#calculating velocity

[er-cryptid]

Velocity Graph from Position Graph [Ex. 1]

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[imaveryevilenby]

i calculated the terminal velocity of a coconut

idk why i did this but I was 0.337 m/s off from the actual answer given by an online calculator so that's cool

[audiart]

Because N has probably never been to school or learned math until the end of the series what would happen if he tried to help porter with math homework?

He's a robot pretty sure he has a built in calculator /lh

Porter is pretty good at math! Not her strongest subject but gets homework done fast (when she remembers)

[hyuneskkami]

[theacedragon0w0]

Brother in christ I didn't suffer through physics class to get CURBSTOMPED BY CALCULUS!

[britomart]

sometimes when i’m doing physics i feel like a renaissance man, but a lot of the time i just feel like a medieval knight being asked about the airspeed velocity of an unladen swallow

[deesi-academia]

oscillations padh padh ke sar ghoom gaya hai

[crunchyfield]

How does Mario Kart 8 Deluxe speed translate into real-life units ?

This something we all have been wondering at some point as a civilized Mario Kart player.

This is also a thing that was pretty much not covered at all within the vast universe of Internet.

So we're going to work it out for the sake of players' curiosity.

Right off the bat, I already see some people coming with the : "No need for experiments, the whole topic is solved 'cause on Mario Kart 8 Deluxe CTGP shows you how fast you drive with a speedometer".

1) There is no way to evaluate, assume anything since the speedometer doesn't display any actual units but numbers/values.

2) Mario Kart 8 Deluxe CTGP is a modified version of the game so go ask its developers for the speedometer's reliability in the first place.

Our main goal here is to authentically/legally (with no other tools than the game provides except for time) find out the real-life scaled coinless speed values (with their respective units) for 50cc, 100cc, 150cc and 200cc.

Let's dive right into the researches :)

First & foremost, we have to understand what speed is.Basically it is a variation of distance for a given amount of time, in other words it is an amount of distance per amount of time.

In this post, we'll only be focusing on the maximum speed of each engine class as it's the most relevant information we wanna know (thus ignoring Instantaneous speed as well as acceleration) :p

Consequently, we will use the following speed formula for constant speed :

(P.S: I wrote unidirectional due to the fact I was in fact implying we are going to test speed/velocity with no direction change during experiments)

Then we want to find a good course to study and to test things out.

Ultimately, we have to choose a track with a simple continuous layout (with no track type variations nor holes/empty areas ==> discontinuous) that could be broken down into different parts to test on.In our case ExciteBike arena fits perfectly experiment wise (especially for its simple layout featuring simple geometric shapes).

Here is ExciteBike arena's map broken down into lines following symmetries (axial symmetry or central symmetry), the map being made from an in-game deep track exploration (note that the track is not well represented nor to-scale, it is only to be seen as a visual help) :

Let's try to frame an estimate of the track's total distance in distance units (probably a unit symbolizing distance which is used in Mario Kart 8 Deluxe wiki) with the following item probability distributions' charts :

Method :

Multiplayer offline (2 players : to disable the position factor as much as possible)/Versus mode/no CPUs, AIs.

2nd player have to be placed on the test line and pick one item at a time and use it before hitting back to the item box (to disable conditional probabilities) to make each case identical and independent as well.Use the frantic items’ probabilities chart (features high probabilities of appearances with the most efficient & cheap amount of tries simplifying experiments) to follow the appearances (items’ appearances are easier to follow than their disappearances) of a given item for a given distance value in distance units, items' appearences to identify (read as colomns and rows intersections for a specific colour, itself for a specific amount of distance) :

Once an item appeared after a certain amount of tries, check its related distance and try to drive back and forth from an apparent track line/current location to another apparent track line till the range tends to no difference (we can identify framed distances more easily using different item modes in favour of it).

Using given items' probabilities (see the charts above) to identify an estimate of a given distance in a given item mode.With the use of the Binomial law, we can consider stochastic variables (like X) associated with items to identify appearances in which trials' success corresponds to those items' presences.

To calculate the number of tries for getting at least one appearance of an item amongst the ones we have got to identify for a given framed distance, we have to solve for the number of trials after mathematically modeling our situation with probabilities :

In our case, finding out the best item setting for each given distances (ranging from 1000 to 5500) with a wanted likelihood of appearance equivalent to 95% :

where :

Sum up all the track's section estimated distances to get the total distance.

Unfortunately, this approach only gives off framed estimates of distances and takes up way too much time & effort for something as uncertain as it is :/ . We'd have to be doing the track measurements in Mario Kart 8 Wii U version to avoid introducing conditional probabilities on top of assuming MK8 tracks are the same lengths as MK8DX tracks (plus, as the items' probabilities (charts) take into account Mario Kart 8 Wii U datas instead of Mario Kart 8 Deluxe's).

I know I did not elaborate much on this part and got a little quick but believe me it's absolutely not necessary to.

(Btw, see Mario Kart 8 items' probability distributions wiki to understand the probility system)

Let's now try out another way to determine ExciteBike arena's track length.

Firstly, we have to measure ExciteBike arena course's length.

