A challenge for the mechanical engineers out there (or any mathematician/physicist/engineer out there for that matter).

The question of measurable benefit from weight reduction in guides has piqued my interest.

As a background/summary: It has been a long time since I took physics, but vibration is in essence a form of energy with frequency and amplitude. A rod is effectively a force sensor and at the same time a lever arm. The rod will translate the force of a fish striking our lure into vibrational energy and transmit this to the nerves in our hands holding the rod. The amplitude of the vibration will determine whether our nerves pick up the signal (low threshold mechanoreceptors in sensory nerves) which if activated will send the signal to the brain (with both intensity and frequency information) that the brain will (through learning and experience) translate into a fish is biting my lure (and eventually all the endorphin release that make us love the sport). Blanks translate the force into frequencies based on the physical properties of the rod (different materials have different vibrational properties), and the most sensitive blanks would have frequencies that our sensory nerves are best at picking up (think of a dog whistle – it may be plenty loud for our canine companions but useless for us to detect).

As a result, anything that decreases the amplitude (or changes the frequency to a non detectable range) to the signal at any point from the lure/bait to our hand will decrease the sensitivity of the rod while anything that increases the amplitude and allows us to distinguish the differences in vibration increases the sensitivity of the rod.
The force of a fish strike has energy. A fishing rod translates this into vibrational energy with an amplitude and frequency (which has movement). The mass of the rod will absorb the vibration with greater mass translating into a lower amplitude movement (but with the same energy). The mass at the tip and the mass at different points along the rod will all have different effects on the dampening of amplitude based on the magnitude of the weight and the distance from the sensor (i.e. our hand). The smaller the amplitude of the vibrational movement, the less likely our sensory nerves in our hand pick it up.

OK, now to the question: Assuming that perceiving the frequency of the vibration is the physical basis for what we call the sensitivity of a rod in determining if a fish, weed or bottom contact, then we should be able to calculate the exact dampening effect of weight based on mass and the distance from the sensor (our hand). If someone can find the correct equation, we should be able to exactly calculate the effect of decreased sensitivity from the differences in mass of titanium Sic guides and Stainless steel aluminum oxide guides. I would recommend using just a standard guide placement chart for distance of each guide to eliminate variability in guide placement between blanks) for the purposes of this calculation.

Anything you add to the naked blank will reduce its efficiency, performance, etc. Not hard to prove this with a simple, practical test. Load up twice as many guides on any rod you have now and go use it. Compare it to the rod when it had only half as many guides. You'll easily discern the difference.

What you feel when you retrieve a lure isn't a vibration - it's the resistance of the lure (or whatever) as you attempt to pull it through the water. You can call this a vibration (cadenced resistance) but lure's don't vibrate (open your tackle box and watch the trays - none of those lures are going to start vibrating no matter how long you watch.

I do not believe that frequency has much if anything to do with sensitivity. But it has a lot to do with casting proficiency, response, recovery, etc. These are the best reasons to build as light as possible, particularly on the upper half of the rod.

...........

Hello Eric.

Here are afew that deal with the weight thing:

Volume/Issue.......Article............Author............Page:
23/4 History: Zero Weight. 38
6/6 How To: Weight or Not To Weight When...(Apologies to William Shakespear) By Rich Forhan. 18
13/3 How To: Weight Reduction. By Bill Colby. 22

