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Lets say magic is capable of summoning fire of varying intensities for different amounts of time, how effective would a shield of wood covered in leather or metal? What would it take to melt or set the shield ablaze? What shield shape would be best at dispersing said heat? And at what point would the heat become fatal to the person holding it?(Suppose the wizard does not know about concentrating heat on a small point, the fire originates from the hand and the user is approximately 20 feet away, the fires heat remains constant throughout the blaze, and it is a flame like that of a propane flamethrower)

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    $\begingroup$ depends on the wood and how the heat is deleivered, oak makes a remarkably good ablative heat sheild, space.stackexchange.com/questions/21442/… As for the perosn underneath it would not be fatal until after the sheild is destroyed. $\endgroup$ – John Jan 5 '18 at 14:59
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    $\begingroup$ What is the fire-summoning process? For example, is it summoned and then projected/thrown, or is it manifested at a point in space - what limitations might there be? Is the fire intensity constant for its duration, or is it subject to decay over that time period? Does the dispersion of heat result in a loss of intensity (logic says that it would, but this is magic fire from nowhere) $\endgroup$ – Lee Leon Jan 5 '18 at 15:04
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    $\begingroup$ To reiterate what Lee Leon said is heating similar to lobbing globs of napalm, a blow torch lance, a laser, ect. Is it contact heating or radiative, is the heating sustained or instantaneous. $\endgroup$ – John Jan 5 '18 at 15:09
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    $\begingroup$ The thing with wood and leather is that they burn easily; moreover, you only have to set aflame a tiny little portion of the wooden shield, it will all burn up. So the magician only has to heat up a tiny little cubic millimeter of wood somewhere on the surface exposed to air... Moreover, wood (and leather) are poor heat conductors, so when heating up that treacherous cubic millimeter the magician doesn't need to worry about the heat being carried away and warming up all the shield. $\endgroup$ – AlexP Jan 5 '18 at 15:09
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    $\begingroup$ wood and leather do not burn as easily as people sometimes think, there is a reason using a laser to burn patterns in wood does not ignite the wood and a reason early fire fighters clothing was made of leather. $\endgroup$ – John Jan 5 '18 at 15:18
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Wood is a good insulator

From that perspective, wood will give you a good deal of protection. Heat transfer is governed by Fourier's law $$q = -k\Delta u.$$

The thermal conductivity ($k$) of wood is about 0.2 W/m/K. Lets say you want to keep heat transfer below 1000 W. That is about a microwave oven's worth of heat. Definitely painful, deadly after a while, but survivable for a short time. The thickness of a shield is maybe 2.5 cm (about an inch), and area is about 0.3 m$^2$ (or 3 square feet). The heat flux is measured in units of W/m$^2$. The temperature gradient $u$ is in units of K/m.

$$\frac{-1000 \text{ W}}{0.3 \text{ m}^2} = -0.2 \frac{\text{W}}{\text{m}\cdot\text{K}}\frac{T \text{ K}}{0.025 \text{ m}}.$$

I solve this as 417 K. Assuming that it is uncomfortably hot on your side of the shield (320 K), that means you can be hit with a constant heat source at around 750 K, hot enough to melt lead, for probably a couple minutes.

Wood is also flammable

Wood will autoignite at around 600 K. Canvas made from cotton will ignite even lower, although I think properly prepared wool would be more fire resistant.

Conclusion

Wood will protect you from a fire, up until the point that the wood itself catches fire. This is around 600 K, which is also around 600 F.

The heat flux needed to ignite wood might be in the 10-50 kW per m$^2$. Considering that our knight behind the shield is seeing 3 kW per m$^2$, it won't take long (less than a minute) for your shield to go up in flames if any of it is made of wood (or canvas or leather).

