This is the NMEA0183 TECHDATA file (version May '91)

Dear reader, the following is an article I wrote on the subject NMEA 0183 interfacing for MAINSHEET, the Catalina and Capri Owners association magazine. It appeared in the May, 1991 issue. You may distribute it freely but please make note of where it came from when you do. Wayne Simpson, <wms@spin.ho.att.com>.

UNDERSTANDING MARINE ELECTRONICS INTERFACING:
the Promise, the Problems

by Wayne Simpson, Technical Editor
International Catalina 27 Association

The coming of the microprocessor to marine electronics has brought with it a promise and a curse. The promise is that two or more devices can share information and so become more valuable and convenient to use. The curse is that not all marine hardware is compatible. To make matters worse, marine electronics manufac turers often make it difficult for the consumer to tell whether any two devices will work together until bought and wired togeth er. Sometimes the result is a happy event. At other times, it can be an exercise in frustration.
An interface is the boundary at which two independent sys tems communicate and interact. When you connect an interface cable from your loran to your autopilot, the wire is like the string between two cans in a play telephone. The wire carries the conversation, but it is the interfaces at each end that do the talking. If the two devices speak the same language and can understand the same words, then they can communicate. Otherwise, they can't. There is a standard for communications in the marine electronics industry, and most manufacturers claim to abide by it, at least in part. Unfortunately this is not always enough.

NMEA 0183: The Marine Interface Standard

In 1980, a group of professionals from the industry met to develop a standard "language" for marine interfaces. The result was the National Marine Electronics Association (NMEA) 0180 standard. It addressed one problem, that of making lorans and autopilots work together, and it was a success. In the following years this standard, revised, broadened, then totally revamped to take into account the wide range of electronics appearing on boats, led to the current NMEA 0183 standard used on almost all equipment today.
The NMEA 0183 standard calls for data communication in the form of coded "sentences." Each sentence begins with the character "$" and ends with a carriage return and line feed (<CR><LF>). These last two characters are "control" characters and are not normally printed (for this reason they are customarily shown enclosed in brackets). Between the beginning and end of each sentence are "fields" of data, each field separated by a comma. The first field in any sentence (field 0) begins with the two letter talker mnemonic code ("talkers" are devices that send out information, "listeners" take it in) followed by the three letter code for the sentence. Data follows in the standard format for that sentence. Here's an example:

field #: 0, 1, 2, 3, 4
sentence: $LCGLL,4001.74,N,07409.43,W<CR><LF>

What is being said here? Lets look at it field by field.
The sentence begins with the start character "$."
Next comes the talker identifier and sentence format code. LC stands for Loran- C, GLL for present position in Lat/Lon.
Field 1 contains the set's current latitude.
Field 2 is either N or S for North or South.
Field 3 is the set's current longitude.
Field 4 is W or E for West or East.
Thus, this sentence reads "Loran-C present position in Lat/Lon: 40 degrees 1.74 minutes North, 74 degrees 9.43 minutes West." A carriage return and line feed close the sentence. The GLL sentence is always displayed in this format. Each type of sentence, and there are many, has its own specific standard format (for a brief catalog of formats, see sidebar: Deciphering the Code). Standard sentences, each in a standard format. This is how NMEA 0183 is intended to work. But compliance with the standard is voluntary. It is up to the manufacturers to decide how they will implement the standard, and to what extent they will comply with it. Because the standard is so broad, there is often more than one way to express the same information, and this can cause problems. There are many different sentences, and few if any talker devices say them all, or adhere strictly to the standard format of those they do. Does your autopilot need information in a form that your loran isn't sending out? How can you tell?
Don't count on there being an adequate explanation in the manuals, because often it isn't there. The owners manual for my loran describes the workings of the interface this way. "The extra connector on the rear panel is a serial data output inter face which can provide loran data to an autopilot, track plotter, or fishfinder. The serial data is in NMEA 0183 format and is transmitted continuously." That's it; the manual makes no other mention of the interface anywhere. Other manuals I have seen are about as descriptive. In a follow-up bulletin nearly a year after I bought it the manufacturer of my loran mentioned what sentences the data output sent (there were four) and what the pin assignments for the output connector were. This section was labeled "for techies only." These interfaces are touted in adver tising copy, but it's clear the manufacturers don't really expect you to use them. In the end, you probably will have to call the manufacturer for a proper explanation of their interface, and ask specifically whether they have tested the devices you have in mind for compatibility.
So far we've discussed only software incompatibilities, but there can be physical ones, too. NMEA 0183 specifies no standard connector, and no two manufacturers seem to use the same one. Usually, the owner will have to buy plugs from the manufacturers and make his own cable.

