Informal DistributionMAY 27 196868-FM64-171FM6/Critical Mission Analysis BranchExtension of the Apollo Mission D (CSM-103/LM-3) launch window using the SPS/DPS ΔV capability

__References__

1. Conway, H. L.; Merriam, R. S.; Spurlin, H. C.; Calvin, C.; MSC Internal Note 68-FM-93 entitled, “Apollo Mission D (AS-502/CSM-103/LM-3) Spacecraft Reference Trajectory, Volume I – Nominal Trajectory”, dated April 30, 1968.

2. Rose, R. G.; MSC memorandum entitles, “Ninth Mission D Flight Operations Plan (FOP) Meeting”, dated April 18, 1968.

__Summary__

A study was conducted to determine the ΔV capability of the SPS/DPS to perform nodal shift and phasing maneuvers so that the launch window for Apollo Mission D could be extended. The results show that the launch window can be extended to approximately 2.75 hours provided the second SPS, third SPS, the docked DPS, and an additional 450 fps SPS burn are designed nominally to optimally shift the line of nodes eastward. Following the nodal shifts, a series of phasing maneuvers (nominally zero for on-time launches) would be then required to complete the launch window extension. Operational considerations (such as non-optimum geographical burn locations to provide MSFN coverage) will prevent full realization of the nodal shift capability; and, as a result, the launch window of 2.75 hours theoretically possible may not be achieved. Redesign of the ΔV maneuvers from that of reference 1 will have no impact on test objectives. The data and analysis leasing to these conclusions are dis- cussed in this memorandum.

__Discussion__

To satisfy requests contained in reference 2, a study was conducted to determine the maximum launch window considering only the ΔV capability of the SPS/DPS to return a vehicle delayed at launch to the nominal lighting and MSFN coverage for the LM-active rendezvous (defined in reference 1). The launch window for the D Mission Reference Trajectory published in reference 1 is less than 1 hour.

There are basically two methods under consideration by which MSFN coverage and lighting requirements during the rendezvous may be satisfied in the event of a launch delay. The first method is to adjust the time from CDH to TPI by small changes in the differential heights during the con- centric coasts of LM-active rendezvous. A study of this technique is currently underway. The second method, which is the subject of this memorandum, is to “rendezvous” the CSM/LM vehicle which may be lifting off late with an imaginary vehicle which lifts off at the nominal time and executes all nominal maneuvers. If the launch delay is long enough (over 15 minutes) then phasing maneuvers (apogee and/or perigee adjust- ments) alone may not reestablish nominal lighting and coverage since out-of-planeness arises due to earth rotation. A nodal shift is then also required, the magnitude of which is directly proportional to the rotation of the earth during the delay period.

__Nodal Shift Requirements__

The nodal shift required is due to the orbital plane of a vehicle launched on time becoming fixed at insertion (neglecting apsidal advancement and nodal regression) while the orbital plane of the delayed vehicle has an eastward shift in the line of nodes equal to the amount of earth's rotation during the delay period. The ΔV required for a nodal correction ΔΩ is given in the following equation:

ΔV = 2V_{X} cos γ_{x} sin __ΔΩ__ sin i
2
where V_{x}, is the inertial velocity at transfer, ft/sec

γ_{x}, is the flight path angle at transfer, degrees

ΔΩ, is the nodal shift required, degrees

i, is the orbital inclination, degrees

For example, from reference 1, if V_{x} = 25771 fps (130 n. mi. circular orbit),
i = 30°, cos γ_{x} = 1, and if ΔΩ = 1°, the ΔV required from equation 1 is
240 fps/deg. The total ΔV available in the D Mission which might practically
be used for nodal shifts amounts to 5050 fps as shown in Tables 1 and 2.
The 5050 fps represents the ΔV from the second SPS, third SPS, the docked
DPS and a 450 fps SPS burn available from presently unused SPS propellant.
If used optimally it will provide a total of about 21.4 degrees of nodal
shift.

In actual flight operations, consideration must be given to locating the SPS burns over MSFN stations (thus not necessarily at maximum Northerly or Southerly latitudes) and as a result the 21.4 degrees of nodal shift represents a theoretical value with 20.0 degrees being an operationally more realistic value. This, figure 1 shows that if the 5050 fps are nominally used to shift the line of nodes eastward then as the launch delay increases (the vehicle rests on the pad for an increasing period of time as the earth rotates at approximately 15 degrees/hour) the ΔV required to shift the plane of the delayed vehicle back to nominal decreases. At about 86 minutes of delay, no nodal shift would be required as shown in figure 1; in this case, the SPS burns required to reduce the CSM mass and accomplish the CSM autopilot test objectives, would be designed so as not to shift the line of node. Delays of over 86 minutes will require shifting the node westward. The magnitude of the shift westward increases until about 2 3/4 hours of delay when the available ΔV for nodal shifts is exceeded. Thus, the launch window for the Apollo Mission D would be 2 3/4 hours. Although such factors as lighting for end of mission and MODE IV aborts also influence the length of the launch window, preliminary studies indicate that the ΔV capability to adjust coverage and lighting for the rendezvous is the most constraining and the other launch window constraints serve only to establish a rather wide 6 hour period in which launch could occur.

__Phasing Requirements__

After correcting the nodal differences between the orbits of a “phantom” vehicle launched on time and a delayed vehicle, the two vehicles are basically in the same orbital plane although not in the same position in the orbit. To correct lighting and coverage, this position difference must be eliminated, and this is accomplished with a series of phasing maneuvers (apogee and/or perigee adjustments to change the orbital period).

Figure 2 illustrates a typical problem which might be encountered in a launch delay. Figure 2 deals with a phasing situation in which the launch delay is about 30 minutes and thus the on-time vehicle is about 120 degrees ahead of the delayed vehicle (the phase angle increasing at about 4 degrees per minute, for a orbital period of approximately 90 minutes).

Two choices are available to the maneuvering (delayed) vehicle once the nodal differential is corrected (Figure 1a and 1b). The first choice is to maneuver to a higher apogee orbit (greater period) and “dwell” for a sufficient time to allow the on-time vehicle to catch up 240°. The second choice is to reduce the apogee altitude and catch up 120° with the on-time vehicle. The problem is now reduced to simply making the proper choice based on minimizing the ΔV expended or the orbit change required.

Figure 3 shows the apogee (or perigee) adjustment (Δh) required for the maneuvering vehicle to catch up (“go below”) or to dwell (“go above”). The magnitude of Δh is approximated by the following relation:

ΔP = 1/50 (Δh) (n)

where

ΔP is the delay time in minutes

Δh is the apogee or perigee adjustment in n. mi.

n is the number of orbits over which the phasing interval is desired

In the D Mission, n is dictated by operational considerations and thus the Δh is determined as a function of n from figure 3. In the example,

Assuming N = 20 then Δh to go above is 150 n. mi. and the Δh to go below is 75 n. mi. The best choice of Δh in this case is Δh = 75 n. mi. provided low perigee problems do not exist (see figure 2c).

__Revision of the D Mission__

To extend the launch window the SPS/DPS burns in reference 1 must be redesigned in both orientation and duration and plans drawn up to accommodate launch delays up to 2.75 hours. Studies are now in progress to identify the operational problems associated with implementing the burn schedule, and reference 1 is currently being updated.

__Conclusion__

Using the SPS/DPS ΔV capability the D Mission launch window can be extended to nearly 2.75 hours. The extension can be accomplished by a series of nodal shifts and phasing burns which must be incorporated into the operational trajectory planning.