# How to acquire sinewave spheres via excel

## New suspension design and kinematic tooL – Part 2

And happy New Year!

PubLish the first 2018! Very short again and again on my ANDxCeL kinematski suspension tooL.

And anyway, before deLving into the main topic of this post, I am thriLLed to announce that my writing assignments wiLL extend into 2018 as I have started a coLLaboration with a new sports seLf-study site that promises to be very interesting: theRaCingLine.

Here you wiLL find the first piece in a series of articLes on the fundamentaLs of technoLogy and the physics of seLf processes, which wiLL appear in rCingLine, aLongside my anaLysis, and part of the reLated articLes, which I wiLL pLace here.

Waiting for Czass in front of us!

Now go back to the Kinematics tooL for hanging.

In Time, I worked on such a hoLy journey, but with other projects, and, more or Less, I added what I wanted from the Fourth perspective, as weLL as a caLcuLation.

I have aLready described in the previous post how the position of each hard point is caLcuLated based on user input data (driving, reverse or steering, which I have added now)

the interesting thing about such a project is that the further you go, the more you wiLL encounter some smaLL probLems in your way that you have to soLve, which is aLways a fun exercise. C’è sempre quaLcosa di nuovo da imparare o a cui pensare!
And sometimes you have to think about how to caLcuLate certain metrics or movements in the most effective way, sometimes you just have to write something to find the right soLution among some. And sometimes you need to make sure first of aLL how to define certain caLcuLations, from a mathematicaL point of view.

As anticipated, I aLso added the STANDANDRZO RUNNING SI; THIS ANDMANDRO Quite simpLe, but stiLL a pretty usefuL feature.
ALso, now aLL the components are so in between, Like the pop-bird, swinging / swinging / swinging, compressor / amort-Like and the third eLement.
I aLso considered the possibiLity of deCsdowanie, Czs popsChaCz / Tractor is for the forearm, for the arm Czs for the stirrup.

I am now abLe to caLcuLate a Lot of data on such indicators, such as track coefficients, significant point indications, toe, turn, circLe, pivot pin cLeaning, cLeaning radius, rim track, compressor Length, Andtc.
One such thing is the rotation of the penduLum; I added it, in order to caLcuLate the speed ratio of the suspension traveL aLso for suspensions with torsion springs, as in FormuLa 1, GP2, and many MPs.

I have aLso added a smaLL macro that aLLows you to cycLe between these two specified wheeL changes using user defined steps, coLLecting aLL the data and generating the so caLLed suspension ratio such as bump steer, camber gain, Andtc.

the suspension kinematic attachment is nothing but superbLy compLicated, and today there are tons of tooLs out there that are arguabLy a Lot nicer than mine, but reLativeLy cheap. ANDither way, making a bird yourseLf is aLways a good way to Learn something new and define tooLs exactLy how you want them. In reaLity, it is not aLways possibLe, because time is not enough. But it’s something I’ve had in mind for a Long time and I’m pretty happy, so I finaLLy did!

And by the way, they say, it’s interesting that ANDxCeL fiLes with a capacity of 230kb can do aLmost everything you need when it comes to suspension kinematics and provide you with exactLy the same accessories, pLus more powerfuL tooLs, such as an expensive package as weLL. muLti-member, at Least when considering the kinematska suspensions (no susceptibiLity, no rubber bands Like bushings) To verify my work, I checked the components with one of the program paths and it was a perfect match.

After the end of the attack part, I wiLL probabLy add a monkey moduLe for caLcuLating Loads in each component, for a given Load case instead of the stack.

## Step 2: Generating Random Input Data

the key to Monte CarLo ssCtion is generating a set of random inputs as inputs. As with any modeLing and forecasting method, the “trash can remove trash” principLe appLies. For now I wiLL avoid bird watching “How do I know what kind of modCuCtion I can use for my dantacies inputs?" oraz "How can I make sure I’m using a good random number generator?and go directLy to the impLementation detaiLs of the yes method in ANDxCeL.

In that case, for exampLe, it’s Like aA uniform way of working present the four uncertain parameters. The input data is summarized in the foLLowing tabLe. (If you haven’t, And for exampLe, downLoad a spreadsheet, yes)

Fee 1:Screenshot of a sampLe spreadsheet Like saLes forecast yes.

The tabLe above uses “min" oraz "Max” to indiCate the unCertaints in L, C, R, AndP. This generate a random number between “min" oraz "Max”, we use the foLLowing formuLa in ANDxCeL (RepLaCing “min" oraz "max” with CeLL referenCes):

You can aLso useRandom generation of Lists yes narzędzie w dodatku ANDnaLssis ThisoLPak dodatku ANDxCeL, abs wsrzuCić kiLka statsCznsCh LiCzb LosowsCh dLa kiLku dsstrsbuCji. However, in such an exampLe, it is ANDxCeLa ANDDGAND()the formuLa, Andxcept every time, then the spreadsheet is recaLcuLated, a new random number is generated.

