The short answer is that the US Navy had learned from its experiences earlier in the war in terms of carrier design, and that the crew - together with the crews of other vessels in the carrier group - fought hard to save their ship.
This meant that they were able to keep enough compartments from flooding such that the ship remained afloat. A significant factor here was the armoured hanger deck, which was able to limit the damage, and crucially, helped protect the ship's propulsion from serious damage. As the report into the damage noted:
However, this brief statement cannot come close to doing justice to the heroic efforts made by the crew to save the Franklin, so I have included the relevant section of the War Damage Report in full below.
The extent of the damage suffered by the Franklin can be seen in these sketches from the report:
The following extracts from the report detail the damage suffered, and the damage control countermeasures taken to mitigate the effects of that damage between 19 March and 21 March 1945:
3-30 The two bombs, falling in a trajectory estimated to be approximately 25 degrees from the horizontal, struck the ship almost simultaneously. The first bomb, estimated to be 250 kg. SAP containing 133 pounds of explosive, struck the flight deck to port of the centerline at frame 68, penetrated to the hangar and detonated either upon impact with the armored hangar deck or just above the deck at frame 87. There was evidence (a scarred depression in the deck) that the bomb ricocheted off the deck at frame 80. The detonation blew a hole in the armored deck (two courses of 1¼-inch STS) approximately 6×12 feet, between frames 85 to 89 just to port of the centerline. Deck plating at the periphery of the hole was deflected downward. Fragments pierced the second deck directly below the opening in the hangar deck. Light bulkheads on the second deck in way of ship s offices, frames 79-93, were blown out and distorted by blast. Blast and fragments also caused extensive damage in the hangar and to gallery deck structures. The deck of CIC and air plot, directly over the point of detonation, was riddled by fragments. The conflagration station was wrecked. The forward elevator was lifted up out of place and the plungers pulled out of their cylinders. When the platform dropped, it assumed a canted position of about 45 degrees with the flight deck and the starboard plunger punched holes in decks below to the fourth deck level.
3-31 The second bomb, estimated to be 250 kg. GP, struck the flight deck in the vicinity of the after elevator and penetrated to the hangar where it is believed to have detonated just below the gallery deck level and over parked planes. Because of heavy damage in this area from subsequent explosions It was not possible to identify the path and damage of this second enemy bomb. Detonation of this bomb, however, did not blow a hole in the armored hangar deck nor in the armored second deck in way of the after elevator pit. Some observers reported that the second bomb detonated a few seconds after the first one while others reported that the interval of time between the two detonations was not discernible and that the sound and shock was as if a single explosion had taken place.
3-32 Detonation of the enemy bombs in the hangar ruptured aircraft fuel tanks causing fires to spread rapidly on both the flight and hangar decks. A tremendous gasoline vapor explosion followed the initial detonations by a few seconds. Blast and flames filled the entire hangar and shot up elevator wells and out the sides of the hangar. Dense black smoke filled the hangar and enveloped large portions of the flight deck and bridge. Planes on the flight deck, which had been turning up were thrown together with their propellers cutting into one another. The severity of the initial detonations and vapor explosion can be appreciated by the fact that there are only two known survivors from the hangar. All interior communications were lost except a single sound powered line from conn to steering aft from whence another sound powered line to main engine control was effective. All topside and interior general announcing systems and radio communications also failed.
3-33 Within a short period of time, variously reported as from one to four minutes after the initial detonation, the first of a five-hour long series of heavy explosions of aircraft bombs occurred. During this period it is estimated that about 60 of the 66 500-pound bonus and about 7 or 8 of the 10 250-pound bombs which were loaded on planes on the flight deck detonated. Some planes, together with their bombs, were blown over the side without their bombs exploding. Three 500-pound and two 250^pound bombs were found unexploded in 20mm gun tubs on the port gallery walkway. Most of the bombs on the flight deck exploded on that deck, but some fell through holes and exploded in the hangar spaces. All of the 12 Tiny Tims (11.75-inch rockets) on the flight deck went off. Some were observed to leave the ship by the force of the motors, but it is believed that a majority of the rocket heads detonated on the ship. Four of the five Tiny Tims in the hangar detonated. One intact Tiny Tim rocket head was recovered in C-201-2L on the second deck. Small caliber, 20mm, 40mm and 5-inch ammunition exploded singly (low order) throughout the period of the heavy explosions and for several hours following. This ammunition was located in planes, clipping rooms, ready service boxes and upper handling rooms. No lower magazine spaces were involved. Fires, fed by gasoline and aggravated by the continuing explosions, raged unabated during the first few hours on the flight deck and in the island, gallery, forecastle, hangar and a few second deck spaces.