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  • $\begingroup$ keep in mind the shape of wood has a large effect on how easy it is to ignite, a flat smooth wood surface is much harder to ignite. firesciencereviews.springeropen.com/articles/10.1186/… Also consider naked wood was very rare on sheilds despite what movies wioud have you believe. $\endgroup$ – John Jan 5 '18 at 15:33
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    $\begingroup$ @John Fourier's equation doesn't care about shape. The point is that wood is a sufficiently good insulator that heat transfer is manageable until autoignition, no matter what temp that is at. $\endgroup$ – kingledion Jan 5 '18 at 15:45
  • $\begingroup$ What I mean is autoignition temprature is changed by shape thus increasing how long it acts as an insulator, and of course it will continue to act as an insulator until it burns through. $\endgroup$ – John Jan 5 '18 at 15:51
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    $\begingroup$ Of course an entirely metal shield has it's own disadvantages... $\endgroup$ – walrus Jan 6 '18 at 0:08
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    $\begingroup$ @walrus Actually, if a shield was padded out with canvas on both sides, then the material transition (canvas -> wood -> canvas, with some air mixed in) would add significantly to the thermal conductivity coefficient. Lets call it a wash. $\endgroup$ – kingledion Jan 6 '18 at 2:53
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Different kinds of wood and different metal alloys have different combustion and melting temperatures. Listing them here would not be productive - you can find results online with a few searches.

The shape of the shield would have negligible effect on heat dispersion. You would need very weird, "unshieldly" shapes to get a useful effect (think of a heat sink, see below).

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As for the effects that would have on the shield bearer...

Wood might make a good thermal insulation layer as long as it doesn't combust. If it does get into combustion, then you have flames on your arm. Enough said... Best option for the poor soul is to unstrap the shield and either jump in a body of water or roll on the floor. If fine sand is available, that can help put down the fires too. The results of such an attack are obvious - depending on how long you got exposed to it, and the amount and kind of clothing between the flames and your arm, you get from small burns to 2nd or 3rd degree ones.

Metal is a worse protection in this case... Most metals are good thermal conductors. You don't have to melt the shield to cause grave damage. Even at 100 degrees Celsius (212 F), you are going to get seriously burned. If the metal goes red hot (around 430 Celsius/800 F), you are sure to get 3rd degree burns.

Burned skin can easily get infected. In medieval Earth people had zero knowledge about antibiotics, and doctors would not wash their hands before helping patients. Unless your world also has some healing spells, people who get their arms burned this way are probably going to need amputations. Ironically, the usual way to close and sterilize the stump resulting from an amputation is through cauterization.

Finally, if you want to kill someone behind a shield with magical fire, it would be much more productive to just burn the person rather than the shield. If the magical fire is delivered in a manner similar to a flame thrower's fire, just aim at the target's feet or around the shield. It would take a very large shield to completely cover someone, but then that person is stuck. If the shield is easily flammable or metallic it's just a matter of time until they get serious hand and forearm burns.

Remember that human hair and most kinds of clothing are flammable, and metal armor is just as conductive as a shield. Burning the shield instead, in a medieval setting, is more likely to cause a slow death and thus is much more cruel than a quick kill.

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  • $\begingroup$ The metal of a shield was rarely in direct contact with the person using it, (wood or leather handles and separating pads are far more common) so heat transfer is minimal. $\endgroup$ – John Jan 5 '18 at 15:37
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    $\begingroup$ @John holding a flaming, or red hot shield by leather straps, with your forearm separated from it by a thin bracer, does not sound confortable. Then there is the matter that you won't want to touch any other part of your body with that shield. If you accidently touch your tigh with it, you'll be limping if you survive. $\endgroup$ – Renan Jan 5 '18 at 15:42
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    $\begingroup$ comfortable no, but not injurious either, not for a while, air and wood is a remarkably poor insulators, the fact that most shields were composite structures also works in your favor. also only some shields were strapped to the arm, just as many are simply carried by a handle. we also don't know the delivery method so it could take quite a long time to ignite or heat said shield. $\endgroup$ – John Jan 5 '18 at 15:47
  • $\begingroup$ @John would you be willing to make that point in a controlled environment? $\endgroup$ – Renan Jan 5 '18 at 15:48
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    $\begingroup$ Since my hobby is blacksmithing I do so all the time. Also consider metal shields are rarely metal all the way through (especially if large) most are metal over wood. $\endgroup$ – John Jan 5 '18 at 15:53
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Shield Construction

