Draft effect on Resistance

Hmmmm..one last attempt. Futile I know..but what the heck!

So, here i stated:

Do you understand this? From your replies, it appears not.

So very over simplistic basic hydrodynamics for you. All in one simple graph, well two actually.

Here, is the change in resistance with a varying LD ratio.



You'll see the more slender the hull the lower the resistance.

And here (graph number two):



You can see the effect of beam to draft ratio. The reason why there is a waffer thin mint's difference between them is...yup...the LD ratio.

But then if wish to start deviating away from pure numbers/theory and go into real practical hydrodynamics, then beam is the key to a successful boat, shown here:



So as the beam increases the stability of the boat increases. Ego, the more narrow the hull the greater the propensity to capsize. Not good!

If you wish to look into the theory of "something" related to a singular discipline of hydrodynamics, then feel free to read up and the voluminous amount of material. It gets heavy but explains all and it is not a 5min read either.

However, if you wish to delve into practical hull design with the end results a vessel on the water, not on paper alone, it is a holistic approach. Since not one single discipline related to a design is perfect. A successfully designed vessel is greater than the sum of it individual parts. Ergo it is all a compromise - often because each discipline is working at variance with the others. Focus on one issue...and you'll get lost, totally, and not understand comments like those from Leo et al. Take a step back and look at the whole picture....then the light starts to shine through...or should!

 

Data per Michelet

Perhaps nothing is wrong. All our experts seem to depend on the formulas which were empirically derived from test tank data over the years. Yet Michelet seems to be telling us that a 67% increase in beam yields only a 7.7% increase in total resistance over a similar hull with same displacement, same wetted area and same friction (less draft). This is rather strong disagreement with the squared relationship usually associated with a change in beam. Think of the fantastic increase in stability in John Perry's example -- Now if we were to have increased beam perhaps only 40 or 50% we might actually show a decrease in resistance -- directly in line with the question I posed in original post --

 

Three different scenarios for comparing "similar" shape hulls with the same length. Water depth is large compared to dimensions of the hulls. Hydrodynamic effects on draft and trim are not considered; ie draft and trim are fixed.

A: Displacement is constant - the product of beam and draft will be constant. If draft is doubled then beam will be halved.

B: Constant beam - displacement is proportional to draft. If draft is doubled then displacement will be doubled.

C: Constant draft - displacement is proportional to beam. If beam is doubled then displacement will be doubled.

For constant draft the wave making resistance will be approximately proportional to the displacement squared as Leo mentions above.

For constant beam the wave making resistance will increase with increasing draft but not as fast as for increasing beam. The deeper the draft the less the increase in wave making resistance for an equal increase in displacement. My guess is the wave making resistance will approach a constant as draft becomes very large.

For constant displacement the wave making resistance will decrease with increasing draft and decreasing beam. As the draft becomes very large the wave making resistance will become small. Asymptotic limit should be zero wave making resistance as the beam approaches zero for extremely large draft.

Remember that wave making resistance decreases with increasing distance below the surface of the source of the wave making.

 

Ad Hoc graphs --

I can get some weird interpretations out of the graphs Ad Hoc presented -- I don't doubt that his first graph of resistance for various L/Ds (to the 1/3 power) while holding B&T constant was plotted from actual test data -- And it clearly states that an increase in the L/D (1/3 power) ratio yields lower resistance -- However, while hull length increases to get a larger L/D (to1/3), displacement also has to increase in order to maintain the B&T both constant -- this means that a longer hull with more weight displacement will have less resistance -- I find this really interesting since it seems to mean that longer heavier boats will require less power -- not much help in resolving my original question -- I had to go through an actual math example to convince myself that the graph was actually telling us this -- Can anyone explain??

 

A longer heavier boat can have less resistance tham a shorter one, at certain speeds, as the result of the infamous "hull speed" factor.

 

Wave making resistance decreases with increasing depth???

Most of what DCockey states above is pertty obvious and I guess we all would agree that a knife blade held vertical should slice right through the water -- But I have some problems with his summary that "Wave making resistance decreases with increasing distance below surface" -- This gets us close to my original question of draft effect on wave making resistance. But I have a hard time accepting the idea that even a streamlined body can be dragged through the water easier than something skimming across it's surface??

 

My understanding is some submarines were or are faster running at depth than on the surface, because despite the increase in wetted surface area, the wave-making resistance is removed.

 

Longer -Heavier vs Hull Speed

Hull speed formula has no weight or displacement factor. But I would agree that depending on speed and wetted area, a long narrow heavy boat might show less resistance than a shorter, wider one, even if the later was lighter and even if the later had less draft.

 

Submarine has no wave resistance

How about a cigar shaped air cannister to float partly submerged with a knife edge vertical rail to support paddler in a seat above water level -- but how to control floatation and how to get any stability w/o an outrigger??

 

Sounds like you are talking about a SWATH.

 

Yes, but I explained that I over-stated the case for the beam-squared
relationship: see DCockey's summary.
Also pay close attention to AdHoc's example where he shows that L/D^(1/3)
is the most important parameter. Once you have that right, most of the rest
amounts to tweaking a bit here and there, and choosing the most attractive
paint colour.

 

Sounds like you have just invented half a SWATH

https://en.wikipedia.org/wiki/Small-waterplane-area_twin_hull

Stability is the problem for a single hull, as you recognized.

 

Not to mention, the higher overall resistance of a Swath compared to a conventional vessel of same Lwl and displacement!!

Nothing in life is for free...

 

Re-inventing the wheel is hard work.

 

jesdreamer, when comparing boats, it is helpful to have some practical measure of merit.

If you use a short list of vessel parameters and operating conditions, such as below -

boat: length, displacement, max beam, max draft, mid ship sectional area, stability (GM).

operating condition: Speed, water depth, sea state, wind vector, fouling.

What you will usually find is when you hold the operating condition fixed and look at "good boats" as you change one boat parameter (such as draft), all the parameters in the boat list will change.

So when some really experienced professionals suggest that you look at the question a bit differently, or relax the constraints you have put on the answer, please try to do that for your own benefit and to keep the thread perking along.

One other point to try to get your head around. Flow disturbance is what creates waves, however, your simple accounting method of equating the distance of flow disturbance to the amount of waves doesn't work. There are hulls which theoretically make no waves at all. All of the energy is recovered, and all of the flow perturbations cancel in a way that produces no waves in the far field. So the rational you proposed of moving more water less far over a greater surface area is not sufficient. You need to know how that affects wave generation specifically. And what looks "similar" to you may not be similar enough as far as wave making goes. So there are proper ways to make this sort of comparison, with practical benefits, and they require some additional freedom in the question and some different qualifications or restrictions in the answer. And happiness is when there is the right combination of both so both a theory and practice yield the same results and new designs can be expected to perform to a certain level with confidence. The folks on this thread want to provide an answer that is useful in predicting performance wrt a range of practical goals. That is why it is such a hard question. It needs to be answered in a context where theory has good agreement with reality, especially for "good boats".