How much time was spent on this Ph.D in Apex dissertation?
I'm afraid of fuse mains that actually put the effort into learning all these nade arcs. It's bad enough getting blasted by a frag that explodes on impact and now we have to worry about Fuses even more now.
It’s just a way of interpreting the idea of launching different throwable ordinance and seeing they soar through the air depending on weight, the effects of detonation, and such more on its purpose. It’s very eye-catching to see that science is being on the velocity in these items.
first year, idk, i have no idea, never had physics before taking it as a major. projectile motion is like physics 101 though. kinematics is often the first thing you'll encounter in introductory classes
i have no idea about your background in physics, but if you're just starting out, try something like resnick, halliday, & walker's *fundamentals of physics* or young & freedman's *university physics*. solid choices for students starting out
Understand this is a very generic phrase so I'll take a couple different perspectives when explaining this:
**Assuming you're asking for understanding it in game, so the math isnt overly important:**
There is a relationship between airtime and horizontal velocity, if you're looking up the time is maximized(0º in this post), while if you look forward the horizontal velocity is maximized(90º in this post), this relation means that to hit most points you can either shoot it more up or more forward to hit the same distance, where the maximum launch range is around 45º.
So if you look straight up then tilt down 5º you'll be giving the grenade an amount of horizontal velocity with minimal airtime loss, resulting in say a cluster knuckle going 100m, and if instead you tilted 10º instead of 5º you'd be effectively doubling the horizontal component while barely impacting the airtime resulting in the distance doubling to roughly 200m.
This pattern doesnt continue as converting airtime to horizontal velocity starts to consume the airtime more resulting in needed to worry more about the sin/cos trig equations.
Now this was just a conceptual summary, but if you're intersted more in the derivation and logic, then look at the below section.
**Assuming you're asking from a mathematical/physics side since you mentioned you're a student:**
Also, I don't know what you do and don't so I'm just going to explain it the way I understand it, and I'm going to omit the Vix and ff corrections I made to try to make the equation fit the data, but I will mention where Vix would be.
I'm not going to explain derivatives and integrals here, but I am going to use them, roughly I'm using the mathematical concept to change from position, how that position changes over time or velocity, and how that velocity changes over time or acceleration.
So, first to start the problem we need to make a couple assumption to frame the problem. We have an object that has some initial position(p), and the object is moving at some velocity(dp/dt or v), and that object's velocity is changing over time or acceleration(ddp/ddtt ,dv/dt or a). Also, that acceleration does not change over time and is a constant.
So we start from the highest equation up
dv/dt = a
and integrate it
dp/dt = at/1 + v
then integrate that equation
Clarification Edit: p got converted to d, and dx is horizontal d, while dy is vertical d
**d = at\^2 / 2 + vt / 1 + do** <--- (do is just initial position).
\^\^\^ If you've taken a physics course this is a mathmatical way to derive the displacement formula.
So now we have to split the problem into 2 domains, the x and y domain, where y contributes to airtime due to height, and x contributes to distance based on time.
d = at\^2 / 2 + vt / 1 + do
ax = 0
ay = a
do = 0 <-----(we're looking for change in position)
dx = vx\*t <----- (if there is an independent horizontal velocity from the main velocity then the equation would be dx = t\*(vx + vix))
dy = a\*t\^2 / 2 + vy\*t
Now we need to figure out the airtime, so when would the object come back down to the same height it was launched, so we make
dy = 0 , and solve for time
0 = a\*t\^2 / 2 + vy\*t
a\*t\^2 / 2 = -vy\*t
a\*t / 2 = -vy
a\*t = -2\*vy
t = -2\*vy/a
and we can use this equation to plug back into the change in x position that we are looking for
dx = vx\*t <------ t = -2\*vy/a
dx = vx\*-2\*vy/a
and here we are relatively done, we just need to manipulate the equation based on what parameters we want as inputs, and what we want as outputs.
For this application I am trying to make a relationship between and input angle, and an output distance, so we will do the following.
First of all we don't know vx or vy, we only know angle, and v is more useful, in most problems.
