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Best speed and course on a river


Keeping Up

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While gently pottering up and down the Thames this summer, a couple of vital questions kept coming back to my mind. My attempts to come up with a definitive answer failed every time, perhaps people here can do better?

Firstly, what is the most economical speed for travelling upstream? Suppose for example the river is flowing at 3mph:

  • if you travel through the water at 2mph you will be going backwards relative to the land
  • if you travel at 3mph you will use a bit more fuel but at least you'll be standing still
  • at 4mph you will be using a lot more fuel but at least you are making 1mph progress
  • at 5mph you will be using lots and lots more fuel but you'll have doubled your land speed to 2mph

and so on. Now, given that the rate of fuel consumption varies (I think) with the cube of your speed through the water, but the length of time for which you use it at that rate is inverseley proportional to your speed relative to the land, what is the best cruising speed for a river which is flowing at 1, 2, 3, or 4 mph?

 

Secondly, when travelling downstream, when should you take the inside line (which is shorter) round a corner, and when should you take the outside line (which will give the greatest assistance from the current which is always faster round the outside of a bend)? I assume this depends on the speed of the river and the speed of the boat, and also on the geometry of the bend, but to what extent assuming of course that the river is fairly wide.

 

There you are - two problems in one post! Now, what about some answers?

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9 minutes ago, Keeping Up said:

Secondly, when travelling downstream, when should you take the inside line (which is shorter) round a corner, and when should you take the outside line (which will give the greatest assistance from the current which is always faster round the outside of a bend)? I assume this depends on the speed of the river and the speed of the boat, and also on the geometry of the bend, but to what extent assuming of course that the river is fairly wide.

 

If you take the inside line you are more likely to run aground. If you take the outside, you will be on the wrong side of the river. Stay in the middle, or just off centre.

Probably doesn't answer your second question, and I'm not smart enough to answer the first.

Edited by rusty69
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41 minutes ago, Keeping Up said:

Firstly, what is the most economical speed for travelling upstream? Suppose for example the river is flowing at 3mph:

  • if you travel through the water at 2mph you will be going backwards relative to the land  If you want to go back to where you were yesterday, do this speed.
  • if you travel at 3mph you will use a bit more fuel but at least you'll be standing still If you do not want to move, and just want to charge your batteries, do this speed
  • at 4mph you will be using a lot more fuel but at least you are making 1mph progress If you want to get there tomorrow, do this speed
  • at 5mph you will be using lots and lots more fuel but you'll have doubled your land speed to 2mph If you want to get there late today, do this speed.

If you want to arrive at a reasonable time do 7 or 8 mph.

If the cost of fuel is your overriding concern when boating, maybe you should consider moving to London &  becoming a CMer.

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If the river is tidal then you will need to factor in the state of the tide to the equation too (inside or outside of a bend might put you on a sand bank!)

Given the variation in the amount of fresh that might be on a river the most economical speed will also vary and whether you are heading upstream or downstream will make a difference to how slow you can go!

Far too many variables for one definitive answer I think

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I think you're overthinking this economy thing. If you're travelling upstream, try to do so when the flow is gentle and then bite the bullet. Most important is that your engine and it's cooling system is up to the job to make your journey safe. Fuel economy is a secondary concern in my book, as we're not talking the Amazon here, just short English river navigations. What I tend to do is set revs at which my engine is happy and my progress is sensible then enjoy the cruise. 

Flow is generally strongest mid stream, so where possible keep right within the confines of depth and safe navigation and you'll be against a lesser flow. Don't cut those inside bends as Rusty said above, as that's usually less depth and you'll also be rounding a blind bend.

Hope that helps.

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If you're taking the Thames as a model. In normal conditions the flow runs at 1 to 1.5 mph Any more than that you're into "increasing stream" and more to "strong stream". For both of these the EA advise NBs  not to cruise - usually because the boat is underpowered and unable to manoeuvre.

So your calculations are of little value as you should be stationary...

Edited by OldGoat
Edited to correct confusion of speed s/be 1 to 1.5 mph.....
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1 hour ago, Keeping Up said:

While gently pottering up and down the Thames this summer, a couple of vital questions kept coming back to my mind. My attempts to come up with a definitive answer failed every time, perhaps people here can do better?

