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Anchors come in various designs. As a general rule, the more versatile the anchor, the less efficient it is. The most inefficient anchor we have is the sinker. It does not penetrate the seabed, and only relies on it's own weight for holding power. The fact that it doesn't penetrate makes it very versatile as it is not dependant on soil condition. One of the most efficient anchors is the plate anchor. The plate itself is not heavy, but because of its position one has to move a lot of dirt to displace the anchor. This is not widely in use due to the difficulty installing them properly.

The design one chooses for an anchor depends on several factors:

Usage Pattern
If you are constantly relocating an anchor, then versatile solutions are important. A fluke anchor or a sinker is most often used. On the other hand, if you are permanently mooring something, then a suction anchor or a plate anchor is a viable solution.
Load direction
If your load is going to be mostly vertical, one could consider a suction anchor, a plate anchor or possibly a sinker. Other anchors can handle huge horizontal loads - especially the fluke anchors.
Holding capacity
Some anchors just get too heavy when you are to secure heavy items. While a sinker might hold your dingy in place, its just not practical to anchor a cruise vessel with a sinker - it just becomes too bulky and heavy.
As one can see, the reason for the fluke anchor beeing the most popular onboard ships is that it is versatile and can handle moderately high loads. It is primarily loaded horizontally - so it is a bit inefficient on large depths - but most ships don't moore at sea anyway. The beauty is of course that retrieval can be made automatic, with a push of a button the anchor can be retreieved and stored onboard.

Important things to remember when designing an anchor is:

Adjustment ability
This is both a pro and a con. Most anchors you want to work without having to adjust for soil condition - just drop it overboard and its ready to use. For specialised anchors though adjustability is a plus. Reliability of the adjustable parts needs to be questioned though. Even if you can adjust to a low holding power, you do not want a part to jam - for example pushing the anchor deeper than you can retrieve it.
Breakout force
When it's time to relocate, the anchor should be as easy to remove as possible. Often this is acomplished by pulling in a seperate wire, or for heavy anchors by using a anchor handling vessel. Most vessels moored downstream of the anchor will move up so that they are over the anchor and then pull straight up. This does not work at all with suction anchors.
Burial depth
The anchors holding power is often a direct function of the level of soil penetration. Quicker and deeper penetration makes for a good anchor.
Penetration resistance
For anchors that use the soil for holding power, it is important to use as little effort as possible in setting up the anchor. Ideally the anchor should slide into the soil and then be ready for use.
Scope
For non-permanent anchors (over-nighters) the ability to work quickly is paramount. If you get 100% efficiency the second it touches the seabed, you got a short-scope anchor. A long-scope anchor is laid out on the seabed, and enough chain is given out so that the anchor can orientate itself properly and dig in.
Stability
As the anchor penetrates the soil, it is important that the anchor does not roll or change direction (if it rolls, it will start digging upwards).
Veering Capability
For single anchor mooring systems it is important that the anchor can handle load that rotates around the anchor. A multi-anchor mooring system does not need this capability, as the moored object is most often in the centre of the anchor pattern.

As an example, here are the various anchor types in use:

Fluke Anchor

The most common anchor, this design relies on a piece of steel to embed itself into the soil. The steel is at an angle to the main shaft, so that when you pull horizontally on the chain, the steel will dig into the soil. It has good holding capacity horizontally, but is easy to pull out vertically or backwards. Ideal for sand and mud seabeds.
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Plate anchor

The plate anchor consists of a steel plate shoved into the seabed at an angle. Once the soil has set around the anchor it can handle great loads due to the amount of soil around the plate. It is fairly easy to remove by pulling on a release chain - but it is most often considered a permanent mooring. Military submarines often use this type of anchor as they can dock onto a floating chain without much noise. The anchor has been preinstalled for this purpose on several locations in the Pacific and Atlantic oceans.
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Sinker

The sinker is very versatile, but inefficient anchor. It can easily be dragged across the seabed. Some sinkers are equipped with a small skirt, this will dig into the seabed and give some extra holding capacity. Sinkers are most often made out of concrete - but scrap iron is often used as well.
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Suction Anchor

This anchor uses a pump to penetrate the seabed. It is shaped like a bucket placed upside down, with the anchor chain placed near the middle of the anchor. Actual chain placement differs from various loading conditions. More horizontal pull gives a lower placement, while vertical pull leads to a top mounted chain. To pull out a suction anchor one needs to shear the soil around the anchor, and also lift the soil embedded inside of it. It is a very efficient anchor because of this. When you actually want to pull it out you connect a hose to the pump and blow it out of the soil. This often requires use of a ROV.
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Penetration anchor

This is an experimental anchor for soft soils. To install the anchor it is dropped from just below the surface. The deployment wings will keep the anchor ontarget while it builds up speed to insert into the soil. During insertion its speed will liquify the soil, slowly slowing it down. When it reaches maximum penetration the soil will begin to solidify again. This might take a week or two, so this is a permanent anchor, not a "for the night" solution.
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