Path of Frost as viewed by an engineer
Intro:
Activates a freezing aura for 10 min that creates ice beneath your feet, allowing party or raid members within 50 yards to walk on water. Usable while mounted, but being attacked or damaged will cancel the effect.
Have you ever wondered how death knights work? Well I'm here to ask and answer one simple question: Just how much power is needed to make Path of Frost work? Now now, I know what you are thinking. "Its magic, it doesn't have to make sense!" Well I say even magic has to behave the laws of simple physics!
(Read more break because its quite long. Sorry if you are on mobile)
We are going to use a human male of average mass for these calculations, although you'll quickly see that the race we choose for this won't make a difference in the long run (68 kg / 150 lb). Lets call him Bob!
Obviously the weight of the mount has to come into consideration as well. While a horse can weigh a hefty 500 kg (1100 lb), WoW is more well known for its huge mounts that sit on top of mailboxes than it is tiny horses. We need more mass. We're talking dragons!
Scientists estimate that large pterodactyls only weighed about 320 kg (700 lb), which while about the right size for a drake mount in WoW, seems a bit light-weight if you ask me. We could use the Stone Drakes in this example as it would undoubtedly weigh much much more, but it would be difficult to come up with an accurate weight for such a beast. So lets use something that we have more information on, yet is still REALLY heavy.
Mammoth mounts!! Yes, these furry guys from WotLK are probably our heaviest mounts, coming in at an estimated 5500 kg (6 tons)! Mammoths will be our token mount for the calculations below.
So lets do some math shall we?
volume:
To find the amount of ice required to keep a mass afloat, we will use the equation:
density of ice * volume of ice = density of ice * volume of ice + mass of load
In order to fully support Bob, we will need 0.682 m^3 of ice. That may not sound like a lot but for a comparison that is 341 2-liter bottles of ice.
Now lets do the same calculation with Bob riding his mammoth mount. This comes out to a whopping 84.0 m^3 of ice....or 42,000 2-liter bottles. If you couldn't tell, this is going to require a LOT of energy.
velocity:
Path of Frost would be pretty worthless if you couldn't get from point A to point B with it, so we need to know how fast a mount can run. From this we can find the mass flow rate and finally start modeling this as a thermodynamic system.
I could't find any information regarding player speed from a google search, but I do remember once in Burning Crusade, I calculated my speed on an epic flying mount using a GPS addon and it came out to approximately 55 mph (24.6 m/s). This was at 380% total speed (100% + 280%). If we assume a ground mount runs at 200% speed, that would come out to be 28.9 mph (12.9 m/s).
cross sectional area:
We need one more property to find the mass flow rate: The cross sectional area of the piece of ice as it's being created. I found this using the required width and length of ice for a person or mammoth to stand on and then going "down" as far as needed to reach the necessary volume. The dimensions for these ice floes are: Bob's ice floe: 1m x 1m x 0.682m Mammoth's Ice floe: 5m x 5m x 3.36m
The cross sectional areas are: Bob: 0.682 m^2 Mammoth: 16.8 m^2
mass flow rate:
Normally we would probably use volumetric flow rate, but for these calculations, using mass is simpler. In short, this is how fast water much be frozen in order to keep the object afloat at full speed.
Using the equation M_dot = density * area * velocity,
We can calculate flow rate. And for just Bob running at 100% speed, he would have to freeze 4108 kilograms of water PER SECOND to stay afloat.
The mammoth is even more asinine, at 101,208 kg/s
heat transfer:
Now we are getting to the meat of this post. Just how much heat must be removed from the water per second? I'll give you a hint. It will be an ungodly amount.
We are going to assume a middle ground for water temperature at 20 degrees Celsius. Although it should be noted that it would take much more energy to use Path of Frost in Tanaris than say Winterspring
It takes 4.2 kJ of energy to cool 1 kg of water from 20 to 0 degrees and an additional 333 kJ to crystallize it into ice for a total of 337.2 kJ/kg.
From all the data we have, we can then create our own formula to find the power requirements for each process:
Power = M_dot * 337.2 kJ/kg
Power required for Bob: 1.385 x 10^6 kilowatts or 1,385 MEGAWATTS Power required for mammoth: 34,127 MEGAWATTS
Overview:
If you don't know what a megawatt is, or don't know how to apply it to every day life, here are some comparisons.
*A nuclear power plant at full capacity produces about 500 MW of power *It would require the combined effort of 3 nuclear power plants for Bob to run across the water himself, not even including his bags or armor. *For Bob to ride his mammoth across the water, he would need almost 70 nuclear reactors in his back pocket. *If Bob rode the mammoth across water for 10 seconds, the energy required for that distance would be equivalent to over 250 atomic bombs
WE'RE NOT DONE YET!!
Path of Frost affects the entire raid right? What if we have 39 other people riding on mammoths with our Death Knight? Oh yes, its about to get interesting.
1.37 MILLION Megawatts required! 2,800 Nuclear reactors equivalent! 10 THOUSAND atomic bombs every 10 seconds!
So now we know that death knights are literal power houses. Where is it coming from? Is it all in the runes? Why can't they channel this power into a single blow to take down Sargeras himself? The world may never know. But we DO know that DKs will be the future power source for Azeroth for years to come.