If you just want "Guides" in general; Here you go!
14/3 Guide & Tiptop Sizing. 28
3/1 Guide and Top Removing Technique. 18
9/5 Guide Classics: Let ELGUS Be Your Guide. By Gene Bullard. 28
14/6 Guide Evolution Design and Properties. By C. Boyd Pfeiffer. 30
20/5 Guide Evolution. 38
4/3 Guide Feet, Prepping Techniques. 22
26/3 Guide Foot Underside Prep. 26
15/6 Guide Height How To Adjust. 14
10/3 Guide Location How To (It's A Process). 28
5/1 Guide Number & Placement. By Tom Kirkman. 30
14/5 Guide Placement System Application. (GPS). 28
5/5 Guide Placement Systems Revisited: Equal Angle System VS New Guide Consept System. 28
15/6 Guide Placement, Spiral . By Joy Dunlap. 10
8/1 Guide Prep Made Easy . By Tom Kirkman. 16
19/1 Guide Replacement. By Tom Kirkman. 26
10/4 Guide Sizing and Placement For Spinning Rods. 28
9/6 Guide Sizing For Your Fly Rod. 28
9/4 Guide Sizing, Don't Use It Just Because They Make It! 30
17/3 Guide Spacing An Engineer's Approach. By Hal Williams / Bill Hall. 26
12/1 Guide Spacing By Story Pole. By Bill Colby. 22
16/4 Guide Spacing By Story Pole. By Bill Colby. 26
2/5 Guide Spacing Grid. By Tom Kirkman. 22
15/2 Guide Spacing The Equal Distance Way. By Rich Forhan. 30
5/3 Guide Spacing, Number and Selection. By Rich Forhan. 10
20/3 Guide Spacing, Number and Selection; as Easy as 5, 6, 7 and 8. By Rich. 10
14/5 Guide Systems of Spinning Rods Has Been An Evolution . By Tom Kirkman. 22
8/3 Guide Weight And Rod Performance. By Emory Harry. 22
21/1 Guide Wraps, Candy Apple. By Jim Wardell. 12
25/3 Guide, Tiptop & Seat Sizing 20
10/6 Guides & Rod Blank Flex. 26
4/5 Guides (Part 1 Of 3). By Tom Kirkman & Don Morton. 16
4/6 Guides (Part 2 Of 3). By Don Morton. 22
14/1 Guides For Fly Rods Past And Present. By C. Boyd Pfeiffer. 16
10/2 Guides, Get The Right Number Right Out Of The Gate (Or Close To It). 28
15/3 Guides, Roller Past & Present. By Boyd Pfeiffer. 28
26/3 Guides: FOOLPROOF! Nine Foot Fly Rod Guide Spacing By Mike Ballard. 28
17/5 Guides: Hallemin Guide Spacing System (HGS). 26
11/5 Guides: Micro, Misinformation and Myths. 16
14/5 Guides: Microwave Guide. By Doug Hannon. 24
3/4 Guides: New Guide Concept Part 1 Spinning Rods. By Tom Kirkman & Lloyd Starush. 10
3/6 Guides: New Guide Concept Part 2 Casting & Fly Rods. By Tom Kirkman & Lloyd Starush. 10
16/2 Guides: NGC Choke Guide Location. By Tom Kirkman. 10
8/2 Guides: Simple Spiral. (Wrap-Around or Acid Wrap). By William "Bill" Colby. 16
2/6 Guides: Single Foot Guides, Taming Them. 16
9/5 Guides: Spinning Guide Sizing. 30
3/5 Guides: Spiral Wrap For Casting Rods. By Ralph O'Quinn. 24
3/4 Guides: Spiral Wrap System, Reflections, Yea or Nay? 30
6/5 Guides: Spiral Wrapping, Making The Transition. By Tom Kirkman. 24
18/2 Guides: Spiral, A Different Way To Do It. By Chris Carrowell. 30
11/2 Guides: Tip-Top Solution For Saltwater. By Dave Sonner. 16


Tight Wraps & Tighter Lines.

Many forum users here will likely remember, and had great respect for Emory Harry, who wrote several articles on sensitivity and was perhaps the strongest proponent of natural frequency in the rod building world. The following is his response to me after I suggested he set aside theory (or misguided application) and try a practical test on the matter-


"In my article on rod sensitivity I wrote “… sensitivity comes down to how much of the energy in the fish’s bite gets to the fisherman’s hand in the form of rod movement.” This is accurate but I overlooked one thing that the editor brought to my attention and which I should have considered before allowing the article to be published.

I focused on impedance and frequency in terms of such movement and failed to consider leverage on the rod from the fish. Tom supplied me with a simple test that added a new twist to how we should look at sensitivity. From the fish’s end the rod is a second order lever and any resistance will be more strongly felt on a longer rod than a shorter rod. I apologize for the error."

Emory Harry

............

Tom Kirkman said, "What you feel when you retrieve a lure isn't a vibration - it's the resistance of the lure (or whatever) as you attempt to pull it through the water. You can call this a vibration (cadenced resistance) but lure's don't vibrate (open your tackle box and watch the trays - none of those lures are going to start vibrating no matter how long you watch."

I have been watching my tackle box trays for hours now and thought I saw some lures vibrating but it was just a huge truck going by my house. Done watching!