A Case History

Two years ago, when I bought my West Marine Vector I loran, I had no intentions of ever using the interface. Why would you want to interface your electronics, anyway? Here's one example. A loran can tell you where you are, what direction to steer to get to your destination, and how far off your intended course track you are. By itself, however, it can't steer the boat. An autopi lot can steer, but on it's own can't compensate for currents or leeway. An autopilot interfaced with a loran can do all these things, and then some. Here's another example. The more you use the magic box, the more you realize the information it gives should be displayed in the cockpit, where the helmsman can have instant access to it. But the cockpit can be a harsh location for electronics and most lorans aren't truly waterproof. A loran "repeater," which echoes steering information on a remote dis play, can provide useful steering information in the cockpit while leaving the loran below in the nav station, safe from sun and spray.
An integrated pilot/navigator system would have been nice, but LEGACY, our 1977 Catalina 27, already had an autopilot, an old style Autohelm 800. It worked perfectly well and I wasn't going to replace it just to have one with an interface. A loran repeater would be handy too, but those available commercially cost as much as a second loran. I toyed with the idea of building a repeater but in the end dismissed the whole thing as not being worth the time, effort, or cost.
Two things happened last summer that changed my opinion on interfacing. First, the old Autohelm failed, and the cost to fix it was almost as much as a new digital autopilot. I went for the new pilot, settling on a Navico Tillerpilot 5000 largely because Autohelm had changed their mounting dimensions and would have required me to change my setup. Navico's dimensions were always very close the old Autohelm's, and would fit without modifica tions.
The new pilot worked well all by itself, but an item on Navico's option list caught my eye. It was a digital hand pro grammer that made the TP5000 a much better pilot. It displayed present heading from the pilot's internal fluxgate compass, allowed you to make course changes in degrees rather than beeps, had an off-course alarm and let you program the pilot's response parameters to better tune them to the boat and conditions. Also at the time, if you bought a pilot and programmer and sent the receipts to Navico, they would send you the loran interface box (which normally cost's $150 at discount) for free.
Second, while at a marine warehouse sale, I came across a KVH model LRX+ loran repeater. It was complete with the warranty card and instruction booklet. It's price was $100, 1/3 the usual discount price. It was NMEA 0183 compatible, and so was my loran. It even had a sheet with a listing of all the lorans the LRX+ had successfully interfaced with. The Vector was there, right at the bottom of the list. Why not?
I took it down to my boat, hooked it up to the NMEA inter face on the back of my loran, programmed a course to a nearby buoy, and waited for the repeater's display to come to life. It did, and showed a bearing that was 12 degrees off! Something in the back of my mind reminded me that the magnetic variation in my area was 12 degrees. The repeater was displaying bearing in de grees true rather than magnetic. Every time I wanted to get a steering course off the display, I would have to do a calculation in my head. The "curse" had visited me.
I was now in the position of having to figure out what the problem was with the repeater. I had no knowledge of the NMEA standard or how it worked, so I called KVH. They said that what ever the loran was sending out over the interface was reported on the display. I called West Marine to find out what the Vector was sending out. They told me that both true and magnetic bearings were sent, and that it was up to the repeater to differentiate between them. I asked KVH for more help, and they offered to upgrade the repeater's software to a newer version at no charge. I sent the repeater off to KVH Industries in Middletown, RI.
While the repeater was away, I took a sample of the Vector's data output using my PC. The procedure is described in the side bar: Listening In, Speaking Out. Here's what I got:

$LCGLL,4004.22,N,07409.78,W
$LCBWC,,4001.80,N,07403.66,W,117,T,129,M,005.2,N,011
$LCAPA,V,A,1.00,R,N,V,V,117,T,011
$LCVTG,,,271,M,02.3,N,,