Wooden shields rarely have exposed wood, they are covered in metal, leather, or painted canvas. Even the few known uncovered viking shields are believed to be burial shields not utility ones. more on viking shield construction and usage.

metal shields are split into two groups as only smaller metal shields were ever solid metal which may not provide any protection depending on how the "fire" is delivered. larger metal shields were metal sheething over wood, some got even more complex, the famous spartan shields were layered wood and leather covered in a layer of bronze. source

Effects on the shield

An agricultural flamethrower (propane) will take quite a long time to burn through a wooden shield and a metal sheathed shield might prevent heat transfer even through prolonged exposure. Gas based torches are remarkably bad at igniting a flat smooth wood surface, to the point it can be used for decorative highlighting of grain. They just do not transfer heat very efficiently if not enclosed. Leather covering will make them far more resistant, to the point it will take minutes of constant exposure to breach the shield. With metal sheathing it may not be able to reach the ignition point of the wood understructure even after several minutes of exposure, especially as the wood will char into an even worse conductor first.

Either type of shield will allow the soldier to close the distance and dispatch the wizard with plenty of time to spare, likely without the shield even igniting even in the worse case scenario. the exception being some painted canvas coated shields as the canvas may ignite even if the wood underneath goes unharmed which should at least provide a decent distraction.

smaller shields and bucklers may not be able to defend against the flame at all depending on how big it is, if they do have the coverage even these solid metal shields will still be able to defend for a considerable amount of time as far as combat is concerned. Again more than enough time for the soldier to close the distance and attack the wizard.

Why this doesn't matter for the flame as a weapon.

The biggest advantage the wizard will have is sight and mobility, as the defender will not be able to see the wizard while using the shield to block the fire. So the wizard can easily move the flame to target the legs or even just step to the side and hit an undefended angle, without the defender being able to react or even know until it is too late. So this flame will still make an effective weapon because shields do not have total coverage. Used with skill the flame will work quite well as a weapon but it will not brute force its way through a shield.

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Given your criteria, the shape, surface, and color of the shield does matter.

The trick is, once shielded from fuel and radiated energy, you want to keep hot AIR away from the target, not the fuel (unless the fuel actually sticks to the shield).

A white or silvery shield would be most effective in deflecting radiated heat away. A black shield would be the worst-case scenario. A slippery shield would prevent the fuel from sticking. Think about police shields, made of composite material, that deflect Molotov cocktails and the burning fuel from them.

The applied heat is not stationary (like a match), it is moving. If you keep the heat moving past the shield, it minimizes the effect. If the shield were appropriately shaped, it would deflect the air flow (and thus the heat energy) around it. I would suggest that a curved narrow shield would be best to deflect the air flow, and thus the majority of the heat. Think a branch moving across a fire vs the same branch stationary over the fire.

And the size and shape of the directed flame is important. Ever try to light a log with a match? But use several matches over a larger surface, you might do it. It is the amount of total heat that matters. A narrow flame jet is not as effective as the same jet with a wider circumference of flame. The total heat energy would be greater. A blow torch capable of burning through metal at close range would not be effective at 20 feet, but a jet engine would. Even a 50,000 BTU furnace burner will not ignite wood at twenty feet. It doesn't have enough force to carry the heat that far. Mind you, an unprotected human would get mighty uncomfortable from just the radiated heat. Remember, water boils at a lower temperature than wood ignites (you can't cause a wood fire by just pouring boiling water at atmospheric pressure over it, no matter HOW much water you use).

The fuel is important. How quickly does it burn? Over 20 feet, will it all have burned up, or will there still be fuel left to burn, and thus to create heat? If the fuel all burns up at source, or just after, all you have is hot air blowing over the shield. To cause damage, it would have to be super-heated air.

Also, it depends on the speed of the flame (the speed of the air flow). An intense flame, but without any force behind it, would not reach 20 feet. Any heat source hot enough to effect the target would be too close to the wizard. Think about standing over a fire, vs standing 20 feet away. So you need a flame with some velocity behind it.

Wood is actually much better at withstanding burning than is metal. A metal beam will deform far earlier than will a wooded beam. Wood doesn't melt, and it doesn't deform and bend under high heat. It maintains its structural integrity until complete failure. It snaps.

