XProfan

English

p.specht

with many physikalischen Vorgängen with nichtlinearen single-Zusammenhängen can self with known Anfangsbedingungen no closed Formeln to Ergebnisberechnung herangezogen go. means must one whom Systemzustand for a designed Time schrittweise calculate. The schweizer Mathematiker Leonhard Euler set moreover already circa 1745 around solid, that moreover a Lineare Näherung sufficient, as long as each Rechenschritte only small enough are. here a suitable application, with the one with the Einzelwerten might try experimenting can, circa z.B. To discern, Why Sternschnuppen mostly in 15-20 km Höhe shine...

Compile Mark Separation

Window Title "Explizites Euler-take action, circa a typischen Kleinmeteor-crash To simulieren"
' details see https://de.wikipedia.org/wiki/Methode_der_kleinen_Schritte
' example to XProfan 11.2a transfer (CL) CopyLeft 2014-01 by P.woodpecker, Wien
Window 0,0-%maxx,%maxy-40:Font 2:set("decimals",5):set("numwidth",18)
declare n&,a_gravi!, rho!, F_Luft!, a_gesamt!, v_neu!, v_alt!, h_neu!, h_alt!
var volume! = 0.04' kg    Typische Eisenmeteor-volume would only ca. 4 gram!
var A! = 0.33' cm²   Querschnittsfläche the Meteors
var v! = 25' km/s  speed on the Startpunkt (Anfangsbedingung, ca. 15 km/s)
var h! = 120' km    Anfangshöhe over reason
var rho_Boden! = 1.2041' kg/m³ =0,0012041 g/cm³ Luftdichte with 20 °C on Meeresniveau
var Cw!=1.18' 0.18 - 1.18 ' Cw = 2*Fw/(rho*A*v^2) Luftwiderstandsbeiwert cw, geschätzt
var dt!=0.1' s = Sec-Zeitschritt the Simulation
Ueberschrift

Repeat

    inc n&' Segment-Nr.
    a_gravi! = 9.80665 * sqr( 6370/(6370 + h!) )' taking off the Gravitation with the Höhe
    rho!=rho_Boden!*exp(-h!/8.4)' Luftdichte in x km Höhe
    F_Luft! = rho!*Cw!*A!*sqr(v!)/2' head-wind-strength
    a_gesamt! = a_gravi! - F_Luft! / volume!' Gesamtbeschleunigung
    v_neu! = v! + a_gesamt! * dt!' Segment-Durchschnittsgeschwindigkeit
    h_neu! = h! - v_neu! * dt!' Seehöhe
    Print h_neu!,n&,v_neu!,a_gravi!,rho!,F_Luft!,a_gesamt!
    casenot (%csrlin+2) mod 4:print
    case %csrlin>26 : were
    v!=v_neu!
    h!=h_neu!

Until h! < -0.5

Waitinput
End

proc were

    waitinput
    cls
    Ueberschrift

endproc

proc Ueberschrift

    print "         Seeöhe [km]      Bahnsegment    speed [km/s],";
    print "     Gravitation,     Luftdichte,       Bremskraft,       Verzögerung\n"

endproc