Sunday, April 28, 2013

No-antenna DXCC

Since I returned to the air at the end of December 2012 I have been using QRP with a newly-purchased and assembled KX3. My antenna is not a real antenna, just an L-network tuner connected to the aluminum eaves trough (you might call it a rain gutter) on my 2-story house. The neighbours might notice a wire running the 1 meter from around the upper-floor window casement to the eaves trough, if they look very very carefully. This is a stealth antenna on steroids.

With my primary interest in DX it was only natural that I'd try to work some despite knowing that it would be difficult. Doable but difficult. Apart from one VE and several W/K stations all my contacts have been DX.

As I continued my casual operating with this minimalist station the countries slowly added up. As the total grew I began to wonder if I could reach 100, the threshold for DXCC. I was not obsessed by the idea, only curious if I could do it, at least before the warm weather arrived and I could proceed with building a real antenna. By "real" I mean an arrangement of conductors designed to effectively work as an antenna rather than a random conductor co-opted and coerced into behaving as one.

I am happy (and exhausted) to report that I have done it. Last week I logged country number 100 -- OA -- and so I have tentatively qualified for DXCC, assuming I actually go ahead and make an application using these criteria (NB: my actual total is over 300), which is not in my plans. It's enough to know I've done it. This goes to show that with a little perseverance, and luck, just how attainable DXCC can be. If I can do it in 4 months with QRP and a no-antenna antenna pretty much anyone can do so.

My most productive band was 20, closely followed by 30 and 15. Both 10 and 40 were well behind. The main reasons 10 was poor were the lower availability of openings and the need for a really low radiation angle. I also suspect, like many tuners, my little MFJ L-network is consuming most of the power, and on 10 meters that was usually 3 watts. Any more and the KX3 folded back due to the excessive RF getting into all the cables. It's due to pretty much having my temporary shack inside the antenna.During periods when conditions were poor (geomagnetic disturbance) I could work almost nothing.

Apart from the early days, the countries did not come easy. There were ample "VE3?" queries from some rare and not-so-rare DX that never did make it into the log. There were a few good catches, including: J5, A7, XT, RI (South Shetland). There are many more common ones I did not log, and these included KL7, ZL and JA. Then there are the frustratingly loud ones that never hear me, such as D3, 5N, and 5U. I did once get a "VE3?" from the D3. Most DXpeditions were out of the question since only rarely can I get through when even so much as one other station is calling. Pile-ups are a no-go. Yet I did occasionally try, sometimes for the practice and sometimes hoping to get lucky.

All 100 contacts were on CW. I did make a few SSB DX contacts. The wider bandwidth (and therefore 8 to 10 db lower SNR) was not friendly to my puny signal.

With this small victory I can proceed with a lighter heart to construct a proper station, including a room dedicated to the shack and actual antennas. My real objective in this DXCC pursuit had been whether the rekindling of my interest in hamming would last. It has.

How speedily station construction will go I am not sure since like for many hams the radio is more of a winter pursuit. Summer is for antenna raising and maintenance, but mostly for non-radio activities. As things stand, the new shack is drywalled and ready for painting. I have enough material on hand to put up simple masts and antennas. If I can pick up a few tower sections to ease construction and maintenance of suitable supports I will do so. One way or another I plan to be fully equipped by the fall.

I may stick with QRP for a while yet. At least it won't be so painful with a real antenna.

Tuesday, April 23, 2013

Basic Site Planning

I have slowed my antenna design plans a little, which is why I've had less to say on the topic recently. The reason is that I am somewhat constrained with what I will use to mount the antenna. Well, not only that but also a variety of related tasks such as building my new shack and dealing with non-radio matters.

The shack-building has gone slow because of the warming weather. I'd rather be outdoors than mucking with drywall in the basement. However I must finish that space since I need to move out of the spare upstairs bedroom. I also have no intention of broaching the walls on the second floor to bring in coax. On the plus side the basement area I'm using was designed for a shack from the start, including a couple of 240 VAC outlets for the amplifiers I no longer have nor intend to buy.

Getting back to mounted antennas at some height, my plans have changed. I was never comfortable with the idea of using the roof as a support -- although it is a good spot -- because it's simply too visible (see picture in this post). There might also be some friction with the city for much the same reason. The policy on this matter was new to me since I've been out of the loop for so many years.