I think there is more to consider then sensitivity, you rod has its own intrinsic power that is subject to forces generated by the casting movement, we expend extra energy starting and stopping this movement. So simply we can accelerate and decelerate using more or less energy and use the energy we do use to throw the lure instead of the blank and extra weight in components.

Tom? If you would do something for me ....... take two rods ..... one that is 1' longer than the other, and lay them both on the floor next to each other. Can you tell me which one is more sensitive? And you can't come back with an answer mentioning length of a lever's affect on its' mechanical advantage. Mechanical advantage only comes into play when a rod (a lever) is in use.

While I wait for an answer ...... I've been watching some lures sitting on the table beside me, for quite some time now. Haven't seen one of them start to vibrate on their own. I'm going to try something. I filled a 5 gallon bucket with water. I'm going to drop one or two of these lures into it, and see what happens. Let's see .... not much room to move a bait around in a bucket of water, so a crankbait won't do. I'll drop this spinnerbait in the bucket, and this 5" Gary Yamamoto Senko in the water and see what they do.

What's this? The arm of the spinnerbait was shaking as the bait was falling, and the Senko was wiggling as it was falling. I put the lures to use, (somewhat) and they started to vibrate.

And I've done this before in past threads, but just so we're clear, I'll do it again

Vibration : 1a : a periodic motion of the particles of an elastic body or medium in alternately opposite directions from the position of equilibrium when that equilibrium has been disturbed (as when a stretched cord produces musical tones or molecules in the air transmit sounds to the ear)

b : the action of vibrating : the state of being vibrated or in vibratory motion: such as (1): oscillation. (2) : a quivering or trembling motion : quiver

When we fish, our lures are attached to a line. What the lure is doing is causing the line to oscillate. Vibrate. The line is running to the rod and causes the rod to vibrate, those vibrations travel down the rod, and the line, and are received by our hand. You can say what we are feeling is leverage all you want, it doesn't change the FACT that the line has been put in a state of oscillation, and it is in FACT, vibrations that we are feeling with the rod.

Once again I have said this in past threads, but it bears repeating.. Just like we use our ears to hear, we use leverage to feel. Increased leverage allows us to feel those vibrations to a greater degree. That is why when you put the two rods that were laying on the floor at the beginning of this post, to use ..... the longer rod, by way of its' increased leverage, will be more sensitive to that input.



Edited 1 time(s). Last edit at 11/25/2024 06:55PM by David Baylor.

Thanks to all for all the info.

Mr. Guist, which periodical are you referencing and are the articles available for download? I am new to the hobby and am not certain

A couple points to clarify.

First when you strike a tuning fork with your hand the sensation you feel in the other hand holding the tuning fork is vibration. The hand you struck it with was not vibrating. The tuning fork translates the kinetic energy into vibration. The length, thickness and material all determine the frequency produced from the strike just like the length, width and materials do in a blank. If you strike the tuning fork and hold onto it the vibration will be short lived like a the constant pull of the resistance of the lure. So, no, I do not believe that the lures in my tackle box are vibrating. Nor do the lures have to vibrate to feel a vibration in the rod when the kinetic energy of a fish striking the lure is translated into vibration in the rod. From a definition standpoint, the cadenced resistance is a form of vibration with the oscillation of more and less resistance being the frequency. The tiny sensations of feeling a little more pull and a little less pull I would classify as a form of vibration as these are picked up by the rod tip and you sense them in your hand. However, if others wish to make a distinction I will concede. However, the variations are still what we pick up in our A delta afferent fibers which are responsible for vibration sensation and proprioception. Regardless of the physics semantics, the neuroscience is vibration and proprioceptive sensation.