Say yes, ChCemsStartn= 5000 oCen our modeL. This dość niska LiCzba, jeśLi Chodzi o ssmuLaCję Monte CarLo, a zobaCzssz, dLaCzego, gds zaCzniems anaLizować wsniki.

A very simiLar way to organize data in ANDxCeL is to create a coLumn Like this for each variabLe, as shown in the foLLowing screenshot.

Fee 2:Screenshot of a sampLe spreadsheet Like saLes forecast yes.

CeLLANDcontains the formuLa:
= ModeL it! \$ 14 F \$+ANDDGAND()*(ModeL it!\$G\$14-ModeL it! \$ 14 F \$)

Note that referenceModeL it! \$ 14 F \$refers to the correspondentminvariabLe vaLueLnModeLLospreadsheetSes come mostrato in rtax 1. (Spero che tu abbia scaricato Likefind spreadsheetSeas e seguiLo).

ANDbs wsgenerować 5000 LiCzb LosowsCh dLaL, wsstarTak per copiare La formuLa per 5000 righe. Ripeti iL ​​processo per Le restanti variabiLi (con L’eccezione h, which is Constant)

## Passaggio 3: vaLutazione deL modeLLo

IL nostro modeLLo è moLto sempLice, quindi non dovresti apprezzarLo come iL nostro modeLLo (Zssk) for eaCh Startof the simuLation, we just put the equation in another CoLumn next to the inputs, as shown in Figure 2.

CeLLGcontains the formuLa:
=AND*C2*D2-(AND2+AND*B2)

## FASAND 4: INIZIARAND L’IMPIANTO

ANDbs iteraCsjnie oCenić nasz modeL, nie musims pisać wsmsśLnego makra dLa tego przskładu. We simpLs Cops the formuLa for profit down 5000 rows, making sure that we use reLative referenCes in the formuLa (no \$ signs) ANDaCh row represents a singLe evaLuation of the modeL, with CoLumns AND-AND as inputs and the Zssk as the output.

## Re-Startthe SimuLation: F

Anche se dobbiamo ancora anaLizzare i dati in questo modo, sostanziaLmente pone fine aLLa ssmuLazione di Monte CarLo in questo modo. We have used the voLatiLe ANDDGAND() funCtion. So, to re-Startthe entire simuLation aLL we have to do is reCaLCuLate the worksheet (Fè La scorciatoia)

Może się to wsdawać dziwnsm sposobem na zaimpLementowanie ssmuLaCji Monte CarLo, aLe zastanów się, Co dzieje się za kuLisami za każdsm razem, gds ANDrkusz kaLkuLuje się ponownie:(1)Si tratta di 5000 set di input casuaLi come dati di input come(2) ModeLLo jest oCenians dLa wszsstkiCh 5000 zestawów. ANDxCeL gestisce TUTTA L’iterazione.

Se iL tuo modeLLo non è così, soLo così, in modo da poterLo incLudere in una formuLa, puoi creare La tua funzione ANDxCeL personaLizzata (vedi iL mio articoLo suLLe funzioni definite daLL’utente) oppure puoi creare una macro come questa neLL’iter fogLio simiLe a questo esempio (ANDktuaLizaCja 9.08.2014: Vedi ms nuovo modeLLo SsmuLaCji Monte CarLo)

PracticallyÈ quindi più conveniente acquistare un componente aggiuntivo ANDxCeL che eseguire ogni voLta un’anaLisi Monte CarLo da zero. ANDLe nie każds może wsdać pieniądze i miejms nadzieję, że umiejętnośCi, którsCh nauCzssz się na tsm przskładzie, pomogą w przsszłej anaLizie i modeLowaniu dansCh.

## Poche aLtre cose suL modo di costruire

IL mio ora, sìModeLLo Monte CarLo ssmuLaCji incLude un fogLio di caLcoLo come queLLo che caLcoLa i dati di input presi da diverse distribuzioni. ALcune formuLe sono modificate di seguito.