Since I also have no intention of installing a tower (at least not for the foreseeable future) my options are more constrained. The diagram below shows my major options.

The drawing is not to scale or accurate (my house has a more complicated layout). It is only intended to show relevant structures in approximate positions. The direction we're looking is west.

Option A is rejected, as I've said. In addition to the visibility issue, especially if I put up delta loops, there is a lesser concern with guying the mast. I do have a plan for that which would suffice nicely for a fibreglass mast plus wire loop, since the wind load would be low. However a yagi is out of the question! I am more concerned that the structure would appear fragile to others even if it is in fact very robust.

Option B is my second choice for where to mount the antennas for 20, 15 and 10 (and maybe 17) meters. This would be either a mast or short "TV" type tower secured to the house below the roof line and anchored to the ground without using any concrete. The antennas themselves would stand clear of the roof although the bottom of any delta loop would be below the roof apex. The eaves are about 6 meters above grade and the roof apex is about 8 meters. The roof pitch is not nearly as steep as shown. The aluminum eaves trough that runs along the south roof line is my present antenna.

There are important considerations when it comes to attached a mast or tower to a building. I do know how I would go about it but will not get into that here. It would make a good subject for a future post. One advantage I have is that my house was custom built so I not only know the structural details, I also have many photographs of the raw frame that I took during construction, including the exact spots where the brackets would be placed.

The base and bracket position has been selected so that the mast/tower does not block any windows (important!). The base will be close to the basement shack. I have a spot selected to open the wall to install a conduit for the coax cables that is convenient, secure and out of the way of accidental encounters.

Options C and D are for masts, or short towers plus masts for 40 and 30 meters. Since I concluded earlier that I am favouring delta loops which come close to the ground (~3 meters up) their supports must be placed in the away from the house and deck. My property is deep (200') but relatively narrow (50'). Fortunately it is long in the north-south direction (350°-170°) so it is easy enough to position a loop broadside to Europe. I did this very thing in the 1980s.

What has changed is the vegetation. I drew the two trees nearest to the C and D to their approximately correct heights. Both were much shorter in 1992. Even though both were decapitated in the 1998 ice storm they have since grown well past those heights. Neither is robust enough to support an antenna but the lower trunks are ideal supports for guy lines. They are each close to the property edges (east and west sides) and almost exactly opposite each other. The space in between is a septic field, which is not the place for a tower base. My old tower was close to D so even the concrete had to be broken out of the bedrock to meet DOE regulations for the new septic system.

Option C would place the north end of the delta loops somewhat close to the house but still well out of the reach of eager fingers. The guy line for the south end of the loop would go a tree or something else farther to the south.

Option D places the loops further away from the house, which is desirable. The problem is that there are two other, larger trees to the south of D (not shown in the diagram). Their trunks are just outside my property lines and they branch out over my property so that they nearly touch at a height of about 10 meters. The squirrels love the arrangement (which didn't exist 20 years ago), using it to practice their acrobatics as they bravely jump the space from one flimsy outer branch to another. They almost always make it.

For a ham these trees are a problem. They are large and old, regularly shedding debris that would surely impact any delta loop or inverted vee that dared to traverse that space. There is also a real risk that one of the trees will come down in future years. Option D is out.

So that's the tentative plan: high band antennas at B and low band antennas at C. The choice for high band antennas is still in flux for a variety of reasons. I'll get to those reasons in a coming post. Regardless of how it goes I will make sure to write about the 20-15-10 delta loop array I've designed. I just don't yet know if I'll build it.

Wednesday, April 17, 2013

Power and Contests

You notice some strange things when you have a puny station as It is not easy to be heard with 10 watts and an eaves trough as a poor excuse for an antenna . Even hearing DX is often a challenge on the high bands.

There are two edge cases I've noticed with this station. One is the DX contest stations that are practically beacons on the bands, day in and day out, irrespective of contests. While I don't know any particulars, many seem to rotate operators into this contest mode of operation as a form of training. They sit on a frequency calling CQ and working any and all callers for hours on end. These are undoubtedly superior stations with excellent antenna systems and high power (QRO).

The antenna systems are easy to guess at since these stations are getting through when others in their areas are far weaker on this end of the path. While I can be less sure of the power they are running it is surely a long, long way from QRP. A strong bit of evidence is that even when quite strong here most of these stations do not hear me when I call. Antennas are reciprocal but power is not.

