Flight Profile
OTRAG
Calculation of the
terminal
velocity (dV) of the KAYSERI rocket
[dV = Isp [Ns/kg] * ln (Mf/Me)]
1.  Mf  first stage: Total mass of the
launcher
Me  first stage: Empty mass of the first
stage + total mass of the second and third stage and payload
2.  Mf  second stage: Total mass of the second and third stage and
payload
Me  second stage: Empty mass of the
second stage + third stage and payload
3.  Mf  third stage: Total mass of the third stage and payload
Me  third stage: Empty mass of the third
stage + payload
Conditions: Prediced data (realistic Isp; thickness of the tanks 1.0 mm; structural mass 17.2 % = one modul 278 kg)  
vac Isp (sec)  =Ns/kg  Mf (kg)  Me (kg)  Mf/Me  ln Mf/Me  Isp * ln (Mf/Me)  
1. (48 CPMs)  ~252.5  2476  104,683  40,267  2.600 
0.95551 
2,366 
2. (12 CPMs)  ~252.5  2476 
26,921 
10,817 
2.489 
0.91188 
2,258 
3. ( 4 CPMs)  ~252.5  2476 
7,480 
2,112 
3,542 
1.26469 
3,131 
dV Total* 
7,755 [m/sec] 
* dV without
losses between 15% and 20% of velocity by gravity, air resistance etc.
Therefore is the real dV nearby 6,400 m/sec for payload 1,000 kg.
Conditions: Optimistic OTRAG data (high Isp; thickness of the tanks 0.5 mm; structural mass 12.2 % = one modul 186 kg)  
vac Isp (sec)  =Ns/kg  Mf (kg)  Me (kg)  Mf/Me  ln Mf/Me  Isp * ln (Mf/Me)  
1. (48 CPMs)  297  2912  98,792  34,376  2.874 
1.05570 
3,074 
2. (12 CPMs)  297  2912 
25,448 
9,344 
2.723 
1.00173 
2,917 
3. ( 4 CPMs)  297  2912 
7,112 
1,744 
4,078 
1.40560 
4,093 
dV Total* 
10,084 [m/sec] 
* dV without
losses between 15% and 20% of velocity by gravity, air resistance etc.
Therefore is the real dV nearby 8,320 m/sec for payload 1,000 kg.