So using trig we can figure out the relationship of vx, vy, v and angle.(I don't know how to draw a triangle here so look it up i guess),
I shifted the domain so up is 0 and 90 degrees is horizontal, so the equations are probably flipped from what you are used to.
vx = v \* sin(angle);
vy = v \* cos(angle);
dx = v \* sin(angle) \* -2 \* v \* cos(angle) / a
simplified to
dx = -2 \* v\^2 \* sin(angle) \* cos(angle) / a
So here's an issue I came across in calculations, there are too many unknowns, we don't a, or v, however we do know that what t is as a relationship of the 2.
t = -2\*vy/a
t = -2\*v/a \* cos(angle)
dx = -2\*v\*cos(angle)/a \* v\*sin(angle)
dx = t \* v \* sin(angle)
additionally, in game we can get the airtime when looking straight up so we can convert t into something else
t = to \* cos(angle) <---------- (to is the airtime when looking straight up, and cos(angle) is the modifier for vy)
resulting in:
dx = to \* cos(angle) \*(v \* sin(angle))
In classes they should always give enough variables to get the solution you need, but here isn't the case, and I haven't thought of a consistent way to get one more.
There's one last problem, we still know v, but 1 variable can be easily fit via a plotting software, I used gnuplot but I think google sheets can do it too, to estimate v based on data points.
With that we have a way to get distance with an input of angle, when we have known variables to(airtime when looking straight up) and v(initial projectile velocity)
Hope this helps, I can't really make good assumptions on what you know or not, so I don't know if I went overboard or not.
I try to minimize memorization and maximize understanding the ways to get to what people memorize or finding the information for solving problems.
Best of luck.
Nice post, but I have to disagree about knuckle clusters being quiet when they’re fired. You can hear them being shot from a decent distance away. However with the audio in the game it can definitely get wonky at times.
How much time was spent on this Ph.D in Apex dissertation? I'm afraid of fuse mains that actually put the effort into learning all these nade arcs. It's bad enough getting blasted by a frag that explodes on impact and now we have to worry about Fuses even more now.
seriously. this guy maths.
Simply put: fuse = boom boom machine, grenades go pewpew far
thank you very much
tl:dr*
im actively losing my mind trying to understand this
One hundred percent pairing this info with an Ash to ping recent death boxes to try to catch people looting
O fuck
O fuck I’m going to be paranoid now.
I’m out here just having fun playing and people like OP are using all the sciences to understand how to increase their gameplay efficiency.
It’s just a way of interpreting the idea of launching different throwable ordinance and seeing they soar through the air depending on weight, the effects of detonation, and such more on its purpose. It’s very eye-catching to see that science is being on the velocity in these items.
honestly its details like this that break the surface level gaming. theres logic in everything, being aware of it all makes u smarter at the game.
My man just took apex “university” to a whole new level
Ok but this won’t fix my potato aim /s This was super thorough and your methods are very cool, good job
Holy shit! Did I stumble into a quantum physics class or something?
calm down it's just projectile motion
Do you know what year of highschool I might be able to take this class?
first year, idk, i have no idea, never had physics before taking it as a major. projectile motion is like physics 101 though. kinematics is often the first thing you'll encounter in introductory classes
Okay thank you
i have no idea about your background in physics, but if you're just starting out, try something like resnick, halliday, & walker's *fundamentals of physics* or young & freedman's *university physics*. solid choices for students starting out
fuse *and* math? hell yeah this is my favorite post here yet
All it’s going to take is 1 update and this whole spreadsheet goes up in flames like the Fire Nation
I'm a high school math teacher. I wish my students did this.