The second case is the weak DX station. My gut reaction is to simply pass them by, reasoning that if I can barely hear them they will surely never hear me. I've proved this many times by tossing in a call and hearing them simply resend their CQ. Not always: sometimes they do hear me and I log a new one. A recent surprise of this sort was working a ZA last week on 20 meters.

It is likely that the ones that do hear me are either running QRP like me, resulting in reciprocity of results, or they have a lower level of noise than I do here. You simply never know. It costs little to make one call and if the weak DX doesn't come back to me or anyone else to just keep spinning the dial. Sometimes I try a few tricks before giving up.

Which brings me back to power and its purpose. Those stations with the big antennas and perhaps even bigger power may seem a bit overindulgent. It is reasonable to ask whether the power is needed when the antennas are so good. Let's also be honest and recognize that not only are a number of these stations running high power, they may be running just a wee bit over the legal limit in their countries.

For the casual operator or even serious DXer with a fantastic antenna farm it is arguably excessive to overdo the power, even if it is kept legal. Breaking through the pile-up for a new one is a proper use of power, but not so much at other times. Every ham makes a judgment call on what suits them. There is no one right answer.

Contests are a different matter. Power has a purpose that has nothing whatsoever to do with pile-up busting. What would seem excessive in other circumstances becomes justifiable in a contest.

Contest stations in the high-power category want to use QRO to maximum advantage. You cannot do this by search-and-pounce (aka hunt-and-peck) as commonly practiced by smaller stations. Sure, you'll work each QSO faster (higher rate) with power but the strategy of search-and-pounce is unproductive other than to add new multipliers

To consistently get big contact totals you must have others call you; that is, create long runs. To run stations you will be the one sitting on a frequency and calling CQ. Others find you and respond. Your success is determined by several factors:
  • The higher your power for a given antenna more stations will hear you.
  • Big signals are more attractive than small ones. If you don't believe it, try it. Tune the band. If you're like most hams you will be attracted to calling the louder stations. It just seems so much easier than digging for the weak ones. Many a rare DX station with a small signal gets few callers.
  • Create elbow room. This one is more controversial. Bands are crowded during a contest and stations are continually jockeying for space. Stations that also want to start a run have to squeeze in where there simply isn't any room. Conflict is inevitable. No one wants to sidle up adjacent to a mega-station since they will not be heard or will be overlooked (see previous point). Power helps the contester hold a frequency, and thus makes it easier to run up the contacts.
As with those DX beacons I opened this post with, the QRO contester is not too concerned with whether they can hear you. That is, they know they will attract many stations they will not be able to copy. They'd surely like to work you, but they are not married to the idea.

This behaviour is similar to the factory trawlers with their giant nets sweeping the ocean currents. They will pick up a lot of unwanted fish (the by-catch). They will readily admit this is unfortunate but will also see it as justifiable since they are getting more of what they want.

I just shrug and move on when they don't hear me. There is no reason to feel offended.

Saturday, April 13, 2013

The Multibander Within

When any antenna is shortened by means of loading elements it tends to become a purely single band antenna. This should not be surprising since the loading elements are specifically tuned to the band of interest, and not for any of the harmonically-related bands. For example, a full-length 40 meters dipole (vertical or horizontal) would be useful at 15 meters with modest tuning.

If we go back to the 40 meter linear-loaded vertical I recently looked at you will find that is truly single band. The following SWR scan covering 40 through 10 meters makes that fact clear.The antenna is mounted 2 meters above average ground.
However that isn't the end of the story. Any conductor can be tuned with a suitable matching network between the transmission line and the feed point; that is, transformed from one impedance to another. We can of course do this in the shack provided that the additional transmission line loss due to high SWR is within reason. From the chart above it should be evident that the SWR at other bands is not within reason.

A matching network at the feed point adds complexity, cost and (most emphatically) loss, but it can be done. However it isn't always exceptionally difficult. The present situation is an interesting case study in that regard. The reason is that the antenna is 13 meters tall, which is ~43 feet. Many hams have heard that a vertical of this height is easy to match on multiple bands with a simple network. It is also a subject of controversy for reasons that only some hams can see.

