Can an Umbrella deflect a Great Wyrm Red Dragon’s Breath?

Supposing your umbrella forces an air current in front of it to shield the user.

If your handle is hollow and pushes the cold air behind you up and out around the outside of the umbrella, one could hope the forced convection will reduce heat transfer sufficiently. Basically, we're making an air curtain in front of the umbrella.

This requires a little bit of machinery or magic inside the umbrella but it seems you have no other choice if this is to work.

Convection formula: P = dQ/dt = h * A * (T − T0) Therefore E = h * A * (T − T0) * Δt

A human can withstand temperatures of 42°C and the breath is at 1246°C meaning T - T0 ≈ -1200°C.

Let's suppose the Wyrm's breath lasts Δt = 45s. Its a big thing and a long human breath is about 15s (I timed myself).

A = 2.5 m^2

Taking into account the calculations made by others on this thread, we have an E = 30 GJ energy transfer. And yeah, there is latent heat of fusion and dissipated energy but a few numbers were taken for worst case scenarios and constraints have been eased since so this is a good order of magnitude. BUT this energy is spread over a 70-ft = 21.3 m cone according to https://www.d20pfsrd.com/bestiary/monster-listings/dragons/dragon/chromatic-red/red-dragon-great-wyrm/ So we are only taking 100 * 2.5 / 21.3^2*pi = 0.175 percent of that because the rest is not directed towards us. We get a final E = 0.00175 * 30 GJ ≈ 50 MJ.

For air on air conducto-convection, we have empirically h = 10.45 − v + 10√v according to https://physics.info/convection/

This gives us v - 10√v = 10.45 - E / (A * (T − T0) * Δt) = 10.45 - 5*10^7 / (2.5 * -1200 * 45) ≈ 380 m/s

So √v = (10 + √(100 + 4*380))/2 ≈ 25 √(m/s) therefore v ≈ 625 m/s. That's a bit under twice the speed of sound in air.

I don't know how permissive your magic/machinery system is but it's theoretically possible. Plus, you can probably modify many these numbers to make it more favourable, especially if the heavy constraints on total energetic output are eased only slightly (a slightly smaller wall means orders of magnitude less energy and therefore orders of magnitude less speed for the air curtain). For example, if you double the breath time, you almost halve the required speed of your air curtain.

The physical model is not perfect but it works well enough to get an idea of the situation and gives a nice proof of concept.

Hope this helps!

This very much depends on the mechanism of how the breath works.

If it's heating by radiation (i.e. some kind of heat ray), then @Ash's answer above gives a convincing 'No'.

However, this kind of answer also prevents the dragon surviving the breath, so we should probably conclude this is not what the rules intended.

It may be better to assume it's more like a flamethrower. Flamethrowers work by squirting out a flammable substance, which is ignited. Thus the heat is generated not at a point, but across the target area, and not instantly, but over a period of time as it burns.

Obviously a very hot flamethrower, something like thermite perhaps.

Would this work?

Thermite has an energy density of 20Mj/L

Let's consider a 10cm square of 4" thick wall. Let's for convenince, metricise this to a 10cm cube of iron. this weighs 7.8kg.

Irons specific heat capacity is 444 J/kgC, and we need to raise it 1523C

444 * 7.8 * 1523 = 5.2MJ.

So a 2.5cm thick layer of thermite could melt through 10cm iron (assuming all the heat goes into the iron). Let's say 50% goes in, and we need a 5cm layer.

So (handwaving away how the dragon stores and fires large quantities of thermite), the breath weapon could be thermite-based.

Can an umbrella deflect this?

A standard umbrella can easily deflect thermite before it is ignited.

It's not impossible for an umbrella to deflect lit thermite, though obviously it'll need to be thicker and heat resistant – it doesn't have to withstand the heat indefinitely, just long enough for the thermite to be deflected. Some kind of fibreglass cloth is likely?

If this leaves you standing in a small clear patch in a large field of thermite, your life expectancy won't be great. But if this protects you from a stream of thermite which otherwise splashes down some distance away, then there's no reason you can't survive.

What if the umbrella were made from the esophaguses of a Great Wyrm Red Dragon? The umbrella might well survive and be found smoking, deep in the wall's crater directly behind where the player -used- to be.

Frame Challenge: The premise of the original thread is wrong

The original theory is as follows:

A pure iron wall has 30 HP per inch of thickness and Hardness 10. A Great Wyrm Red has a breath weapon that does 24d10 Fire Damage in a 70 ft. cone. Maximum damage is 240, which is halved against objects for 120, which is then dropped by 10 because of Hardness. So it's technically a little less than 4 inches thick that can be liquified. A 70 ft. cone has a maximum straight horizontal line in it of something like 80 ft., and everything in the AOE takes full damage.

Which someone disputed as

4 inch thick Iron has 120HP and hardness 10, and a Great wyrm breath weapon does 24d10 damage in a 70' cone which averages at 132 damage.

However fire would do half damage to objects (I personally wouldn't say that iron walls are particularly vulnerable to fire) which after hardness would be 56 damage so a basic MM great wyrm red dragon would probably heat the metal thoroughly but not completely destroy it.

I would go with the second method with averaged damage (as commonly you don't roll and use the average in a lot of DnD situations for sake of speed) in which case it would heat the metal but not destroy it meaning the breath is much less than expected heat wise.

~600 C is a lot less destructive than the initial 1243 C. However what is commonly stated in the RPG stack is DND is not a physics simulator thus, we can also assume that these measurements were not really thought out in terms of physics in general.

