%% $Id: santa_claus.m,v 1.2 2004/01/01 01:26:32 forman Exp forman $
%%
%% Description:
%% The energy required for Santa Claus to deliver his gifts on Christmas.
%%
%% Author:        Michael Forman <Michael.Forman@Colorado.EDU>
%% URL:           http://www.Michael-Forman.com
%% Creation Date:  Date: 2003/12/19 10:14:23 GMT
%% Last Revision: $Date: 2004/01/01 01:26:32 $ 
%% Revision:      $Revision: 1.2 $
%%
%% Copyright (C) 1999-2004 Michael Forman.  All rights reserved.
%% This program is free software; you can redistribute it
%% and/or modify it under the same terms as Perl itself.
%% Please see the Perl Artistic License.
%%
%% Category: Matlab
%% Rating:   2/5
%%
%% <meta name="title" content="The Physics of Santa Claus.">
%% <meta name="description" content="The physics of Santa Claus.">
%% <meta name="abstract" content="The physics of Santa Claus.">
%% <meta name="keywords" content="matlab script Santa Claus physics delivery">
%

mdc = 1.2e9;		% 1.2 billion people in MDC
a = 0.8;		% correlation between MDC membership and belief in SC
b = 0.25;		% children in MDC population
k = a*b*mdc;		% number of kids = correlation * percent kids * pop
f = 0.51;		% kids per household
n = f*k;		% number households with kids

to = 32*60*60;		% travel time in seconds
th = to/n;		% time per household
tt = 0.5*th;		% time in transit per household

Ae = 1.5e14;		% total land area of earth
Ar = Ae/10;		% area where 90% of travel will be
Ah = Ar/n;		% area per household
rh = sqrt(Ah/(2*pi));	% household radius (assuming local flat earth)
dh = 2*rh;		% distance between homes
dt = dh*n;		% total distance traveled

va = dh/tt; 		% average house-to-house speed
vs = 340;		% speed of sound at sea level is 340 m/s
rs = va/vs;		% mach number

mt = 1;			% toy weight in kg
mi = mt*k;		% initial toy mass
m  = mi/2;		% avg toy mass


e = 0.5;		% efficiency
a = 2*(dh/2)/(tt/2)^2;	% accelerate half way there
F = m*a;		% force
W = F*dh/2;		% work
W = 2*W;		% work for accel and decel
W = W/e;		% account for efficiency
Wt = W*n;		% total energy for all households

We = 1.5*8.661e18;	% total world E consumption = 1.5 * U.S. consumption
rW = Wt/We;		% ratio of Santa to world E consumption

P = Wt/to;		% average power output over total time of flight

rg = 1000;		% flight altitude
As = P/(4*pi*rg^2)	% power density on sphere (W/m)

Pu = 3.826e26;		% power output of sun
ru = 6.955e8;		% radius of sun
Au = Pu/(4*pi*ru^2);	% power density on surface of sun (W/m)

rA = As/Au		% ratio of santa power density and sun surface p den