A relativity calculator for finding the Lorentz factor at various velocities

Relativity.elm

module Relativity exposing (main)

import Html exposing (..)
import Html.Attributes exposing (style, src, min, max, type_, value)
import Html.Events exposing (onClick, onInput, onMouseEnter, onMouseDown, onMouseUp)


type Msg
    = SetMacro String
    | SetMedium String
    | SetMicro String


type alias Model =
    { macro : Float
    , medium : Float
    , micro : Float
    }


init : ( Model, Cmd Msg )
init =
    ( Model 50 0 35
    , Cmd.none
    )


update : Msg -> Model -> ( Model, Cmd Msg )
update msg model =
    case msg of
        SetMacro x ->
            { model | macro = Result.withDefault 0 (String.toFloat x) } ! []

        SetMedium x ->
            { model | medium = Result.withDefault 0 (String.toFloat x) } ! []

        SetMicro x ->
            { model | micro = Result.withDefault 0 (String.toFloat x) } ! []


view : Model -> Html Msg
view model =
    let
        v =
            totalSpeed model

        c =
            299792458
    in
        div [ Html.Attributes.style [ ( "font-family", "'Bitter', 'Nunito', 'Helvetica Neue', 'Helvetica', sans-serif" ), ( "font-size", "18px" ), ( "color", "#333333" ), ( "background", "whitesmoke" ), ( "padding", "16px" ) ] ]
            [ p []
                [ text <| "Macro velocity: " ++ toString model.macro ++ "% of c" ]
            , Html.node
                "style"
                [ type_ "text/css" ]
                [ Html.text "@import url('https://fonts.googleapis.com/css?family=Bitter')" ]
            , input
                [ type_ "range"
                , Html.Attributes.min "0"
                , Html.Attributes.max "99"
                , Html.Attributes.step "1"
                , Html.Attributes.style [ ( "width", "95%" ) ]
                , onInput SetMacro
                ]
                []
            , p [] [ text <| "Medium velocity: " ++ toString model.medium ++ "m/s" ]
            , input
                [ type_ "range"
                , Html.Attributes.min "0"
                , Html.Attributes.max (toString (c / 100 - 1000))
                , Html.Attributes.style [ ( "width", "95%" ) ]
                , onInput SetMedium
                ]
                []
            , p [] [ text <| "Micro velocity: " ++ toString model.micro ++ "m/s" ]
            , input
                [ type_ "range"
                , Html.Attributes.min "0"
                , Html.Attributes.max "1000"
                , Html.Attributes.step "1"
                , Html.Attributes.style [ ( "width", "95%" ) ]
                , onInput SetMicro
                ]
                []
            , p [] [ text <| "Total velocity: " ++ toString v ++ "m/s" ]
            , p [] [ text <| "Total velocity as percentage: " ++ toString (100 * v / c) ++ "%c" ]
            , p [] [ text <| "Lorentz factor: " ++ toString (1 / ((sqrt (1 - ((v * v) / (c * c)))))) ]
            , p [] [ text <| "Inverse Lorentz factor: " ++ toString (((sqrt (1 - ((v * v) / (c * c)))))) ]
            ]


totalSpeed model =
    2997924.58 * model.macro + model.medium + model.micro


main : Program Never Model Msg
main =
    Html.program
        { init = init
        , update = update
        , view = view
        , subscriptions = \_ -> Sub.none
        }