And leather is actually very good at protecting against flames. Blacksmiths and welders use leather gloves and aprons for a reason. I have never seen a blacksmith using a metal apron or a chain metal glove.

So, a white or silver curved wooden shield protected by leather (on the inside?) would withstand a prolonged attack.

Unless the wizard could maintain the flame for some time, directed at the target (would the target, a person, really just stand there?) for probably a minute or so, I would suggest that the target could get to the wizard faster than the shield would ignite. And even if the shield DID ignite, it would continue to offer protection until completely burned through.

But change the wizard's weapon to a ball of flame, or a very wide flame (wider than the shield), that will encompass the entire target, and you have a completely different story. The flame does not have to burn through the shield, it (and the heat) goes around it. It's the hot air that wouldn't be stopped. Drop the target into a furnace, and even a ceramic heat shield and perfect insulator will be immaterial, unless the target is COMPLETELY surrounded by the shield.

Really, the best protection against a fire-breathing dragon would be a wooden shield, not metal armor. That's why they make saunas out of wood, not metal.

Edit

My background team has reminded me that there is one other danger besides radiated heat, air temperature, and fuel load.

Traditionally, sulfur and brimstone have been referred to in fantasy worlds.

These burning substances add toxic fumes and carbon monoxide poisoning to the mix. No shield (unless equipped with a respirator) will protect a warrior from products of combustion, particularly sulfur dioxide. If the wizard uses a sulfur based fuel, all survivability analysis and bets are off.

It's not usually the fire that kills, it is the toxic fumes.

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  • $\begingroup$ So based on what you said would a wooden shield with a highly polished reflective metal outer covering that is curved or pointed to direct the heat around the target with a leather interior work the best? $\endgroup$ – Christopher Void Jan 5 '18 at 18:22
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    $\begingroup$ I am not sure I would use metal at all. Perhaps a ceramic coating. Metal conducts the heat into the wood. Many a house fire has been caused when the wood stove is placed on a metal shield, and the wood ignites by heat conduction under the shield. Heat shields on stoves always require an air gap between the heat shield and any combustible material for that reason. Asbestos shields were much better, until they found out about asbestos and cancer. But polished slate tiles would work. Maybe a polished silver coating, if they have that technology. $\endgroup$ – Justin Thyme Jan 5 '18 at 18:32
  • $\begingroup$ But yes, you need to protect against the burning fuel, radiant heat, and the hot air flow. $\endgroup$ – Justin Thyme Jan 5 '18 at 18:33
  • $\begingroup$ I should have clarified that these shields would be used in combat with non magic foes as well so they need to be able to take hits without the coating breaking, so what would you say would be optimum then? $\endgroup$ – Christopher Void Jan 5 '18 at 18:34
  • $\begingroup$ I would go with slate tiles, if the warriors were strong enough to carry them. Otherwise, wood and leather layering. Wood splits, but the leather binds it and disperses the impact energy. Modern ceramics are really impact resistant, but the technology is rather recent. Police and military armor uses ceramic tiles. Even if they crack, they still continue to offer protection. The wood offers structural integrity, which ceramics do not have. $\endgroup$ – Justin Thyme Jan 5 '18 at 18:40
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Some sort of flame acting on some sort of metal, leather or wood for some amount of time... Make a decision about what you want the answer to be for your story and then justify it.

If you want people to survive, a thin layer of steel (better) or leather over a wooden shield will protect them from quite a bit. The heavier the wood, the harder it is to get it to start burning, but the higher its probable thermal conductivity. There will be an upper limit on how heavy the shield can be for the user. A steel shield would probably be the worst because as it heats up, it burns the warrior until they drop the shield. A purely wooden shield would vary from light and terrible to heavy and ok (though perhaps too heavy to use) depending on the type of wood. Leather, tanned with vegetable extracts, is actually a pretty great flame retardant.

The wise spell caster will aim around the shield and strafe to flank, so the wise warrior will probably not face down a spell caster alone, no matter their shield.

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  • $\begingroup$ its funny you should say that last part as i have been thinking about group tactics for fighting mages. $\endgroup$ – Christopher Void Jan 5 '18 at 19:20

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