Defining a flight envelope for the Saturn V - Apollo
Picture illustrating the meaning of the parameters
Figure 1
The Flight path angle and the Velocity are two of the most significant performance parameters to monitor the flight trajectory of a launch vehicle.
NASA's internal note no. 68-FM-305:
"An envelope of Saturn V malfunction trajectories which can achieve orbit"
On this page is discussed an internal note (ref. 1, title mentioned above) prepared by the TRW Systems Group and the Flight Analysis Branch of NASA's Mission Planning And Analysis Division. The internal note was released in December 1968.
This internal note concludes with a recommendation to include graphical information, containing the launch vehicle's abort envelope, in the plotboards used by the flight dynamic officer in the Mission Operations Control Room.
The purpose of the abort envelope was to provide the flight dynamics officer with an early indication that a vehicle, which is slowly diverging from a nominal trajectory, will not reach a contingency orbit.
The recommendation was intended to be used for the Apollo 8 mission, the first manned Apollo - Saturn V mission.

The primary plot boards used by the flight dynamic officer were:

  1. An Altitude versus Downrange distance chart
  2. A Flight path angle versus Space-fixed velocity chart
These concluding graphs, containing abort envelopes, which were recommended to integrate with these primary plotboards, can be found in figure 7 and 8.

Flight envelope
The abort or flight envelope is determined by considering all the trajectories for a malfunctioning launch vehicle which can attain a contingency orbit. Those trajectories which deviate the most from the nominal trajectory are decisive for the shape of the abort envelope.

The construction of such an abort envelope would allow flight controllers and the flight crew to anticipate malfunctions which result in relatively slow diverging flight trajectories, which might be an early indication of an impending abort situation.

Malfunctions which cause an immediate abort situation were monitored and detected by the Emergency Detection System (EDS), were of a different category and were not taken into consideration in determining the abort envelope.

Step 1 in defining the abort envelope
The first step in defining the abort envelope is determining the operational and physical constraints which must be considered when the malfunction trajectories are identified, which will shape the envelope. These constraints are actually defining the outer limits of the envelope.
The constraints are depicted in figure 2.

Saturn V Flight Envelope Determination angle-vel plot Step 1

Figure derived from reference 1 figure 5.
Saturn V Flight Envelope Determination angle-vel plot Step 1
Figures 2a and 2b
Step 1: Determining operational and physical constraints

The set of flight trajectories which deviate from the nominal trajectory but will result in an orbit insertion are constrained by some physical limits and an orbit insertion requirement.

  1. The breakup limit of the Saturn V launch vehicle.
  2. The minimum time needed to orient the Command Module to the correct entry attitude following abort initiation and Service Module separation is 100 seconds. It thus means that the minimum time of free fall between abort initiation and hitting the reentry interface at an altitude of 100 km is 100 seconds.
  3. Maximum entry load of 16 G.
  4. The actual orbital insertion altitude must be within 19 kliometers (10 nautical miles) of that specified by the operational trajectory.
  5. The inertial flight path angle at orbit insertion must be within 2 degrees of that specified by the operational trajectory.

Step 2 in defining the abort envelope
In figure 3 a table of malfunctions is listed which have been taken into consideration. But simulation studies have revealed that only a selection of these malfunctions are contributing to defining the abort envelope.
The malfunctions which resulted in fatal failures are not mentioned in the list.
These simulation studies were carried out in 1967 and 1968 by the TRW Systems Group by using the TRW Saturn Launch Simulating Program.

The malfunctions which eventually were found to contribute to defining the abort envelope are:

  1. ST-124-M2 inertial platform: loss of X-axis accelerometer
  2. ST-124-M2 inertial platform: gyro drift
  3. ST-124-M2 inertial platform: loss of inertial attitude reference
  4. S-IC stage engine actuator hardover
  5. Premature shutdown of an S-IC stage engine
  6. S-II stage engine actuator hardover
  7. Failure of an S-II engine to ignite
(The ST-124-M2 inertial platform is located in the Instrument Unit, panel 21. see drawing)

Failure modes
Figure 3
Candidate malfunctions which can contribute to defining the abort limits

Simulation studies have shown that only a selection of the malfunctions listed above contribute to defining the abort limits.
The NASA note is, however, not very exhaustive in providing information about the selection criteria. For example, the reasoning why failure mode F12 (loss of one S-IVB APS engine) has not been taken into consideration has not been reported in the note. It is possible that such a malfunction was considered fatal and was therefore left out because it would not have contributed to defining the envelope for obvious reasons.

The failure modes 5 through 8 are related to actuator malfunctions. Figure 4 is helpful in picturing the impact of a hydraulic actuator failure. These actuators are used for thrust vector control by gimbaling the thrust engines.

The dark red numbers in the fifth column of the table shown above are referring to the curve numbers in figures 5 and 6.

S-IC Polarity Table

Figure based on reference 2 figure 7-15.
Figure 4
Thrust vector control

The four outer engines of the S-IC stage were equipped with hydraulic actuators to control the thrust vector by which the flight trajectory could be controlled.
Engine no.5, the center engine, was fixed; its thrust vector was pointed along the roll axis of the launch vehicle.

The actuators were orientated in such a way that each of them could induce a yaw movement or a pitch movement.
Combinations of actuator movements would result in a combination of yaw and pitch movements. The actuators were numbered; in the table shown above is laid down which actuator movements were required for the various rotational movements along the Yaw, Pitch and Roll axes.

