Max hull speed

[Richard D]

During other threads people have said that max hull speed is 1.5 x the square root of the length of the boats waterline, in feet, mind you some said 1.4 also. This surely cannot be very accurate as it takes no notice of how sleek the shape is.Is there perhaps a slightly more complex formula that takes other things into account such as weight etc.

Richard

 

[VicS]

In knots?

I have 1.5 to give it in knots but I have edited the reference to read 1.34 times the square root of the waterline length.

For small craft of " normal shape" !

 

[Tranona]

During other threads people have said that max hull speed is 1.5 x the square root of the length of the boats waterline, in feet, mind you some said 1.4 also. This surely cannot be very accurate as it takes no notice of how sleek the shape is.Is there perhaps a slightly more complex formula that takes other things into account such as weight etc.

Richard

It is not "accurate", but just an empirical estimation. Suggest you google hull speed and lose yourself for a couple of hours in the theory. BTW it is not "maximum" - it is just the point at which the power required to get out of the hulls' own waves increases dramatically - so it is only an estimation of the maximum displacement hull speed. It can be exceeded either by breaking away from the waves (planing) or applying excess power.

 

[rob2]

Yes and no - the formla can be adjusted a little with the 1.4 or 1.5 multiplier. But the formula calculates the maximum displacement speed, which is the point at which the bow and stern waves are exactly matched to the waterline. To go faster, the bow must rise over the wave - well actually the wave is generated further back than the bow so the boat can plane.

The difference is that a sleek hull will require less power to achieve this speed.

Rob.

 

[Richard D]

Ok thanks will use 1.34. So how accurate do you think this formula is considering all the diff shapes and keels, rudders, props etc as these must cause diff amounts of drag.

Richard

 

[Richard D]

Yes , I understand the argument about the power needed to go faster becomes impossible to supply but if you compare all boats on the same formula up to this brick wall, you are getting a true comparison. Coming back to my last post surely hull shape, keel, rudders etc must have a baring due to drag.

Richard

 

[Richard D]

The formula is based on the water line, how do you measure this, or is is something you need to find from the maker as they have determined it?

 

[Twister_Ken]

Ok thanks will use 1.34. So how accurate do you think this formula is considering all the diff shapes and keels, rudders, props etc as these must cause diff amounts of drag.

Richard

Drag doesn't matter when it comes to determining max displacement speed. If you have a draggy boat, you just need more power to reach displacement speed, but you'll get there eventually.

 

[MaranaF]

The formula is based on the water line, how do you measure this, or is is something you need to find from the maker as they have determined it?

Unless you want a result accurate to a few decimal places an estimate of waterline length is good enough. If you want to know exactly then wait till your out of the water next and drop a plumb line from each end of the waterline on to the ground and measure it there.

For the pedants... Yes it does have to be on the level and it does change as the boat speed changes.

An old mathematical rule of thumb is the answer should have one less significant figure than the least accurate number used in the equation, for example if your boat is 25.00' long then the sum is sq'root 25 x 1.35 = 6.7kn Note this is not 6.75 as you will see on the calculator, we have removed the lease significant digit...

Does that help?

 

[Lakesailor]

Long, slender hull shapes are easier to drive. Steam launches use this to achieve high speeds with limited power. Typically the faster ones will have a 10:1 lwl/beam ratio

 

[jdc]

More sophisticated calculation

There are more sophisticated methods for calculating resistance (aka total drag - forgive the pun;-) as a function of hull speed than simple 1.4 x sqrt(LWL). Whether more useful for any practical purpose is another matter...

Available from the web there is a program called HullDrag/32 for instance which breaks it down into elements of viscous and residual (wave), and makes allowance for keel, rudder and excess roughness among other factors.

You can also use a cruder formula for wave making drag as follows:

F_num = U / sqrt(g * L);
Cw = 0.0022 * exp((F_num - 0.33) / 0.057);
Rw = 0.5 * rho * U .^2 * S .* Cw;

where F_num is the dimensionless Froude number,
U is speed in m/s
g is acceleration due to gravity
L is LWL
rho is density of (sea) water
S is surface area of hull, including keel

Embedded constants (0.0022 etc) are my estimates from fitting a simple formula to a more complex integral.

To illustrate this for my boat (42', longish keel, big skeg and rudder) see this graph. The red stars are from the Hulldrag/32 program and the smooth red, blue and green curves are from my simplified formula. Blue is viscous (frictional) drag, green is wave drag and red is the total. LWL for me is 10.2m (33.4'). Agreement is quite good.

