Hand sharpening vs. Using a system

I think that those guys are professional grinders and that can use their tools to levells we cannot. They probebly work 16 hours per day 6 days per week and that they started to work when they was about 6 years old.

I use very little pressure, sometimes i even lift up the sharpener to get less weight. When I make precission grinding I sometimes add special weight pieces so that the pressure stay the same withbaton s small variations as possible.

Long blades needs support from below. That makes it important to have also a wide grinding table. I have construct myvtoolsmy Chef so I can have very wide grinding tables - and I have also other types of support if needed. Yes, it is important that the blade do not move in any direction.

Yes, what precision is needed? Is 1/100 part if 1 degrees enough - or do we need 1/1000 part of 1 degree :)
For a standard beltknife I think 1 degree precission are enough. For a scalpell we need a better precission then that to reach - and understand - to make the perfect edge on scalpells. We also need something that can meassure thise small angles. Perhaps that is the next step ?

I have made a tool that can sharpen icedrills, its name is IcePal.
The best thing with IcePal is that no one can have a opinion about the edge quality after that IcePal have sharpen the edge. Only the ice can tell the quality of the edge. Ice drills drill - or not. There is nothing in between, it works - or it do not work.
Ice drill edges have three dimension edges. The edge angle change from 40-20 degrees along the edge. The edge is screwed - and also concave. IcePal shapens all three dimensions at the same time.
A knife edge have only 1 dimension on its edge...and people have trouble to get knife edges sharp.

Thomas
 
This is one of the more interesting threads I've read in a while. Nice to see a conversation that is based on real, substantial experience with freehand sharpening and with sharpening tools, and with folks from different perspectives staying civil and just continuing the discussion. Please continue, it's a great read. :D

Responding to the OP's question: How do you guys sharpen your knives and why?

In my case, 100% manual sharpening. About 90% of that is unguided freehand on stones, with about 10% being cases where I still use Sharpmaker for some things that, to me, it just makes easier and faster. Like recurves, serrations, or cases where I want to set a very cosmetically consistent 15 degree bevel. I've been chatting in PMs with a few folks like Heavyhanded about eventually getting into a belt sander ONLY for cases where I want to grind and change the blade profile, basically for fast metal removal/shaping but not really for sharpening. Currently I'm investigating one of the Kalamazoo 1/42 belt sanders, I think they are well made, run at a lower speed that's good for sharpening, and there's a wide variety of belts/abrasives available to use with that. I considered a KOWS unit with the BGA, as I know some here think highly of it, but when I consider my main use will be not sharpening but fast blade grinding, I think a larger belt and more powerful unit, with more choice of abrasives, will get that job done more efficiently.

I don't view my results or approach as superior to any other method. I can see there are folks who become master sharpeners and get fantastic results using manual guided systems like WE/EP, and other get the same using powered systems whether specialized belt sanders, wheel grinders, or even KOWS. My motives for going to freehand are not because I think I can get better results than a skilled user of a guided or powered system. It's also not because of any illusion that one can get a perfectly flat v-beveled edge (anybody who freehand sharpens for a bit will realize there's always a degree of convex, even when your edge looks 'mostly' flat--it's a question of degree and there will be some convex present).