Secondly, yes, I absolutely agree with the point from Mr. Kirkman who commented to Emory Harry about length and leverage. A longer rod will have more of an effect in both sensitivity as well as be affected more by weight the farther the mass is from the fulcrum. This is why I specifically mentioned using a standard guide placement chart so that the added weight at each distance is calculated separately. 1gm of weight at the rod tip will have far more effect than 1gm 20 inches from the tip of the reel spool i.e. the farther away from the fulcrum, the weight has the more effect with the tip having the greatest magnifier. The weight of the blank, especially at the tip will also have an effect. For example (I made the math easy I know these values are not the actual weight of the tip of the blank), if the tip of the blank weighed 10gm adding 1 gm (10%) to it will be less noticed than if the tip weighed 0.5 gm and you added a 1 gm weight (increased by 200%). As I mentioned, "A rod is a force sensor as well as a lever arm." However if the length of the rod were the only factor, a fiberglass blank, a bamboo stick and a steel rod of the same length and width would all have the same sensitivity which I think we can all agree do not. Thus all the factors must be taken into account. I can attest that the tip of my old fiberglass rods move fine with weeds and fish strikes, and the rods are just as long as other rods but I can not always tell a fish and a weed apart apart, thus a lever arm is not sufficient to explain sensitivity. There is another sensation transmitted through the blank that allows people to tell the difference. I believe this to be the vibrational properties of the blank which is why the materials a blank is made of is so important.

As a third point, although the recommendation above is a very simple experiment in design, it is not a practical one for me to build on an expensive blank with twice the titanium guides fish for a day and then strip off half of them and fish for another day. I would not trust that I would not damage a very high quality blank. Doubling up on cheap heavy guides on a cheap insensitive blank would not be a fair comparison. I absolutely believe that there will be a difference, but when does it matter? The micro guides, whether titanium vs steel vs carbon fiber are a tiny weight. What if the calculation shows that 90% of the effect are from the weight of the stripper (which is like half the weight of all the guides using the anglers resource system) and the tip top. Then the only two things that really have to be titanium are the first stripper guide and the tip top. Now that could save money for freshwater fishermen (in saltwater I would always choose titanium for the corrosion protection). On a side note, if any of the manufacturers want to donate a couple high end blanks and titanium guides (I will chip in and cover the SS guides), I sure am willing to do a comparison experiment! I'll even recruit local fisherman to blind test them (my son's high school has a bass fishing team)! ;)

An interesting point is that the sensation may be picked up more at the wrist than the fingertips (at least according to some online comments) which would potentially indicate proprioception changes with slight oscillation in wrist position is a major factor (a slower frequency and different waveform) -- but if that were the only factor, than carbon grips and CCT reel seats should not have any greater sensitivity.

Unfortunately, since I have mainly fished cheap 20 year old fiberglass rods (my nicest rod this summer was an uglystick), I certainly cannot make any comment based on experience. I am still building on cheap clearance parts and blanks as I build my skillset until I don't fear screwing up on the more expensive stuff. As a newbie I am asking for advice from experienced anglers and rod builders and do not always appreciate derogatory comments as if I am hallucinating about lures moving in a tackle box. In fact it is not even an appropriate comparison. I have also been looking at my tuning fork and it hasn't moved at all. Yet I certainly know it translates a physical strike into a calculatable vibration. If I used the lure in a tackle box example and applied it to rods, I might as well say that an NRX+ sitting in a rod holder in the basement is sensing as much as an Uglystick right next to it and thus it is no more sensitive -- because in this example they are both detecting no energy. A lure moving through the water is a far more appropriate comparison. The movement of the lure translates into a energy waveform with frequency and amplitude transmitted in the line which is then converted by the rod into another oscillating waveform which finally gets to the sensory endings in your hand and wrist. The stretching and compression activating the LTMRs in your sensory nerves are what you feel and activate the same whether you call it vibration or oscillating resistance.

Mr. Guist, I really would like to look at those articles, if you have a link I would greatly appreciate it. Or at least the name of the journal.

Where can I find the articles from Emory Harry?

Alright, enough writing, the family is waiting for me so we can watch a Thanksgiving special. Happy Thanksgiving everyone!



Edited 1 time(s). Last edit at 11/26/2024 01:39AM by Eric Hernandez.

Eric,

The problem is that nothing you're discussing replicates a real world fishing situation. There are all sorts of "tests" out there that seek to prove this or that, but very few actually have any connection to what we actually do with a fishing rod. For years we've had people believing that rod spine can be orientated to stop rod twist due to tests where the blank is flexed by hand, but this does not replicated what actually happens on the water where load is applied not your hand on the blank, but via a line passing through line guides (lever arms). These are two completely different scenarios.