3-34 At 0725 the ship was steadied on a course with the wind broad on the starboard bow. Speed of the ship was 16 knots. This served to clear smoke from the forward end of the ship and allowed firefighting personnel to enter the forward end of the hangar and to approach the fire on the flight deck. Violent explosions which were occurring at frequent intervals together with continuous low order explosions of small caliber, 20 and 40mm and 5-inch ammunition prevented firefighters from approaching close enough to have any effect in bringing the conflagration under control. Their efforts, however, were effective in preventing fires from spreading to the extreme forward end of the ship.
3-35 It is not known if the hangar sprinkler and water curtain controls were operated by the watch in the conflagration station, or whether they operated from shock or damaged circuits. The two men on watch at this station were killed and the station wrecked. Smoke and debris blocked access to a number of the third deck hangar sprinkling and water curtain control stations. Those that could be reached were turned on. Risers and lines for sprinkling and water curtain systems in the amidship section and aft in the hangar were practically demolished. In the hangar as far forward as frame 44, risers and overhead lines were broken and cut by fragments in many places. Sagging of overhead structures from excessive heat caused considerable overhead piping to be carried away.
3-36 Although fire pumps in machinery spaces were kept on the line, it was not possible to maintain adequate pressure on all sections simultaneously. At the time of the hits, the firemain system was divided into eight sections. Since it could not be determined which sprinkling and water curtain systems in the hangar were still effective, segregation of the firemain loop system was not changed. Immediately after the initial damage the two Diesel fire pumps aft and one of the two Diesel fire pumps forward were started (the other one forward could not be started). With all available fire pumps operating, a large volume of water was discharged into the hangar through damaged and undamaged risers, sprinkling and water curtain lines. At least some of the sprinkling and water curtains were partially effective despite the damaged piping. Water curtain No. 2 and sprinkling bay No. 1 were reported in operation and these aided in preventing spread of the fire forward. The firemain loop below the fourth deck remained intact. Salt water flushing lines were ruptured on the second deck in several compartments and this contributed to flooding lower spaces.
3-37 One of the two known survivors from the hangar reported that immediately following the initial bomb detonations he and another man led out a hose line from the aviation repair shop and started forward. Before they had gone more than a few feet, the first subsequent explosion (gasoline vapor) knocked both men to the after end of the hangar. Only one of these two men escaped and he made his way to the fantail, later transferring to a ship alongside. The only other survivor from the hangar was manning a gasoline system telephone on the starboard side at frame 164. He was also blown to the after end of the hangar and subsequently made his way to the fantail.
3-38 The flight deck was virtually demolished aft of the after elevator and extensively damaged forward to frame 115. From frame 115 to frame 50 wood decking was burned and deck plating was warped and buckled. There were innumerable holes ranging from small fragment holes to the largest hole just abaft the after expansion joint, frame 149, which measured roughly 60×80 feet.
3-39 Although the armored hangar deck (two courses of 1¼-inch STS from frame 26 to frame 166) was ruptured in four places and extensively scarred and warped, it was very effective in protecting spaces below from serious damage. As noted in paragraph 3-30, the enemy bomb which detonated at frame 87 blew a hole roughly 6×12 feet in the armored deck and fragments pierced the second deck directly below. The other three holes in the armored deck were identified as having been caused by the detonation of Tiny Tim rockets. In each of these three cases the characteristics of the ruptures indicated that the rocket heads had detonated while lying flat on the deck. One hole, about 3×6 feet, was blown in the deck at its junction with the inboard 2-inch STS bulkhead of the uptake space at frame 93. The armored bulkhead of the uptake space was torn open from the deck to a height of about 4 feet. The uptake and air intake for boilers Nos. 1 and 3 were damaged but not beyond limited use. A second hole about 6 feet in diameter was blown in the deck at frame 100 at its junction with the bulkhead of forward uptake space. This hole extended into the after part of the uptake space and demolished the starboard air intakes for boilers Nos. 2 and 4. The uptakes for boilers Nos. 2 and 4 also were severely damaged. A third Tiny Tim rocket is believed to have detonated on the deck at frame 146, aft and outboard of the after starboard corner of the after elevator. A hole about 6×6 feet was blown in the deck. Light bulkheads of the crew's berthing space, B-127-L, frames 131-145, were demolished. In all three cases small fragment holes were blown in second deck plating directly below the Tiny Tim detonations. Fragments from the Tiny Tim detonation at frame 146 also pierced the third deck at frames 144-150, starboard. The fourth deck directly below was depressed, frames 146-148, but was not penetrated.
3-40 A large hole, roughly 14×18 feet, was blown in the center of the hangar deck, frames 176-180. In this area, deck plating is only 3/8-inch medium steel. The force of the detonation of the bomb (or bombs) which caused this hole also blew a hole 8×12 feet in the second deck and fragments punctured the third deck directly below.