My main issues for going to manual freehand sharpening are:
  • Can sharpen anywhere (as others said).
  • Speed. Folks using other systems will dispute this I'm sure, but to me, when I'm in a mood to sharpen, I enjoy just being able to grab a knife and a stone and get to it. Don't need a bunch of fancy settings, attachments, swapping out stones, clamps, belts, etc. The setup and teardown times are very minimal, and because I usually only eyeball the 'settings' (edge angle, etc), I can just get to down to sharpening very fast, and finish very fast if I want to. Now if doing major blade grinding--totally agreed, you want powered gear for that, I've tried doing a total blade reprofile by hand, it takes forever.
  • Simplicity and lower startup cost. Although it is very easy to get into freehand sharpening and blow a lot of money on stones you don't need, and some of us probably do that. :rolleyes: But, it is ALSO possible to get into it for a very minimal startup cost, just a handful of quality stones, and you'll have all you'd ever need. They don't take up much space, don't cost much, are easy to setup, easy to maintain, and unlike guided systems that are constantly changing, you don't have to worry about your stones becoming outdated and no longer supported.
  • Satisfaction. I enjoy doing something with my hands precisely because it is NOT controlled by a machine, or software. It's hard to describe, just get a sense of satisfaction in still retaining a few old world manual skills, even though most of the world around us is becoming completely mechanized and automated. Sharpening is not my profession, so I'm not in a hurry, and not charging people for the work, so I'm not really under any pressure to get cosmetically perfect edges.
  • Great results. As above, I wouldn't claim I can get any better results doing freehand than skilled sharpeners with other methods. Of course not. However....I can get very, very sharp edges, and without a lot of time and fancy stropping steps required. I actually do better now with freehand than I've ever done with any past guided device including Sharpmaker. It's partly due to learning, and partly due to being able to select any abrasive I want and use the best one for the job. I am getting edges that are sharper than any application I currently need from a knife, and plenty durable, and don't look too bad either. :p There is always some degree of discernible convex in my hand-sharpened edges, but that is actually ok, as HH cited above, a small degree of convex at the edge can actually enhance cutting performance. And I agree with 42 and others that for freehand cutting applications: the quality of edges one can get by freehand sharpening are more than adequate. A higher degree of precision is not necessary or required, though of course if one wants that (for cosmetic or other reasons) and willing to spend all the $$ and hassle for the setup, more power to them!
When I look at the whole balance of costs, needs, and results--I still come down on the side of favoring freehand sharpening for ordinary sharpening needs. It's simple, fast, gets the job done, and fun to build the skill. The only place I'd look to get a powered sharpener is for specialty jobs like blade grinding where it would really speed up the process.
 
Maximus83,

I like manual sharpening. I did that for 40 years. I lived in the high mountains innthe north part of Sweden with the Sami people for 20 years and my knifes was my only tools and I use them dor eveeything I did, from making things to repair things, skin games and butcher them to butcher fish - and I use them when I was eating. Every evening I sit beside my fire and maintained the edge and it become a sort of Nirvana.

I lived like this about 6 month per year. It was total wilderness so everything was made by hand with the help of handtools, axes, knifes, chissel, saws and so on - when I was home - and with my knifes when I was out in the mountains.

When sharpen by freehand daily during 6 month was a good school - I could se what happens to the edge - and how everything adds up. When I understood whats happend I start to leran how fo avoid it. My edges was to start with flat, they become convex - and I learned how to hold them in 3 degrees convex sphere in that way that the xutting edge angle did not change. This was in the early sixties. I started then to think about how to construct a sharpening tool that was small and strong and that could grind both flat and convex edges in any wanted edge angle. Manyvyeqrs later I make my first sharpening tool, it tqke ne 3 years on more then full time and I named my tool "Edge" that later become EdgePal from that tool when I have made some more tools. One of my grinds like to have a Edge tool so I made one dor him, his friend like to have one also - and I am still on that road...

I like to identify sharpening problem and then make tools and solution that solves that problem, dor example the bended or angled guide rod that nake it possible to grind convex edges with full control of the edge angle and the convex sphere. Today this is my hobby

Well, my tool edge and al the construction work I have done during 3 years and more then 200 prototypes with all testnings leran me a lot of things. One thing was the differance between a freehand sharpened edge and a edge that was made with a sharpening tool. There was no tools for axes so I construct my tool AxePal with its magnetic fot, and later IcePal and last, Chef and Forest.

Besides those tools have a make very special tools for very special needs and some xomplete solutions dor companys that use edge tools and machineparts in their production - and now they can sharpen them their selfs.

I am also a knife maker thins the sixties and I have also work a lot with wood, especially curly birch.

So, that was a little about my background - and why I make sharpening tools :)

For me is sharpening skill not to make an edge as sharp as possible - it is to make an edge as sharp it need to be for its purpouse = balanced between sharpness and retention. If you can so it by hand or with a tool do not matter, so it any way you like - and are you happy with the result - I am happy also :)

Thomas
 
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Freehand on various stones, Sharpmaker (enhanced by Congress Tools), or Edge Pro depending on the amount of work or refinement required.
 
As I have write above, edges develops out of needs (and use). If you are happy with your edges, dont change anything, keep doing what you are doing.

I like to know what edge angle my knifes have. When I change the edge angle I do it for a reason, i need to change the edge becouse my needs have changed - and I change my edge to what My needs are. I know the result of the change before I change the edge and I know what levell of sharpness I need to have. But that is me - and my needs.

