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Best speed and course on a river


Keeping Up

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On 12/15/2017 at 14:44, Alan de Enfield said:

Surely the most economic routes and speeds must encompass more than just  fuel usage.

Time must play an important part in the calculation :

If (for example) you are only achieving 0.5mph SoG and you have 20 miles to go to your destination, then it will take you 40 hours (2 days), this could then involve having to take on extra crew for the 'night shift', or paying for moorings for at least one night (maybe 2 nights), it could also mean you losing a days wages if you arrive back a day later than expected.

If (for example) you are achieving 4 mph SoG and you have 20 miles to go to your destination, then it will take you 5 hours. It may use a considerable amount more fuel, but you save additional crew costs, mooring costs and loss of wages.

So, which is the most economical speed ?

When Keeping Up posed the fuel question, he provided a formula in which the rate of consumption was proportional to speed.  Whilst the formula doubtless had it shortcomings, it did allow the calculations to be run.

So to answer your question, you would need to set out the various costs which are to be taken into consideration and the the circumstances in which they are incurred.   In the world of commercial haulage, wages are a significant factor. 

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33 minutes ago, Tacet said:

When Keeping Up posed the fuel question, he provided a formula in which the rate of consumption was proportional to speed. 

He never said this!  He said, ab initio, that consumption was proportional to RPM cubed.  We are agreed that RPM is proportional to speed. ( roughly)

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40 minutes ago, Tacet said:

When Keeping Up posed the fuel question, he provided a formula in which the rate of consumption was proportional to speed.  Whilst the formula doubtless had it shortcomings, it did allow the calculations to be run.

 

4 minutes ago, mross said:

He never said this!  He said, ab initio, that consumption was proportional to RPM cubed.  We are agreed that RPM is proportional to speed. ( roughly)

In post 1 (aka ab initio)

On 12/13/2017 at 10:16, Keeping Up said:

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,

 

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2 hours ago, mross said:

So, are you admitting that you were mistaken?  Your quote is exactly what I said!

My quote of you is indeed exactly what you said -  as a result of my quoting you exactly.

When Keeping Up said that "the rate of fuel consumption varies (I think) with the cube of your speed through the water" I thought he meant that "the rate of consumption was proportional to speed", which is what I said.    And I can't see any reference to RPM at ab initio.

I may well be mistaken - but at the moment, can't see just how and would ask you to explain more simply, please.

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9 hours ago, Tacet said:

My quote of you is indeed exactly what you said -  as a result of my quoting you exactly.

When Keeping Up said that "the rate of fuel consumption varies (I think) with the cube of your speed through the water" I thought he meant that "the rate of consumption was proportional to speed", which is what I said.    And I can't see any reference to RPM at ab initio.

I may well be mistaken - but at the moment, can't see just how and would ask you to explain more simply, please.

In post 51, you said, "When Keeping Up posed the fuel question, he provided a formula in which the rate of consumption was proportional to speed."

but he didn't, he said speed cubed.

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5 hours ago, mross said:

In post 51, you said, "When Keeping Up posed the fuel question, he provided a formula in which the rate of consumption was proportional to speed."

but he didn't, he said speed cubed.

Thanks,  I see now.   I accept the formula shows an exponential rather than a linear relationship and apologise for any confusion.

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I recon you want to be about a third out from the bank on the inside of the curve, 

assuming a perfect u shaped profile.

If there was no "friction" from the bottom or sides, if you were drifting it wouldn't matter where you were.

once you start moving independently, the shortest distance starts to become relevant. ie the inside of the curve, the more independent speed the more relevant it becomes.

When "friction is taken into consideration, anywhere outside from the center will not be the fastest route.

If you take the profile into consideration it could completely muck up the above.  

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1 hour ago, rasputin said:

I recon you want to be about a third out from the bank on the inside of the curve, 

assuming a perfect u shaped profile.

If there was no "friction" from the bottom or sides, if you were drifting it wouldn't matter where you were.

once you start moving independently, the shortest distance starts to become relevant. ie the inside of the curve, the more independent speed the more relevant it becomes.

When "friction is taken into consideration, anywhere outside from the center will not be the fastest route.

If you take the profile into consideration it could completely muck up the above.  

Possibly ... but I don't know. Let me propose a set of numbers, and maybe those whose knowledge of rivers is more "in depth" than mine can comment as to whether they are realistic or not.

Imagine a river, 100ft wide, flowing at 2mph around a long 180o bend whose inner radius is 200ft; thus its outer radius is 300ft. The distance around the inside of the bend (ignoring the possibility of grounding) is 628 ft, and around the outside of the bend it is 942 ft

The river speed on the inside of the bend is much less than 2mph, say 0.5mph; the river speed on the outside of the bend will be similarly more than 2mph, say 3mph.