This linear-loaded antenna isn't quite a simple 43-footer since it has already been loaded to resonate on 40 meters. Even so it does show evidence of other resonances, resonances which are not especially evident from the above SWR chart. The actual R and X values do indicate some promise, though you'd have to plot them on a Smith chart to see that.

I "eyeballed" the values and decided to, metaphorically speaking, roll the dice. In EZNEC I connected a λ/2 length (calculated at 7.1 MHz) of open-wire transmission line. This is equivalent to making a full circle around the Smith chart, bringing the impedance right back to what it is at the feed point, though only on 40 meters (but is exact only for zero-loss line). At every other frequency there will be a net reactance that will transform the impedance.

After only a few minutes of fiddling with values in EZNEC I settled on 300Ω open-wire line, and I fed the antenna near the bottom rather than at the centre. The shift downward changes the values of E and I (and phase) at the feed point, which shifts the impedance (Z = E / I). Here is the resulting SWR chart from 7 to 30 MHz.
Notice how we've made visible some otherwise hidden easy matches. This was done no more sophisticated a matching network than a hunk of open-wire line. This is a bit like that trick in old detective movies where the hero lightly rubs a pencil lead over the criminal's notepad to highlight the depressions, and the message, from the previously removed top sheet.

Some of the SWR dips are useful, such as on 30, 17 and 12 meters, but not all. That isn't too bad for a roll of the dice, and it shows the matching potential of the 43-foot vertical. However, please keep in mind this is only a thought experiment not a serious antenna design.
  • The feed line introduces loss, including on 40 meters. The SWR is high on that section of open-wire line. In most cases the loss is modest, but first make sure of it.
  • Even without shifting the feed point the antenna is not electrically symmetrical on bands above 40 meters. That means you will have a challenge, perhaps an impossible one, keeping the open-wire line from becoming a part of the antenna (i.e. radiating).
  • A λ/2 of open-wire line at 40 meters is close to 20 meters long. In most stations that is a problem since the entire run isn't that long. It also needs to be mounted carefully to avoid a variety of problems. that was a long discussion about matching. But the match doesn't matter unless the pattern is what you want; first get the pattern right, then and only then work on the match.

The pattern on a multi-band antenna is always a challenge. The pattern of any antenna with an electrical length much longer than λ/2 is never simple, and can get quirky, with lobes and nulls in various directions, as you go ever higher in frequency.

For an especially bad example, let's look at how this antenna performs on 17 meters. With our "magical" feed line addition there is an attractive resonance near 18.1 MHz that draws our interest.

Ground losses are high at -9 db, which is considerably worse than on 40 meters; the pattern is asymmetric; and, there is also substantial radiation at higher angles, which does not suit my focus on DX. These figures become clear when we have EZNEC show us the currents on this antenna. Notice the position of the current maxima and minima: the bulk of the antenna's radiation comes from the bottom loading wire. This does not help us get a decent pattern.

So, again, don't be deceived by low SWR. The pattern matters. The antenna will certainly work, but will fare worse than many others.

Sunday, April 7, 2013


DXing with QRP to a tuner-fed aluminum eaves trough isn't easy. My country count plateaued at 90 countries when the HF conditions turned poor over the past little while. Mind you I am counting from late December when I reestablished a station, not all time with this call, which is well over 300 countries.

I am interested in seeing whether I can work 100 countries with this pathetic station before I finally am able to erect some real antennas. It's certainly possible, but it's been getting difficult as my total rises. In the last 24 hours I had a run of luck working 3 new ones, including two in central Asia. Over-the-pole conditions on 20 meters have been good of late. So now I'm at 93 worked, with many new band-countries.

When I say it isn't easy, I mean it is really difficult. Sometimes I get lucky and some weak and rare (to me) DX station comes back on the first call. Most often I get silence in response: I am just not heard.

In many of the in-between cases I am heard but not at all well. The most common response I get, when I get one at all, is "VE3?". Occasionally this converts into a good QSO though more frequently the other station gives up in frustration. I understand; I, too, get frustrated.

It reminds me of those long graveyard shifts trying to make contest contacts at a multi-single or multi-multi operation on 40 meters SSB. With a beam and a kilowatt there were many that heard me though far fewer were copyable on my end. Hour after long hour I'd repeatedly struggle to pull another call out of the noise, sometimes successfully and sometimes not. The log would fill slowly, too slowly, while waiting for sunrise and the high bands to open. Others would get that thrill as I trundled off for a few hours of sleep. In 30 minutes that lucky operator would surpass my hard-won contact totals.

