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Propulsion Power


Antrepat

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It's my naive impression that a lot of rule-of-thumbing goes on when it comes to selecting engines or motors of an appropriate power for a boat of a particular length, beam, hull design, material, and weight.  This impression has been formed having tried to work out how much power is really being deployed, and finding that no one anywhere seems to have published any specific data about this except for a guy with deep pockets, a battery that could power a village, and a small nuclear power station for a generator.  What's the drag for a narrow boat, a barge, a cruiser?  How does it vary with hull surface condition, length or draught?  If anyone knows, they don't seem to be saying, unless you count Lynch Motors' article or this chap who went round in circles on here trying to work something out a few years ago.  I could also be that boat builders and designers keep this kind of lore close to their chests so that the punters don't get ideas above their station.

 

This is probably where someone will pop up and post a link to a comprehensive public database and reveal the inadequacy of my web searching skill, but anyway, I did find what seemed to be a reasonable way of estimating and I thought it might be interesting to share it on here.  It's quite possible that this is a widely-known method and all I'll get is eye-rolling sighs and muttering of "another clueless newbie", but here we go.  I'm not a physicist, I'm not a mathematician, and I'm not a marine engineer, but this is what I've found out.

 

For about 150 years the horse was the predominant way to move a narrow boat, and although an unfettered horse will walk at 4mph, obviously pulling a 50-ton boat it's going to go a bit slower.  Lots of people seem to have wondered how fast passenger flyboats went (about 10mph, apparently - allegedly they got them to plane, which is pretty cool) but there wasn't much about how fast a regular plodder went.  2-3mph, reckons the blog of Whilton Marina.  A typical horse can do work at a rate of about 750W (actually 745.7W, or 33,000lb-ft/min - 50% more than the average pit pony, according to Mr Watt's observations), and this one horsepower seems to have fair validity, so it's a good start to assume that about 750W will move a laden wooden 72ft working narrow boat at perhaps 2mph, and an unladen one at perhaps 3mph.  I know the mass in itself doesn't limit the speed, but a laden boat would sit lower in the water so would have more drag.  It would of course also be harder to get going.

 

The power you need to move something at a constant speed with a resistive force (drag) is the exact counter-force required multiplied by the speed: P = Fv.  As the speed changes, the drag changes with the square of the speed, and is also a product of the cross-sectional (wetted) area of the hull (2.1*0.6=1.26 m^2), the density of the water (997 kg/m^3), and a factor called the drag coefficient.

 

The drag coefficient represents how the object's shape (boat hull) and the fluid behave.  We know that 745.7W will move a narrow boat at 2-3 mph, we know the density of water and the cross-sectional area of the typical hull, so we know the force that power was overcoming.  I believe that all means we can calculate the drag coefficient (https://en.wikipedia.org/wiki/Drag_(physics)) because F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{D}\,A.  (That's force = 1/2 x density x speed squared x drag coefficient x area.)

 

Suppose the speed is actually 2.5mph (1.12 m/s) - a bit of allowance for the fact that today's boats have steel hulls (a bit smoother?) and are nowhere near as heavy and hence low in the water as a laden working boat.  The power is 745.7W so, by P = Fv, the force applied at that speed is 667 N.  Now that we know that, we can calculate the drag coefficient CD as 0.8505.

 

There you go, the estimated and very approximate drag coefficient of a 72ft narrow boat; but wait, maybe I don't want to go at 2.5mph.  How much power do I need to go at other speeds?  Well, now we know the coefficient, we can just plug all the speeds into the force equation:

image.png.0834519fb131c85de075521790fc04fb.png

According to that, 10hp out the propeller would get you 5mph.  I don't know what the efficiency is of a typical diesel drive but I've heard it's not great, with loss through heat, mechanical friction and fluid viscosity in the engine.  The 40ft narrow boat I went on holiday on in October (Chas Hardern's terrific Thorin) slugged up to Ellesmere against the current and took a lot of welly to make 3mph - and Thorin is not underpowered by any means.  An electric drive with 50% efficiency would need to deliver 20hp continuous (yes, I know the canal limit is 4mph) to hold that speed.  Things I've read have talked of maybe 3hp to maintain a fair canal speed, and that does approximately fit in with the data here, but the chap with the big generator took proper measurements and reckoned 2.5kW for 3mph, 6kW for 3.5mph and 13kW for 4mph.  He was measuring his Amps, so this is before drive mechanical losses and electrical heat dissipation - just as well, since otherwise it implies a drag coefficient of 6.5, and with that, you'd need about seven horses to get your boat to 2.5mph, and to pull out the control rods of the nuclear power station to get to 4mph.  I'm going to assume that the steeper, deeper curve from the input power measurements is owing to system losses growing faster as power consumption increases.

