How viable are non-magical flaming weapons? Like, coating the sword with a flammable substance and then setting it on fire. Would the trouble be worth it for the increased damage? Would they be more dangerous for the yielder? Would the fire negatively affect the blade?
No. At least not, that example. Also flaming arrows are out. The physics involved mean they either self-extinguish on launch, or they’ll ignite the user (I don’t remember which, and I kinda think it’s the former.)
That said, there are a lot of historical and modern military applications for flame.
The modern examples that come immediately to mind are napalm, dragon’s breath shells, and Molotov cocktails.
Napalm is, basically, jellied gasoline. It will burn, it will stick when it lands, and it will keep burning. Set something on fire and watch it melt. Napalm is, quite frankly, pretty terrifying stuff, and while the exact chemical formula is recent, the concept of launching burning liquids at people is not, going all the way back to Greek Fire. No one is exactly sure what Greek Fire was, but it would burn, could be lobbed onto ships or people you didn’t like, while burning, and would not stop burning once it arrived.
Molotov Cocktails are a medium ground here. You load a bottle up with alcohol, use an alcohol soaked rag as a fuse, light, and throw. There’s a little bit more going on here though. Alcohol solutions are only directly flammable if they’re more than 50% alcohol by volume. Most hard liquor is around 80 proof (40%), but, the vapors put off by the solution are still flammable (down to around 20%, if I remember correctly). So you can use a bottle of vodka as an improvised incendiary device. (Fair warning, it’s been a long time since I took a chemistry class, so those exact percentages may be a bit off.)
In spite of being named after a Russian Revolutionary, the idea of setting something on fire and chucking it someplace is not a new concept.
I know you can launch flaming payloads with a trebuchet, put them roughly where you want them, and set the area on fire. I’m not 100% sure of the military history, but it was used for centuries. Anything that will break apart on impact will spread the flame over a decent area and get a good blaze going.
Hot shots originally referred to cannonballs that were preheated before firing, with the intention of it igniting enemy structures or ships. This isn’t something we still think about (outside of the term “hotshot” seeping into idiomatic usage), but it did work, apparently.
The modern equivalent would be incendiary ammunition. There’s a lot of variety here, and they range from phosphorous rounds, which will ignite on contact with moisture, including the moisture in the air, to dragon’s breath shells which eject a mixture of highly flammable metals, such as magnesium, or potassium, which will ignite on contact with moisture.
Phosphorous was also a popular component for incendiary grenades, mortars, and other explosives. For example, one of the US military’s versions of a Molotov in WWII was produced by dissolving phosphorous and rubber (as a thickener) in gasoline). This mixture would self ignite on contact with the atmosphere (when the glass broke).
One variant of modern incendiary grenades use a Thermite variant
to eject molten iron on detonation.
So far as it goes, most flare guns fire a 12 gauge shotgun shell. While the plastic ones won’t survive trying to put a conventional shell down range, the flare shell itself can result in horrific, and fatal, burns.
If you want a melee weapon to set someone on fire, you might be able to achieve that safely by heating the blade or using something like a thermal lance. The problem with simply coating a sword with oil and lighting it up is, they tend to drip. And, when you’re swinging the sword around, you’ll end up with burning oil getting splashed everywhere, including on the user. This is, “a very bad thing.”
Of course, shoving a torch in someone’s face is also a very bad thing, for them, and fits the definition provided.
So, the short answer is, yes there are a lot of real applications for setting someone on fire, especially when they’re all the way over there and walking is too much effort. Setting your own sword on fire is not a great idea, however.