The pattern of four sentences repeated itself every two seconds. Close inspection of this string revealed the problem. In order to work with a wide variety of lorans, the KVH repeater's program accepts data from several different sentences, two of which, BWC (bearing to waypoint along great circle) and APA (autopilot format A), appear in the above sample. Look closely at the APA sentence. Data fields 8 and 9 display the bearing and whether it represents degrees true or magnetic. The standard format for APA is degrees magnetic, in this example it is degrees true. There was a bug in the Vector's software.
Why couldn't the repeater see that the bearing was in de grees true and disregard it? Most of these programs are "comma counters." They recognise a sentence of interest from the ad dress, then count commas until they get to the field in which they expect to find data they need. They don't look at the fields telling whether the information is true, magnetic, east, or west.
The people at KVH felt confident that the software upgrade would cure this condition but when the repeater came back, my problem was still there. I called West. The problem was their doing in the first place, maybe they would fix it. Unfortunately for me, the Vector I was made obsolete by the Vector II the previous year. West planned no more software upgrades for the Vector I, and it would be prohibitively expensive for them to rewrite the software in response to this one complaint. I could, perhaps, install the Vector II software (which corrected this bug) but then I would lose some of the features the Vector I had that the Vector II lacked. I decided it wasn't worth it.
There was still some confusion over exactly what data fields the repeater was looking at. To find out, I wrote a loran simula tor program for my computer (see sidebar). I coded the data in each of the three fields that displayed bearing, giving each a different value, and was able to prove that the repeater was looking at the APA sentence for it's bearing to display.
Once again, I called KVH. Rob Solomon, one of KVH's techni cal people who had stayed with me throughout this ordeal, was certain the new software didn't look at APA for bearing. He wanted to look further into the problem, but was unsure when he would be able to find the time to do so. It was early February, war had just broken out in the Persian Gulf and KVH was in the midst of delivering 15,000 of it's DataScopes to Desert Storm personnel. He promised to look at the LRX+'s software when things quieted down. Oddly enough, he called back in an hour with the LRX+'s program listing in hand. He told me absolutely that the new software did not look at APA for bearing. Back to the drawing board...
I went home that night and ran my simulator again. There was no mistake. I wrote a letter to Rob at KVH. In it I included everything I knew about the problem, a sample of the Vector's data output, the listing of my simulator program, and the version number of the software EPROM ("Erasable Programmable Read Only Memory," the chip which stores the software) installed in my repeater. I sent it off by FAX the following day. A few days later, I called Rob to see if he had gotten the letter. He had, but had not yet read it. When he did, he saw that I hadn't been given the software he asked for. He sent a new EPROM chip in the mail (the right one, this time) for me to put in myself. I did, and it worked as promised. My problem was solved, but only after five months had passed and I had spent many hours on testing and investigation.
I had better luck regarding the autopilot. Late last summer, wisened by my experience with the repeater (I had just begun the process of sorting out it's troubles), I called West Marine and spoke to Dave Wells, their technical support person for the Vector. I was determined to find out whether the loran/autopilot interface would work before I bought it. He told me the Vector and the Navico pilot were compatible. He had tested them himself. I bought the programmer and sent away for the junction box. When it arrived, the manual informed me that my pilot would require a software upgrade from the factory in order to work properly with my loran (sound familiar?). It was by then late fall and I would not be needing the pilot for months, so I sent it off to Navico's Largo, FL plant. When it came back, I hooked the loran, pilot, programmer and junction box together in my study to see what would happen. The system worked as advertised. This time, the "promise" was fulfilled.

Conclusions and Recommendations

My story has a happy ending. Come spring, I will be install ing my new toys and enjoying them all summer. Others who try this may not be so fortunate. The NMEA system can work, but there is no guarantee in any particular case that it will. My repeater adventure shows what sort of problems you can have, and to what lengths you may have to go in order to solve them.
My recommendations are these: Do your homework before you buy. If you are buying from a supplier who will do the installa tion for you, make sure he will guarantee the satisfactory opera tion of the interface. If you will do the installation yourself, try to arrange for a full credit return in the event the inter faces prove to be incompatible. Call the manufacturers and ask questions. Take the time to understand what the NMEA 0183 stand ard is and how it works.
If you find that you've been stuck anyway all is not com pletely lost. A company called Maricom Electronics, at 2911 River Drive, Thunderbolt, GA 31404 (phone (912) 354-4542) markets what it calls a "Universal Marine Interface." For just under $400, this box claims to take data in any format that any talker might emit and put it into a form any listener will understand. In the absence of less extreme solutions, this may be worth trying.