David,

No the lures did not vibrate. They were moved by gravity and what you saw were the lures resisting that movement. Yes, a rod that is a foot longer than another will be more sensitive than the other one.There are no magic vibrations traveling through the line and the rod. It's all about movement. You pull on one end and the other end moves, or the other end moves and pulls on the opposite end. If you put slack in the line nothing that you do to that lure is going to be felt on the rod end. So yes, it is indeed all about lever mechanics. Emory set aside his similar theories on vibration for a few minutes and actually tried it. He found out that the longer rod is indeed more "sensitive" due to lever mechanics. Movement is the only thing you can feel and all this supposed shaking, vibrating, etc. on a slack (non tensioned) line is never going to be felt by the angler because it's not going to resist or create movement from/to the rod.

.........



Edited 1 time(s). Last edit at 11/26/2024 01:03PM by Tom Kirkman.

Hello Eric.

All the listed articles are from "RodMaker Magazine".

As far as copies goes, you might want to check with Tom and his people at "RodMaker Magazine", the page is listed under sponsors.

The most can be had on the CD's, but I'm sure he has a bunch of different magazines for back order.

I mostly put the info out there for people who want to know where to find info on a range of subjects.

Hope it was helpful.


Tight Wraps & Tighter Lines.

I have fished for tunafish but never for tuningforks. The so called tests that some are doing might as well just go back to the old Adam's Apple sensitivity test where you will find that ash and hickory are just as sensitive as graphite. Some would say even more sensitive than graphite.

Mike,

I'm sure you spoke in jest but the old "Adams Apple" sensitivity test is much more similar to what so many here do in order to try and determine sensitivity.

.............

Eric Hernandez Wrote:
-------------------------------------------------------
> ...
> Blanks translate the force into frequencies based
> on the physical properties of the rod (different
> materials have different vibrational properties),
> and the most sensitive blanks would have
> frequencies that our sensory nerves are best at
> picking up (think of a dog whistle – it may be
> plenty loud for our canine companions but useless
> for us to detect).

This also would apply to humans...at what threshold is MORE sensitive basically useless?
One rod could measure more sensitive than another with piezoelectric sensors', but can we really differentiate them with our limited feel.
I have been fishing with plenty of people who lack the skill of feeling a bite.

> ....
> The mass ... based on the magnitude of
> the weight and the distance from the sensor (i.e.
> our hand)

Here you're assuming that weight is the dampening agent....it's not. It's the material.
For example.... look at cork. Burl cork (heavier) would transmit vibration better than just plain cork.
When we start looking at guide ring material and frame material...I think we're getting at a point where we are at our limit of being able to tell.
I'm not saying that Ti doesn't have its place...it does. It light, its corrosion resistant and stronger than aluminum.

I've made several different devices that measure sensitivity, and I'm convinced that were just beating a dead horse.
If you want more sensitivity use braid and fluorocarbon...this would improve the touch more than any component ever could.

There is a large part of sensitivity that is learned as a skill.
Put the same rod in the hand of a guy who fishes once a year vs a guy who fishes every day.

Just so I'm clear .......... we're to ignore the Merriam - Webster definition of the word vibration. We're to ignore what the bait is causing the line to do. And we aren't to consider the level of damping attributed to a slack line.

We're to ignore physics in those instances, yet we're to use physics as proof that a longer rod (a longer lever) will be more sensitive to input at its' end, than a shorter rod (a shorter lever)


This whole exchange has me thinking of some words from an Aldo Nova song .......... "life is just a fantasy, can you live this fantasy life"

Some can ...... but I can't.

Have fun .....

I’ve used both Fuji titanium and stainless steel KR guides on a bunch of casting and spinning rods. Personally, I can’t feel a performance difference between them, but that’s my opinion. However, I can say that I do feel a difference between a KR concept layout vs other types of guide layouts. Again, my opinion. For rods that are primarily going to be used in saltwater I use titanium guides, and stainless guides for those used in fresh water.
Norm

David Baylor Wrote:
-------------------------------------------------------
> Just so I'm clear .......... we're to ignore the
> Merriam - Webster definition of the word
> vibration. We're to ignore what the bait is
> causing the line to do. And we aren't to consider
> the level of damping attributed to a slack line.
>
> We're to ignore physics in those instances, yet
> we're to use physics as proof that a longer rod (a
> longer lever) will be more sensitive to input at
> its' end, than a shorter rod (a shorter lever)
>
>
> This whole exchange has me thinking of some words
> from an Aldo Nova song .......... "life is just a
> fantasy, can you live this fantasy life"
>
> Some can ...... but I can't.
>
> Have fun .....