I could claim this is "payback" time where I get to be the one with the weak signal trying to work the bigger stations, but the reality is that it is no fun at either end of the QSO.

Some operators give up quite easily and will log the first or second guess at my call. I have gone into DX logs as VE3UN, VE7VN, VE3STN (try this on CW and you'll understand), XE3VN, VA3VN, among others. Of course these are all inferior outcomes to being VE3?, since it at least means the DX operator is still trying to get it right.

Alternatively I should perhaps explore getting a special suffix. After all, special prefixes have become routine. Just listen to what was on the bands during the recent WPX contest. How much of a stretch is it to try for a special suffix. I'll bet you've guessed what I'm thinking: my preferred suffix is "?".

Then, when the DX comes back with "VE3?" I can shout back "QSL, QSL!!". This could greatly accelerate my ascension to the DXCC Honor Roll. Or perhaps nothing more than a lot of very confused hams.

Monday, April 1, 2013

Comparing Those Short 40 Meter Verticals

After all of that modelling it is now time to see what it can tell us about antenna choices for 40 meter DXing. First, to recap, here are the antennas I modelled along with links to the posts where each was discussed:
  • Linear-loaded vertical
  • Lazy-H vertical
  • Linear-loaded quad and delta loops
To make the comparison fair each is placed at about the same height (3 meters) over the same ground (good suburban, medium ground). Each is tuned for the low end of the band, aiming for resonance (zero feed point reactance) around 7.075 to 7.100 MHz, and adjusted for best match for 50Ω coax. It is assumed in each model that there are no obstructions (conductive or absorptive) between antenna and horizon, and that the transmission line is completely isolated from the antenna using one or more high-resistance common-mode chokes.

Although we have made the model simple with respect to the environment the reality is never like that. It is nevertheless critical and a common enough problem in many vertical installations. I therefore will use as one figure of merit the height of the average antenna current: higher is better.

Just to finish off these (important) preliminaries I want to summarize what the antennas do have in common:
  • Omnidirectional - Despite asymmetries in all the antennas, they are all effectively omnidirectional. The worst case is a maximum-to-minimum gain differential of 2 to 3 db for the vertically-polarized loops.
  • Match sensitivity - Matching and resonant frequency are very sensitive to even small adjustments to antenna height. Environment is also likely to be a significant factor. In all cases it is therefore desirable to make the antennas easy to adjust in place. Some suggestions are in the articles. The loops are hardest to adjust.
Where the antennas differ most profoundly is in their construction, which impacts visual appeal (this can be important in many situations), cost of materials, and weather survivability. If you need to purchase aluminum tubing you might be shocked at the prices. Individual hams don't have the bulk buying power of commercial operations. I have a bunch of aluminum stored away in the form of older antenna that I can re-purpose. Fibreglass non-conductive masts that should suit this application are available from companies such as Spiderbeam. Insulated heavy-gauge wire is widely available and comparatively cheap.

Now then, after all of that lead up over two weeks you may be expecting to hear me say something profound about which antenna is best, worst, etc. This is difficult, and did not turn out as I expected. This was a learning experience for me, and perhaps for you as well.

If you were following along you might have noticed one glaring fact: the patterns of all these antennas are almost identical! Sure, we got good matches to 50Ω coax, but that was easy and not especially important. What I want is to find the best possible DX performer for 40 meters. Yet in every case the low-angle gain ends up somewhere in the vicinity of 0.25 dbi at 15° elevation.

The performance difference, such as it is, can only be found in modest differences in the height of the average current. Since all antennas are mounted at the same low height this mostly comes about by how high the antenna reaches. For the two "true" verticals the average is at the centre point, which are 9.5 and 8 meters for the linear-loading vertical and Lazy-H, respectively, since each is mounted 3 meters up. Due to its squat construction the quad loop has its current centre up only 6.3 meters. The more complex delta loop has its average somewhere around 10.4 meters up, which is not too different from the verticals.

On the basis of this and its complex construction I won't hesitate to eliminate the quad from consideration. Of course it can be placed higher above ground without exceeding the top height of the other antennas but it then becomes more unwieldy and fragile.