When you sharpen by freehand you do not know what edge angle you give your knife. You know that your knife get around, for example, 20 degrees. It can be 18-22 degrees. If you are skilled, 19-21 degrees.
When I grind a edge I decide the edge angle to be for example 20 degrees - and I get 20 degrees. Not 19,5or 20,5 degrees. Of cause, I often use Angle Cube and Angle Cube are not exact, it varius +/- 0,1 degrees. If needed I can calculate the angle so I get exactly 20 degrees - but I do not do that often.

My point is still, if you do not know what edge angle there is on your knife, and change the edge angle, you do not know where you started, you do not know where you landed,myror do not know the distance you have travel - and what can you learn from not knowing what you have done?

When you know what you have done you can also evaluate what you have done - and that give you knowledge and understanding about how edges work and warns.
Once again - but that is me - i allways try to learn more...

I like to know the history about things, what did my forefathers do and why, what tools sid they use, and why. I experiment a lot, try things - and when I make things I use the monkey method = sucsess by failur. I make a lot of prototypes and test then hard. When I constructed my tool Chef I made more then 200 prototypes. That is a lot if prototypes - but I have not got any reason to change Chef for 10 years, i did my misstakes on my prototypes.

To understand what I write about, by two Mora knifes of the same modell. The edge holds 11 degrees per side = total 22 degrees. There is a very tiny hooning edge that holds around 3 degrees higher angle = 14 degrees. Change the honing edge 1 degree higher = to 15 degrees on one of ghe knifes - and use both knifes in the same piece of wood and just whittle in the wood. Notice the differance in performance and more power you need with the knife who have the steeper angle.

You dont feel it at once - but you will feel it after some minutes, especially when you change back to the Knife with the lower edge angle. And - that is just 2 degrees differance....

Thomas
 
Good discussion. On some I sharpen, I know the angle and on some I'm close. As long as the bevels are even and fully apexed the knife will be sharp. Will a customer using the knife be able to tell which cut better and longer? I doubt it. They do know if it's sharp. So, the burrs must be removed. I do all freehand.
Many knives I sharpen are badly convexed and recurved. Plus, have nicks in the blade with a flattened point or broke. Try working all that out on a clamp in device, in 15 minutes with a 8" scimitar blade. Sabatiers are easier because no belly. At shows I see vendors with a angle device. Rarely someone who freehands. Persons doing business calls in the parking lot do mostly freehand. Some I see are talented with stones and
can rework a broken tip knife to look new. Blending in the bevel to match the existing one. Talk about a learned talent... These type conversations we will only read here in Blade Forums. No one engages me in one out in the real world. Still, it's what we are about. DM
 
I sharpen freehand, but occasionally use an angle guide (Buck Honemaster). Works for me.
Ed, I talk with some who use the Buck Honemaster. It was patented in 1978. Since you have one hang on to it. It's not often I see them for sale. The last year Buck offered in their catalog was 1985 / 86. They were well built. DM
 
1. Sharpening tools where the knife are fixed on the grinding table and tye sharpening angle are locked give 100% flat edges if a straight guide rod are used, it CAN not be anything else then flat, the law of fysics rules.

2. If the knife is not fixed in its position, or, if the angle is not locked - it do not give a flat edge. The edge WILL be convex and the cutting edge WILL not be straight.

These are facts.

In this thread freehanders and tool users have write about both freehand sharpening and sharpening with a sharpening tool.

Freehanders have write that it is impossible to hold a constant angle by freehand and that they varius in angle with, at least, 1,5 degrees per side = 3 degrees total.
I am a tool user and I say that the wobble cant come below 3 degrees becouse 34 joints innthe human body are involved innfreehand sharpening.

Freehanders have told that to be a good freehander omlott of experiance are needed = many years of freehand sharpening - and - with that - it is atill impossible to make a 100% flat edge.

With a sharpening tool, where both the knife and the angle are locked - any one can make a 100% flat edge the first time they use the this tool.

Internet is amazing. Anyone can clime anything - and it is very hard to control what is clamed...