 

My boat is diddy, only 30', so how does the drag vary with boat length?  I thought about this and I realised there are two components: the skin drag, which is the friction of the water passing the hull and is going to be proportional to length, and what I suppose you'd call the bow force, the effort required to push the water aside at the bow.  Most narrow boats seem to have basically the same bow shape (please don't jump on me, experts, this is just a convenient assumption) so I think it's a fair assumption that some component of the drag is actually constant between narrow boats regardless of length, at a given speed.  I have absolutely no idea what size this component is so I guessed at 20% of the total drag at my reference speed of 2.5mph.

 

I set up my spreadsheet to scale a proportion of the calculated drag force with length, but to include an unscaled component which I set as 20% of the 2.5mph force, and I recalculated for 30/72.

image.png.2daa8ed631257df90f6b56cdc569f0ad.png

If some lunatic came up with the totally bonkers idea of trying to make a 30' narrow boat electric, he could now see that pushing 4kW of power would be needed for a continuous 4mph at 50% efficiency, and that eight hours of that would need 26kWh of power, and that even if he did manage to cram 1kW of solar on that roof between the vents and the gas flue and the stove chimney and the hatch, he'd probably only get 2kWh out of it on a grey day, and he'd be running a generator for 7 hours of the day, so he'd be best slowing the blazes down to 3mph where he'd only need 11kWh (14.6kWh allowing for domestic loads and bursts of full power).

 

I had a lot of fun doing this, and it might be complete rubbish, but it would probably be fun also to have a discussion about it, if anyone wants to comment.  Please, please let's not rehearse the old arguments about diesel vs electric.  I know all that and this is just an idea I'm exploring for amusement during lockdown!

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You are perhaps overthinking a bit.I am sure you know your sums but I don't.

To be down to earth,my last narrowboat was 30ft,and weighed about 8 proper tons.Fitted with a BMC 1500 which rumour has it produces 30hp,but driving a prop and being old,I would guess 20 ish.

A comfortable rumble gave 3-4 knots,and flat out if i could tolerate the noise,smoke and vibration,for long about 7knots.Used a squirt over a litre per hour at canal speed,and flat out I don't know,as I couldn't stand the racket for long.

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15 minutes ago, Mad Harold said:

You are perhaps overthinking a bit.

 

My last narrowboat was 30ft,and weighed about 8 proper tons.Fitted with a BMC 1500 which rumour has it produces 30hp,but driving a prop and being old,I would guess 20 ish.

A comfortable rumble gave 3-4 knots,and flat out if i could tolerate the noise,smoke and vibration,for long about 7knots.Used a squirt over a litre per hour at canal speed,and flat out I don't know,as I couldn't stand the racket for long.

 

Wouldn't be the first time I'd overthought things, Harold.  Yes, I bet that did set teeth chattering a bit.

 

What you've recorded fits in pretty well, so this is good validation data, thanks.  My sums are saying 8.7kW for 7mph for a 30ft, which is about 12hp - this is plausible if you reckon your 1500 was giving you 20ish before post-engine mechanical and prop losses.  Propeller efficiency is the next thing I'm curious about...

 

Perhaps see you on the C&H in due course.

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The VicProp calculator will work out the power required to propel a boat at a given speed.

https://vicprop.com/displacement_size_new.php/?m=1

 

But I believe this uses empirical relationships which were developed for 'boat-shaped' boats moving in open water. Narrowboat hulls are not a typical boat shape, and operate mainly in constrained channels, so the relationships are probably less valid.

Edited by David Mack
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2 minutes ago, dmr said:

Hear are some power curves from somebody who has actually measured it:.....

 

https://nb-firecrest.co.uk/tag/power-curve/

 

..........Dave

Yeah, that's the nuclear power guy I was referring to.  His data were measured as Amps input, whereas I'm doing mechanical work output, and I think that's why his data are steeper and more deeply curved: the system losses are presumably non-linear as you crank things up, so that non-linearity compounds the non-linearity of the drag and the result is power into the motor which goes up very fast beyond a certain speed.  I don't know if it's exponential but it could easily be x^4 rather than x^2 (if I'm thinking this through right).

