SUMMARY: Single Stage Rockets

The total mass of the rocket stage can be considered to be the sum of several parts:

ML: Mass of the payload MP: Mass of the propellant MS: Structural mass

The structural mass includes all other mass but the payload and the propellant. This includes engine, guidance system and control equipment and fuel tanks. Other texts use different definitions to divide the rocket into various fractions, but these groupings are most common. The initial mass of the rocket is written as the sum of these components:

M o  M L  M P  M S 1

If the rocket consumes all its propellant during firing, the burnout mass is:

M b  M L  M S  M o  M P 2

These variables may be arranged in several important ratios, as summarized below:

Symbol Ratio Description M M Mass Ratio: initial mass / mass at the R R  o  o end of the thrust period. Want this 3 M M  M b L S ratio large. Payload Ratio: ratio of payload to M L M L everything but payload. Want this     4 M o  M L M P  M S large, but larger the payload, the lower maximum attainable velocity. M M  M Structural Coefficient: ratio of the    S  b L structural weight to everything but 5 M  M M  M P S o L the payload. Want this small.

M P M P Propellant Ratio: Ratio of propellant     6 M P  M S M o  M L to everything but the payload.

We can also write the mass ratio as:

1  7 R    

Note that the structural and payload ratios are related by:

  1  8

1 SUMMARY: Multistage Rockets

Some key points about rocket staging:  A multistage rocket is a series of individual vehicles or stages each with its own structure, tanks and engines. The stages are connected so that each operates in series and accelerates the remaining stages and payload before being detached and discarded.  The stages are numbered in the order of firing.  The payload for any particular stage is simply the mass of all subsequent stages.

th Moi: Total initial mass of the i stage prior to firing, including its effective payload th Mbi: Total mass of the i stage after burnout, including its effective payload ML: Payload of the last stage to fire th Msi: Structural mass of the i stage alone, including the mass of its engine, controls, and instruments.

By slightly modifying the ratios defined in equations 1-8, we can examine multistage rockets. Remember, that the payload of any stage is simply the mass of all subsequent stages.

th The payload ratio, i, of the i stage is:

M o(i1) 9 i  M oi  M o(i1)

The structural coefficient of the ith stage is:

M si 10  i  M oi  M o(i1)

M bi  M o(i1) 10.1  i  M oi  M o(i1)

The last expression holds if the ith stage contains no propellant at burnout. The mass ratio of the ith stage can be written as:

M oi 11 Ri  M bi

1 i 11.1 Ri   i  i