The Electra Glide, or FL series, is easily the most iconic Harley-Davidson. Favoured by law-enforcement agencies and horizon chasers around the world, it’s pretty much the company’s signature model and, with its distinctive “batwing” fairing, is instantly recognizable. In one form or another, it’s been in the company’s lineup since 1941.

These days, it represents the pinnacle of motorcycle luxury and refinement for the Milwaukee manufacturer. Offered in a dozen trim and equipment levels, it can be had with things like hands-free Bluetooth, rider-passenger intercom, iPod presets, and a 25-watt sound system. My test bike, the Ultra Limited Low, had all of the above, as well as cruise control, adjustable air vents, and an information screen mounted above the handlebars.

Power, as always, is delivered by an air-cooled V-twin that in this case displaces 1,700 cc and features fuel injection, twin overhead camshafts, and a six-speed transmission. This is the classic Harley drive train—traditional yet up-to-date at the same time. Definitely not the fastest bike on the road, it still has more than enough power to provide flawless all-day cruising while returning surprisingly frugal fuel economy. It has a 5.6 litres per 100 kilometres combined fuel rating—a figure that always catches me off guard. Despite its heft and oversize dimensions, it’s still a remarkably cheap way to get around.

It also has the most important ingredient of all in spades: presence. Whether it’s muffled or not, the Electra Glide announces itself as soon as it arrives. Admit it—when a Harley pulls up, you look. The Ultra is a visually stunning piece of equipment that still has gravitas other manufacturers can only imitate. This is one of the reasons law enforcement still favours the Electra Glide. For whatever reason, motorists take it more seriously than other makes. Both BMW and Honda have taken a serious run at this market, and it’s still owned by Harley.

The other reason cops like the Electra Glide so much is that it has unmatched low-speed stability. This is a bike that can almost stand on its own—without a kickstand. Not quite, of course, but in traffic and during low-speed trolling, it’s firmly planted and rock-steady. There are other, equally sybaritic touring bikes out there—the Honda Goldwing and the BMW K1600, for example—that are faster, but they can’t match the FL when it comes to dead-slow crawling.

That said, if the Electra Glide does decide to topple over, there’s no bringing it back. At almost 400 kilograms (880 pounds), once this puppy starts to go, it’s all over but the crying—a fact I was conscious of the whole time I had it.

As well, for shorter riders, it can be a bit of a stretch. My bike had the “low” option, which drops the seat height down to 740 millimetres (29 inches). This is an excellent feature for those who are a little inseam-challenged, but it’s still a bit of a reach to get both feet flat on the ground.

But the bike has so much going for it and is so enjoyable to ride, we can put up with its various shortcomings. Crack the throttle and you’ve got endless amounts of torque and takeoff power. On the highway, it’s a smooth, stable dreadnought that eats up the kilometres effortlessly and has you in one of the most comfortable saddles ever bolted to a motorcycle. I struggled somewhat with the infotainment setup, which can be risky during highway riding, and learned to have everything ready to go before I hit the blacktop. Handlebar controls make things like volume control and station selection straightforward enough, but you don’t want to be fiddling around with buttons and knobs while clipping along at freeway speed.

I also couldn’t help but feel that the Electra Glide is a bit of a dinosaur. Yes, it’s a joy to ride and has years of research and development and rider experience behind it, but I found myself wondering just how long bikes of this size can hang on. For older riders, the Electra Glide may be the cat’s pyjamas, but younger riders might not appreciate its charms and could view it as an oversize, bloated piece of rolling furniture. It’s no secret that Harley’s traditional customer base is fading, and the company is addressing this by bringing out models like the Street series specifically to bring younger riders into the fold.

And then there’s the price. With a two-tone paint job, my Ultra Limited Low will run you $34,279 before extras—$32,999 for the basic-black version. This makes it one of the most expensive standard-production motorcycles on the market.