So, to end this never ending discussion about how good freehandsharpener people are - a demand is necesarry (in my mand). When a person clime that he, or she, can hold a constant angle, or, can come below 3 degrees wobble, they have ro prod it with a video with the laser toll I show a drawing of earlyer in this thread. Without this video their clime is only a clime = it is not a fact. With showing it on a video with the laser pen - the clime will be a fact - and facts are allways interesting to discuss becouse from facts can we learn.

I have discuss on forums thins 15 years back in time. There is many myths in sharpening - and not so many facts. I am interested in discussing facts - not myths.

Convex edges have been discussed long time and they was seen as superial all other types of edges by a lot of people, today, after about 10-12 years discussions are convex edges back to fakta again, it is only a type of edge along other types of edges, good dor some things - and bad fo other things - ans that is exactly why we have different types of edges. No edge type is superial other edge types. This discussion took 10-12 years - and sometimes this discussion was really hard.

Freehand sharpening means wobble. i say tyat you cannot come below 3 degrees wobble - please, prove me wrong with facts - not myths. Show a video where you prove that you can come below 3 degrees wobble = where you are in the video, the sharpener and knife are inthe video - and the fd point are innthe video, all in the same time - and where the red dot stay in the horisontal line on the target. THAT is a prof of your skill - and a fact. Everything else is only a clime...

Let US not mix facts with myths.

All over the world, humans have, for thousends of years, search facts, from facts canntake innovate things. Precision is needed everywhere - the only thing where precision is NOT needed is in the sharpening process :)
People even dis not know that their forefathers use both guides and sharpening tools and that we can tra k them back at least 6000 years.
In most forums freehanders clime how good they are and that they wobble "just a little" (for 10 years ago many clime that they did not wobble at all and that their results was better then what sharpening tool can perform).

Then - i have no problems with freehand sharpening. I did that during 40 years - and I was happy with the result, it worked fine for me, then.
As I have wrote before in this thread - if you are happy with your edges - keep doing what you are doing, dont change anything. You fullfill your needs.

Accept that other people are other needs. Dont write that higher quality is bit needed - write that YOU dont need higher quality.

the three most important things in sharpwning and knfe use are: edge angle, edge angle and edge angle.
Sharpening skill for me is to be able to give a knife the edge angle I want the knife to have and to balance the sharpness with the wanted retention so that the knife hold its sharpness as long time as possible.

I can discuss this things with very few people becouse most people today sont have a clue what edge angle they have on their knifes... They are happy that their knifes are sharp....

The next thing is that in the west world 90% if the population lives in citys, on forums 99% if the members lives in citys. City people edges holds around 40 degrees total. Traditional edges holds around 20 degrees total. That is perfextly normal with both edge Nikes bexouse city people Alice and cuts in harder material then traditionals do = the edges have developed out of needs abd out of use, harder materials needs steeper angles.
But - traditional old knife knowledge have not survive in citys.

This can be explained best with a new type of knife: the survival knife :)
A survivel knife shall be tough,nit shall hold ro chop with, batoon with, bend with, been used as a throwing knife ans hold to be used as a spearhead - and of cause hold to make up fire with.

In reality: if you ever come in a survival situation you really need to take care about yiur knife becouse your life depends perhaps on your knife abd that your knife works and that your knife are sharp. NEVER chop, throw, batoon, bend with your knife. Use your knife to make tools you canbchop, throw, batton and bend with. Uf thise rools broke, use your knife and make a new tool. If your knife broke - you probebly will die.
Was that a understandble explanation?

So, today we have two big knife developing lines, the traditional line and the city living line - and they are veey different needs in this two lines.

Go back a few deccades, as hunting knifes folders was never used. Today, city hunters use folders as hunting knifes - traditionals never use folders as hunting knifes.

IF a folder are used as a hunting knife this dolder needs to be taken apart and it must be cleaned and then boiled in at least 20 minutes - all parts. If this is nit done - I will never eat anything this folder have been in contact with. Still, folders are today used as hunting knifes...

I dont know how many times people have explain for me how good their knife are or how fantastic quality its steel have "I have use this knife for 20 years and it is the best knife in the world" they say (or similar). When I read the blade I can se that the fakturie edge is still there = this knife have never been sharpened = this man have carryed this knife in his belt for 20 years - but never use the knife... This is very common...