All this leaves us to ask why these antennas perform so similarly? It turns out the reason is simple enough: the low angle performance is determined by ground, not the antenna! If you want more gain it is necessary to add more elements to create a vertical array. That is not what I want to do, though many hams have followed this route to great success.

What if we raise the vertical higher off the ground? As already mentioned the match will change, but here we will ignore that and focus on the pattern. It turns out you need to add quite a lot of height to get a significant change in the pattern. For illustrative purposes here is the pattern of the Lazy-H raised to 20 meters above ground; its top will be at 33 meters.

The pattern plot is educational. Total losses are cut to -3.6 db, or about 2 db better than when mounted at 3 meters. Unfortunately this helps little since that additional gain goes into higher-angle radiation. That's great is you want to operate a contest like the ARRL Sweepstakes, but helps little with DX. If that's your objective, put up a dipole.

At our target elevation of 15° the gain is actually slightly less than it was before. The lesson here is that you cannot outsmart Mother Earth; if you want better low-angle performance you'll have to move somewhere with better ground. All you've really gained is a clear shot to the horizon, which is helpful but unlikely to justify the construction of a massive tower. If you do have such a tower it will be far better to choose a dipole or yagi.

The antenna would also have to be lengthened since the change in height shifts the resonance upward to 7.175 MHz. We would also have to move the feed point to near the bottom of the vertical element to regain a 50Ω impedance. However these are merely details.

The big factor is ground loss. This is worth attention and so I took the trouble to model the Lazy-H (at its original 3 meters height) over various grounds. While not modelled, the other verticals in this comparison should be similar.

If you use EZNEC I made the results easily reproducible by using the standard set of ground options that come with the application. In the following table the first 2 columns are the ground conductance and dielectric constants, ranging from extremely poor ground at the top to salt water at the bottom. The final 2 columns are the net gain at 15° and total ground loss. The choice of 15° is done to ease comparisons at a typical DX take-off angle, just keep in mind the elevation of maximum gain ranges from about 20° down to 5°.

Gain at 15°Total Loss
0.0013-2.9 dbi-7.4 db
0.0015-2.1 dbi-6.7 db
0.00210-1.1 dbi-6.0 db
0.00213-0.6 dbi-5.6 db
0.00513-0.6 dbi-5.9 db
0.00613-0.6 dbi-5.8 db
0.007512-0.5 dbi-5.8 db
0.01140 dbi-5.4 db
0.03201.7 dbi-4.0 db
0.001802.3 dbi-3.3 db
5815.0 dbi-0.7 db

The differences in gain and loss are substantial across the full range of ground types. However unless you are one of the rare hams sited on a seashore that final row is pretty useless. In my case the second-last row (fresh water) isn't far wrong for a range of useful directions since I am very close to Lac Déschènes, which is a widening of the Ottawa River. I took the following photograph from the peak of my roof with the camera about 9 meters above ground and looking towards Europe (north-east). As you can see the fresh water is a little bit "hard" this time of year.

Apart from the water scenarios the range of gains and losses are quite modest at under 1 S-unit. I would therefore not be inclined to worry too much about ground quality. I do believe it is important to get above obstructions, many examples of which can be seen in the above photograph. Current averages much below the height of the photograph can result in attenuation, perhaps a lot, although I have no easy way to prove it.

Comparing all these short verticals to a full size, vertically-polarized delta loop at the same 3 meters height shows a modest advantage. At 15° there is about 1 db advantage favouring the delta loop, with a comparable average current height of ~10 meters. The gain is -3 db off the ends when compared to the broadside directions.

The final comparison I want to make is to an inverted-vee. This is the only horizontal antenna I will use in this analysis since it has comparable construction requirements. Like the other antennas it is a single, half-wave wire element, and it will be mounted using a similarly sized mast. The legs will be set 90° apart and the apex at 13 meters.

I won't reproduce the patterns of the inverted-vee here since I've shown almost the very same plots previously. In the broadside direction it shows a gain of -0.7 dbi at an elevation of 15°. Despite its low ground loss almost all the radiation goes out at high angles due to its low height, which is not only useless for DX it will increase QRM from domestic stations. I'd rather hear the DX, not the pile-up.

Where does this leave us? The two short verticals options look interesting but not too much. For myself I still favour the full-sized delta loop. This exercise has set my mind at ease about previously-unexplored alternatives.