A challenge to you engineering types.

[river runner]

From reading some of the threads and posts at this site, it seems to me that one of the most fundamental questions in boating has not been definitevely answered. How do you locate the LCB. By this, I don't mean calculating where the LCB is on a design, but where it should be on a design.
For all objects that travel through fluids, the teardrop shape offers the least amount of drag, except for two exceptions: Those that travel faster than sound and those that travel on the surface of a fluid. Here, obviously, we are concerned with vessels that travel on the surface of water.
My understanding is that the reason surface ships aren't teardrop shaped is because of wave-making resistance. For now, let's restrict this discussion to displacement vessels. You planing and multihull types can fight it out later.
It seems logical to me, that at slower speeds, before much of a wave is created, something appraoching a teardrop might actuallly have less drag, but as speed increases and a wave is created, moving the LCB aft would make sense.
Assuming I'm right, seems like there shoud be a table giving you the best location for the LCB for a given speed-length ratio, just as you can look up the best prismatic coefficient for a specific speed-length ratio. Then there should be a way of matching the best prismatic to the best LCB.

[jehardiman]

That question has been answered for over 100 years for the bodies, i.e. ships, that it is worth while to go get the answer for. You need to go read a copy of The Speed and Power of Ships by D.W. Taylor published in 1910. In boats it really doesn't matter because you can just throw power at it, i.e. the cost of finding the the last 10% of the powering answer costs 9 times as much as finding the first 90%; and that last 10% is always going to be hidden in waves, current, and wind anyway. Just increase sail area or put the next size motor in and call it good.

And no, a teardrop shape is not the least drag for motion in a fluid below mach; it is the most efficient; different things. And yes, ther are tables for optimum LCB and prismatic coeff based on Fn. Just go to a good NA&ME school and all the mystery will be revealed.

[DCockey]

Originally Posted by river runner

....
For all objects that travel through fluids, the teardrop shape offers the least amount of drag, except for two exceptions: Those that travel faster than sound and those that travel on the surface of a fluid.
.....

That premise is fundamentally incorrect. I realize it's been repeated many times so it "must be true", but experiments have shown it not to be.

[DCockey]

Originally Posted by jehardiman

.... And no, a teardrop shape is not the least drag for motion in a fluid below mach; it is the most efficient; different things. ....

What do you mean by "most efficient"?

[jehardiman]

Originally Posted by DCockey

What do you mean by "most efficient"?

Highest displacement to expeneded energy ratio including all stability factors for a body fully submerged in the fluid. Basically it takes the least amount of energy to move the maximum mass a given distance at speed less than mach. Notice I didn't say what speed, as that is the issue. This is the whole transport efficiency (ton-NM/kWh) issue that makes ships larger and larger.

FWIW, a cargo ship is ~8 times more energy efficient than a human walking.

[Doug Lord]

Originally Posted by river runner

From reading some of the threads and posts at this site, it seems to me that one of the most fundamental questions in boating has not been definitevely answered. How do you locate the LCB. By this, I don't mean calculating where the LCB is on a design, but where it should be on a design.
For all objects that travel through fluids, the teardrop shape offers the least amount of drag, except for two exceptions: Those that travel faster than sound and those that travel on the surface of a fluid. Here, obviously, we are concerned with vessels that travel on the surface of water.
My understanding is that the reason surface ships aren't teardrop shaped is because of wave-making resistance. For now, let's restrict this discussion to displacement vessels. You planing and multihull types can fight it out later.
It seems logical to me, that at slower speeds, before much of a wave is created, something appraoching a teardrop might actuallly have less drag, but as speed increases and a wave is created, moving the LCB aft would make sense.
Assuming I'm right, seems like there shoud be a table giving you the best location for the LCB for a given speed-length ratio, just as you can look up the best prismatic coefficient for a specific speed-length ratio. Then there should be a way of matching the best prismatic to the best LCB.

===============
There is a table in Principles of Yacht Design by Larsson and Eliasson that does exactly that: page 81-Figure 5.25-"Resistance increase due to non-optimum LCB location".

[DCockey]

Originally Posted by jehardiman

Highest displacement to expeneded energy ratio including all stability factors for a body fully submerged in the fluid. Basically it takes the least amount of energy to move the maximum mass a given distance at speed less than mach. Notice I didn't say what speed, as that is the issue. This is the whole transport efficiency (ton-NM/kWh) issue that makes ships larger and larger.

FWIW, a cargo ship is ~8 times more energy efficient than a human walking.

Thanks for the reply. Are all "tear drop" shapes the same, or is there an optimum diameter to length ratio and profile, presumably dependent on Reynolds number?

[Alik]

The question of optimum LCB is answered in most of systematic series and regression methods for resistance prediction, where LCB is a parameter of series. For general guideline, there is a graph:

[water addict]

Principles of Naval Architecture from SNAME or Hydrodynamics in Ship Design, Harold Saunders has the "design lane" for where the LCB should be.

[jehardiman]

Originally Posted by DCockey

Thanks for the reply. Are all "tear drop" shapes the same, or is there an optimum diameter to length ratio and profile, presumably dependent on Reynolds number?

Actually it is the entrance ellipsoid and aft taper ratios that are dependent on Rn and Fn,(remembering that Rn is effectively constant for bodies of usable size) and that what you are manipulating is the pressure wave speed in the fluid to speed of advance

[DCockey]

Originally Posted by jehardiman

Actually it is the entrance ellipsoid and aft taper ratios that are dependent on Rn and Fn,(remembering that Rn is effectively constant for bodies of usable size) and that what you are manipulating is the pressure wave speed in the fluid to speed of advance

For a fully submerged body which is deep enough that free surface effects are insiginificant Froude number is not meaningful (unless in a density gradient). So the shape would be selected to minimize viscous drag with preventing separation as a priority.

[jehardiman]

Froude number is always meaningful, it is just what you attach it to. I use it in submerged bodies all the time because it relates to the speed of a moving pressure distrubance, depth is irrelevant.

[DCockey]

Originally Posted by jehardiman

Froude number is always meaningful, it is just what you attach it to. I use it in submerged bodies all the time because it relates to the speed of a moving pressure distrubance, depth is irrelevant.

Very interesting. I've always understood Froude number as the ratio of vessel speed to a gravity wave speed, and understood that when submerged in uniform density fluid sufficiently far from a free surface gravity waves are negligable.

[jehardiman]

Originally Posted by DCockey

Very interesting. I've always understood Froude number as the ratio of vessel speed to a gravity wave speed, and understood that when submerged in uniform density fluid sufficiently far from a free surface gravity waves are negligable.

"Deeply Submerged" and "negligable" are the operative words. For real life diameters, depths and speed, that is not always the case. Moving pressure disturbances always prodice gravity waves on the surface and pressure gradients below, wether they are mesurable is a different topic. Go read Lamb to see where the "infinite fluid" simplification gets made. FWIW, I never consider it "wavemaking drag", it is pressure drag period. The surface wave is just the manifestation of the pressure disturbance at the interface. It is always there.