Have a problem to solve, or a solution to share? Send your comments and queries to the address above. If you require a quick answer, please include a self addressed, stamped envelope. Your submissions on computer disk (IBM format, any size) will make my job easier, but your paper submissions are, as always, welcomed and appreciated. Until next time...

NMEA 0183: DECIPHERING THE CODE

The "language" of NMEA 0183 is extensive but not difficult to understand. The ground rules are these: maximum sentence length is 80 characters including the starting "$", the terminating <CR><LF>, and everything in between. Minimum number of data fields is two, including the address field (talker identifier and sentence format). If data for any field is unavailable, a "null" field, two commas with nothing between them (",,") can be sent instead.
Here is a sampling of two letter talker identifier codes. There are others, for everything from satellite communications to atomic clocks, but these are some of the most familiar to the recreational sailor.

LC Loran-C
GP GPS
TR Transit SATNAV
AP Autopilot (magnetic)
HC Magnetic heading compass
RA Radar
SD Depth sounder
VW Mechanical speed log

Now for some of the more common sentences that might be spoken by your LORAN, SATNAV, or GPS. This is not a complete listing, but should illustrate how the system works. In the following examples, the character "#" will denote some number (0-9). Remember that each of these sentences would be preceded by the start character "$" and the two letter talker ID. Each also would be followed by the sentence terminator, <CR><LF>.

Geographic Location in Lat/Lon

field #: 0 1 2 3 4
sentence: GLL,####.##,N,#####.##,W

1, Lat (deg, min, hundredths); 2, North or South; 3, Lon; 4, West or East.
Geographic Location in Time Differences

field #: 0 1 2 3 4 5
sentence: GTD,#####.#,#####.#,#####.#,#####.#,#####.#

1-5, TD's for secondaries 1 through 5, respectively.
Bearing to Dest wpt from Origin wpt

field #: 0 1 2 3 4 5 6
sentence: BOD,###,T,###,M,####,####

1-2, brg,True; 3-4, brg, Mag; 5, dest wpt; 6, org wpt.
Vector Track and Speed Over Ground (SOG)

field #: 0 1 2 3 4 5 6 7 8
sentence: VTG,###,T,###,M,##.#,N,##.#,K

1-2, brg, True; 3-4, brg, Mag; 5-6, speed, kNots; 7-8, speed, Kilometers/hr.
Cross Track Error

field #: 0 1 2 3 4 5
sentence: XTE,A,A,#.##,L,N

1, blink/SNR (A=valid, V=invalid); 2, cycle lock (A/V); 3-5, dist off, Left or Right, Nautical miles or Kilometers.
Autopilot (format A)

field #: 0 1 2 3 4 5 6 7 8 9 10
sentence: APA,A,A,#.##,L,N,A,A,###,M,####

1, blink/SNR (A/V); 2 cycle lock (A/V); 3-5, dist off, Left or Right, Nautical miles or Kilometers; 6-7, arrival circle, arrival perpendicular (A/V); 8-9, brg, Magnetic; 10, dest wpt.
Bearing to Waypoint along Great Circle

fld: 0 1 2 3 4 5 6 7 8 9 10 11 12
sen: BWC,HHMMSS,####.##,N,#####.##,W,###,T,###,M,###.#,N,####

1, Hours, Minutes, Seconds of universal time code; 2-3, Lat, N/S; 4-5, Lon, W/E; 6-7, brg, True; 8-9, brg, Mag; 10-12, range, Nautical miles or Kilometers, dest wpt.

BWR: Bearing to Waypoint, Rhumbline, BPI: Bearing to Point of Interest, all follow data field format of BWC.

For a full explanation of the NMEA 0183 standard, you can write or call the NMEA. For a fee, they will send you the their 36 page booklet "NMEA 0183 Standard for Interfacing Marine Elec tronic Navigational Devices." The address is: National Marine Electronics Association, PO Box 50040, Mobile, AL 36605. Phone (205) 473-1793.