Firstly, what is the most economical speed for travelling upstream? Suppose for example the river is flowing at 3mph:

  • if you travel through the water at 2mph you will be going backwards relative to the land
  • if you travel at 3mph you will use a bit more fuel but at least you'll be standing still
  • at 4mph you will be using a lot more fuel but at least you are making 1mph progress
  • at 5mph you will be using lots and lots more fuel but you'll have doubled your land speed to 2mph

and so on. Now, given that the rate of fuel consumption varies (I think) with the cube of your speed through the water, but the length of time for which you use it at that rate is inverseley proportional to your speed relative to the land, what is the best cruising speed for a river which is flowing at 1, 2, 3, or 4 mph?

 

Secondly, when travelling downstream, when should you take the inside line (which is shorter) round a corner, and when should you take the outside line (which will give the greatest assistance from the current which is always faster round the outside of a bend)? I assume this depends on the speed of the river and the speed of the boat, and also on the geometry of the bend, but to what extent assuming of course that the river is fairly wide.

 

There you are - two problems in one post! Now, what about some answers?

Going downstream, the most economical arrangement (in fuel, if not repairs) is to turn-off the engine.  It doesn't matter which line you take on the bends.

To answer the upstream question, you would need to be clear whether the rate of fuel consumption (that increases with the cube of the speed) is by time or by distance.  I think this rule-of-thumb is usually taken to be by time.  

  

Edited by Tacet
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Going upstream, the speed must be greater than the current to make progress.  Increasing speed will increase the hourly consumption but shorten the journey time.  If the current is 2 knots and you increase the speed through the water from 3 knots to 5 knots you will increase ground speed from 1 knot to 3 knots so journey time will be reduced by a factor of 3.  But fuel consumption will increase by a factor of *4.6.  So the optimum speed must be less than this.  Of course, increasing speed in calm water always causes costs to rise. 

Going upstream, there will be an optimum speed and a formula could be written to calculate it, but life is too short!

*(5/3)^3

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4 hours ago, OldGoat said:

If you're taking the Thames as a model. In normal conditions the flow runs at 1 1.5 mph Any more than that you're into "increasing stream" and more to "strong stream". For both of these the EA advise NBs  not to cruise - usually because the boat is underpowered and unable to manoeuvre.

So your calculations are of little value as you should be stationary...

I don't think the Thames even in normal conditions runs at 11.5mph.   Not much chance of a narrow boat going upstream then. I think you really meant 1.5mph. :lol:

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I would have thought travel through the water at a speed that the boat is comfortable at, likely to be 4 to 5mph in a NB. If you are going upstream you will travel over the ground a bit slower and if going down you will be a bit faster.

If the current is up at 3mph or more your main consideration would be safety not economy but you would certainly have to be careful not to overheat your engine and that depends on your individual boat so as others have said ... too many variables!

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49 minutes ago, Flyboy said:

I don't think the Thames even in normal conditions runs at 11.5mph.   Not much chance of a narrow boat going upstream then. I think you really meant 1.5mph. :lol:

I read old goat's "1  1.5" as 1-1.5 which I expect is what he meant. It was a bit less of a leap than removing the space to read it as an unfeasible 11.5 knots. :P

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I'm fairly sure it is the consumption per unit time that increases with the cube of the speed (I think, and that ignores the fact that even at tickover in neutral some fuel is consumed) - but by drawing some graphs I make it that the most economical speed is about 1.5 times the value of the current, although of course I could have miscalculated there. So if the current is 2mph the best speed is 3mph, if it is 3mph the best is 4.5mph, and so on. Of course not only may I have got it wrong, but also when cruising the river during the summer I had neither the time nor inclination to use pen, paper, and Excel spreadsheet!

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For me its easy on the Thames. Loddon has a Beta 2203 so about 1500rpm upstream, 5mph, 1350/1400 rpm  downstream, 5mph. I did forget which way I was going  and ran 1500rpm downstream and got warned by the EA.      Twice:o

Edited by Loddon
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1 hour ago, Keeping Up said:

I'm fairly sure it is the consumption per unit time that increases with the cube of the speed (I think, and that ignores the fact that even at tickover in neutral some fuel is consumed) - but by drawing some graphs I make it that the most economical speed is about 1.5 times the value of the current, although of course I could have miscalculated there. So if the current is 2mph the best speed is 3mph, if it is 3mph the best is 4.5mph, and so on. Of course not only may I have got it wrong, but also when cruising the river during the summer I had neither the time nor inclination to use pen, paper, and Excel spreadsheet!