Secondly, if we take a close look at Mario Kart 8 Deluxe player's statistics menu, we clearly see there is a traveled distance counter which displays this total traveled distance in kilometers (Km).

That means we can measure ExciteBike arena course's length but we have to do many races to get some decimal places out, doing the course over 100 times (driving in the middle of the road to get a fair estimate) should be enough for the experiments (a decameter accuracy is not a big deal simply because doing 1000 times a course to get a meter accuracy is useless since a few meters are negligible, e.g when you measure how tall you are you clearly not take millimeters into account as they almost make no signaficant differences to your height.. same goes for race tracks...)

Dividing the distance we obtain after 100 courses (took me about 3.5 hours straight btw) by 100 then by 3 (because there are 3 laps per course) indicates ExciteBike arena course's approximated length is 947 m (0.947 km).

Some people might be wondering why I do not use max speed values (in 150cc) from the Mario Kart 8 Deluxe wiki to determine ExciteBike arena's length in distance units but to my mind using undefined units (sorry not sorry but the wiki did not explained what a "distance unit" necessarily symbolizes in the game distance nor how it's been measured, same story with the "frame") for both distance and time isn't the best way to go for since those said values were provided by some people's tests not by developers themselves.Unless explained, we are not going to use distance units nor frames but rather in-game units for both distance and time (we'll be using the game's stopwatch in time trial mode).

Secondly, notice that the track consists of semi-cercles merged to a rectangle on each side of it like this :

We wanna apply pixel measurements to be able to quantify different proportions of the track :

Knowing the length of the used bars and using perimeter formulas we get the track's total length in pixels :

Then we have to take a specific portion of the track as long as possible with visually distinguishable eye marks from which we can get the experiments started (just as follows) :

To measure its length, we can place 2 players at both eye marks to determine the distance in-between the 2 players' map icons' barycenters in pixels (to make the barycenter thing easier, we only use Tanooki Mario's map icon since the shape is quite similar to a circle) :

And get that length in meters too :

To set up the experiments, we have to take a combination with a level 10 of speed (3.25 speed stat bars), an average speed stat level combination :

We'll place the vehicle a certain amount of distance back from the first eye mark and make it use a mushroom to get to top speed quickly when its effect fades away while driving straight (no tilt to be as accurate as possible).Besides, we'll count the elapsed time using time trial's time display for 150cc & 200cc and external time counters for 50cc & 100cc (pardon the low quality) :

This way we can apply the average speed formula because the speed will remain constant during the tests, we can make a sequence of 20 values for each engine class (50cc, 100cc, 150cc & 200cc) and calculate top speed related to every single value :

Eventually, we can average out the top speed values in real-life units for every engine class as follows :

Suffice-it-to-say there are uncertainties but after correctly and identically performing experiments those shouldn't be a big problem, we could estimate those using variance and standard deviation :

So here we are with an interesting outlook on Mario karts' (bikes', ATVs' & all) top speed values (coinless), 200cc is just outrightly wicked fast irl (you'd definitely get pulled over in the motorway lol) :$

At least this info should calm down Mario Kart 8 Deluxe haters always obliviously claiming it's slow asf x)

Sidenote: For sUsSy BaKaS, We were obviously talking about ground speed (tbh I don't see people driving underwater, in anti-gravity nor airborne lol) as we tried to reach for a realistic approach.

Overall, all values are approximations (fair ones) but I curiously really wanted to get my hands on this topic as no one did it so far in the vast world that is internet :)

[croded]

bro might be a professional fanfic writer (his favourite tag is the canon divergence tag)

peak philosophy in ao3 tags

[wannabe-paladin]

Imperial measurements are cottagecore and the metric system is dark academia. Is this anything

[ianmiller42]

Guidance Waves

And now for something different from usual: theoretical physics. If that turns you off, so be it, but the reason I am excited is I have now published my ebook ��Guidance Waves 2nd Edition”, which I claim is an alternative theory for quantum mechanics. Which raises the question, what does it need to do to be an alternative theory? First, before everyone turns off completely, the main equation is…

[muirneach]

im trying to do river basin calculations and physics n shit And i have to go to a documentary screening about police brutality in a minute. and meanwhile carlos is losing a tennis match

[iamhollywood]

if i have to do calculus for one more second i'm going to throw myself off a cliff

[whats-in-a-sentence]

I won't bore you with the calculations but the results come out as follows:

"The Stars in their Courses" - Isaac Asimov

[licorishh]

I desperately need a Subnautica-esque open world game set in deep space like BADLY

[little-p-eng-engineering]

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Little P.Eng. for Discrete Element Modeling (DEM) Services: Unveiling the Power of Simulation

The Importance of Discrete Element Modeling (DEM) Studies and What Problems It Can Solve

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Discrete Element Modeling

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Particle behavior

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PFC (Particle Flow Code)

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Rocky DEM

Yade

Abaqus

Ansys Rocky

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Particle velocity

Shear forces

Normal forces

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Torsional moments

Acceleration

Material scatter

Flow simulation

Wear patterns

Center loading

Equipment design

Production line optimization

Safety protocols

Computational simulations

Input parameters

Simulation accuracy

Bulk Material Handling & Processing

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