The fantasy is believing that inputing signals into a rod tip via a speaker, Adams Apple, etc., etc., are in any way similar to what's going on when you retrieve a lure through the water with a rod. The two are not the same.

So ignore those things that do not replicate what happens in a real fishing situation and pay attention to what happens when you pull something through the water - it resists you due to the drag of water, bottom surface, current, itself, etc.. And if you're pulling it with a lever, then lever mechanics are in full play. Even Emory Harry realized this once he tried a practical, real world test.

Here's one of several you can try for yourself - cast out a crankbait or spinnerbait and point the rod directly at the lure as you retrieve it with the reel. Try to keep the line straight so that it makes very little contact with the rod and line guides. You won't feel much at all. Then, begin raising the rod tip (introduce a lever) and suddenly you'll feel the thumping (cadenced resistance) of the lure as you retrieve it. The reason why is simple - you're holding a second order lever. And the longer that lever is, the more that thumping (resistance) will be magnified.

................



Edited 1 time(s). Last edit at 11/26/2024 08:48PM by Tom Kirkman.

Tom Kirkman Wrote:
-------------------------------------------------------
>
> The fantasy is believing that inputing signals
> into a rod tip via a speaker, Adams Apple, etc.,
> etc., are in any way similar to what's going on
> when you retrieve a lure through the water with a
> rod. The two are not the same.
>

It’s a little stunning that this paradigm won’t die or even wane regardless of how many times it gets covered. A rod isn’t a guitar string, speaker cone, tuning fork, or any other resonance device. A very few fast strikes that don’t end in a hookup that dampens, and striking the rod on a gunwale, is about all that sets up vibrations. Neither of those events allow for setting the hook.

Tom Kirkman Wrote:

>
> The fantasy is believing that inputing signals
> into a rod tip via a speaker, Adams Apple, etc.,
> etc., are in any way similar to what's going on
> when you retrieve a lure through the water with a
> rod. The two are not the same.
>
> So ignore those things that do not replicate what
> happens in a real fishing situation and pay
> attention to what happens when you pull something
> through the water - it resists you due to the drag
> of water, bottom surface, current, itself, etc..
> And if you're pulling it with a lever, then lever
> mechanics are in full play. Even Emory Harry
> realized this once he tried a practical, real
> world test.
>
> Here's one of several you can try for yourself -
> cast out a crankbait or spinnerbait and point the
> rod directly at the lure as you retrieve it with
> the reel. Try to keep the line straight so that it
> makes very little contact with the rod and line
> guides. You won't feel much at all. Then, begin
> raising the rod tip (introduce a lever) and
> suddenly you'll feel the thumping (cadenced
> resistance) of the lure as you retrieve it. The
> reason why is simple - you're holding a second
> order lever. And the longer that lever is, the
> more that thumping (resistance) will be
> magnified.
>
> ................


You are correct and the higher you raise the rod and the greater the angle between the line and the rod tip becomes the stronger these so called vibrations will be. The fact that you can increase or decrease how strongly you feel what's on the end of the line simply by changing the length of the effective lever should be enough to convince anyone that sensitivity really is all about the lever in play. Take a six foot carbon bass rod that you think is really sensitive and cast out a big colorado blade spinnerbait and wind it back in. Then throw the same spinnerbait out on a nine foot glass plugging rod and wind it back in on that rod. The vibrations will be double what they were on the six foot rod.

David,

The line isn't vibrating. It's simply connecting the resistance of the lure to the angler.

Go perform one of the practical tests. If the line is "vibrating" and therefore causing the rod to "vibrate," why do those vibrations become increasingly stronger felt when you raise the rod tip higher and higher? The strength or intensity of what you call the "vibrations" hasn't changed - same lure and same line. The only thing changing in that instance is the length of the effective lever.

Surely you don't believe that a plastic worm "vibrates" and yet its movement along a lake bottom (resistance) is more strongly felt with a longer rod than with a shorter rod. No vibrations whatsoever but you can feel it. Why is that? It's not vibrating and if it's not resistance, what are you feeling?

..............

This has been a very informative thread, love it every time.



Edited 1 time(s). Last edit at 11/27/2024 06:40PM by Lynn Behler.