Show us yer graphs (and calculations)!

Slower is always better unless you want to incorporate standing costs as in charter agreements.  

When you include fixed costs like crew wages, it's fairly easy to prove that the most economical speed is that at which your in-port costs are doubled.

Edited by mross
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1 hour ago, Loddon said:

For me its easy on the Thames. Loddon has a Beta 2203 so about 1500rpm upstream, 5mph, 1350/1400 rpm  downstream, 5mph. I did forget which way I was going  and ran 1500rpm downstream and got warned by the EA.      Twice:o

Yes, the EA speed limits are based on Speed over Land ,in Full Flood conditions it can be difficult to achieve 5 MPH going upstream without making Wash and Running Down Stream it is all too easy to exceed the limit on a Slightly raised Tick over!

Full Flood speed is @5 MPH on the wide and broader bits and 8-9 MPH on the Narrow or Shallow sections(Upper Thames)

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20 minutes ago, mross said:

Show us yer graphs (and calculations)!

Slower is always better unless you want to incorporate standing costs as in charter agreements.  

When you include fixed costs like crew wages, it's fairly easy to prove that the most economical speed is that at which your in-port costs are doubled.

Slower isn't better if it means you're moving backwards!

 

If the river speed is Vb and the boat speed is Vb, the land speed VL is given by VL=Vb-Vr

The consumption rate C is proportional to the cube of the speed, thus C=K*(Vb cubed)

The travelling time T is the distance S divided by the land speed VL, tuis T=S/VL

The diesel used is C*T which is K*(Vb cubed)*S/VL which is K*S*(Vb cubed)/(Vb-Vr)

Given that the distance is a constant for any journey and assigning an arbitrary value of K*S = 1 (it doesn't matter what the value is, we are just looking for the minimum) I plotted a table of values for this formula, with the boat speed Vb as the horizontal axis and the river speed Vr as the vertical.

image.png.eb55fa5985798a1b866c27aaacf9543c.png

I can't make the graphs look good on screen but looking at the table it looks as if the least diesel always occurs where I have highlighted is always with the boat speed around 1.5 times the river speed

Of course this may be all pure rubbish

 

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43 minutes ago, Keeping Up said:

Slower isn't better if it means you're moving backwards!

 

If the river speed is Vb and the boat speed is Vb, the land speed VL is given by VL=Vb-Vr

The consumption rate C is proportional to the cube of the speed, thus C=K*(Vb cubed)

The travelling time T is the distance S divided by the land speed VL, tuis T=S/VL

The diesel used is C*T which is K*(Vb cubed)*S/VL which is K*S*(Vb cubed)/(Vb-Vr)

Given that the distance is a constant for any journey and assigning an arbitrary value of K*S = 1 (it doesn't matter what the value is, we are just looking for the minimum) I plotted a table of values for this formula, with the boat speed Vb as the horizontal axis and the river speed Vr as the vertical.

image.png.eb55fa5985798a1b866c27aaacf9543c.png

I can't make the graphs look good on screen but looking at the table it looks as if the least diesel always occurs where I have highlighted is always with the boat speed around 1.5 times the river speed

Of course this may be all pure rubbish

 

But what are the figures in green?  Total fuel for the journey, fuel per mile, fuel per hour?

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3 minutes ago, mross said:

But what are the figures in green?  Total fuel for the journey, fuel per mile, fuel per hour?

I couldnt work it out as well.

...but thinking about it, it looks like fuel 'equivalent' for the journey. Cant have an absolute value as dont know the value of K.

Edited by Dr Bob
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4 minutes ago, mross said:

But what are the figures in green?  Total fuel for the journey, fuel per mile, fuel per hour?

Sorry, every figure in the table is the cost per unit distance. Thus every row represents the cost for a given journey, for that river speed, at different boat speeds. The figures in green are where I have manually highlighted the lowest figure in that row. Looking to see where they occur, they are always where the boat speed (column) is about 1.5 times the river speed (row).

Does that clarify it?

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