Hope this useful!

 

[Tranona]

Yes , I understand the argument about the power needed to go faster becomes impossible to supply but if you compare all boats on the same formula up to this brick wall, you are getting a true comparison. Coming back to my last post surely hull shape, keel, rudders etc must have a baring due to drag.

Richard

No, as Ken says drag just affects the amount of power required. Similarly weight is almost irrelevant - again offset by power. Length beam ratios do have an impact as the examples of long thin powerboats and multhulls show.

There is very little difference between different hull shapes - and for sailing yachts both engine and sailpower is usually sufficient to meet the displacement point when at full power - although under sail it is easier to overpower on certain points of sail, and therefore start to break away, particularly if helped by waves.

Under engine, most yacht auxilliaries have only just sufficient power to achieve "hull speed", but even if overpowered, for example with a 40hp instead of 30hp, that extra 10hp is insufficient to make much difference at the maximum. You can often see that in practice with yachts creating huge bow waves - but not going any faster than if they back off 3 or 400 revs.

Still not sure why you want a "true comparison" - the only factor that influences the point is waterline length - the longer the faster. Not all boats achieve with the same waterline length achieve the same speed because of lack of power in relation to weight and drag.

 

[mitiempo]

There are boats like in the pics posted by Lakesailor that are not as bound by the 1.34 number. They are not true displacement but semi-displacement boats. They are able without a huge increase in horsepower to achieve faster speeds than the 1.34 suggests without having to climb over the hump of their bow wave. Long and narrow means also that the "hull speed" of 1.34 is reached with less power as drag is reduced.

 

[maxcampbell]

accurate

Don't you mean "precise"?

Sorry, just wanted to join in.

 

[sailorman]

The formula is based on the water line, how do you measure this, or is is something you need to find from the maker as they have determined it?

as the hull heels the wl increases thre fore the hull spd increases, this led to the quirky designs under the IOR

 

[MaranaF]

Don't you mean "precise"?

Sorry, just wanted to join in.

Pedant.

 

[VicS]

Long, slender hull shapes are easier to drive. Steam launches use this to achieve high speeds with limited power. Typically the faster ones will have a 10:1 lwl/beam ratio

The formula applies to hulls of "normal shape". that proabably excludes the steam launches.

Pierrette is 44 ft long x 6'6" beam. Said to be capable of 20mph when new

 

[Lakesailor]

Mosquito is 46' with 6'ish beam. The 17 mph recorded on Windermere was a politically correct kind of statement, apparently.

 

[jdc]

rowing viiis

The formula applies to hulls of "normal shape". that proabably excludes the steam launches.

Pierrette is 44 ft long x 6'6" beam. Said to be capable of 20mph when new

I think the formulae also apply, or at least the normal analyses are used, for rowing viiis, which are nearly 20m long and only ~60cm wide at the widest point. Google will oblige. The thing is that viiis, despite being of extreme aspect ratio are still entirely displaement craft, so the near exponential increase in drag with velocity still applies.

As I know too well from a lifetime going backwards, the speed of an viii when racing is well above the hull limit which is one reason there are such slight differences in speed - maybe 30m in a 3000m race or 1% - in a bumps or head race despite, I assume, much bigger differences in fitness or power output between crews. Simply put, to go a tiny amount faster one needs to do loads more work.

 

[westernman]

I think the formulae also apply, or at least the normal analyses are used, for rowing viiis, which are nearly 20m long and only ~60cm wide at the widest point. Google will oblige. The thing is that viiis, despite being of extreme aspect ratio are still entirely displaement craft, so the near exponential increase in drag with velocity still applies.

As I know too well from a lifetime going backwards, the speed of an viii when racing is well above the hull limit which is one reason there are such slight differences in speed - maybe 30m in a 3000m race or 1% - in a bumps or head race despite, I assume, much bigger differences in fitness or power output between crews. Simply put, to go a tiny amount faster one needs to do loads more work.

A good VIII does 2000m in 5min 30 seconds. I.e. 21.8 km/h or about 11.8 knots. An Empacher VIII has a waterline length 16.92m long. I.e. 55.51ft.

This is a bit faster than 1.34 * SQRT(LWL) = 9.98 knots.
However, we know that this formula does not apply to hulls which are very much longer than their width.

If this displacement speed was a limiting factor we would see a trend to much longer VIII's. The fact that the first choice for many years for top flight international crews, the Empacher VII is actually shorter than some eights in production suggests that other factors such as skin friction are more important.