Let us imagine a boat travelling downstream at 2mph through the water. If it takes the inside line its speed over land is 0.5+2=2.5mph but around the outside it is 3+2=5mph. These correspond to 3.7 and 7.3 ft per second respectively. So if it takes the inside line it will take 628/3.7=169 seconds, but if it takes the outside of the bend it will take 942/7.3=129 seconds.

Thus taking the outside of the bend is quicker by 40 seconds in this case.

  • Greenie 1
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That may well be about right.  But the figures are the key, of course.

Assuming your river is a constant width and profile round the bend and down the straights (straits?), the numbers you adopt have the start of an implication that less water is flowing round the bend than on the straights, which would be interesting.

My feeling, based on no figures at all, is that the faster flow is worth more than the short cut.  The faster flow accelerates the boat and the momentum will last a bit beyond the curve.  Or is that not logical?

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The Power demand for both the propeller and Craft speed is in theory V^3 (cubed) that goes for car, boat and plane. (with some modification)

The diesel Engine specific fuel consumption is not linear with Power, an mecanical injected Engine that most have use as said earlier here about 0.22 liter per HP at best

but at low rpm/Power it can be a lot more  closer to idle at 10% power it can be 0.3 L/HP

with Electronic injection and or big slow reeving engines it will be well under 0.2 L/HP

Items on the Engine and the Engine itself need some fuel at any rpm to run, like generator load, pumps...

I often see tha equation V^2.8 on boats that will take incount with increased fuel at lower Power settings.

Carson speed is the best time - fuel efficient speed about 1.31 times higher then minimum fuel/distance

 

 

Liter Diesel per HP-h (Power in %)

L_HPh.jpg

Grace and Favour fuel / RPM see the rpm^2.8877 in red, and the theory ^3 in black

Grace and Favour.jpg

My Winga 25 with Penta MD II we see that rpm is not linear with speed, (if the rev counter is ok)

OLIVIA speed RPM.jpg

Edited by Dalslandia
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Thanks Dalslandia that's all fascinating. I'd not heard of Carson Speed before, but it seems totally relevant here.

If I understand correctly, the "best" travelling speed upstream will be about TWICE the speed of the current, unless this is slow enough to bring the engine revs down close to tickover.

Given that on most narrowboats the speed at tickover is around 2mph it suggests that for a slow-moving river with 1mph of current the best speed through the water is a little over 2mph, say 2.5, but for a river with 2mph of flow it would be best to travel at 4mph. I like this, it feels somehow about right.

 

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Did some work on Allan's spread sheet, and struggled with excels poor ability to give the correct equation for a curve, but honestly so did my CASIO calculater too, that normally is very correct, this on the specific fuel usage curve. it is a bit wavy in the curve, but it is boat right?

with the idea that the propeller rpm vs boat speed isn't linear but Close to and vary the fuel useage with Power related to propeller rpm and not speed, but the speed give the rpm...

the result is a bit scattered but in general at very low speed the best boat speed is 2,5 units higher then the river speed, at still Waters the boat best speed is some 2.5-2.75 units, and after that it looks like 2-3 knots higher boat speed then river speed is ulimate not counting time as a cost.

i set the top speed to 10, may that be km/h mph or knots as long as the river flow is in the same units.

By using some 100 hp at 10 knots the Power needed at my privat boats top speed seems to line up pretty good (6.5 knots) and using 0.22 liter per HP and some 0.6+ liter at idle it look good.

 

 

 

Allans_Riverspeeds.xlsx

Edited by Dalslandia
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Don't worry about the extra fuel used going upstream as you will get it back in fuel saved when you travel downstream.

On a tidal river there is, of course, a potential to obtain assistance from the tide both directions - if you time your journey accordingly.

I don't know about the Thames but there are charts for the Trent which show you where the channel is. Deviate from that at your own risk. The channel is usually on the outside of a bend - but not always.

 

 

  • Greenie 1
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1 hour ago, MartynG said:

Don't worry about the extra fuel used going upstream as you will get it back in fuel saved when you travel downstream.

On a tidal river there is, of course, a potential to obtain assistance from the tide both directions - if you time your journey accordingly.

I don't know about the Thames but there are charts for the Trent which show you where the channel is. Deviate from that at your own risk. The channel is usually on the outside of a bend - but not always.

 

 

Yes I've got those.

Coming up the tidal Trent a few years ago, when there was a LOT of fresh, I moved over to make room for an oncoming fully-loaded sand barge and instead it cur straight across Scotchman's Shoal without even touching it!

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