Rocket propulsion

The principle of rocket thrust goes back to the ancient Chinese and their brilliant firework displays. Then and now it is based on Newton’s second law, applied to the exhaust stream with the velocity c and the mass flow m (see Example 5.6):

F = me

Instead of providing the exhaust velocity, usually the specific impulse /sp is given. It is defined as the ratio of the impulse delivered, divided by the propellant weight consumed

FAt _ F mg0At mg„

where g0 is Earth’s gravity acceleration referenced to the fixed, standard value g0 = 9.80665 m/s2. Solving for F yields the alternate thrust equation

F = Ispthgo (8.24)

The exhaust velocity is therefore related to the specific impulse by c = Isvg0- Specific impulse provides an important characterization of the rocket engine and its propellant. Typical values are given in Table 8.1 for double-based solid propel­lants like nitrocellulose (NC) and nitroglycerin (NG) and liquid bipropellants like hydrazine (N2 H4) and oxygen (O2).

The thrust of a missile is usually given at sea level. A correction has to be made for the thrust at altitude. Suppose FsL is the sea-level thrust; a term is added that corrects for the fact that the pressure at altitude pAt is less than the pressure at sea level psh – With the exhaust nozzle area Ae the thrust at altitude is

FAit = Fsl + (Psl — Раі)Ає (8.25)

For solid propellant the sea-level thrust is most likely given as a function of bum time and possibly of propellant temperature. A simple table look-up routine will suffice. If only specific impulse and propellant bum rate are known, Eq. (8.24) will provide the thrust. This equation also serves the liquid propellant rocket motor. You just need to include a multiplying factor that represents the throttle ratio (values between zero and one). To complete the propulsion model, the expended propellant is monitored for updating the vehicle’s mass.