LISTENING IN, SPEAKING OUT:
Using your Home Computer to Monitor NMEA Communications

The data that comes out of your loran or other NMEA equipped gear is in the same format as that from your personal computer. It is possible, and very easy to take a look at what your talkers are saying, and to speak to your listeners in a form they can understand.
To listen in, you need a PC equipped with a serial (RS-232) interface and modem program (such as HAYES SmartCom or CTRM). If your program has a data capture feature, you can read data from the line into a file for later use.
To make the connection, connect the NMEA signal line (line A, output, etc) to the RS-232 "receive data" line (#2 on 9 pin or #3 on 25 pin connectors), and the NMEA ground line (line B, return, etc) to the RS-232 "signal ground" (#5 on 9 pin or #7 on 25 pin connectors).
The statistics for NMEA 0183 are as follows: 4800 baud, 8 data bits, 1 stop bit, no parity. Set your modem program for these parameters. Switch on your loran (or other talker), start the modem program, and the data should come pouring in.
One note of caution regarding radionavigation receivers: they are very sensitive to the kind of RF interference computers, fluorescent lights, TV's and other such things cause. Your re ceiver may not be able to lock on to it's transmitters with these things operating nearby, and you may have to set up the receiver in another room and connect it with a long cable for it to work properly.
Speaking to your listeners is only slightly more complicat ed. You need to send the data strings over and over again at a repetition rate of once every few seconds (but no faster than once every second). For this, I wrote a short simulator program in BASIC that does the job, and allows me to program in the text I want to send. The connection is different, also. This time you will have to connect the NMEA signal line to RS-232 "transmit data" (#3 on 9 pin or #2 on 25 pin connectors), and NMEA ground to RS-232 signal ground (as before). In addition, you probably will have to bring the RS-232 "data set ready" (DSR) terminal to a low voltage. You can do this by inserting a jumper between "data terminal ready" (DTR, normally #4 on 9 pin or #20 on 25 pin) and DSR (#6 on 9 or 25 pin setups).
Here is the text of my NMEA 0183 simulator program:

005 REM LORAN SIMULATOR PROGRAM - Wayne Simpson, 1991
010 OPEN "com2:4800,n,8,1,RS" FOR OUTPUT AS#1
015 REM setup RS-232 to parameters and disable request to send
100 A$="$LCGLL,4004.22,N,07409.78,W"
110 B$="$LCBWC,,4001.80,N,07403.66,W,100,T,200,M,005.2,N,011"
120 C$="$LCAPA,V,A,0.25,R,N,V,V,300,T,011"
130 D$="$LCVTG,,,268,M,02.1,N,,"
140 E$=""
200 PRINT A$ 'print GLL statement to screen
205 PRINT#1,A$ 'send GLL over interface
210 PRINT B$ 'BWC to screen
215 PRINT#1,B$ 'BWC to interface
220 PRINT C$ 'APA to screen
225 PRINT#1,C$ 'APA to interface
230 PRINT D$ 'VTG to screen
235 PRINT#1,D$ 'VTG to interface
240 PRINT E$ 'empty line to screen
245 PRINT#1,E$ 'empty line to interface
300 FOR I=1 TO 12000
310 NEXT
320 GOTO 200
330 REM line 300 provides the 2 second rep rate
340 REM line 320 repeats the transmission over and over
350 REM use ctrl-brk keystroke to terminate transmission

Load this program into your computer, substitute into the A$-E$ variables whatever it is you want to say, and run it. You are now speaking NMEA, and can do a fair job of troubleshooting interface problems this way.

Nota bene: the Magellan NAV5000D GPS and some other GPS's only send NMEA data after having a position fix. So setting things up indoors to try to debug connectors won't generate any data on the cable.

(The following is a short excerpt from a ~200K document I have on NMEA 0183)

TABLE 4 - TALKER IDENTIFIER MNEMONICS (Address Characters 1 and 2)