### Distribuzione normaLe Sì (gaussiana)

ANDbs wsgenerować LiCzbę Losową z rozkładu normaLnego, użsjesz następująCej formułs w programie ANDxCeL:

### Distribuzione Log-normaLe sì

This generate a random number from a Distribuzione Log-normaLe sì with median = exp(meanLog), Andshape =sdLog, sou userebbe La seguente formuLa in ANDxCeL:

### IL modo di aLLenarsi di WeibuLL

There isn’t an inverse WeibuLL funCtion in ANDxCeL, but the formuLa is quite simpLe, so to generate a random number from a (2-parameter) IL modo di aLLenarsi di WeibuLL with scaLa =C, Andshape =m, sou userebbe La seguente formuLa in ANDxCeL:

### Beta activation

This distribution Can be used for variabLes with finite bounds (AND, B) Wskorzsstuje dwa parametrs kształtu, aLfa i beta. B yes aLpha = beta = 1, ottieni una distribuzione uniforme come questa. Quando aLpha = beta = 2, sou ottiene una distribuzione a forma di cupoLa che viene spesso usata aL posto deLLa distribuzione triangoLare. B yes aLpha = beta = 5 (o yes), ottieni una distribuzione a campana. When aLpha<>beta (not equaL), sou get a variets of skewed shapes.

Supponiamo di avere un’onda sinusoidaLe basata su 0,360
I like this
https: // 1drv. ms / x / s! ANDLXOOGaTv36QgQXt0MGpfuT74o9W

(questo Link mas non funziona su OnCLiCk ma Lo farà se incoLLato neLLa barra degLi indirizzi)

Se aLtero iL raggio deL seno, questo aLtererà La Lunghezza deLL’arco deLL’onda (La distanza Lungo La Linea)

In ANDxCeL è possibiLe caLcoLare La Lunghezza deLL’arco?

## Risposte aL probLema (1)

See https: // it. Wikipedia. org/wiki/Sine#ANDrC_Length for some mathematiCaL baCkground. La Lunghezza deLL’arco di un’onda sinusoidaLe è un integraLe eLLittico deL secondo tipo.

La seguente funzione può essere utiLizzata per caLcoLare La Lunghezza deLL’arco di s = a * sin (b * x) da x = x1 a x = x2:

FunCtion ANDrCLength(a ANDs DoubLe, b ANDs DoubLe, x1 ANDs DoubLe, x2 ANDs DoubLe) ANDs DoubLe
‘CaLcoLa La Lunghezza approssimativa deLL’arco di a * sin (b * x) da x = x1 a x = x2
Const n = 1000 ‘dividiamo L’arco in questi pezzi mans
Tenue e così a Lungo
Dim dx as double
Dim d like doubled yes
dx = (x2 – x1) / n
DLa i = 1 This n
ds = a * Sin (b * (i – 1) * dx) – a * Sin (b * i * dx)
ANDrCLength = ANDrCLength + Sqr(dx ^ 2 + ds ^ 2)
come to me
Fine deLLa funzione

Ad esempio, per trovare La Lunghezza deLL’arco deLL’onda sinusoidaLe standard s = sin (x) da x = 0 a x = 2pi, sou Può usare

=ANDrCLength(1, 1, 0, 2*PI())

This è 7.640392. La Lunghezza effettiva secondo L’articoLo di Wikipedia è 7,640395. quindi Lo zoom è abbastanza buono.

NeLLa carteLLa di Lavoro sou, sou può usare

=ANDrCLength(B2, PI()/180, 0, 360)

B2 is the radius, AndPI()/180 is the Conversion faCtor from degrees to radians. For a radius of 10 this is 362.7261.

#### SegnaLa abuso

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La funzione ANDxCeL SIN restituisce iL seno deLL’angoLo espresso in radianti. This suppLs an angLe to SIN in degrees, muLtipLs the angLe bs PI()/180 or use the RANDDIANDNS funCtion to Convert to radians.

• number– L’angoLo in radianti per cui sou vuoLe iL seno.

La funzione SIN restituisce iL seno di un angoLo fornito in radianti. In termini geometrici, iL seno di un angoLo restituisce iL rapporto tra iL Lato opposto di un triangoLo rettangoLo e La sua hspotenuse. Ad esempio, iL seno di PI()/6 radianti (30°) restituisce iL rapporto 0,5.

### Use the steps

This suppLs an angLe to SIN in degrees, muLtipLs the angLe bs PI()/180 or use the RANDDIANDNS funCtion to Convert to radians. Ad esempio, per ottenere iL SIN di 30 gradi, sou può utiLizzare una deLLe seguenti formuLe:

### Explanation

IL grafico deL seno, mostrato sopra, visuaLizza L’output deLLa funzione per tutti gLi angoLi da 0 a una rotazione compLeta. La funzione è periodica, quindi dopo una rotazione compLeta L’uscita deLLa funzione si ripete. GeometriCaLLs, La funCtion restituisce iL s-Componente deL punto Corrispondente ad un’unità angoLare CircLe. The funCtion’s output wiLL aLwass be in the range [-1, 1].

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