Even if with the current values , my SSTO don't go to LEO, I hope
it will be an good help to every one interested in SSTO .
1)
Why using a model on spreadsheet and not something done in
Mathematica or C++?
Because Mathematica or C++ required highly
trained people and Mathematica is a costly commercial product that no
one use at home.
Instead everybody who use Internet can read Excel
or Works files (or even download compatible spreadsheets).
Plus :
Spreadsheet have proven along the years an capability to make quickly
models of various kind and help to test instantly various hypothesis,
increasing dramatically productivity of mere mortals!
Spreadsheet
success story exist because there is no loop in spreadsheet, all
loops are developed and you are not required to be Einstein or
Hawkings to understand complex phenomenon because they are exposed
under your eyes.
In some ways Visicalc inventors changed more our
world than Nasa scientists! (and it cost far least :)
2) If you
don't use Mathematica, C++, Fortran (giggle) or spreadsheets you must
do mathematics analysis using calculus.
Even if this is something
every educated young adult studied in classroom, the same adult
nearly forgot all this stuff at the age of 30, because no one use
calculus in real life, even engineers use numerical analysis because
of the high computational power of today computers (old timers
remember that Pentium series is more powerful than the 80' Cray I or
II).
Numerical analysis must follow the same rules than calculus :
Work on small quantities and be cautious about the use of formulas
and units (ever see endless and frightful quarrels about ISP or
remember Mars Polar Lander?). You must not use short cuts like delta
V, this is not correct but lazy thinking, there is no excuses, after
all it's not you who really work hard but the computer!
I test
every formulae against another to hunt bugs, but I am sure there is a
lot of bugs there even after all my efforts!
ALL
references apply to rocket1.htm
1) Just for fun there
is some errors, good luck!
2) To avoid circular references,
formulae in some cells refer not to the same row, but to the previous
row.
3) Precision can be attained only with small steps.
Exhaust speed =
3500 : The value in m/sec for Kerosene and Liquid oxygen (RP1
and LOX)
Length of combustion
chamber = volume of combustion chamber / Aerodynamic
surface of the rocket (m^2)
volume of combustion
chamber =35*(3,14*(Throat diameter/2)^2)
Length
of tanks (LOX+RP1)
= ((Mass of propellant /1080)*9,8) / Aerodynamic surface of the
rocket
The various mass are in kilograms.
Don't confuse weight and mass!
For the sake of simplicity the
total mass is added from the payload mass and the propellants
mass.
Ejected Mass per second = This is
the important stuff!
It's the mass of gas that is ejected backward
by the rocket, by the law of the conservation of impulse and
knowledge of Exhaust speed of the gas you can compute the speed of
the rocket (provided that you compute the new mass of the rocket
because of the loss of the gas mass).
Theoretical
speed with rocket equation = The rocket equation help compute
the speed of a rocket from an initial state to a final state with
three variables : Exhaust speed, initial mass and final mass.
This
is the theoretical speed in vacuum and far away from any gravity
well.
Real speed (w. air drag and weight)
= an attempt to compute a more realistic value for speed with respect
to gravity and air drag.
Force de propulsion
(dm*Ex_speed) = A weak point in my calcs! I never retrieve where I
found this formulae but it work better than another derivation of
Newton's law so...
The last six formulas
are an attempt to verify the efficiency of rockets as an engine
motor. Carnot must be happy even steam engines make better use of
energy!
Someone really smart must start thinking on something less
dispendious of this world fossils energy.
In my dreams I sometime
think that a conventional thermal motor using mechanic or electric
mean to accelerate exhaust gas of the thermic motor to 6000m/sec
might be something as highly disgracious but as useful as a railway
engine!
Air drag = =(Real speed^2)*(Aerodynamic
surface)*(Atmospheric Density)*0,4
This formulae is the classical
one for a rocket speed slower than the sound speed. There is other
formulas one for larger than sound speed, and one another for air
drag in semi vacuum.
I use this one because of simplicity and
there was so much simplifications elsewhere and so much things not
incorporated in the model (wind by example) that it was inconsistent
to use here a complicated formulae.
Atmospheric Density = (last step atmospheric
density)*EXP((Altitude above ground) / 25000)
This is not the
usual formulae, this one is simpler and seem as accurate.
System :m/kg/sec 

Fact. rég. l'accélération 

0,0045 
Vertical depuis le sol 

Ratio dry_M/M_plein 

0,090909091 
Surface aérodyn. (m^2) 
3 
Vmax (m/sec) 

0 
Exhaust speed 
3500 
Gmax 

1,0 
Length of combustion chamber 
volume of combustion chamber 

#VALEUR! 

Length of tanks (LOX+RP1) 
7,56 

Throat diameter 
#VALEUR! 