        TALKER DEVICE                                        IDENTIFIER

        AUTOPILOT:              General                         *AG
                                Magnetic                         AP
        COMMUNICATIONS:         Digital Selective Calling (DSC) *CD
                                Satellite                       *CS
                                Radio-Telephone (MF/HF)         *CT
                                Radio-Telephone (VHF)           *CV
                                Scanning Receiver               *CX
        DECCA Navigation                                         DE
        Direction Finder                                        *DF
        Electronic Chart Display & Information System (ECDIS)    EC
        Emergancy Position Indicating Beacon (EPIRB)            *EP
        Engineroom Monitoring Systems                            ER
        Global Positioning System (GPS)                          GP
        HEADING SENSORS:        Compass, Magnetic               *HC
                                Gyro, North Seeking             *HE
                                Gyro, Non-North Seeking          HN
        Integrated Instrumentation                               II
        Integrated Navigation                                    IN
        LORAN:                  Loran-A                          LA
                                Loran-C                          LC
        OMEGA Navigation System                                  OM
        Proprietary Code                                         P
        Radar and/or ARPA                                       *RA
        Sounder, depth                                          *SD
        Electronic positioning system, other/general             TR
        Sounder, scanning                                        SS
        Turn Rate Indicator                                     *TI
        TRANSIT Navigation System                                TR
        VELOCITY SENSORS:       Doppler, other/general          *VD
                                Speed Log, Water, Magnetic       VM
                                Speed Log, Water, Mechanical     VW
        TRANSDUCER                                               YX
        TIMEKEEPERS, TIME/DATE: Atomic Clock                     ZA
                                Chronometer                      ZC
                                Quartz                           ZQ
                                Radio Update, WWV or WWVH        ZV
        Weather Instruments                                      WI


*
 Designated by I.E.C. for use with I.M.O. marine electronic
 devices. This is the minimum requirement for equipment that is
 specified by I.M.O. to meet S.O.L.A.S. regulations.

TABLE 5 - APPROVED SENTENCE FORMATTERS

        AAM - Waypoint Arrival Alarm............................... 22
        ALM - GPS Almanac Data..................................... 22
        APB - Autopilot Sentence "B"............................... 23
       *ASD - Autopilot System Data................................ 23
        BEC - Bearing & Distance to Waypoint, Dead Reckoning....... 23
        BOD - Bearing, Origin to Destination....................... 24
        BWC - Bearing & Distance to Waypoint, Great Circle......... 24
        BWR - Bearing & Distance to Waypoint, Rhumb Line........... 24
        BWW - Bearing, Waypoint to Waypoint........................ 24
        DBT - Depth Below Transducer............................... 24
        DCN - Decca Position....................................... 25
       *DPT - Depth................................................ 25
       *FSI - Frequency Set Information............................ 25
        GGA - Global Positioning System Fix Data................... 26
        GLC - Geographic Position, Loran-C......................... 26
        GLL - Geographic Position, Latitude/Longitude.............. 27
        GSA - GPS DOP and Active Satellites........................ 27
        GSV - GPS Satellites in View............................... 27
        GXA - TRANSIT Position..................................... 28
       *HDG - Heading, Deviation & Variation....................... 28
       *HDT - Heading, True........................................ 28
        HSC - Heading Steering Command............................. 28
        LCD - Loran-C Signal Data.................................. 29
        MTW - Water Temperature.................................... 29
       *MWV - Wind Speed and Angle................................. 29
        OLN - Omega Lane Numbers................................... 29
       *OSD - Own Ship Data........................................ 30
        RMA - Recommend Minimum Specific Loran-C Data.............. 30
        RMB - Recommend Minimum Navigation Information............. 31
        RMC - Recommend Minimum Specific GPS/TRANSIT Data.......... 31
       *ROT - Rate of Turn......................................... 32
       *RPM - Revolutions.......................................... 32
       *RSA - Rudder Sensor Angle.................................. 32
       *RSD - RADAR System Data.................................... 32
        RTE - Routes............................................... 33
       *SFI - Scanning Frequency Information....................... 33
        STN - Multiple Data ID..................................... 34
        TRF - TRANSIT Fix Data..................................... 34
       *TTM - Tracked Target Message............................... 35
       *VBW - Dual Ground/Water Speed.............................. 35
        VDR - Set and Drift........................................ 35
        VHW - Water Speed and Heading.............................. 35
        VLW - Distance Traveled through the Water.................. 36
        VPW - Speed, Measured Parallel to Wind..................... 36
        VTG - Track Made Good and Ground Speed..................... 36
        WCV - Waypoint Closure Velocity............................ 36
        WNC - Distance, Waypoint to Waypoint....................... 36
        WPL - Waypoint Location.................................... 36


If you have comments or suggestions about the WWW-pages of Yacht-L or if you want to contact me personally, email me with or without attachments at E.R.Kooi@XS4all.NL
Last updated: 010716 Back to the top of this page or the homepage of Yacht-L