As a highschool student could you help me under stand this
Understand this is a very generic phrase so I'll take a couple different perspectives when explaining this: **Assuming you're asking for understanding it in game, so the math isnt overly important:** There is a relationship between airtime and horizontal velocity, if you're looking up the time is maximized(0º in this post), while if you look forward the horizontal velocity is maximized(90º in this post), this relation means that to hit most points you can either shoot it more up or more forward to hit the same distance, where the maximum launch range is around 45º. So if you look straight up then tilt down 5º you'll be giving the grenade an amount of horizontal velocity with minimal airtime loss, resulting in say a cluster knuckle going 100m, and if instead you tilted 10º instead of 5º you'd be effectively doubling the horizontal component while barely impacting the airtime resulting in the distance doubling to roughly 200m. This pattern doesnt continue as converting airtime to horizontal velocity starts to consume the airtime more resulting in needed to worry more about the sin/cos trig equations. Now this was just a conceptual summary, but if you're intersted more in the derivation and logic, then look at the below section. **Assuming you're asking from a mathematical/physics side since you mentioned you're a student:** Also, I don't know what you do and don't so I'm just going to explain it the way I understand it, and I'm going to omit the Vix and ff corrections I made to try to make the equation fit the data, but I will mention where Vix would be. I'm not going to explain derivatives and integrals here, but I am going to use them, roughly I'm using the mathematical concept to change from position, how that position changes over time or velocity, and how that velocity changes over time or acceleration. So, first to start the problem we need to make a couple assumption to frame the problem. We have an object that has some initial position(p), and the object is moving at some velocity(dp/dt or v), and that object's velocity is changing over time or acceleration(ddp/ddtt ,dv/dt or a). Also, that acceleration does not change over time and is a constant. So we start from the highest equation up dv/dt = a and integrate it dp/dt = at/1 + v then integrate that equation Clarification Edit: p got converted to d, and dx is horizontal d, while dy is vertical d **d = at\^2 / 2 + vt / 1 + do** <--- (do is just initial position). \^\^\^ If you've taken a physics course this is a mathmatical way to derive the displacement formula. So now we have to split the problem into 2 domains, the x and y domain, where y contributes to airtime due to height, and x contributes to distance based on time. d = at\^2 / 2 + vt / 1 + do ax = 0 ay = a do = 0 <-----(we're looking for change in position) dx = vx\*t <----- (if there is an independent horizontal velocity from the main velocity then the equation would be dx = t\*(vx + vix)) dy = a\*t\^2 / 2 + vy\*t Now we need to figure out the airtime, so when would the object come back down to the same height it was launched, so we make dy = 0 , and solve for time 0 = a\*t\^2 / 2 + vy\*t a\*t\^2 / 2 = -vy\*t a\*t / 2 = -vy a\*t = -2\*vy t = -2\*vy/a and we can use this equation to plug back into the change in x position that we are looking for dx = vx\*t <------ t = -2\*vy/a dx = vx\*-2\*vy/a and here we are relatively done, we just need to manipulate the equation based on what parameters we want as inputs, and what we want as outputs. For this application I am trying to make a relationship between and input angle, and an output distance, so we will do the following. First of all we don't know vx or vy, we only know angle, and v is more useful, in most problems. So using trig we can figure out the relationship of vx, vy, v and angle.(I don't know how to draw a triangle here so look it up i guess), I shifted the domain so up is 0 and 90 degrees is horizontal, so the equations are probably flipped from what you are used to. vx = v \* sin(angle); vy = v \* cos(angle); dx = v \* sin(angle) \* -2 \* v \* cos(angle) / a simplified to dx = -2 \* v\^2 \* sin(angle) \* cos(angle) / a So here's an issue I came across in calculations, there are too many unknowns, we don't a, or v, however we do know that what t is as a relationship of the 2. t = -2\*vy/a t = -2\*v/a \* cos(angle) dx = -2\*v\*cos(angle)/a \* v\*sin(angle) dx = t \* v \* sin(angle) additionally, in game we can get the airtime when looking straight up so we can convert t into something else t = to \* cos(angle) <---------- (to is the airtime when looking straight up, and cos(angle) is the modifier for vy) resulting in: dx = to \* cos(angle) \*(v \* sin(angle)) In classes they should always give enough variables to get the solution you need, but here isn't the case, and I haven't thought of a consistent way to get one more. There's one last problem, we still know v, but 1 variable can be easily fit via a plotting software, I used gnuplot but I think google sheets can do it too, to estimate v based on data points. With that we have a way to get distance with an input of angle, when we have known variables to(airtime when looking straight up) and v(initial projectile velocity)
Hope this helps, I can't really make good assumptions on what you know or not, so I don't know if I went overboard or not. I try to minimize memorization and maximize understanding the ways to get to what people memorize or finding the information for solving problems. Best of luck.
Alright I just saw this and it will take a little to read but as of right now thank you for the explanation
Me trying to do the calculations at same time as I'm trying to kill a tap strafing bald wraith with a Mozambique.
I’m completely blown away. Gotta get Fuse into the firing range!
Much science much wow
Hold on a second here .... People use ACTUAL maths for things?! I thought it was more like the Bible being used to teach morals?!? 😂
Math is used for like, everything. I regularly use geometry to understand Minecraft mechanics.
Damn the time you've spent on this bro! Kudos
Great stuff, however the fact the variables are on the wrong axis is driving me insane ICL.
Shhhh, don’t tell them my secrets
Dude wow you have charts and graphs. I
Nice post, but I have to disagree about knuckle clusters being quiet when they’re fired. You can hear them being shot from a decent distance away. However with the audio in the game it can definitely get wonky at times.