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5 minutes ago, David Mack said:

The VicProp calculator will work out the power required to propel a boat at a given speed.

https://vicprop.com/displacement_size_new.php/?m=1

 

But I believe this uses empirical relationships which were developed for 'boat-shaped' boats moving in open water. Narrowboat hulls are not a typical boat shape, and operate mainly in constrained channels, so the relationships are probably less valid.

Interesting, I hadn't come across that one.  Yes, I think you're right, it seems aimed more at shaplier hulls in perhaps deeper and wider channels.

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4 minutes ago, Antrepat said:

Yeah, that's the nuclear power guy I was referring to.  His data were measured as Amps input, whereas I'm doing mechanical work output, and I think that's why his data are steeper and more deeply curved: the system losses are presumably non-linear as you crank things up, so that non-linearity compounds the non-linearity of the drag and the result is power into the motor which goes up very fast beyond a certain speed.  I don't know if it's exponential but it could easily be x^4 rather than x^2 (if I'm thinking this through right).

 

The losses will be non linear but I doubt exponential. However a decent electric motor is pretty efficient so I would think his figures are not too far from true mechanical input to his prop.

Prop losses are likely much much greater than electric motor losses.

 

...........Dave

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3 minutes ago, Antrepat said:

Interesting, I hadn't come across that one.  Yes, I think you're right, it seems aimed more at shaplier hulls in perhaps deeper and wider channels.

 

As David Mack says, this calculator is for boaty boats on open water, the data in the link that I provided shows that there is a huge difference between open water and canals.

 

A narrowboat is a very short(and not very good) boaty boat with a huge flat sided bit inserted between the front boaty bit and the back boaty bit, and this rather confuses that prop calc.

 

...............Dave

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3 minutes ago, dmr said:

 

The losses will be non linear but I doubt exponential. However a decent electric motor is pretty efficient so I would think his figures are not too far from true mechanical input to his prop.

Prop losses are likely much much greater than electric motor losses.

 

...........Dave

Maybe he should try a different prop.  3mph with all that enormous welly behind him seems a pretty poor show.

 

It does make me wonder whether narrow boat hulls have truly adapted to the mechanised era - they've only had about 130 years to experiment, after all - or whether the bow shape remains essentially optimised for horse speeds.

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5 minutes ago, Antrepat said:

Maybe he should try a different prop.  3mph with all that enormous welly behind him seems a pretty poor show.

 

It does make me wonder whether narrow boat hulls have truly adapted to the mechanised era - they've only had about 130 years to experiment, after all - or whether the bow shape remains essentially optimised for horse speeds.

 

For canal cruising the speed is limited by the canal, whether the power comes from a horse or an engine/motor is not a big factor.

During the 200 years of the canals some optimisations have been done, such as the josher bow shape. For both  working boats and most leisure boats getting the maimum internal volume is a big factor which pretty much dictates the flat sides. A better shaped front and back loses a bit of space but can help the drag, but in a canal getting all the water round the side of a long boat will always need a lot of power.

 

A bigger prop might help that electric boat, bigger slower props are more efficient, but maybe he already has the biggest he can fit. Electric motors do give a bit more scope for prop optimisation, but I still reckon his figures are not a bad indication of how much mechanical power is needed to push a boat through water.

 

..............Dave

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14 minutes ago, dmr said:

A narrowboat is a very short(and not very good) boaty boat with a huge flat sided bit inserted between the front boaty bit and the back boaty bit, and this rather confuses that prop calc.

I made a total guess at what proportion of the drag was the bow pushing the water aside, and what proportion was skin drag.  Does anyone have any ideas how we could advance from a total guess to something with a bit more basis?

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I wonder if the reason few go into such detail is that tinkering around with the various variables in equations make little difference in the real world and then the shallow water effect comes along and trumps the lot? If narrowboats were long distance or high speed vessels working in deep water  things might be different.

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6 minutes ago, Sea Dog said:

I wonder if the reason few go into such detail is that tinkering around with the various variables in equations make little difference in the real world and then the shallow water effect comes along and trumps the lot? If narrowboats were long distance or high speed vessels working in deep water  things might be different.