The five engines of the S-II stage were arranged in a similar way.

Saturn V Flight Envelope Determination angle-vel plot Step 2

Figure based on reference 1 figure 3.
Figure 5
Step 2a: Identifying malfunction trajectories which can achieve orbit insertion in an inertial flight path angle - velocity chart

Only malfunction trajectories are shown here which contribute to defining the flight envelope.

Early engine shutdown
Failure mode 10 (curve no.4) was only applicable for the Apollo 8 mission, which seems obvious since the NASA note was prepared with this mission in mind.
The lift-off mass of the Apollo 8 launch vehicle was 2750 Tons. It could even afford to lose one engine at lift-off. Four engines delivering a total thrust of 2800 Tons were sufficient for lift-off.
However, for the other Apollo missions, 9 through 17, the mass at lift-off ranged between 2866 and 2896 Tons. The moment at which those missions could afford to lose one engine ranged between 7.7 and 9.7 seconds after lift-off.

Note
According to the simulations, a shutdown of an S-IC stage engine at 3 seconds results in a curve (no.4) which is closer to the nominal one than the curve (no.5) which represents the situation in which an engine has shut down at 60 seconds. But in both cases the inertial flight path angle is smaller than in the nominal case.
In general, when thrust is lost in midflight, which results in a lower thrust-to-weight ratio (TWR), it is preferred to increase the pitch rate (to have a more aggressive gravity turn) to start gaining lateral velocity sooner and spend less fuel to fight gravity. This is a more efficient use of propellants and necessary for achieving an orbit.
Curve 5 reflects this programmed flight behaviour.
It will, however, result in a significantly lower altitude at S-IC stage burn-out compared to the nominal trajectory.
Curve 5 shows that the S-II and S-IV stages would have been used to achieve the target altitude by reducing the pitch rate to obtain a higher vertical thrust-to-lateral thrust ratio compared to the nominal trajectory.

Inertial platform failure
If the inertial platform fails in about the first 320 seconds of flight, a (contingency) orbit cannot be achieved. But if this failure occurs later in the boost flight, an acceptable orbit can be achieved. The range of possible trajectories can be found in between the trajectories 7 and 8.

Saturn V Flight Envelope Determination altitude-range plot Step 2

Figure based on reference 1 figure 4.
Figure 6
Step 2b: Identifying malfunction trajectories which can achieve orbit insertion in an altitude - range chart

As discussed in the caption of figure 5, a shutdown of an S-IC engine at 60 seconds (curve no.5) apparently results in an early reduction of the inertial flight path angle and therefore in a much lower ascent trajectory. This malfunction appeared to contribute significantly to defining the abort envelope.

Note that curve 2 has been truncated as in reference 1, for reasons unknown.

Conclusion of the NASA note (ref.1)
In figures 7 and 8 are shown the abort or flight envelopes, which are the results of the TRW flight simulation studies.

The NASA note ends with a recommendation to have these envelopes incorporated in the Flight Dynamics Officer's Inertial Flight Path Angle vs. Inertial Velocity and Altitude vs. Range plotboards to enhance the decision-making process when a launch vehicle is gradually deviating from its nominal trajectory and is approaching the edge of the envelope beyond which an orbit cannot be achieved.

Saturn V Flight Envelope flight path angle - velocity
Figure 7
Flight path angle versus Velocity abort limit lines

This abort or flight envelope is the result of figure 2a + 5: the operational constraints + the result of the TRW simulation studies in defining the abort limits.

The lower abort limit is shaped by curve no.5 in figure 5 and is overlapping an outer limit. This curve violates the rule that the red-colored outer limits must not be exceeded. The risks involved were probably considered manageable. However, this violation might entail that if in that particular part of the trajectory a booster failure would prompt a (mode II) abort, there would have been less than 100 seconds left between the moment of spacecraft separation and the start of the reentry procedure. This would have jeopardized a controlled start of the reentry.

Saturn V Flight Envelope altitude-range
Figure 8
Altitude versus Range abort limit lines

This abort or flight envelope is the result of figure 2b + 6: the operational constraints + the result of the TRW simulation studies in defining the abort limits.

Saturn V Flight Envelope altitude-range
Figure 9
Plot screens in the Mission Operations Control Room to monitor the ascent trajectory of the Saturn V.

Wide-angle view of the Mission Operations Control Room just after lift-off of Apollo 15.
The plots on the large screens are intended to enable the flight controllers to ascertain whether the Saturn V remains within its flight envelope. Altitude, downrange distance, inertial flight path angle and velocity are the most important parameters for the assessment.

The 2nd and the 3rd plot screens from right to left are also intended to oversee the several abort mode regions in a flight path angle versus velocity plot. An abort will result in a landing into the Atlantic Ocean of the Command Module or a contingency orbit for the Command & Service Module.
These plots are discussed in more detail on the page "Saturn V - Apollo   Launch Aborts".


Acronyms
EDS Emergency Detection System

References
  1. An envelope of Saturn V malfunction trajectories which can achieve orbit
    MSC Internal note No. 68-FM-305, 16 December 1968
    TRW Systems Group
    by H.G. Schaeffer, V.A. Dulock, J.J. White
    Commisioned by:
    NASA, Manned Spacecraft Center
    Mission Planning and Analysis Division

  2. Saturn V Flight Manual SA-506
    George C. Marshall Space Flight Center
    MSFC-MAN-506, 25 February 1969



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