A used knifes blade are more or less grinded away after some years use. All traditionals knows this - few city people do. Traditionals can read a blade and se how it have been use, often ro what it have been used - and how many times it have been sharpened. When a knife is used it gets dull - and it need to be sharpened, every sharpening take away material from the blade - and the vlade gets more and more narrow.
When I lived innthe mountains a knife hold for me 5 years, after 5 years the blade was so much sharpened that I did not trust the knife - and it was time for a new knife.

When People come to you and talk about how much they use their knifes, read the blade, in normal use for me about 1 millimeter of the blade width are grinded away per year. You can se this where the blade go in to the handle. The where tells how much the knife are used - not the knifes owner...
If the owner climes that he have use this knife a lot - you know how much...

I think what I have just wrote can be seen as provocative. It is NOT written to be provocative at all, it is written becouse I like to be able to discuss facts - not Myths and climes. Read it with a positive mind please.

Thomas
 
I use both
when it needs a bevel set, or some real work on the edge, or i get the urge to polish it up - i use a fixed angle system

after that, if i just need to sharpen or touch up an edge that is already set - freehand.

learning to really sharpen using the fixed angle system, by reading and researching on this forum, has increased my understanding and my freehand abilities.
 
I got an EP when I started. The ergonomics and the fiddle factor were not for me. Standing there with my head down and grinding away; change hands an repeat. Change stones, fiddle and repeat. Uuugh!
I had a set of 2x6 DMT stones and started freehanding. Ahhh!
 
The best I can come to by way of comparison would be hand sharpen something and put it on a jig, make a few passes and see where they don't match up.

I actually did just this when I was building my guided system, and most often I lost the angle at the belly. At the tip and heel the angle was close enough the scratch pattern overground in a few passes. The belly normally needs more work but still probably under 2 minutes/side.

I could try to fit in a test of this sort in near term, but unfortunately I'm busy wringing out the guided option for doing convex hair shears on my guided widget and that's going to be my priority for a few :p. Hey, the cosmetics count!

Another maybe more pertinent test would be to have people who believe they are good at both, sharpen em up and see if they can tell a difference in quality or longevity of the actual edge in use.

I myself did not, but I did notice once the edge was set on the system, follow up sharpenings removed very little steel - probably less than freehand but hard to tell. Another test would be needed...
 
Hi David,

I am very tierd after my treatment against my cancer - but I feel my self stronger and stronger - but it Is a slow progress - but never the less it is a positive progress :)
 
Heavy Handed, i think it would be very good to try to kill all myths - and that it will benefit everybody that sharpens their knifes.

Freehand sharpening is good enough for most people - but after some time, depending on how often they sharpen their knifes, the edge will be so convex that the edge so not function any more - and that point are named reprofilling = get the edge back to the starting point again. This is the point when all small "wrongs' have add up to a big wrong :)

We must also understand that some people never come to this point, they do not sharpen their knife so often that this become a problem for them - but others can identify this problem after some weeks of using the knife.

Most people clime that they use their knife "a lot". But what is "a lot" ?
I think that a butcher who use his knife 8 hour a day 5 days per week use his knife a lot. He can warn out a knife in a week. Dor me it takes 5 years - so I do not use my knife a lot compare to a butcher. I use my knife a little. Perhaps 5 minutes per day now. That means that I need 96 days to use my knife compare what a butcher use his knife per day...

If you use your knife 1 minute per day... You need to use your knife 480 days compare to a butchers day off work.

To se what I am talkning about needs some good instruments, you, or I, cannot freehand sharpen a knife and then compare it with a sharpening tool. The differance is to small and it is very hard to se the differance - but after 10 or 15 freehand sharpenings it is visibel - if you use permanent magic pen (this pen give ink on the blade that is 1/100 part of 1 mm thick when it have been in use for a while - and a white board pens ink is 100% thicker = 2/100 part of 1 mm). One more thing, to compare this the freehand sharpening must be in wanted degrees, let's say 15 degrees - and then be compared in a tool in 15 degrees - that tells the quality of the freehand 15 degrees.

About the belly and the tip..
My tool Chef have allways a distance between the cutting edge and the pivot point if 28 cm. To meassure this distance are simple becouse there is markings for this distance on the guide rod, it takes only some seconds to meassure the distance and adjust for the belly and tip so that they holds the same edge angle as the straight part if the edge do. Alternative, in this fixed distance, 28 cm, 1 degree = 25 mm = 1". If the blade is 15 mm wide - the change will get 0,5 degree lower angle on the tip compare to the straight part of the edge - and most people can live with that I think...

