Recently I have been playing this game called League of Legends (LoL). I’m pretty sure that loads of guys out there play LoL. So I was checking out some info about the game. So in this game, there are 3 maps or Fields of Justice. The first one is Summoner’s Rift, the second being Twisted Treeline and the third is called Howling Abyss. But wait, I’m not here to tell you about LoL. If so why would I label it under ‘Science’? Ok here comes the interesting part. In the description of Howling Abyss LoL said that at screams could be heard in the wind and those were rumoured to be those of warriors who got pushed into the bottomless abyss. So I was thinking “Since its a bottomless pit, the warriors who fell in the abyss wont hit the ground and die so how long will it take for them to die and if they screamed when they died, how long would the screams take to reach the top?”
Ok so the first part’s really simple: How long would they take to die? Assuming there are no flying creatures that eat them up, they did not cry, sweat, pee or breathe through their mouth and they were regular humans, they would take 3 days to die of dehydration.
So that’s part 1 answered, now for part 2. Here’s where it starts to get difficult. How long would their final scream take to reach the top? firstly we have to find out how far down they would have travelled. So assuming they were falling like a skydiver (horizontally) we can find the projected area or the area which is in contact of the air below them. The average male Body Surface Area ( BSA )is 1.9 m^2 therefore to calculate the projected area, we can take the BSA divided by 2 as only one side of their bodies are in contact with the air. therefore the projected area would be 0.95 m^2. Next we have to find their mass. Assuming they were very fit and they had the most ideal body weight according to the Body Mass Index (BMI) and they were average American males in the United States of America who have an average height of 1.763 m, they would have a mass of around 150 pounds or 68.0389 kg. Now we have all the data we need to calculate the terminal velocity of the warriors or the speed they will be at when they stop accelerating. The formula for terminal velocity is as follows:
Vt= Terminal velocity
m=Mass of falling object
g= Acceleration due to gravity
p(rho)= Density of fluid which the object is travelling through (in this case, air)
A= Projected area
Cd= Drag coefficient
So what do all these mean? well we have been through practically everything except for the drag coefficient. So what is drag coefficient? Drag coefficient is a value which cannot be calculated. It is the value which puts the force generated by drag into account. The drag coefficient of a man is 1.0-1.3. Lets assume that our warriors have a drag coefficient of 1.2, not too skinny yet not too fat. The acceleration due to gravity on Earth is 9.8m/s^2 and the density of air at room temperature (25 degrees Celsius) is 1.1839 kg/m^3 so with everything in SI units we can calculate the terminal velocity of the warriors. The final answer is 54.44492062 m/s assuming all our calculations are right and in SI units. this can be rounded off to 54.4m/s (3 s.f.). The next part that we have to solve is the acceleration period. so from 0m/s to 54.4 m/s how long would it take? Once again assuming that the acceleration due to gravity is around 9.8 m/s^2 as on earth, all we have to do is divide 9.8m/s^2 from 54.4 m/s. The result we arrive at is 5.551020408 s. to find the distance travelled during this time, all we have to do is imagine that all this data is being plotted on a distance time graph and find the area during the acceleration period.
1/2*5.551020408 s*54.4 m/s =150.9877551 m
This can once again be rounded off to 151 m ( 3 s.f.)
Now lets move on to the part where we deal with the duration of the freefall. Assuming that they took EXACTLY 3 days to die of dehydration, they would take 24 h*3= 72 h to die. Now we minus the 5.551020408 s from the 72 h. 72 h = 72 h*60 min = 4320 min =4320 min* 60 s= 259200 s
259200 s – 5.551020408 s = 259194.449 s (my calculator only has this many decimals)
Therefore we can assume that our warriors remained at terminal velocity for 259194.449 s.
So to find the distance they travelled at terminal velocity, all we have to do is:
259194.449 s* 54.4m/s= 14100178.02 m
So our warriors travelled a total distance of:
14100178.02 m + 151 m = 14100329.02 m
Finally to calculate the time taken for the sound to reach the top, we have to divide the distance travelled by the speed of sound which is Mach 1 or 346.13 m/s at room temperature (25 degrees Celsius).
14100329.02 m / 346.13 m/s = 40737.09018 s
That is how long the sound would take to reach the place where our warriors fell from. Converting it to hours : 11.3159 h
So there’s the answer!
If you have anything else, like a science question of some sort or you found a mistake in my calculations and want me to rectify it, please post it in the comments section or you could send me a message via the contact me form!
Thanks for reading!
Clyde Lhui 🙂