 

I dare say you're right, particularly about the slog that a narrow, shallow channel can create.  I've done this partly as lockdown entertainment (haven't been allowed to go to the boat since October, what with Tier restrictions, lockdown, Tier restrictions, more lockdown) and partly because, despite the massive variables and confounding factors you're correct in noting, I wanted a way at least to find the right ballpark if it came to deciding the right size of battery, the right power of motor.  For example, Lynch say their Marlin 5 motor (5kW) is suitable for narrow boats up to 40ft, but the nuclear man's measurements (although I think his boat must be much bigger) suggest half that power for 3mph but not even 3.5mph at full power.  Obviously that motor is insufficient for his size of boat, but I also wanted a way of extrapolating data like his for a boat of a different size.  Just to get some idea.

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A decent basic text on Naval Architecture will help you  here.  Barnaby is the usual suggestion, though it is getting old.  Things like  block coefficient, transverse coefficient  and Froude number are all in the mix for powering decisions.

 

You are right about the two main elements of drag.  The bow part is usually called wave making drag and is predominant above a particular, hull form and length dependent, speed.   Skin friction is next, usually and then things like form drag.

 

The basic hydrodynamics of a narrow boat in a narrow canal mean that wave drag starts earlier than in open water and is predominant very quickly.  ( The water should go under the boat, but cannot, so it has to go round the sides).

Usually from 1-2 mph up. By ~4 mph you are using more power to make waves than to propel the boat.

 

Most canal pleasure craft are over ballasted  with a flat counter in, not on, the water.  That creates lots of form drag.  You can see the water trying to follow the boat in many instances. It is worse with a square transom type counter.

 

Finally, propeller efficiency is not as good as the ideal  by a long way.  That again is down to a rectangular boat in  a narrow, shallow channel.  A "block" of water is effectively being dragged along with the boat so prop slip is increased.  This lowers propulsive efficiency and you need to put more power into the prop to get the same amount onto the water. 

 

As an aside, Watt's definition of a horsepower was deliberately generous, to the customer, not the hoss.  Watt wanted his users to see that his engines were more effective than a gin with the same nominal number of horses.   So he overstated the amount of work that one, real,  horse could do.

 

N

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Has anyone mentioned that in many cases the bottom portion of the narrowboat hull is moving through a mud slurry that is denser and more viscous than water. I think that and the severely restricted waterway cross-sectional dimensions that vary so much makes any attempt to do as the OP seems to desire pretty much a waste of time. I think rule of thumb based on experience rules here rather than physics and maths.

 

Without any instruments the difference in boat/engine performance between say the GU and Ashby is noticeable, as it is on the South Oxford when the water levels fall.

 

As WWW said years ago it probably takes about 3 HP to drive a narrowboat at typical canal speed but then what's typical. Others say about 6 HP and i would not argue with either.

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Just now, Tony Brooks said:

Has anyone mentioned that in many cases the bottom portion of the narrowboat hull is moving through a mud slurry that is denser and more viscous than water. I think that and the severely restricted waterway cross-sectional dimensions that vary so much makes any attempt to do as the OP seems to desire pretty much a waste of time. I think rule of thumb based on experience rules here rather than physics and maths.

 

Without any instruments the difference in boat/engine performance between say the GU and Ashby is noticeable, as it is on the South Oxford when the water levels fall.

 

As WWW said years ago it probably takes about 3 HP to drive a narrowboat at typical canal speed but then what's typical. Others say about 6 HP and i would not argue with either.

 

Barnaby states that drag is increased by 150% when the depth of the water is 1.5 x the draught (compared to 20% at 5 x draught) at low speeds for a barge form vessel.  That implies a depth of 3-5 feet of clear water (not the "mud slurry" that Tony refers to) is required to achieve 150% drag. This would be the exception not the rule most canals so the drag is likely to be worse than that.  Even so, that doesn't mean narrowboats need 50 bhp which seems to be an emerging trend!

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9 hours ago, Antrepat said:

 

I dare say you're right, particularly about the slog that a narrow, shallow channel can create.  I've done this partly as lockdown entertainment (haven't been allowed to go to the boat since October, what with Tier restrictions, lockdown, Tier restrictions, more lockdown) and partly because, despite the massive variables and confounding factors you're correct in noting, I wanted a way at least to find the right ballpark if it came to deciding the right size of battery, the right power of motor.  For example, Lynch say their Marlin 5 motor (5kW) is suitable for narrow boats up to 40ft, but the nuclear man's measurements (although I think his boat must be much bigger) suggest half that power for 3mph but not even 3.5mph at full power.  Obviously that motor is insufficient for his size of boat, but I also wanted a way of extrapolating data like his for a boat of a different size.  Just to get some idea.

