General increase of fuel consumption related to weight.

In this times where batteries are no longer only for toys I'm curious how much fuel will be burned because the increase in wetted surface(considering it's not replacing ballast)
Is there a rough factor describing increase with increased weight?

 

I'm greatly disappointed if no one here has an rough estimate for a displacement hull. 50% error is good enough.

 

You should perhaps have provided more detail about the type of boat. There is more involved than an Increase in wetted area.

 

Consider how disappointed can feel someone, who would want to help, when someone asks such a vague question without giving any information, for not being able to answer. Could you, please, focus your question a little more?

 

My question is vague because I have no specific boat in mind. Therefore I also expect a vague and not accurate answer. Would fuel consumption increase 1 or 50% if weight was increases by 5%?

 

A lot nearer to 1 than 50, but without some background as to what your interest in it is, it is not a fruitful discussion. Suffice to say, boats with low speed potential, are more forgiving of weight increases.

 

As you have no interest in precision, I will tell you that, contrary to what Mr Efficiency thinks, I think it may be closer to 50% (for the ship I have in mind).

 

It will depend on the hull and on the speed. The faster you go the closer the drag increase will be to weight increase. When you increase displacement you are always increasing wetted surface, but likely also LWL and all parameters describing hull form and its resistance.

I happen to have the same 8.2 m sailboat defined as 2140 kg and 3399 kg (59% increase in displacement, including crew etc) in my VPP. The LWL is 7.13 and 7.59 m. The wetted surface increased by 19%. The drag increased 16% at 3 knots, 18% at 4 knots, 16% at 5 knots, 23% at 6 knots, 33% at 7 knots, 46% at 8 knots and 56% at 9 knots. Normal cruising speed with 10 hp diesel is 5.5-5.8 knots for this boat (at 3399 kg) and top speed 6.4 knots.

A good rule of thumb for sailboats is that 10% increase in weight decreases average performance by 1%. Note that is not equal to 1% increase in drag.

 

Gentlemen, I must recommend a re-reading of the classics; "Principles of Naval Architecture" for instance. In the displacement mode, Froude's Circle-K and Circle-C show the resistance correlation to (displacement)^2/3. For a 10% displacement increase, the resistance (and consequently the energy consumption) will increase by roughly 6.6% at constant speed and lwl.

For operation at higher Froude numbers (read planing), the exponent is closer to 5/6, or 0,833, giving a power constant = P/(v^2*D^0,833). In Joakim's case with 59% displacement increase, the drag increase would then be 47%.

 

Then making the vessel bigger makes things even more interesting. Comparing the 8.2 m sailboat at 3399 kg to a 10.8 m sailboat at 6701 kg (97% more weight and 50% more wetted suface) of quite similar, but not the same design. The drag change at 3 knots +38%, 4 +35%, 5 +29% , 6 + 16%, 7 -12%, 8 -14% and 9 + 8%.

For a displacement hull there is no general correlation for displacement change and resistance, since the hull is not the same after adding displacement. And at different speeds the ratio of friction drag to total drag changes dramatically (and depends on the roughness of the hull).

A planing hull is a bit simpler in this matter at full planing speeds and with a prismatic hull.

 

For a 5% increase in weight to increase drag by over 25% would be an unusual vessel, to say the least. What was it you had in mind ? All I can imagine is a planing hull that is struggling to stay on plane, and the addition of the extra 5% at a rearward position causes it to fall off into a "hump" mode.

 

Yes, indeed, a boat in a situation of equilibrium (whichever you may suppose), which is broken by a slight addition of weight or by a slight displacement of the center of gravity.
(Monohull in situation of planning, catamaran on foils, ...submarine with zero buoyancy near the surface, ....)

 

We may never know what piqued the OP's interest, TANSL, something tells me he is pondering the effect of loading a small boat up with heavy batteries, and wants to know when it becomes unwise to add more.

 

Sure if the OP gives more details someone could give a more appropriate answer to his problem. But that depends on him.