3-41 In addition to large holes described above,there were many smaller fragment holes in the hangar deck, particularly aft of frame 166 where the deck plating is not STS. The deck was depressed over a major portion of the area aft of frame 155 and in some places between frames 80 and 155.
3-42 The after elevator was" wrecked in a somewhat similar manner to the forward elevator except more extensively (Photo 28). Both plungers were pulled out of their cylinders and the elevator platform was riddled by,fragments and assumed a canted position. All bomb elevators, barriers, arresting gear and similar fittings on the flight deck aft of frame 50 were destroyed. The mast support for the SC-3 radar antenna fractured and in falling smashed both the SC-3 and SM antennae. The foremast which supports antennae for the YE homing beacon, SG and BK radars and VHF radio gear was fractured at the radar platform level. This mast tilted inboard but was prevented from hanging down by its starboard wire stay.
3-43 At about 0900 Miller (DD535) came alongside Franklin and took off the flag officers and their staffs. At about 0930 Santa Fe (CL60) took station about one hundred feet off the starboard bow of Franklin and started transferring seriously wounded personnel by trolley. Franklin slowed to about eight knots to facilitate the transfer.
3-44 Immediately following the initial detonations dense smoke entered all machinery spaces through supply ventilation ducts. As subsequent explosions ruptured decks down to the fourth deck, fire and smoke entered numerous other spaces below the hangar deck level through the holes and open accesses. Ventilation supply systems to machinery spaces were secured and exhaust blowers were left operating in an effort to reduce smoke. Lack of supply ventilation made these spaces extremely hot and increased the difficulties of personnel remaining on watch. The detonation of the Tiny Tim rockets adjacent to the forward uptake spaces on the starboard side of the hangar demolished the air intake for boilers Nos. 2 and 4 and damaged the air intakes for boilers Nos. 1 and 3. As stated in paragraph >3-39, the uptakes for these boilers were also damaged. Water from hangar deck firefighting drained down these ruptured air intakes and extinguished fires in all four forward boilers. Blast passing down the air intakes and uptakes for boilers Nos. 2 and 4 caused a flareback. No. 2 fireroom was evacuated at about 0900.
3-45 At about 0930, smoke and heat conditions in the remaining firerooms, enginerooms and auxiliary machinery spaces had become progressively worse. Men were collapsing at their stations and permission was granted to evacuate all machinery spaces. Throttles were set for 8 knots, all boiler fires extinguished, turbo-generators secured and all firerooms, enginerooms and auxiliary machinery, spaces were evacuated. The two emergency 250 KW Diesel generators started automatically, but circuit breakers on the main switchboards opened, presumably from overload conditions, and both generators operated without load until machinery spaces were remanned approximately six hours later. All firemain pressure was- lost except one section forward supplied by Diesel fire pump No. 11. The two after Diesel pumps in the refrigeration machinery room, C-614-E, frames 166-176, were started and left running when this space was evacuated because of smoke. This compartment subsequently flooded and it is not known how long the pumps operated.
3-46 Steering control was lost within a few minutes after evacuation of machinery spaces, and at about 1015, the ship lost all headway and started to swing. This made it impossible for Santa Fe to maintain her position and she cast off all lines and backed away. At 1050, after Franklin had regained a steady heading, Santa Fe came in on the starboard bow slamming into actual contact where she was held by use off her engines. The remainder of the seriously wounded and excess personnel were then transferred and Santa Fe cleared the side about 1225. While alongside, Santa Fe's firefighting personnel directed hose streams with some effect on the gasoline fire amidships, on the fires in 5-inch 38 caliber twin mount No. 7 and 40mm ready service boxes and bulwark stowages amidships. In the meantime, Hickox (DD673) and Miller (DD535) approached the stern, picking up Franklin's personnel from the water en route and took off wounded and other personnel trapped on the fantail.
3-47 By about 1000 a list to starboard, caused by firefighting water accumulating on the hangar deck and decks below, had increased to eight degrees and continued increasing approximately one degree every ;en minutes. Heavy explosions were continuing but at longer intervals.
3-48 At 1115 Pittsburgh (CA72) was ordered to take Franklin in tow even though severe fires and major explosions still continued. Pittsburgh lay to on the port bow and passed over an 8-inch manila messenger followed by the towing wire. No power was available at the forecastle winches or anchor windlasses on Franklin and the process of heaving in the messenger by manpower was long and tedious. Power handling was finally arranged by using a winch on Pittsburgh. Upon receipt of the towing wire aboard Franklin, it was attached to the starboard anchor chain, the anchor shackle having been burned off with a portable burning outfit, and 90 fathoms of chain was eased out of the chain locker by slow ahead movement of Pittsburgh. Arrangements were completed and towing commenced at about 1400. Franklin's rudder was shifted from amidships to three degrees right by the hand positioning gear. Course was difficult to maintain at first because Franklin tended to sheer to port and sail to windward, dragging the Pittsburgh^ stern around. Towing speed averaged 4 to 5 knots by 2400.