 

Most people like to fit engines of about 30Hp, though increasingly think that 40Hp is preferable.

Some boats have old vintage engines of about 18Hp and these do struggle a bit on a river.

I am talking of 57 foot type boats here rather than smaller shallower ones.

The electric motor sellers rather tell us that the motors that they can produce are adequate, and sometimes even point out that smaller motors are fine because they produce full torque at zero speed (great in a locomotive, irrelevant in a boat). I would not want a boat with a 5hp electric motor.

 

My own view is that for serious boating about 30Hp is needed, especially to cope with rivers, emergency stops and getting "unstuck". Its actually quite difficult to do this with an electric motor, in part because we like to limit voltage to 48. At some point some more adventurous people might start using higher voltages.

 

...............Dave

 

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The average diesel engine of 30 HP rating would produce this power at revs in excess of 2500 RPM, maybe 3500 RPM.

How many of us would run at that speed? So at say 1200 RPM the engine is producing substantially less than its peak power rating. Add to that power taken to drive the alternator/s and water pump you can see why the 30 HP figure is used.

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4 minutes ago, dmr said:

 

Most people like to fit engines of about 30Hp, though increasingly think that 40Hp is preferable.

 

 

 

Maybe I'm cynical but I think this is being driven by the manufacturers, not because boating dynamics have changed little over 200 years. 

 

"We can do 40bhp for £10 more than a 30bhp (because we don't really sell many 30's and make more money on 40's because we sell loads of those in to the machinery industry)".

2 minutes ago, Tracy D'arth said:

The average diesel engine of 30 HP rating would produce this power at revs in excess of 2500 RPM, maybe 3500 RPM.

How many of us would run at that speed? So at say 1200 RPM the engine is producing substantially less than its peak power rating. Add to that power taken to drive the alternator/s and water pump you can see why the 30 HP figure is used.

 

A good point about power take off as boats become even more loaded with electrickery.  Maybe that's why bhp is increasing?

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Glad to have stimulated such an interesting debate.

 

Thank you for the book recommendations and the benefit of deep knowledge and experience.  I wonder if the actual maths has changed between the earlier and more recent book?

 

I very much take the point made about shallow draft, the impact on viscosity and the fluid dynamics of a rather cuboid craft in a narrow, shallow channel.  At the extremes, this almost makes the boat like a loose-fitting piston in a half-cylinder.  The nuclear boat owner's data shows the difference between a canal and a river: the free-flowing of water around and presumably under the boat on a river leads to very significantly less power being needed.  Whilst it's true that my boat will most likely be on rivers and river navigations - Aire & Calder, Calder & Hebble, Huddersfield Broad are my closest waterways - I wouldn't want it to let me down if I were to venture onto the narrow system from Huddersfield; and I bet the Rochdale and the L&L have got pretty shallow with so little navigation over the past year too.

 

I also take the point that these variables make folly of assuming any kind of precision.  I never intended to reject experience, wisdom and a well-founded rule of thumb, I just wanted to explore whether it is feasible to model the situation despite the variables (and without needing a degree in engineering).

 

What's been said about real power delivered out of the propellor is interesting too.  It seems that hardcore whirling about beyond a certain amount of power is futile owing to the fluid dynamics of the channel and the fundamental inefficiency of a propeller especially in shallow water.  Tracy D'Arth mentioned a rule of thumb that you won't succeed in applying more than about 5hp no matter what you do.  I suspect the tendency towards bigger engines is owing to engine salemanship, like someone suggested, and questionable assumptions, rather than evidence that more and more power really helps do anything other than stir up the silt and cause cavitation and climate change.

 

I did read that the Horsepower is suspected of being overstated, but the Wikipedia article does suggest some evidence that it might not be as overstated as some have suggested.  Fundamentally, my idea of starting from what a horse can do was simply to try to calibrate things, in the absence of empirical data.  The rule of thumb is surely: err on the side of caution.

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15 minutes ago, Antrepat said:

Thank you for the book recommendations and the benefit of deep knowledge and experience.  I wonder if the actual maths has changed between the earlier and more recent book?

 

I doubt very much the maths has changed but the units of measure will have.

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