About convex edges on scissors.
I invented the bended/angled guide rod that give true convex edgesL I did this for around 15 years ago, during 2017 some of my "competitors" have come out with some variations of my invention, instead of a bend or angle they use a knee - and that is perfectly ok for me that have copyright on my invention.
You can use a knee, or discuss other solutions with me to get convex edges to scissors. I am happy to help you.

Yes, that is correct, to make, and then maintain edges with tools take away very little material from the edge, far less then forehand sharpening do. Every maintapainens sharpening is a continuing if the first sharpening you did - in exact the correct angle.

Thomas
 
I would be happy to share a video/pics of my newest widget and of the current one I use for guided sharpening!

I do have a bit of issue re the loss of angle over time. I do not believe this happens with skilled persons, at least not reliably. That is another thing I was able to check with my Beta versions - I shoot for freehand between 26 and 30 degrees, 28 being optimum. That is what the angle had to be set for to hit the bevel square on every knife I put to it, with exception of pronounced bellies that were a few degrees less acute. I was surprised, but not entirely.
 
HeavyHanded,
You can send anything to me and it will be safe with me - and from me :)

Skill or experiance do not help with this wobble, you, and I, wobble at least 3 degrees when we sharpen freehand - but you do not se it at once, you see it over time - but it starts the first time you sharpen your edge - in the same way, the drip destroys stone over time - and it starts with the first drip.

The cutting edge will get a steeper and steeper Angle. Then you have to regrind the edge - and when you do that you have to take away a lot of material from the blade to get back to where this edge started.
When using tools, this so not hapend. Every maintaining sharpening is a continuing of the first sharpening - and you never need to regrind the edge becouse the edge angle will not change.

If you use a sharpening tool - and then maintain that edge by freehand, the edge WILL be convex, and when you use the sharpening tool again you have to correct that started convex edge back to flat -and you must remove a lot of material from the edge to do that. IF you outdoors use only a fine ceramic sharpener for sharpening and sharpen as little as possible - you can correct the edge with your tool and you will take away less material this way.

To avoid hard discussions, if you are happy with your edges after sharpening them, please keep doing what you are doing, don't change anything :)

thomas
 
The cutting edge will get a steeper and steeper Angle. Then you have to regrind the edge - and when you do that you have to take away a lot of material from the blade to get back to where this edge started.


thomas

I believe we've had this exact discussion before. Normally I always work from the shoulder to the edge. Oftentimes I find my edge trying to become more acute over time, not less. If I have to reset on a coarse stone it does not take long. There is perhaps a slight increase in the amount of steel removed freehand. I have sharpened items for other people and seen this, and I used to be guilty of it myself, that's why I always work from shoulder to apex.

I won't argue the basics - you get a more precise angle using a widget, but whether this translates to a better performing edge I am not convinced. A degree or two per side, usually on the microbevel, won't make or break offhand cutting performance.
 
I believe we've had this exact discussion before. Normally I always work from the shoulder to the edge. Oftentimes I find my edge trying to become more acute over time, not less. If I have to reset on a coarse stone it does not take long. There is perhaps a slight increase in the amount of steel removed freehand. I have sharpened items for other people and seen this, and I used to be guilty of it myself, that's why I always work from shoulder to apex.

I won't argue the basics - you get a more precise angle using a widget, but whether this translates to a better performing edge I am not convinced. A degree or two per side, usually on the microbevel, won't make or break offhand cutting performance.

Knowing how human hand has wobble, erring to the more acute side and listening to the shoulder (like taught by HeavyHanded HeavyHanded & @Obsessed with Edges) will prevent it getting more obtuse over time. This aspect alone will change the equation. Same skill all good shooters and archer use: adapt to compensate the tendency. It’s not precise, but it’s enough.

I do agree it likely remove metal more than using jig. Although I’d say over time, the jig will need to be adjusted to keep same angle as the blade width is reduced by every sharpening session. It’s like chasing/removing burr: only how much (also depends on the level of magnification) the error/margin is still tolerable.

Again, I don’t see any issue or disagreements, just sharing different perspectives and tactics to achieve the edge we prefer. To have good understanding of each system limitation and use accordingly is important.

I enjoy the discussion ;)
 
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