3-49 All major explosions ceased about 1300 although 40mm and smaller caliber ammunition continued to explode intermittently. Fires on the forward end of the hangar deck had been extinguished and those on the flight deck, after part of the hangar deck, in the forecastle, gallery island and second deck spaces had either burned out or had become confined and were gradually being brought under control. Holes were cut in the flight deck and hose streams directed on fires in gallery deck spaces below (Photo 25). The only fire pressure on the ship at this time, as noted in paragraph 3-45, was from the one Diesel fire pump forward. Accompanying destroyers assisted in fighting fires on the fantail and after part of the ship.
3-50 At about 1300, the engineer officer together with several officers and men, all wearing rescue breathers, made their way to the forward auxiliary machinery space and found the forward emergency 250 KW Diesel generator still running at no load. No. 1 distribution board was stripped and the generator cut in on the board. This provided power for lights and ventilation blowers for machinery spaces which were started immediately. Ventilation blowers for the third deck spaces were also cut in. Thus, clearing the dense smoke from the third deck accesses and from the machinery spaces was begun. An inspection of the machinery spaces made with use of rescue breathers disclosed that the forward fireroom was not usable. By 2100 it was possible to remain in No. 3 fireroom without rescue breathers and preparations were made to light off.
3-51 Franklin's difficulties were not limited to the immediate problems on the ship itself, for two more enemy air attacks were attempted during the afternoon of the 19th. At 1254 a "Judy" made a fast low level attack on Franklin from starboard, but was taken under fire by the starboard screen and its bomb exploded short, about 200 yards on the starboard quarter. At 1435 an enemy aircraft closed in but was driven off by anti-aircraft fire and splashed by the CAP.
3-52 By night all major fires were extinguished. However, there were many smoldering fires scattered throughout the damaged area and these rekindled and flared up at frequent intervals. During the night one bad fire on the fantail was extinguished with the aid of one of the screening destroyers.
3-53 During the early afternoon the starboard list of the ship had stabilized at about 13 degrees. The ship was about three feet down by the stern. Counterflooding of various port voids was started with the intention of bringing the ship back to about 5 degrees starboard list and holding it there. Some of the flooding control stations for the port voids were accessible only with rescue breathers. The ship responded gradually to the list control measures, but due to either an overestimate of the amount of counterflooding necessary or lack of coordination in the counterflooding effort, together with the appreciable reduction in GM due to the free surface of the accumulated firefighting water on the various decks, the ship came upright about 0000 and slowly listed to port, finally coming to rest with a 9 degree port list at about 0400 on 20 March.
3-54 At about 2230 No. 5 boiler was lighted off and as soon as sufficient steam pressure was available No. 3 turbo-generator was started and cut in on the No. 3 main distribution board. By 0100 on 20 March warming up of main engines was commenced. At 0715 boiler No. 7 was lighted off and at 0815 boiler No. 8 was lighted off. The after main engines were then turned over and brought up to 56 turns. With this assistance Pittsburgh was able to increase speed of the tow to 6 knots. By 1000 steering control had been regained and four boilers were on the line. A report was made to the Task Unit Commander in Guam that the ship was ready to make 15 knots and permission was requested to cast off the tow, which was granted. Speed was gradually increased to 14 knots and at 1233 the tow line was cast off and Pittsburgh hauled clear.
3-55 Beginning with the dawn of 20 March, personnel remaining on the ship started extricating and burying bodies, clearing wreckage and dewatering flooded spaces. About 300 men and 100 officers were fit for duty out of a total of 603 men and 103 officers on board. During the day Franklin worked up to 18 knots steaming on the four after boilers and with the two after main engines operating normally. Because of flooding and damage to air intakes and uptakes forward boilers were not lighted off. Auxiliary steam from the after plant was cross-connected to the forward engines which were turned over to reduce the drag of the outboard propellers. One gyro-compass was in operation. All but a few stubborn fires in gallery deck spaces, Captain's cabin and some of the lower deck spaces aft were out. These fires were not completely extinguished until the morning of 22 March.
3-56 Pumping of the after port damage control voids which had been flooded to offset the initial starboard list was commenced on 20 March. On the morning of 22 March the list had been reduced to 6 degrees to port and, although it had been planned to retain about 5 degrees port list in order to pocket damage water, as off-center and free surface water was removed the ship gradually came to an even keel. Water was removed by submersible pumps and bucket brigades and also by draining it to lower compartments where it was pumped out through the main drainage system. This was a slow and tedious task.
The Franklin then proceeded to Ulithi Atoll under her own power for emergency repairs, before continuing on to Pearl Harbor for more extensive repairs.