Sens du vol 
V 
V 
V 
V 
Time in sec after launch 
0 
2 
5 
10 
Total Weight 
27005,00 
SI(C11*(C29(C29*(B14/11000)))> 0;C11*(C29(C29*(B14/11000)));0) 
SI(D11*(D29(D29*(C14/11000)))> 0;D11*(D29(D29*(C14/11000)));0) 
SI(E11*(E29(E29*(D14/11000)))> 0;E11*(E29(E29*(D14/11000)));0) 
Total mass 
2750 
C12+$L1 
D12+$L1 
E12+$L1 
Mass of propellant 
2500 
SI(B12(C13*(C9B9))> 0;B12(C13*(C9B9));0) 
SI(C12(D13*(D9C9))> 0;C12(D13*(D9C9));0) 
SI(D12(E13*(E9D9))> 0;D12(E13*(E9D9));0) 
Ejected Mass per second 
8,00 
SI(B12>0;(B11*$E$1);0) 
SI(C12>0;(C11*$E$1);0) 
SI(D12>0;(D11*$E$1);0) 
Real speed (w. air drag and weight) 
0 
((C18*(C9B9))/C11)+B14 
((D18*(D9C9))/D11)+C14 
((E18*(E9D9))/E11)+D14 
Theory with rocket equ. 

$B4*LN($B11/C11) 
$B4*LN($B11/D11) 
$B4*LN($B11/E11) 
Apparent number of G 
1,00 
((C18/C11)+C29)/9,82 
((D18/D11)+D29)/9,82 
((E18/E11)+E29)/9,82 
Force de propulsion (dm*Ex_speed) 
0,00 
(C13*$B4) 
(D13*$B4) 
(E13*$B4) 
Force de propulsion nette 
0,00 
C17C25C10 
D17D25D10 
E17E25E10 
Kinetic energy gained (millions of Joules) 
0 
(0,5*C11*(C14*C14))/1000000 
(0,5*D11*(D14*D14))/1000000 
(0,5*E11*(E14*E14))/1000000 
Equiv motor in KW gained 

(C19/(3,6))/((C9$B9)/3600) 
(D19/(3,6))/((D9$B9)/3600) 
(E19/(3,6))/((E9$B9)/3600) 
Caloric energy used 
0 
42*($B$12C12)*9,82 
42*($B$12D12)*9,82 
42*($B$12E12)*9,82 
Equiv motor in KW used 

(C21/(3,6))/((C9$B9)/3600) 
(D21/(3,6))/((D9$B9)/3600) 
(E21/(3,6))/((E9$B9)/3600) 
Kinetic energy in propellant 

((0,5*C13*($B$4^2))/1000000)+B23 
((0,5*D13*($B$4^2))/1000000)+C23 
((0,5*E13*($B$4^2))/1000000)+D23 
Ratio gained/used 

C19/(Somme($B21:C21)) 
D19/(Somme($B21:D21)) 
E19/(Somme($B21:E21)) 
Air drag 
0 
(B14^2)*($B$3)*(C28)*0,4 
(C14^2)*($B$3)*(D28)*0,4 
(D14^2)*($B$3)*(E28)*0,4 
Altitude above ground 
0 
SI(C8 "V";(C14*(C9B9))+B26;SI((C14*(C9B9))> (B14*(B9A9));(C14*(C9B9)*pente)+B26;B26(C14*(C9B9)*pente))) 
SI(D8 "V";(D14*(D9C9))+C26;SI((D14*(D9C9))> (C14*(C9B9));(D14*(D9C9)*pente)+C26;C26(D14*(D9C9)*pente))) 
SI(E8 "V";(E14*(E9D9))+D26;SI((E14*(E9D9))> (D14*(D9C9));(E14*(E9D9)*pente)+D26;D26(E14*(E9D9)*pente))) 
Max alt possible ballisticly 

SI(C13>0;(C14^2)/(2*C29)+C26;B27) 
SI(D13>0;(D14^2)/(2*D29)+D26;C27) 
SI(E13>0;(E14^2)/(2*E29)+E26;D27) 
Atmosphéric Density 
1 
B28*EXP(B26/25000) 
C28*EXP(C26/25000) 
D28*EXP(D26/25000) 
G at altitude 

9,82*((($L$4*1000)^2)/((B26+($L$4*1000))^2)) 
9,82*((($L$4*1000)^2)/((C26+($L$4*1000))^2)) 
9,82*((($L$4*1000)^2)/((D26+($L$4*1000))^2)) 
Altitude from Earth center 
6500 
C26+$L$4 
D26+$L$4 
E26+$L$4 
Horizontal distance from start point 

SI(C8 "H";pente*(C26B26);0)+B31 
SI(D8 "H";pente*(D26C26);0)+C31 
SI(E8 "H";pente*(E26D26);0)+D31 
Horizontal distance in hour 

#VALEUR! 
#VALEUR! 
#VALEUR! 
Dernière mise à jour le 30/12/99
Par Le Rouzic Jean Pierre
Email:
jeanpierre.lerouzic@wanadoo.fr