Jump to content

Boat Speed/Power Maths


clbrof

Featured Posts

Hi

 

What are some of the governing laws (maths not 4mph limit etc) that limit a boats speed, also is it possible to work out a rough speed dependent on engine power?

 

Does double speed quadruple drag apply to boats?

 

Thanks

Link to comment
Share on other sites

I believe there are several things which govern a boats speed. Hull length is the obvious one but on most canals and rivers in England probably not the major factor.

The volume of water that the boat is travelling through has a big effect, a large boat in a small channel will travel slower than a small boat in the same channel.

Power factors work the same as far as I know for boats, as they do with cars or even hi-fi. Twice the power will not equal twice the speed for any given boat.

Link to comment
Share on other sites

In principle a Narrowboat is a displacement boat - however it is not acting as a typical displacement boat in that it is a 'floating brick' and has no 'depth' in the water (no keel)

There is a formula for 'proper' displacement boats.:

 

Generally, the larger the boat, the faster it can go. For a displacement boat, a heavy deep-keel boat, the maximum speed a given hull can attain is called "hull speed" and is largely dependent on the waterline length of the boat. Hull speed is expressed as 1.34 X the square root of LWL, or length of waterline. If a cruising sailboat has a waterline length of 36 feet, she should be able to sail 1.34 x 6, or approximately eight knots.

 

With a displacement boat you cannot exceed the hull design speed, just increasing power (bigger engine) just increases the size of the bow wave but does not increase the speed of the boat. As a guideline, to achieve max hull design speed you need 1hp per 4 tonnes of displacement.

Link to comment
Share on other sites

A displacement boats speed does increase as the bow wave increases or the bow wave wouldn't increase. Not by much I admit, but little by little, until if enough power is turned on the boat will bury itself in its own trough and sink.

Years ago the ship QE2 was delayed by storms on its way up the US eastern seaboard to New York and was steaming almost flat out when the hull struck the sea bed and damaged the stern gear. The sea was shallow just there which the ship normally sailed over safely at a moderate cruising speed. But because of its extra speed which had lowered it by an extra 9ft or so in the water it struck bottom. The ship had to be docked. Crew incompetence, perhaps they thought it would rise up and plane.

Link to comment
Share on other sites

Most of the empirical data out there is for boats in open water. In the restricted channels most of us boat in your speed is more limited, and any attempt to go faster will use a lot more fuel, with little if any increase in speed. Sometimes cutting the revs can result in going faster, due to the reduction in pulling the stern down.

Link to comment
Share on other sites

With a displacement boat you cannot exceed the hull design speed, just increasing power (bigger engine) just increases the size of the bow wave but does not increase the speed of the boat.

 

A popular myth but completely untrue. Adding more power will always make a boat go faster, but is subject to diminishing returns. The returns diminish pretty steadily. "Hull speed" is just the speed at which the wavelength of the bow wave happens to match the length of the hull. There's no vertical cliff in the speed/power curve at that speed.

 

Good writeup here, including some of the history of where this notion came from: http://www.boatdesign.net/forums/boat-design/hull-speed-1220.html

Link to comment
Share on other sites

If it helps, my 33', 6 tonne, 20" draught nb could barely make the 5mph speed limit when I timed it past the markers on the Thames. My, probably over-propped, Vetus M3.10 claims 20hp at 3k rpm but I could only get, a very noisy, 2,800 rpm. All other traffic was overtaking me.

 

To reach the hull limiting speed in open, deep water would require at least twice as much power. On a narrow, shallow canal or river, like the upper Thames you can see the bow wave meeting the stern wave creating an obvious depression near the stern. A little more power and you are making a breaking wash and going slower.

 

Alan

Link to comment
Share on other sites

If it helps, my 33', 6 tonne, 20" draught nb could barely make the 5mph speed limit when I timed it past the markers on the Thames. My, probably over-propped, Vetus M3.10 claims 20hp at 3k rpm but I could only get, a very noisy, 2,800 rpm. All other traffic was overtaking me.

 

To reach the hull limiting speed in open, deep water would require at least twice as much power. On a narrow, shallow canal or river, like the upper Thames you can see the bow wave meeting the stern wave creating an obvious depression near the stern. A little more power and you are making a breaking wash and going slower.

 

At 33' your hull speed is 7.76 knots or about 9mph. At 60' that goes up to 12mph. Narrowboats are not generally going anywhere near hull speed.

Link to comment
Share on other sites

When below "max hull speed" speed increase with increase in power ^1/3 or 3th Root of P

so double power (x2) speed goes up with 26%

in reality I seen speed goes up with 2.8 or 2.9 root factor

 

can also be used the other way, how much power does it take to go ??% faster?

and even to increase propeller RPM,

= V1/V0 ^3 (cube factor)

 

drag goes up with square factor! Thrust goes down linear with speed

 

So if we increase speed from 3 to 4 (sort doesn't matter) 4/3= 1,3333^3 = 2,37 times more power and fuel is needed

 

This doesn't account for shallow or narrow waters

Edited by Dalslandia
Link to comment
Share on other sites

The limits in a small cross-section waterway like a canal are completely different to open water, since the displaced water has to flow backwards between the hull and the canal banks/bed -- if the canal is narrow you can easily see a downhill slope on the water level from bow to stern by looking at the drop in bank water level. So you're effectively going uphill, which absorbs a *lot* of power. For a long narrowboat in a narrow canal this kicks in much sooner than the open-water hull limit. Even if the canal is wider but it's shallow, the problem then becomes the stern "sitting down" under power, more throttle just makes it dig in deeper but hardly increases speed.

Link to comment
Share on other sites

When below "max hull speed" speed increase with increase in power ^1/3 or 3th Root of P

so double power (x2) speed goes up with 26%

in reality I seen speed goes up with 2.8 or 2.9 root factor

 

can also be used the other way, how much power does it take to go ??% faster?

and even to increase propeller RPM,

= V1/V0 ^3 (cube factor)

 

drag goes up with square factor! Thrust goes down linear with speed

 

So if we increase speed from 3 to 4 (sort doesn't matter) 4/3= 1,3333^3 = 2,37 times more power and fuel is needed

 

This doesn't account for shallow or narrow waters

And for another way of looking at things, see how much less fuel you use by going just a little slower.

  • Greenie 1
Link to comment
Share on other sites

I try to do 6.0 - 6.3 kts on the lakes, for 2,5 h of a total 5 h trip.

if I go 7 kts average, 0,85 kts more

it would take almost 50% more fuel on the lakes that's 20 litre a day, or 1500-2000 litre per season

Edited by Dalslandia
Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.