then the propellers would either be overloading the engine in the beginning or slipping at the end, leading to inefficiencies. Again, this is not important for displacement vessels as most long-range cruisers are, but one of the big issues if you want to have a planing cruising range of 2,2000 nm at displacement speed. Then you would actually have to change propellers halfway. Not impossible but definitely not typical. I think this is by far the biggest variable factor.

So, I come up with two conclusions a) range at planing speeds largely depends on fuel% of displacement. Newer engines and lower-v help increase this by 5-10% at best; b) fuel efficiency discussions and comparison between boats are close to useless - it is much better to look at displacement and if you care about fuel efficiency, choose a boat that has low enough displacement for your target nmpg. Ignore everything else.

And the last thought... it could be possible to cover 2,200 nm at 15-20 knots without refueling provided you have a sea state that allows you to maintain that speed and that you have a boat that can safely carry 40-45% fuel. This would mean, for a 50 ft cruiser with dry displacement of 14 tons to add 6 tons of fuel. I do not think that is realistic. Variable pitch propellers would be needed or the propellers would need to be changed a couple of times during the trip.

 

A boat with a length of 16 m, a beam of 4 m, a draft of 0.83 m and a displacement of 33 tons can have a tonne per cm of immersion of between 400 and 500 kg/cm. This means that the 6 tons of fuel, when consumed, would produce a reduction in draft of about 15 or 12 cm (may be 20 cm, it doesn´t matter). This does not seem to be a difference that requires changing propellers. Perhaps some outboard motors, with a device on the transom that allows the height of the motors to be varied, would be sufficient.
NOTE: All the above data are merely a supposition, for comparison of fast boats of similar length, so they should not be taken as absolute truths. But they give an idea of the dimensions of the problem.

 

Any reference to "Crouch formula" is nonsense, since that formula is not dimensionless. Take a look at the "admiralty constant" instead as a start; it demonstrates the drag/lift ratio over the Froude volume number. You will then have a formula in the form of [power/(speed^2*volume^(5/6))]. Here you can then introduce factors for power as function of fuel flow and propulsion efficiency, which will show a better correlation to reality.

 

A range formula based on fuel mass ratio is similar to the Tsiolkovsky Rocket Formula, where
deltav=ve*ln(fuelm/emptym)
So not an intrinsically pointless exercise, but certainly not practical. Just in my own boat, my best mileage was 17l/100km, at 2.5 knots, and my worst was 125l/100km at 11knots. A ratio of 7.35, in the same boat under the same conditions. I don't think you can derive a formula that can generate a meaningful output. The most you could hope for is curve fitting after a prohibitive amount of empirical work.

 

It is not a propeller issue, but the fuel necessary. 150 foot yachts have a hard time achieving that range and speed.

 

i agree with gonzo, re: aspects that affect fuel efficiency, including significant issues like planing surface deadrise, appendages (lower/drive unit(s), topside drags, and others...

 

There are free to use prop calculators to estimate speeds with the weight and water length then you have to examine the engine curves on horsepower for every hundred RPMs and fuel curve at that RPM and you can start getting a reasonable idea on fuel burn.

 

You could not desing a 30 foot boat with that range. The formula is not dimensionless.

 

I agree
Most off the people are trying to get us to answer what is possible without working out the details on their own.
600 mile range is possible for a 30 ft boat for 20 knots

I will chew on this and see if I can push it more extreme just to entertain for fun.

 

Even though it would not be a boat I would ever want to take on a trip you could get close to the range in a too thin ,shallow,narrow 30 ft boat with a single diesel in the lower rpm achieving the 20 knots with 325 gallons of fuel

30 ft
29.6 water length
8 ft water beam
1.3 ft draft
Single 209 HP diesel @2200
1.5 to 1 reduction gear
Single bearing on shaft
22 d x22 p prop
20 knots
325 gallons of fuel
Inverters with an extra battery to not have generator using fuel

Your just giving up on all the features to make it a nice comfortable anything

Just an entertaining thought



Almost no accommodations
No seaworthiness
Thin skin
Minimal structure

If the only criteria was range

 

1.5 gallons per hour at 1800rpms
3.25 gallons per hour available
2200 RPMs achieving 21 knots