The Wall Would Explode Before it Melts

You can not "melt" the wall in any thematically satisfying and meaningful since of the word. Ash's energy calculations do a good job of expressing how much thermal energy it would take to melt the wall, but they do not tell the whole story.

Here are a few practical points that it misses:

1. He is off by a few order of magnitude when converting J to Kilotons. By his calculations, it would be a 0.007762kT blast, or roughly the energy force of a really big conventional explosive missile.

2. High energy fires condensed into a small area create explosive forces that blast the steel away as you "melt" it. Basically you are doing this to the wall, but at about 1,000,000:1 scale. This means there are forces at play which may not require you to fully melt the metal to remove it.

3. When shooting fire across a room, you create more heat than is absorbed by the target.

With these 3 factors added together it is REALLY hard to say how accurate a simple thermodynamics equation will be; so, instead I will assume that a dragon's breath would probably have a similar thermal efficiency to an Oxyacetylene torch, then we can do some calculations to figure out how much energy is actually going into the metal.

It was surprisingly hard to find the energy efficiency of an Oxyacetylene torch, but after running through a long rabbit hole of various sources I've found that:

• Oxyacetylene torches produce ~1585.26 kJ/cuft of fuel
• You can cut a 1/4" channel through about 10.9 ft of 1/2" thick steel per cuft of fuel
• This means you need about 1163.49 kJ/cuin of steel to heat/blast your way through the wall.
• Using a 90" tall wall you have a total volume of @ 345,600 cu inches to remove.
• This requires a total energy of ~402,103,380kJ. Compared to Ash's equations, this means you are actually outputting about 12.38 times as much energy as it takes to just melt the steel to do so by heat blasting it. While this is still no nuclear bomb, it is roughly equivalent to blasting the wall with 10,544 liters of burning jet fuel. That is 17.6 liters per sqft.

So, to answer your question, with a normal umbrella having an 8-10sqft surface area, standing in the dragon's spray means you getting pelted with the equivalent of ~140-180 liters of high velocity jet fuel. Even if the Dragon's breath failed to ignite, it would probably buckle your umbrella under the sheer force of getting hit by whatever fuel it it breathing at you. If your umbrella were able to take the force of getting hit by the dragon's breath, you would then have to be able to survive the explosive force of that much fuel combustion in such a small place. Even if you could survive that, you are then looking at a sudden wave of heat that is going to be hotter than the surface of the sun coming at you from all angles.

The only way I see your hero surviving this is if he is wearing and entire suit made out of starlite or similar material. Starlite can protect a person from 5 minutes of sustained blow torch heat; so, it can probably protect you from the heat of a dragon's breath as long as you can solve for how to make it durable enough not to crack under the explosive force... also you're hero will need to be super human tough to survive the explosive forces being transferred through the armor.

Umbrella vs a kiloton nuclear warhead.

Even ones made of unobtainium and blessed by all the gods will be vaporised in an instant.

Lets take a look at that wall melting, and try to work out the power in the dragons breath

So, melting point of iron is 1538 degrees C

Lets assume Earth global average temperature at the spot the attack happened (15 degrees C).

Irons specific heat capacity is 444 J/kgC. Irons density is 7874kg/m^3

Your wall that was melted was 24.384m ('80ft') * 10cm ('4 inches') * ...? Assuming the wall is a standard medievil fortification the wall height was 2.5m minimum. (But it could be up to 6m). We're going 2.5m here just to give the umbrella the best chance.

So we have $24.384 cdot 0.1 cdot 2.5 = 6.1 m^3$ of iron.

The wall weighs 48031.4kg.

So to heat that wall by one degree, you need 21325941.6 joules of energy.

... But we need it heat it up by 1523 degrees.

So the energy contained in the breath is: 32479409056.8 joules!

That number means nothing, so I suggest refering to Wikipedia's helpful "Orders of magnitude" page, which shows us that:

• This is just under a kiloton nuke.
• This is bit over a Massive Ordnance Air Blast Bomb, the largest non nuclear bomb ever created.
• This is a bit over the impact of an A380 at cruising speed - 560 tonnes at 511 knots

Also remember this is just the energy that hit the wall - the breath also heated up the air, the ground, the dragon, and the poor people behind it.

(Edit: Corrected a maths error, I had originally calculated this as over the strength of a Hiroshima bomb, it's actually about an order of magnitude below this.).

No you can't

The breath is simply too hot. If it hits the umbrella and it holds, you'll still be exposed to incredible heat from all sides where the breath goes past you. It is able to liquify 4 inches of metal on an 80 feet surface! Assuming steel, that is 1510C or 2750F! But it's much, much hotter, as it can liquify 4 inches deep. In. A. Breath. The flash heating will probably cook you alive. Where it hits the ground or surroundings it'll likely liquify the material, likely giving off lots of toxic funes that'll rob you from breath or poison you, likely both. This will also add to the heat flying around you.

The umbrella might not protect you fully as well, making you in even more dire straights.

Make the umbrella with something akin to the Shuttle thermal protection system

The black HRSI tiles provided protection against temperatures up to 1,260 °C. [...] These tiles were such poor heat conductors that one could hold one by the edges while it was still red hot. [...] The HRSI tile was composed of high purity silica fibers. Ninety percent of the volume of the tile was empty space, giving it a very low density (140 kg/m3)

For comparison water has a density of 1000 kg/m3.

Just be sure that the deflected breathe doesn't bounce back on some other nearby surface.

I can't find information on their price per square meter, but from the answer to this question I infer it is not prohibitively high, if jewelers can use it as soldering base.